id
int64 0
458k
| file_name
stringlengths 4
119
| file_path
stringlengths 14
227
| content
stringlengths 24
9.96M
| size
int64 24
9.96M
| language
stringclasses 1
value | extension
stringclasses 14
values | total_lines
int64 1
219k
| avg_line_length
float64 2.52
4.63M
| max_line_length
int64 5
9.91M
| alphanum_fraction
float64 0
1
| repo_name
stringlengths 7
101
| repo_stars
int64 100
139k
| repo_forks
int64 0
26.4k
| repo_open_issues
int64 0
2.27k
| repo_license
stringclasses 12
values | repo_extraction_date
stringclasses 433
values |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2,288,600 | yba_ams_py_controller.py | TshineZheng_Filamentor/src/impl/yba_ams_py_controller.py | import json
import select
import socket
import threading
import time
from src.impl.yba_ams_controller import YBAAMSController
from src.utils.log import LOGE, LOGI
class YBAAMSPYController(YBAAMSController):
"""YBA-AMS-Python 版本，用 python 复刻原版，增加内存指令
Args:
YBAAMSController (_type_): _description_
Returns:
_type_: _description_
"""
@staticmethod
def type_name() -> str:
return "yba_ams_py"
def __init__(self, ip: str, port: int, channel_count: int):
super().__init__(ip, port, channel_count)
self.broken_detect_thread = None
def connect(self):
super().connect()
self.broken_detect_thread = threading.Thread(target=self.recive_loop, name=f"yba-ams-py({self.ip}) recive_loop")
self.broken_detect_thread.start()
self.ams_gc()
def disconnect(self):
super().disconnect()
if self.broken_detect_thread:
try:
self.broken_detect_thread.join()
except Exception as e:
pass
self.broken_detect_thread = None
def recive_loop(self):
while self.is_running:
time.sleep(0.1)
if self.sock is None:
break
try:
r, _, _ = select.select([self.sock], [], [])
do_read = bool(r)
except socket.error:
pass
if do_read:
try:
data = b''
while True:
if self.sock is None:
break
packet = self.sock.recv(1024) # 一次接收1024字节
if not packet:
break
data += packet
latest = data[-1:]
if latest == b'\x04':
break
if len(data) != 0:
data = str(data[:-1], 'utf-8')
try:
json_obj = json.loads(data)
type = None
msg_data = None
if 'type' in json_obj:
type = json_obj['type']
if 'data' in json_obj:
msg_data = json_obj['data']
if type != None:
self.on_recv(type, msg_data)
except Exception as e:
pass
except Exception as e:
LOGE(f"接收数据失败: {e}")
time.sleep(1)
pass
def on_recv(self, type: int, data):
if type == 0:
LOGI(f'ESP Info : {data}')
elif type == 1:
LOGI(f'ESP Info: {data}')
def ams_gc(self) -> str:
self.send_ams(b'\x2f\x2f\xff\xfe\xff')
def get_system_status(self) -> str:
self.send_ams(b'\x2f\x2f\xff\xfe\xfe')
def ams_sync(self):
ams_sync = b'\x2f\x2f\xff\xfe\x02' + self.channel_total.to_bytes(1, 'big')
for i in range(self.channel_total):
ams_sync += self.ch_state[i].to_bytes(1, 'big')
self.send_ams(ams_sync)
def heartbeat(self):
while self.is_running:
if self.sock is not None:
self.ams_sync()
time.sleep(1)
| 3,488 | Python | .py | 93 | 22.44086 | 120 | 0.463393 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,601 | gcode_util.py | TshineZheng_Filamentor/src/utils/gcode_util.py |
class GCodeInfo(object):
def __init__(self):
from src import consts
self.first_channel = 0
self.layer_height = consts.LAYER_HEIGHT
def decodeFromZipUrl(zip_url: str, file_path: str) -> GCodeInfo:
import requests
import zipfile
import io
# 发送GET请求并获取ZIP文件的内容
response = requests.get(zip_url)
# 确保请求成功
if response.status_code == 200:
ret = GCodeInfo()
# 使用BytesIO读取下载的内容
zip_data = io.BytesIO(response.content)
# 使用zipfile读取ZIP文件
with zipfile.ZipFile(zip_data) as zip_file:
# 获取ZIP文件中的所有文件名列表
file_names = zip_file.namelist()
# 遍历文件名列表
for file_name in file_names:
# 如果文件名符合您要查找的路径
if file_path == file_name:
# 打开文本文件
with zip_file.open(file_name) as file:
# 逐行读取文件内容
for line in file:
# 将bytes转换为str
line_str = line.decode('utf-8')
# 检查是否包含特定字符串
if line_str.startswith('M620 S'):
# 找到匹配的行，返回内容
text = line_str.strip()
import re
# 正则表达式模式，用于匹配'M620 S'后面的数字，直到遇到非数字字符
pattern = r'M620 S(\d+)'
# 搜索匹配的内容
match = re.search(pattern, text)
# 如果找到匹配项，则提取数字
if match:
number = match.group(1)
print(number) # 输出匹配到的数字
ret.first_channel = int(int(number))
return ret
elif line_str.startswith('; layer_height = '):
value = line_str.split('=')[1].strip()
ret.layer_height = float(value)
return None
| 2,421 | Python | .py | 49 | 23.22449 | 74 | 0.429481 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,602 | front.py | TshineZheng_Filamentor/src/utils/front.py | import requests
import zipfile
import os
def unzip_file(zip_path, extract_path):
with zipfile.ZipFile(zip_path, 'r') as zip_ref:
zip_ref.extractall(extract_path)
print(f"文件已解压到 {extract_path}")
if os.path.exists('web'):
exit('前端已存在，如果要更新，请删除 web 文件夹后重新运行本脚本')
print('正在下载前端资源...')
# GitHub 用户名和仓库名
owner = "TshineZheng"
repo = "FilamentorApp"
# GitHub API URL
url = f"https://api.github.com/repos/{owner}/{repo}/releases/latest"
# 获取最新的 release 信息
response = requests.get(url)
release_data = response.json()
# 获取最新的 release 的资产（文件）
assets = release_data['assets']
for asset in assets:
download_url = asset['browser_download_url']
print(f"下载 URL: {download_url}")
# 下载文件
file_response = requests.get(download_url)
file_name = asset['name']
with open(file_name, 'wb') as f:
f.write(file_response.content)
print(f"文件 {file_name} 已下载")
unzip_file('web.zip', 'web/')
os.remove('web.zip')
| 1,106 | Python | .py | 31 | 27.483871 | 68 | 0.704846 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,603 | persist.py | TshineZheng_Filamentor/src/utils/persist.py | import os
from src.consts import STORAGE_PATH
def update_printer_channel(printer_id: str, channel: int):
with open(f'{STORAGE_PATH}{printer_id}.channel', 'w') as f:
f.write(str(channel))
def get_printer_channel(printer_id: str) -> int:
# 如果文件不存在，则返回 0
if not os.path.exists(f'{STORAGE_PATH}{printer_id}.channel'):
return 0
try:
with open(f'{STORAGE_PATH}{printer_id}.channel', 'r') as f:
return int(f.read())
except:
return 0 | 519 | Python | .py | 14 | 29.428571 | 67 | 0.644958 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,604 | log.py | TshineZheng_Filamentor/src/utils/log.py | from abc import abstractmethod
from typing import Any
from loguru import logger as LOG
import src.consts
def LOGI(msg, *args: Any, **kwargs: Any):
LOG.info(msg, *args, **kwargs)
def LOGW(msg, *args: Any, **kwargs: Any):
LOG.info(msg, *args, **kwargs)
def LOGE(msg, *args: Any, **kwargs: Any):
LOG.error(msg, *args, **kwargs)
def LOGD(msg, *args: Any, **kwargs: Any):
LOG.debug(msg, *args, **kwargs)
LOG.add(
sink = f'{src.consts.STORAGE_PATH}/logs/filamentor.log',
enqueue=True,
rotation='1 days',
retention='1 weeks',
encoding='utf-8',
backtrace=True,
diagnose=True,
compression='zip'
)
class TAGLOG:
@abstractmethod
def tag(self):
return ''
def LOGI(self, msg, *args: Any, **kwargs: Any):
LOGI(self.__mix_msg__(msg), *args, **kwargs)
def LOGW(self, msg, *args: Any, **kwargs: Any):
LOGW(self.__mix_msg__(msg), *args, **kwargs)
def LOGE(self, msg, *args: Any, **kwargs: Any):
LOGE(self.__mix_msg__(msg), *args, **kwargs)
def LOGD(self, msg, *args: Any, **kwargs: Any):
LOGD(self.__mix_msg__(msg), *args, **kwargs)
def __mix_msg__(self, msg:str):
if self.tag == '' or self.tag is None:
return msg
return f'{self.tag()} | {msg}' | 1,286 | Python | .py | 38 | 28.684211 | 60 | 0.60778 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,605 | singleton.py | TshineZheng_Filamentor/src/utils/singleton.py | class Singleton(type):
_instances = {}
def __call__(cls, *args, **kwargs):
if cls not in cls._instances:
cls._instances[cls] = super(Singleton, cls).__call__(*args, **kwargs)
return cls._instances[cls] | 237 | Python | .py | 6 | 32.666667 | 81 | 0.586207 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,606 | json_util.py | TshineZheng_Filamentor/src/utils/json_util.py | def ast(json_data: dict, key: str, value):
if key in json_data:
if json_data[key] == value:
return True
return False | 144 | Python | .py | 5 | 22.4 | 42 | 0.592857 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,607 | net_util.py | TshineZheng_Filamentor/src/utils/net_util.py | def get_ip_address():
import socket
hostname = socket.gethostname()
ip_address = socket.gethostbyname(hostname)
return ip_address
| 146 | Python | .py | 5 | 25 | 47 | 0.730496 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,608 | models.py | TshineZheng_Filamentor/src/web/models.py | from datetime import datetime
from typing import Any
from zoneinfo import ZoneInfo
from fastapi.encoders import jsonable_encoder
from pydantic import BaseModel as bm, ConfigDict, model_validator
def convert_datetime_to_gmt(dt: datetime) -> str:
if not dt.tzinfo:
dt = dt.replace(tzinfo=ZoneInfo("UTC"))
return dt.strftime("%Y-%m-%dT%H:%M:%S%z")
class BaseModel(bm):
model_config = ConfigDict(
json_encoders={datetime: convert_datetime_to_gmt},
populate_by_name=True,
)
@model_validator(mode="before")
@classmethod
def set_null_microseconds(cls, data: dict[str, Any]) -> dict[str, Any]:
datetime_fields = {
k: v.replace(microsecond=0)
for k, v in data.items()
if isinstance(v, datetime)
}
return {**data, **datetime_fields}
def serializable_dict(self, **kwargs):
"""Return a dict which contains only serializable fields."""
default_dict = self.model_dump()
return jsonable_encoder(default_dict)
| 1,044 | Python | .py | 27 | 32.111111 | 75 | 0.668322 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,609 | front.py | TshineZheng_Filamentor/src/web/front.py |
import http.server
from typing import Any
from src.utils.net_util import get_ip_address
front_server: http.server.HTTPServer = None
class FrontHandler(http.server.SimpleHTTPRequestHandler):
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs, directory='web')
def log_message(self, format: str, *args: Any) -> None:
pass
def start():
import os
import threading
if os.path.exists('web'):
global front_server
front_server = http.server.HTTPServer(('', 8001), FrontHandler)
threading.Thread(target=front_server.serve_forever).start()
myip = get_ip_address()
print("========================================")
print(f"| 管理页面: http://{myip}:8001 |")
print(f"| 接口文档: http://{myip}:7170/docs |")
print("========================================")
def stop():
if front_server:
front_server.shutdown()
| 954 | Python | .py | 24 | 32.916667 | 71 | 0.58204 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,610 | __init__.py | TshineZheng_Filamentor/src/web/__init__.py | from src.web.controller.router import router as controller_router
from src.web.sys.router import router as sys_router
from src.web.printer.router import router as printer_router
from fastapi.middleware.cors import CORSMiddleware
from fastapi import APIRouter, FastAPI
import json
import logging
from fastapi import Request
from fastapi.responses import JSONResponse
from starlette.middleware.base import BaseHTTPMiddleware, RequestResponseEndpoint
class ResponseMiddleware(BaseHTTPMiddleware):
async def dispatch(self, request: Request, call_next: RequestResponseEndpoint):
response = await call_next(request)
if not request.url.path.startswith("/api"):
return response
# 获取响应内容
response_body = [section async for section in response.body_iterator]
response_body = b''.join(response_body).decode('utf-8')
# 尝试解析响应内容为 JSON 对象
try:
response_data = json.loads(response_body)
except json.JSONDecodeError:
response_data = response_body
# 根据状态码包装响应内容
if response.status_code == 200:
new_response = JSONResponse(
status_code=response.status_code,
content={
"code": response.status_code,
"message": "success",
"data": response_data
}
)
else:
msg = 'unknown error'
if 'detail' in response_data:
if isinstance(response_data['detail'], str):
msg = response_data['detail']
elif isinstance(response_data['detail'], list):
detail = response_data['detail'][0]
if 'msg' in detail:
msg = detail['msg']
new_response = JSONResponse(
status_code=response.status_code,
content={
"code": response.status_code,
"message": msg,
"data": None,
"error": response_data
}
)
# 返回新的响应对象
return new_response
class EndpointFilter(logging.Filter):
def filter(self, record: logging.LogRecord) -> bool:
return record.args and len(record.args) >= 3 and record.args[2] != "/api/sys/sync"
def init(fast_api: FastAPI):
# Add filter to the logger
logging.getLogger("uvicorn.access").addFilter(EndpointFilter())
fast_api.add_middleware(ResponseMiddleware)
fast_api.add_middleware(
CORSMiddleware,
allow_origins=["*"],
allow_credentials=True,
allow_methods=["*"],
allow_headers=["*"]
)
api_router = APIRouter()
api_router.include_router(sys_router, prefix='/sys')
api_router.include_router(printer_router, prefix='/printer')
api_router.include_router(controller_router, prefix='/controller')
fast_api.include_router(api_router, prefix="/api")
| 3,049 | Python | .py | 72 | 30.944444 | 90 | 0.615651 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,611 | exceptions.py | TshineZheng_Filamentor/src/web/exceptions.py | from typing import Any
from fastapi import HTTPException, status
class DetailedHTTPException(HTTPException):
STATUS_CODE = status.HTTP_500_INTERNAL_SERVER_ERROR
DETAIL = "Server error"
def __init__(self, **kwargs: dict[str, Any]) -> None:
super().__init__(status_code=self.STATUS_CODE, detail=self.DETAIL, **kwargs)
class PermissionDenied(DetailedHTTPException):
STATUS_CODE = status.HTTP_403_FORBIDDEN
DETAIL = "Permission denied"
class NotFound(DetailedHTTPException):
STATUS_CODE = status.HTTP_404_NOT_FOUND
class BadRequest(DetailedHTTPException):
STATUS_CODE = status.HTTP_400_BAD_REQUEST
DETAIL = "Bad Request"
class NotAuthenticated(DetailedHTTPException):
STATUS_CODE = status.HTTP_401_UNAUTHORIZED
DETAIL = "User not authenticated"
def __init__(self) -> None:
super().__init__(headers={"WWW-Authenticate": "Bearer"})
| 899 | Python | .py | 20 | 40.3 | 84 | 0.73903 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,612 | router.py | TshineZheng_Filamentor/src/web/sys/router.py | from typing import List
from fastapi import APIRouter, Depends
from src.ams_core import ams_list
from src.app_config import DetectRelation, IDBrokenDetect, config
router = APIRouter()
@router.get('/config')
async def get_config():
d = config.to_dict()
detect_list = d['detect_list']
detect_relation_list = d['detect_relations']
# 将所有打印机和控制器自带的断料检测器构造出来，还有关系
for printer in config.printer_list:
if printer.client.filament_broken_detect() is not None:
detect_list.append(IDBrokenDetect(printer.id, printer.client.filament_broken_detect(), printer.alias).to_dict())
detect_relation_list.append(DetectRelation(printer.id, printer.id).to_dict())
# FIXME： 控制器断料检测器绑定打印机的逻辑不对，断料检测器应该和通道或者控制器绑定，而不是和打印机绑定
for c in config.controller_list:
if c.controller.get_broken_detect() is not None:
detect_list.append(IDBrokenDetect(c.id, c.controller.get_broken_detect(), c.alias).to_dict())
detect_relation_list.append(DetectRelation(printer.id, c.id).to_dict())
return d
@router.get('/sync')
async def sync():
controller_state: List[dict] = []
ams_info: List[dict] = []
detect_info: List[dict] = []
for printer in config.printer_list:
if printer.client.filament_broken_detect() is not None:
detect_info.append({
'detect_id': printer.id,
'is_broken': printer.client.filament_broken_detect().is_filament_broken()
})
for c in config.controller_list:
controller_state.append(
{
'controller_id': c.id,
'channel_states': c.controller.get_channel_states()
}
)
if c.controller.get_broken_detect() is not None:
detect_info.append({
'detect_id': c.id,
'is_broken': c.controller.get_broken_detect().is_filament_broken()
})
for p in ams_list:
ams_info.append({
'printer_id': p.use_printer,
'fila_cur': p.fila_cur,
'cur_task': p.task_name
})
for d in config.detect_list:
detect_info.append({
'detect_id': d.id,
'is_broken': d.detect.is_filament_broken()
})
return {'ams': ams_info, 'controller': controller_state, 'detect': detect_info}
| 2,511 | Python | .py | 56 | 33.053571 | 124 | 0.62069 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,613 | schemas.py | TshineZheng_Filamentor/src/web/controller/schemas.py | from src.web.models import BaseModel
class ControllerChannelModel(BaseModel):
controller_id: str
channel: int
class YBAAMSControllerModel(BaseModel):
ip: str
port: int
channel_total: int
class YBASingleBufferControllerModel(BaseModel):
fila_broken_safe_time: int
ip: str
port: int
channel_total: int
| 342 | Python | .py | 13 | 22.076923 | 48 | 0.76161 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,614 | dependencies.py | TshineZheng_Filamentor/src/web/controller/dependencies.py | from typing import List
from fastapi import Depends, Query
from src.controller import ChannelAction
from src.impl.yba_ams_controller import YBAAMSController
from src.impl.yba_ams_py_controller import YBAAMSPYController
from src.impl.yba_ams_servo_controller import YBAAMSServoController
from src.impl.yba_single_buffer_controller import YBASingleBufferController
from src.web.controller.exceptions import ChannelDuplicate, ControllerChannelBinded, ControllerChannelActionError, ControllerChannelNotFoundError, ControllerChannelUnBinded, ControllerNotFoundError, ControllerTypeNotMatch
from src.app_config import config
from src.web.controller.schemas import ControllerChannelModel
async def valid_controller_type(controller_type: str) -> str:
if controller_type == YBAAMSPYController.type_name():
return controller_type
elif controller_type == YBAAMSServoController.type_name():
return controller_type
elif controller_type == YBAAMSController.type_name():
return controller_type
elif controller_type == YBASingleBufferController.type_name():
return controller_type
else:
raise ControllerTypeNotMatch()
async def valid_controller_id_exist(controller_id: str) -> str:
for c in config.controller_list:
if c.id == controller_id:
return controller_id
raise ControllerNotFoundError()
async def valid_controller_channel(channel: int, controller_id: str = Depends(valid_controller_id_exist)) -> ControllerChannelModel:
for c in config.controller_list:
if c.id == controller_id:
if 0 <= channel < c.controller.channel_total:
return ControllerChannelModel(controller_id=controller_id, channel=channel)
raise ControllerChannelNotFoundError()
async def valid_channel_binded(channels: List[int] = Query(alias='channels'), controller_id: str = Depends(valid_controller_id_exist)) -> List[ControllerChannelModel]:
if len(channels) != len(set(channels)):
raise ChannelDuplicate()
for channel in channels:
await valid_controller_channel(channel, controller_id)
for c in config.channel_relations:
for channel in channels:
if c.controller_id == controller_id and c.channel == channel:
raise ControllerChannelBinded()
return [ControllerChannelModel(controller_id=controller_id, channel=channel) for channel in channels]
async def valid_channel_unbinded(channel: int, controller_id: str = Depends(valid_controller_id_exist)) -> ControllerChannelModel:
for c in config.channel_relations:
if c.controller_id == controller_id and c.channel == channel:
return ControllerChannelModel(controller_id=controller_id, channel=channel)
raise ControllerChannelUnBinded()
async def valid_channel_action(action: int) -> ChannelAction:
if action == ChannelAction.PUSH.value or action == ChannelAction.PULL.value or action == ChannelAction.STOP.value:
return ChannelAction(action)
raise ControllerChannelActionError()
| 3,042 | Python | .py | 51 | 53.529412 | 221 | 0.765972 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,615 | router.py | TshineZheng_Filamentor/src/web/controller/router.py | from typing import List, Union
from fastapi import APIRouter, Depends
from src.controller import ChannelAction
from src.web.controller import service
from src.web.controller.dependencies import valid_channel_binded, valid_channel_unbinded, valid_controller_channel, valid_controller_id_exist, valid_controller_type, valid_channel_action
from src.web.controller.schemas import ControllerChannelModel, YBAAMSControllerModel, YBASingleBufferControllerModel
from src.web.printer.dependencies import valid_ams_printer_task, valid_printer_id_exist
router = APIRouter()
@router.put('/', dependencies=[Depends(valid_ams_printer_task)])
async def add_controller(
alias: str,
info: Union[YBASingleBufferControllerModel, YBAAMSControllerModel],
type: str = Depends(valid_controller_type)
):
await service.add_controller(type, alias, info)
@router.delete('/', dependencies=[Depends(valid_ams_printer_task)])
async def delete_controller(
id: str = Depends(valid_controller_id_exist),
):
await service.remove_controller(id)
@router.post('/bind_printer', dependencies=[Depends(valid_ams_printer_task)])
async def bind_printer(
printer_id: str = Depends(valid_printer_id_exist),
channels: List[ControllerChannelModel] = Depends(valid_channel_binded),
):
await service.bind_printer(printer_id=printer_id, channels=channels)
@router.post('/unbind_printer', dependencies=[Depends(valid_ams_printer_task)])
async def unbind_printer(
printer_id: str = Depends(valid_printer_id_exist),
channel: ControllerChannelModel = Depends(valid_channel_unbinded),
):
await service.unbind_printer(controller_id=channel.controller_id, printer_id=printer_id, channel=channel.channel)
@router.post('/control', dependencies=[Depends(valid_ams_printer_task)])
async def controll(
channel: ControllerChannelModel = Depends(valid_controller_channel),
action: ChannelAction = Depends(valid_channel_action),
):
await service.controll(channel.controller_id, channel.channel, action)
| 2,032 | Python | .py | 38 | 50.026316 | 186 | 0.786471 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,616 | service.py | TshineZheng_Filamentor/src/web/controller/service.py | from typing import List, Union
import uuid
from src.controller import ChannelAction, Controller
from src.web.controller.exceptions import ControllerTaken
from src.app_config import config
import src.core_services as core_services
from src.web.controller.schemas import ControllerChannelModel, YBAAMSControllerModel
async def add_controller(type: str, alias: str, info: Union[YBAAMSControllerModel]) -> Controller:
contorller = Controller.generate_controller(type, info.model_dump())
for c in config.controller_list:
if c.controller == contorller:
raise ControllerTaken()
# TODO: 需要验证控制器是否可用
config.add_controller(f'{type}_{uuid.uuid1()}', contorller, alias)
config.save()
core_services.restart()
async def remove_controller(id: str):
config.remove_controller(id)
config.save()
core_services.restart()
async def bind_printer(printer_id: str, channels: List[ControllerChannelModel]):
for c in channels:
config.add_channel_setting(printer_id, c.controller_id, c.channel)
config.save()
core_services.restart()
async def unbind_printer(controller_id: str, printer_id: str, channel: int):
config.remove_channel_setting(printer_id, controller_id, channel)
config.save()
core_services.restart()
async def controll(controller_id: str, channel: int, action: int):
config.get_controller(controller_id).control(
channel, ChannelAction(action))
| 1,468 | Python | .py | 32 | 40.625 | 98 | 0.757857 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,617 | exceptions.py | TshineZheng_Filamentor/src/web/controller/exceptions.py | from src.web.exceptions import BadRequest
class ControllerTypeNotMatch(BadRequest):
DETAIL = "控制器类型不支持"
class ControllerNotFoundError(BadRequest):
DETAIL = "控制器不存在"
class ControllerChannelNotFoundError(BadRequest):
DETAIL = "控制器通道不存在"
class ControllerChannelBinded(BadRequest):
DETAIL = "控制器通道已绑定"
class ControllerChannelUnBinded(BadRequest):
DETAIL = "控制器通道未绑定"
class ControllerTaken(BadRequest):
DETAIL = "控制器已存在"
class ControllerInfoError(BadRequest):
DETAIL = "控制器信息有误"
class ControllerChannelActionError(BadRequest):
DETAIL = "控制器通道动作有误"
class ChannelDuplicate(BadRequest):
DETAIL = "请求设置的通道有重复" | 786 | Python | .py | 19 | 30.631579 | 49 | 0.802589 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,618 | schemas.py | TshineZheng_Filamentor/src/web/printer/schemas.py | from src.web.models import BaseModel
class BambuPrinterModel(BaseModel):
printer_ip: str
lan_password: str
device_serial: str | 139 | Python | .py | 5 | 24.2 | 36 | 0.774436 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,619 | dependencies.py | TshineZheng_Filamentor/src/web/printer/dependencies.py |
from typing import Union
from fastapi import Depends
from src.impl.bambu_client import BambuClient
from src.printer_client import PrinterClient
from src.web.exceptions import DetailedHTTPException
from src.web.printer.exceptions import ChannelNotFoundError, PrinterHasTaskError, PrinterInfoError, PrinterNotFoundError, PrinterTaken, PrinterTypeNotMatch
from src.app_config import config
import src.core_services as core_services
from src.web.printer.schemas import BambuPrinterModel
async def valid_printer_type(type:str) -> str:
if type == BambuClient.type_name():
return BambuClient.type_name()
else:
raise PrinterTypeNotMatch()
async def valid_printer_taken(info: Union[BambuPrinterModel], type: str = Depends(valid_printer_type)) -> PrinterClient:
printer_client: PrinterClient = None
if type == BambuClient.type_name():
try:
printer_client = BambuClient(info)
except:
raise PrinterInfoError()
if printer_client is None:
raise DetailedHTTPException(status_code=500, detail="未知错误")
for p in config.printer_list:
if p.client == printer_client:
raise PrinterTaken()
return printer_client
async def valid_printer_id_exist(printer_id:str):
for p in config.printer_list:
if p.id == printer_id:
return printer_id
raise PrinterNotFoundError()
async def valid_printer_channel(printer_id : str, channel_index: int) -> int:
channels = config.get_printer_channel_settings(printer_id)
if 0 <= channel_index < len(channels):
return channel_index
raise ChannelNotFoundError()
async def valid_ams_printer_task():
#TODO: 最好能分开打印机判断
if core_services.hasPrintTaskRunning():
raise PrinterHasTaskError()
| 1,829 | Python | .py | 41 | 37.707317 | 155 | 0.74158 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,620 | router.py | TshineZheng_Filamentor/src/web/printer/router.py | from fastapi import APIRouter, Depends
from src.controller import ChannelAction
from src.printer_client import PrinterClient
from src.web.controller.dependencies import valid_channel_action
from src.web.printer.dependencies import valid_ams_printer_task, valid_printer_channel, valid_printer_id_exist, valid_printer_taken
import src.web.printer.service as service
router = APIRouter()
@router.put('/', dependencies=[Depends(valid_ams_printer_task)])
async def create_printer(alias: str, change_temp: int, printer: PrinterClient = Depends(valid_printer_taken)):
id = await service.create_printer(printer, alias=alias, change_temp=change_temp),
return {'id': id}
@router.delete('/', dependencies=[Depends(valid_ams_printer_task)])
async def delete_printer(
printer_id: str = Depends(valid_printer_id_exist),
):
await service.delete_printer(printer_id)
return {'id': printer_id}
@router.post('/set_channel', dependencies=[Depends(valid_ams_printer_task)])
async def set_channel(
printer_id: str = Depends(valid_printer_id_exist),
printer_channel: int = Depends(valid_printer_channel)):
# await service.update_printer_channel(printer_id, printer_channel)
await service.channel_control(printer_id, printer_channel, ChannelAction.NONE)
@ router.post('/set_change_temp')
async def set_change_temp(
change_temp: int,
printer_id: str = Depends(valid_printer_id_exist),
):
await service.update_printer_change_temp(printer_id, change_temp)
@router.post('/edit_channel_filament_setting')
async def edit_channel_filament_setting(
filament_type: str,
filament_color: str,
printer_id: str = Depends(valid_printer_id_exist),
printer_channel: int = Depends(valid_printer_channel),
):
await service.edit_channel_filament_setting(printer_id, printer_channel, filament_type, filament_color)
@router.post('/channel_control', dependencies=[Depends(valid_ams_printer_task)])
async def channel_control(
printer_id: str = Depends(valid_printer_id_exist),
printer_channel: int = Depends(valid_printer_channel),
action: ChannelAction = Depends(valid_channel_action),
):
await service.channel_control(printer_id, printer_channel, action)
| 2,215 | Python | .py | 44 | 46.954545 | 131 | 0.764133 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,621 | service.py | TshineZheng_Filamentor/src/web/printer/service.py | import uuid
from src.controller import ChannelAction
from src.printer_client import PrinterClient
from src.utils import persist
from src.app_config import config
import src.core_services as core_services
from src.ams_core import ams_list
async def create_printer(printerClient: PrinterClient, alias: str, change_temp: int) -> str:
id = f'{printerClient.type_name()}_{uuid.uuid1()}'
# TODO：需要验证打印是否可用
config.add_printer(id, printerClient, alias, change_temp)
config.save()
core_services.restart()
return id
async def delete_printer(printer_id: str) -> str:
config.remove_printer(printer_id)
config.save()
core_services.restart()
return printer_id
async def update_printer_channel(printer_id: str, channel_index: int):
persist.update_printer_channel(printer_id, channel_index)
core_services.restart()
async def update_printer_change_temp(printer_id: str, change_temp: int):
config.set_printer_change_tem(printer_id, change_temp)
config.save()
for p in ams_list:
if p.use_printer == printer_id:
p.change_tem = change_temp
async def edit_channel_filament_setting(printer_id: str, channel: int, filament_type: str, filament_color: str):
channels = config.get_printer_channel_settings(printer_id)
channels[channel].filament_type = filament_type
channels[channel].filament_color = filament_color
config.save()
async def channel_control(printer_id: str, printer_channel: int, action: ChannelAction):
from src.ams_core import ams_list
# TODO: 这里写死 0了，应该调整为通过id获取 ams
ams_list[0].update_cur_fila(printer_channel)
ams_list[0].driver_control(printer_channel, action)
| 1,735 | Python | .py | 38 | 39.921053 | 112 | 0.747698 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,622 | exceptions.py | TshineZheng_Filamentor/src/web/printer/exceptions.py | from src.web.exceptions import BadRequest, NotFound
class PrinterNotFoundError(BadRequest):
DETAIL = "没有对应的打印机"
class ChannelNotFoundError(BadRequest):
DETAIL = '没有对应的通道'
class PrinterTaken(BadRequest):
DETAIL = '打印机已存在'
class PrinterTypeNotMatch(BadRequest):
DETAIL = '打印机类型不支持'
class PrinterHasTaskError(BadRequest):
DETAIL = '打印机打印中，无法调用该接口，请在没有打印任务时再操作'
class PrinterInfoError(BadRequest):
DETAIL = '打印机信息有误'
| 574 | Python | .py | 13 | 30.769231 | 51 | 0.794811 | TshineZheng/Filamentor | 8 | 2 | 0 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,623 | setup.py | SUSE_klp-build/setup.py | import setuptools
with open("README.md", "r") as f:
long_description = f.read()
setuptools.setup(
name="klp-build",
version="0.0.1",
author="Marcos Paulo de Souza",
author_email="[email protected]",
description="The kernel livepatching creation tool",
long_description=long_description,
long_description_content_type="text/markdown",
url="https://gitlab.suse.de/live-patching/klp-build",
packages=setuptools.find_packages(exclude=["tests"]),
package_data={"scripts": ["run-kgr-test.sh"]},
python_requires=">=3.6",
classifiers=[
"Programming Language :: Python :: 3",
"Intended Audience :: Developers",
],
entry_points={
"console_scripts": ["klp-build=klpbuild.main:main"],
},
install_requires=[
"configparser",
"cached_property",
"GitPython",
"lxml",
"mako",
"markupsafe",
"natsort",
"osc-tiny",
"requests",
"filelock",
"pyelftools",
"zstandard"
],
)
| 1,047 | Python | .py | 37 | 22.027027 | 60 | 0.608739 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,624 | .pylintrc | SUSE_klp-build/.pylintrc | [MASTER]
# A comma-separated list of package or module names from where C extensions may
# be loaded. Extensions are loading into the active Python interpreter and may
# run arbitrary code.
extension-pkg-allow-list=
# A comma-separated list of package or module names from where C extensions may
# be loaded. Extensions are loading into the active Python interpreter and may
# run arbitrary code. (This is an alternative name to extension-pkg-allow-list
# for backward compatibility.)
extension-pkg-whitelist=
# Return non-zero exit code if any of these messages/categories are detected,
# even if score is above --fail-under value. Syntax same as enable. Messages
# specified are enabled, while categories only check already-enabled messages.
fail-on=
# Specify a score threshold to be exceeded before program exits with error.
fail-under=9.0
# Files or directories to be skipped. They should be base names, not paths.
ignore=CVS
# Add files or directories matching the regex patterns to the ignore-list. The
# regex matches against paths and can be in Posix or Windows format.
ignore-paths=
# Files or directories matching the regex patterns are skipped. The regex
# matches against base names, not paths. The default value ignores emacs file
# locks
ignore-patterns=^\.#
# Python code to execute, usually for sys.path manipulation such as
# pygtk.require().
#init-hook=
# Use multiple processes to speed up Pylint. Specifying 0 will auto-detect the
# number of processors available to use.
jobs=1
# Control the amount of potential inferred values when inferring a single
# object. This can help the performance when dealing with large functions or
# complex, nested conditions.
limit-inference-results=100
# List of plugins (as comma separated values of python module names) to load,
# usually to register additional checkers.
load-plugins=
# Pickle collected data for later comparisons.
persistent=yes
# Minimum Python version to use for version dependent checks. Will default to
# the version used to run pylint.
py-version=3.6
# Discover python modules and packages in the file system subtree.
recursive=no
# When enabled, pylint would attempt to guess common misconfiguration and emit
# user-friendly hints instead of false-positive error messages.
suggestion-mode=yes
# Allow loading of arbitrary C extensions. Extensions are imported into the
# active Python interpreter and may run arbitrary code.
unsafe-load-any-extension=no
[MESSAGES CONTROL]
# Only show warnings with the listed confidence levels. Leave empty to show
# all. Valid levels: HIGH, CONTROL_FLOW, INFERENCE, INFERENCE_FAILURE,
# UNDEFINED.
confidence=
# Disable the message, report, category or checker with the given id(s). You
# can either give multiple identifiers separated by comma (,) or put this
# option multiple times (only on the command line, not in the configuration
# file where it should appear only once). You can also use "--disable=all" to
# disable everything first and then re-enable specific checks. For example, if
# you want to run only the similarities checker, you can use "--disable=all
# --enable=similarities". If you want to run only the classes checker, but have
# no Warning level messages displayed, use "--disable=all --enable=classes
# --disable=W".
disable=raw-checker-failed,
bad-inline-option,
locally-disabled,
file-ignored,
suppressed-message,
useless-suppression,
deprecated-pragma,
use-symbolic-message-instead,
missing-function-docstring,
missing-module-docstring,
missing-class-docstring,
line-too-long,
wrong-import-position,
unspecified-encoding,
fixme,
# Enable the message, report, category or checker with the given id(s). You can
# either give multiple identifier separated by comma (,) or put this option
# multiple time (only on the command line, not in the configuration file where
# it should appear only once). See also the "--disable" option for examples.
enable=c-extension-no-member
[REPORTS]
# Python expression which should return a score less than or equal to 10. You
# have access to the variables 'fatal', 'error', 'warning', 'refactor',
# 'convention', and 'info' which contain the number of messages in each
# category, as well as 'statement' which is the total number of statements
# analyzed. This score is used by the global evaluation report (RP0004).
evaluation=max(0, 0 if fatal else 10.0 - ((float(5 * error + warning + refactor + convention) / statement) * 10))
# Template used to display messages. This is a python new-style format string
# used to format the message information. See doc for all details.
#msg-template=
# Set the output format. Available formats are text, parseable, colorized, json
# and msvs (visual studio). You can also give a reporter class, e.g.
# mypackage.mymodule.MyReporterClass.
output-format=text
# Tells whether to display a full report or only the messages.
reports=no
# Activate the evaluation score.
score=yes
[REFACTORING]
# Maximum number of nested blocks for function / method body
max-nested-blocks=5
# Complete name of functions that never returns. When checking for
# inconsistent-return-statements if a never returning function is called then
# it will be considered as an explicit return statement and no message will be
# printed.
never-returning-functions=sys.exit,argparse.parse_error
[FORMAT]
# Expected format of line ending, e.g. empty (any line ending), LF or CRLF.
expected-line-ending-format=
# Regexp for a line that is allowed to be longer than the limit.
ignore-long-lines=^\s*(# )?<?https?://\S+>?$
# Number of spaces of indent required inside a hanging or continued line.
indent-after-paren=4
# String used as indentation unit. This is usually " " (4 spaces) or "\t" (1
# tab).
indent-string=' '
# Maximum number of characters on a single line.
max-line-length=120
# Maximum number of lines in a module.
max-module-lines=1000
# Allow the body of a class to be on the same line as the declaration if body
# contains single statement.
single-line-class-stmt=no
# Allow the body of an if to be on the same line as the test if there is no
# else.
single-line-if-stmt=no
[LOGGING]
# The type of string formatting that logging methods do. `old` means using %
# formatting, `new` is for `{}` formatting.
logging-format-style=old
# Logging modules to check that the string format arguments are in logging
# function parameter format.
logging-modules=logging
[MISCELLANEOUS]
# List of note tags to take in consideration, separated by a comma.
notes=FIXME,
XXX,
TODO
# Regular expression of note tags to take in consideration.
#notes-rgx=
[SIMILARITIES]
# Comments are removed from the similarity computation
ignore-comments=yes
# Docstrings are removed from the similarity computation
ignore-docstrings=yes
# Imports are removed from the similarity computation
ignore-imports=yes
# Signatures are removed from the similarity computation
ignore-signatures=no
# Minimum lines number of a similarity.
min-similarity-lines=4
[SPELLING]
# Limits count of emitted suggestions for spelling mistakes.
max-spelling-suggestions=4
# Spelling dictionary name. Available dictionaries: none. To make it work,
# install the 'python-enchant' package.
spelling-dict=
# List of comma separated words that should be considered directives if they
# appear and the beginning of a comment and should not be checked.
spelling-ignore-comment-directives=fmt: on,fmt: off,noqa:,noqa,nosec,isort:skip,mypy:
# List of comma separated words that should not be checked.
spelling-ignore-words=
# A path to a file that contains the private dictionary; one word per line.
spelling-private-dict-file=
# Tells whether to store unknown words to the private dictionary (see the
# --spelling-private-dict-file option) instead of raising a message.
spelling-store-unknown-words=no
[STRING]
# This flag controls whether inconsistent-quotes generates a warning when the
# character used as a quote delimiter is used inconsistently within a module.
check-quote-consistency=no
# This flag controls whether the implicit-str-concat should generate a warning
# on implicit string concatenation in sequences defined over several lines.
check-str-concat-over-line-jumps=no
[TYPECHECK]
# List of decorators that produce context managers, such as
# contextlib.contextmanager. Add to this list to register other decorators that
# produce valid context managers.
contextmanager-decorators=contextlib.contextmanager
# List of members which are set dynamically and missed by pylint inference
# system, and so shouldn't trigger E1101 when accessed. Python regular
# expressions are accepted.
generated-members=
# Tells whether missing members accessed in mixin class should be ignored. A
# class is considered mixin if its name matches the mixin-class-rgx option.
ignore-mixin-members=yes
# Tells whether to warn about missing members when the owner of the attribute
# is inferred to be None.
ignore-none=yes
# This flag controls whether pylint should warn about no-member and similar
# checks whenever an opaque object is returned when inferring. The inference
# can return multiple potential results while evaluating a Python object, but
# some branches might not be evaluated, which results in partial inference. In
# that case, it might be useful to still emit no-member and other checks for
# the rest of the inferred objects.
ignore-on-opaque-inference=yes
# List of class names for which member attributes should not be checked (useful
# for classes with dynamically set attributes). This supports the use of
# qualified names.
ignored-classes=optparse.Values,thread._local,_thread._local
# List of module names for which member attributes should not be checked
# (useful for modules/projects where namespaces are manipulated during runtime
# and thus existing member attributes cannot be deduced by static analysis). It
# supports qualified module names, as well as Unix pattern matching.
ignored-modules=
# Show a hint with possible names when a member name was not found. The aspect
# of finding the hint is based on edit distance.
missing-member-hint=yes
# The minimum edit distance a name should have in order to be considered a
# similar match for a missing member name.
missing-member-hint-distance=1
# The total number of similar names that should be taken in consideration when
# showing a hint for a missing member.
missing-member-max-choices=1
# Regex pattern to define which classes are considered mixins ignore-mixin-
# members is set to 'yes'
mixin-class-rgx=.*[Mm]ixin
# List of decorators that change the signature of a decorated function.
signature-mutators=
[VARIABLES]
# List of additional names supposed to be defined in builtins. Remember that
# you should avoid defining new builtins when possible.
additional-builtins=
# Tells whether unused global variables should be treated as a violation.
allow-global-unused-variables=yes
# List of names allowed to shadow builtins
allowed-redefined-builtins=
# List of strings which can identify a callback function by name. A callback
# name must start or end with one of those strings.
callbacks=cb_,
_cb
# A regular expression matching the name of dummy variables (i.e. expected to
# not be used).
dummy-variables-rgx=_+$|(_[a-zA-Z0-9_]*[a-zA-Z0-9]+?$)|dummy|^ignored_|^unused_
# Argument names that match this expression will be ignored. Default to name
# with leading underscore.
ignored-argument-names=_.*|^ignored_|^unused_
# Tells whether we should check for unused import in __init__ files.
init-import=no
# List of qualified module names which can have objects that can redefine
# builtins.
redefining-builtins-modules=six.moves,past.builtins,future.builtins,builtins,io
[BASIC]
# Naming style matching correct argument names.
argument-naming-style=snake_case
# Regular expression matching correct argument names. Overrides argument-
# naming-style. If left empty, argument names will be checked with the set
# naming style.
#argument-rgx=
# Naming style matching correct attribute names.
attr-naming-style=snake_case
# Regular expression matching correct attribute names. Overrides attr-naming-
# style. If left empty, attribute names will be checked with the set naming
# style.
#attr-rgx=
# Bad variable names which should always be refused, separated by a comma.
bad-names=foo,
bar,
baz,
toto,
tutu,
tata
# Bad variable names regexes, separated by a comma. If names match any regex,
# they will always be refused
bad-names-rgxs=
# Naming style matching correct class attribute names.
class-attribute-naming-style=any
# Regular expression matching correct class attribute names. Overrides class-
# attribute-naming-style. If left empty, class attribute names will be checked
# with the set naming style.
#class-attribute-rgx=
# Naming style matching correct class constant names.
class-const-naming-style=UPPER_CASE
# Regular expression matching correct class constant names. Overrides class-
# const-naming-style. If left empty, class constant names will be checked with
# the set naming style.
#class-const-rgx=
# Naming style matching correct class names.
class-naming-style=PascalCase
# Regular expression matching correct class names. Overrides class-naming-
# style. If left empty, class names will be checked with the set naming style.
#class-rgx=
# Naming style matching correct constant names.
const-naming-style=UPPER_CASE
# Regular expression matching correct constant names. Overrides const-naming-
# style. If left empty, constant names will be checked with the set naming
# style.
#const-rgx=
# Minimum line length for functions/classes that require docstrings, shorter
# ones are exempt.
docstring-min-length=-1
# Naming style matching correct function names.
function-naming-style=snake_case
# Regular expression matching correct function names. Overrides function-
# naming-style. If left empty, function names will be checked with the set
# naming style.
#function-rgx=
# Good variable names which should always be accepted, separated by a comma.
good-names=i,
j,
k,
f,
e,
el
ex,
ok,
Run,
_
# Good variable names regexes, separated by a comma. If names match any regex,
# they will always be accepted
good-names-rgxs=
# Include a hint for the correct naming format with invalid-name.
include-naming-hint=no
# Naming style matching correct inline iteration names.
inlinevar-naming-style=any
# Regular expression matching correct inline iteration names. Overrides
# inlinevar-naming-style. If left empty, inline iteration names will be checked
# with the set naming style.
#inlinevar-rgx=
# Naming style matching correct method names.
method-naming-style=snake_case
# Regular expression matching correct method names. Overrides method-naming-
# style. If left empty, method names will be checked with the set naming style.
#method-rgx=
# Naming style matching correct module names.
module-naming-style=snake_case
# Regular expression matching correct module names. Overrides module-naming-
# style. If left empty, module names will be checked with the set naming style.
#module-rgx=
# Colon-delimited sets of names that determine each other's naming style when
# the name regexes allow several styles.
name-group=
# Regular expression which should only match function or class names that do
# not require a docstring.
no-docstring-rgx=^_
# List of decorators that produce properties, such as abc.abstractproperty. Add
# to this list to register other decorators that produce valid properties.
# These decorators are taken in consideration only for invalid-name.
property-classes=abc.abstractproperty
# Regular expression matching correct type variable names. If left empty, type
# variable names will be checked with the set naming style.
#typevar-rgx=
# Naming style matching correct variable names.
variable-naming-style=snake_case
# Regular expression matching correct variable names. Overrides variable-
# naming-style. If left empty, variable names will be checked with the set
# naming style.
#variable-rgx=
[DESIGN]
# List of regular expressions of class ancestor names to ignore when counting
# public methods (see R0903)
exclude-too-few-public-methods=
# List of qualified class names to ignore when counting class parents (see
# R0901)
ignored-parents=
# Maximum number of arguments for function / method.
max-args=5
# Maximum number of attributes for a class (see R0902).
max-attributes=7
# Maximum number of boolean expressions in an if statement (see R0916).
max-bool-expr=5
# Maximum number of branch for function / method body.
max-branches=12
# Maximum number of locals for function / method body.
max-locals=15
# Maximum number of parents for a class (see R0901).
max-parents=7
# Maximum number of public methods for a class (see R0904).
max-public-methods=20
# Maximum number of return / yield for function / method body.
max-returns=6
# Maximum number of statements in function / method body.
max-statements=50
# Minimum number of public methods for a class (see R0903).
min-public-methods=2
[IMPORTS]
# List of modules that can be imported at any level, not just the top level
# one.
allow-any-import-level=
# Allow wildcard imports from modules that define __all__.
allow-wildcard-with-all=no
# Analyse import fallback blocks. This can be used to support both Python 2 and
# 3 compatible code, which means that the block might have code that exists
# only in one or another interpreter, leading to false positives when analysed.
analyse-fallback-blocks=no
# Deprecated modules which should not be used, separated by a comma.
deprecated-modules=
# Output a graph (.gv or any supported image format) of external dependencies
# to the given file (report RP0402 must not be disabled).
ext-import-graph=
# Output a graph (.gv or any supported image format) of all (i.e. internal and
# external) dependencies to the given file (report RP0402 must not be
# disabled).
import-graph=
# Output a graph (.gv or any supported image format) of internal dependencies
# to the given file (report RP0402 must not be disabled).
int-import-graph=
# Force import order to recognize a module as part of the standard
# compatibility libraries.
known-standard-library=
# Force import order to recognize a module as part of a third party library.
known-third-party=enchant
# Couples of modules and preferred modules, separated by a comma.
preferred-modules=
[CLASSES]
# Warn about protected attribute access inside special methods
check-protected-access-in-special-methods=no
# List of method names used to declare (i.e. assign) instance attributes.
defining-attr-methods=__init__,
__new__,
setUp,
__post_init__
# List of member names, which should be excluded from the protected access
# warning.
exclude-protected=_asdict,
_fields,
_replace,
_source,
_make
# List of valid names for the first argument in a class method.
valid-classmethod-first-arg=cls
# List of valid names for the first argument in a metaclass class method.
valid-metaclass-classmethod-first-arg=cls
[EXCEPTIONS]
# Exceptions that will emit a warning when being caught. Defaults to
# "BaseException, Exception".
overgeneral-exceptions=builtins.BaseException,
builtins.Exception
| 19,598 | Python | .py | 433 | 42.859122 | 113 | 0.785338 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,625 | test_setup.py | SUSE_klp-build/tests/test_setup.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza
import json
import logging
from pathlib import Path
import pytest
from klpbuild.setup import Setup
import klpbuild.utils as utils
from tests.utils import get_workdir
lp = "bsc9999999"
cs = "15.5u19"
def test_missing_file_funcs():
with pytest.raises(ValueError, match=r"You need to specify at least one of the file-funcs variants!"):
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None, mod_file_funcs=[],
conf_mod_file_funcs=[], file_funcs=[], mod_arg="vmlinux", conf=None,
archs=utils.ARCHS, skips=None, no_check=False).setup_project_files()
def test_missing_conf_prefix():
with pytest.raises(ValueError, match=r"Please specify --conf with CONFIG_ prefix"):
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None, mod_file_funcs=[],
conf_mod_file_funcs=[], file_funcs=[], conf="TUN", mod_arg="vmlinux",
archs=utils.ARCHS, skips=None, no_check=False).setup_project_files()
# Check for multiple variants of file-funcs
def test_file_funcs_ok():
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None, conf="CONFIG_TUN",
mod_arg="tun", mod_file_funcs=[], conf_mod_file_funcs=[],
file_funcs = [["drivers/net/tun.c", "tun_chr_ioctl", "tun_free_netdev"]],
archs=utils.ARCHS, skips=None, no_check=False).setup_project_files()
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None,
conf="CONFIG_TUN", file_funcs=[], conf_mod_file_funcs=[], mod_arg=None,
mod_file_funcs = [["tun", "drivers/net/tun.c", "tun_chr_ioctl", "tun_free_netdev"]],
archs=utils.ARCHS, skips=None, no_check=False).setup_project_files()
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None,
conf="CONFIG_TUN", mod_file_funcs=[], file_funcs=[], mod_arg=None,
conf_mod_file_funcs = [["CONFIG_TUN", "tun", "drivers/net/tun.c", "tun_chr_ioctl", "tun_free_netdev"]],
archs=utils.ARCHS, skips=None, no_check=False).setup_project_files()
def test_non_existent_file():
with pytest.raises(RuntimeError, match=r".*: File drivers/net/tuna.c not found on .*"):
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None, conf="CONFIG_TUN",
mod_arg="tun", mod_file_funcs=[], conf_mod_file_funcs=[],
file_funcs = [["drivers/net/tuna.c", "tun_chr_ioctl", "tun_free_netdev"]],
archs=utils.ARCHS, skips=None, no_check=False).setup_project_files()
def test_non_existent_module():
with pytest.raises(RuntimeError, match=r"Module not found: tuna"):
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None, conf="CONFIG_TUN",
mod_arg="tuna", mod_file_funcs=[], conf_mod_file_funcs=[],
file_funcs = [["drivers/net/tun.c", "tun_chr_ioctl", "tun_free_netdev"]],
archs=utils.ARCHS, skips=None, no_check=False).setup_project_files()
def test_invalid_sym(caplog):
with caplog.at_level(logging.WARNING):
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None, conf="CONFIG_TUN",
mod_arg="tun", mod_file_funcs=[], conf_mod_file_funcs=[],
file_funcs = [["drivers/net/tun.c", "tun_chr_ioctll", "tun_free_netdev"]],
archs=utils.ARCHS, skips=None, no_check=False).setup_project_files()
assert "Symbols tun_chr_ioctll not found on tun" in caplog.text
def test_check_conf_mod_file_funcs():
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None, mod_arg="sch_qfq",
conf="CONFIG_TUN", mod_file_funcs=[], file_funcs=[],
conf_mod_file_funcs = [["CONFIG_TUN", "tun", "drivers/net/tun.c", "tun_chr_ioctl", "tun_free_netdev"]],
archs=[utils.ARCH], skips=None, no_check=False).setup_project_files()
def test_check_conf_mod_file_funcs():
# Check that passing mod-file-funcs can create entries differently from general
# --module and --file-funcs
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None, mod_arg="sch_qfq",
conf="CONFIG_NET_SCH_QFQ", conf_mod_file_funcs=[],
file_funcs=[["net/sched/sch_qfq.c", "qfq_change_class"]],
mod_file_funcs=[["btsdio", "drivers/bluetooth/btsdio.c", "btsdio_probe", "btsdio_remove"]],
archs=[utils.ARCH], skips=None, no_check=False).setup_project_files()
with open(Path(get_workdir(lp, cs), "codestreams.json")) as f:
data = json.loads(f.read())[cs]["files"]
sch = data["net/sched/sch_qfq.c"]
bts = data["drivers/bluetooth/btsdio.c"]
assert sch["conf"] == bts["conf"]
assert sch["module"] == "sch_qfq"
assert bts["module"] == "btsdio"
# Rerun setup and now conf and module should be different
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None, mod_arg="sch_qfq",
conf="CONFIG_NET_SCH_QFQ", mod_file_funcs=[],
file_funcs=[["net/sched/sch_qfq.c", "qfq_change_class"]],
conf_mod_file_funcs = [ ["CONFIG_BT_HCIBTSDIO", "btsdio",
"drivers/bluetooth/btsdio.c", "btsdio_probe",
"btsdio_remove"] ],
archs=[utils.ARCH], skips=None, no_check=False).setup_project_files()
with open(Path(get_workdir(lp, cs), "codestreams.json")) as f:
data = json.loads(f.read())[cs]["files"]
sch = data["net/sched/sch_qfq.c"]
bts = data["drivers/bluetooth/btsdio.c"]
assert sch["conf"] == "CONFIG_NET_SCH_QFQ"
assert sch["module"] == "sch_qfq"
assert bts["conf"] == "CONFIG_BT_HCIBTSDIO"
assert bts["module"] == "btsdio"
| 5,619 | Python | .py | 92 | 53.054348 | 113 | 0.638248 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,626 | test_extract.py | SUSE_klp-build/tests/test_extract.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza
from klpbuild.extractor import Extractor
from klpbuild.setup import Setup
import klpbuild.utils as utils
import logging
def test_detect_file_without_ftrace_support(caplog):
lp = "bsc9999999"
cs = "15.6u0"
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None,
file_funcs=[["lib/seq_buf.c", "seq_buf_putmem_hex"]],
mod_file_funcs=[], conf_mod_file_funcs=[], mod_arg="vmlinux",
conf="CONFIG_SMP",
archs=[utils.ARCH], skips=None, no_check=False).setup_project_files()
with caplog.at_level(logging.WARNING):
Extractor(lp_name=lp, lp_filter=cs, apply_patches=False, app="ce",
avoid_ext=[], ignore_errors=False).run()
assert "lib/seq_buf.o is not compiled with livepatch support (-pg flag)" in caplog.text
| 906 | Python | .py | 20 | 39.35 | 91 | 0.678409 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,627 | test_utils.py | SUSE_klp-build/tests/test_utils.py | import klpbuild.utils as utils
from klpbuild.codestream import Codestream
def test_group_classify():
assert utils.classify_codestreams(["15.2u10", "15.2u11", "15.3u10", "15.3u12"]) == \
["15.2u10-11", "15.3u10-12"]
assert utils.classify_codestreams([Codestream("", 15, 2, 10, False),
Codestream("", 15, 2, 11, False),
Codestream("", 15, 3, 10, False),
Codestream("", 15, 3, 12, False)]) == \
["15.2u10-11", "15.3u10-12"]
| 631 | Python | .py | 10 | 41.1 | 88 | 0.452342 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,628 | test_ksrc.py | SUSE_klp-build/tests/test_ksrc.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza
from klpbuild.ksrc import GitHelper
import pytest
def test_multiline_upstream_commit_subject():
_, subj = GitHelper.get_commit_data("49c47cc21b5b")
assert subj == "net: tls: fix possible race condition between do_tls_getsockopt_conf() and do_tls_setsockopt_conf()"
# This CVE is already covered on all codestreams
def test_scan_all_cs_patched(caplog):
with pytest.raises(SystemExit):
GitHelper("bsc_check", "").scan("2022-48801", "", False)
assert "All supported codestreams are already patched" not in caplog.text
| 648 | Python | .py | 14 | 43.285714 | 120 | 0.749206 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,629 | utils.py | SUSE_klp-build/tests/utils.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza
from pathlib import Path
from klpbuild.config import Config
def get_workdir(lp_name, lp_filter):
return Config(lp_name, lp_filter).lp_path
def get_file_content(lp_name, filter, fname=None):
# Check the generated LP files
path = Path(get_workdir(lp_name, filter), "ce", filter, "lp")
if not fname:
fname = f'livepatch_{lp_name}.c'
with open(Path(path, fname)) as f:
return f.read()
| 528 | Python | .py | 15 | 31.4 | 65 | 0.700197 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,630 | test_config.py | SUSE_klp-build/tests/test_config.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
from klpbuild.codestream import Codestream
from klpbuild.config import Config
from tests.utils import get_file_content, get_workdir
def test_filter():
lp = "bsc9999999"
def to_cs(cs_list):
ret = []
for cs in cs_list:
ret.append(Codestream.from_cs("", cs))
return ret
# Same output because filter and skip were not informed
assert Config(lp, "").filter_cs(to_cs(["12.5u10", "15.6u10"])) == to_cs(["12.5u10", "15.6u10"])
# Filter only one codestream
assert Config(lp, "12.5u10").filter_cs(to_cs(["12.5u10", "12.5u11", "15.6u10"])) == \
to_cs(["12.5u10"])
# Filter codestreams using regex
assert Config(lp, "12.5u1[01]").filter_cs(to_cs(["12.5u10", "12.5u11", "15.6u10"])) \
== to_cs(["12.5u10", "12.5u11"])
assert Config(lp, "12.5u1[01]|15.6u10").filter_cs(to_cs(["12.5u10",
"12.5u11",
"15.6u10"])) \
== to_cs(["12.5u10", "12.5u11", "15.6u10"])
# Use skip with filter
assert Config(lp, "12.5u1[01]", skips="15.6u10").filter_cs(to_cs(["12.5u10",
"12.5u11",
"15.6u10"])) \
== to_cs(["12.5u10", "12.5u11"])
# Use skip with filter
assert Config(lp, "12.5u1[01]", skips="15.6").filter_cs(to_cs(["12.5u10",
"12.5u11",
"15.6u12",
"15.6u13"])) \
== to_cs(["12.5u10", "12.5u11"])
# filter is off, but skip will also only filter the 12.5 ones
assert Config(lp, "", skips="15.6").filter_cs(to_cs(["12.5u10", "12.5u11",
"15.6u12", "15.6u13"])) \
== to_cs(["12.5u10", "12.5u11"])
assert Config(lp, "", skips="15.6u13").filter_cs(to_cs(["12.5u10",
"12.5u11",
"15.6u12",
"15.6u13"])) \
== to_cs(["12.5u10", "12.5u11", "15.6u12"])
| 2,766 | Python | .py | 46 | 34.521739 | 99 | 0.384985 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,631 | test_templ.py | SUSE_klp-build/tests/test_templ.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza
from klpbuild.extractor import Extractor
from klpbuild.setup import Setup
import klpbuild.utils as utils
from tests.utils import get_file_content
def test_templ_with_externalized_vars():
lp = "bsc9999999"
cs = "15.5u19"
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None,
file_funcs=[["fs/proc/cmdline.c", "cmdline_proc_show"]],
mod_file_funcs=[], conf_mod_file_funcs=[], mod_arg="vmlinux",
conf="CONFIG_PROC_FS",
archs=utils.ARCHS, skips=None, no_check=False).setup_project_files()
Extractor(lp_name=lp, lp_filter=cs, apply_patches=False, app="ce",
avoid_ext=[], ignore_errors=False).run()
# As we passed vmlinux as module, we don't have the module notifier and
# LP_MODULE, linux/module.h is not included
# As the code is using the default archs, which is all of them, the
# IS_ENABLED macro shouldn't exist
content = get_file_content(lp, cs)
for check in ["LP_MODULE", "module_notify", "linux/module.h", "#if IS_ENABLED"]:
assert check not in content
# For this file and symbol, there is one symbol to be looked up, so
# klp_funcs should be present
assert "klp_funcs" in content
def test_templ_without_externalized_vars():
lp = "bsc9999999"
cs = "15.5u19"
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None,
file_funcs=[["net/ipv6/rpl.c", "ipv6_rpl_srh_size"]],
mod_file_funcs=[], conf_mod_file_funcs=[], mod_arg="vmlinux",
conf="CONFIG_IPV6",
archs=[utils.ARCH], skips=None, no_check=False).setup_project_files()
Extractor(lp_name=lp, lp_filter=cs, apply_patches=False, app="ce",
avoid_ext=[], ignore_errors=False).run()
# As we passed vmlinux as module, we don't have the module notifier and
# LP_MODULE, linux/module.h is not included
# For this file and symbol, no externalized symbols are used, so
# klp_funcs shouldn't be preset.
content = get_file_content(lp, cs)
for check in ["LP_MODULE", "module_notify", "linux/module.h", "klp_funcs"]:
assert check not in content
# As the config only targets x86_64, IS_ENABLED should be set
assert "#if IS_ENABLED" in content
# For multifile patches, a third file will be generated and called
# livepatch_XXX, and alongside this file the other files will have the prefix
# bscXXXXXXX.
def test_check_header_file_included():
lp = "bsc9999999"
cs = "15.5u17"
Setup(lp_name=lp, lp_filter=cs, data_dir=None, cve=None,
file_funcs=[["net/ipv6/rpl.c", "ipv6_rpl_srh_size"], ["kernel/events/core.c", "perf_event_exec"]],
mod_file_funcs=[], conf_mod_file_funcs=[], mod_arg="vmlinux",
conf="CONFIG_IPV6",
archs=[utils.ARCH], skips=None, no_check=False).setup_project_files()
Extractor(lp_name=lp, lp_filter=cs, apply_patches=False, app="ce",
avoid_ext=[], ignore_errors=False).run()
# test the livepatch_ prefix file
assert "Upstream commit:" in get_file_content(lp, cs)
# Check the other two files
assert "Upstream commit:" not in get_file_content(lp, cs, f"{lp}_kernel_events_core.c")
assert "Upstream commit:" not in get_file_content(lp, cs, f"{lp}_net_ipv6_rpl.c")
| 3,376 | Python | .py | 65 | 45.507692 | 108 | 0.667476 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,632 | codestream.py | SUSE_klp-build/klpbuild/codestream.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
from pathlib import Path
import re
from klpbuild.utils import ARCH
class Codestream:
__slots__ = ("data_path", "sle", "sp", "update", "rt", "ktype", "project",
"kernel", "archs", "files", "modules", "repo")
def __init__(self, data_path, sle, sp, update, rt, project="", kernel="",
archs=[], files={}, modules={}):
self.data_path = data_path
self.sle = sle
self.sp = sp
self.update = update
self.rt = rt
self.ktype = "-rt" if rt else "-default"
self.project = project
self.kernel = kernel
self.archs = archs
self.files = files
self.modules = modules
self.repo = self.get_repo()
@classmethod
def from_codestream(cls, data_path, cs, proj, kernel):
# Parse SLE15-SP2_Update_25 to 15.2u25
rt = "rt" if "-RT" in cs else ""
sle, _, u = cs.replace("SLE", "").replace("-RT", "").split("_")
if "-SP" in sle:
sle, sp = sle.split("-SP")
else:
sp = "0"
return cls(data_path, int(sle), int(sp), int(u), rt, proj, kernel)
@classmethod
def from_cs(cls, data_path, cs):
match = re.search(r"(\d+)\.(\d+)(rt)?u(\d+)", cs)
return cls(data_path, int(match.group(1)), int(match.group(2)), int(match.group(4)), match.group(3))
@classmethod
def from_data(cls, data_path, data):
return cls(data_path, data["sle"], data["sp"], data["update"], data["rt"],
data["project"], data["kernel"], data["archs"], data["files"],
data["modules"])
def __eq__(self, cs):
return self.sle == cs.sle and \
self.sp == cs.sp and \
self.update == cs.update and \
self.rt == cs.rt
def get_data_dir(self, arch):
# For the SLE usage, it should point to the place where the codestreams
# are downloaded
return Path(self.data_path, arch)
def get_sdir(self, arch=ARCH):
# Only -rt codestreams have a suffix for source directory
ktype = self.ktype.replace("-default", "")
return Path(self.get_data_dir(arch), "usr", "src", f"linux-{self.kernel}{ktype}")
def get_odir(self):
return Path(f"{self.get_sdir(ARCH)}-obj", ARCH, self.ktype.replace("-", ""))
def get_ipa_file(self, fname):
return Path(self.get_odir(), f"{fname}.000i.ipa-clones")
def get_boot_file(self, file, arch=ARCH):
assert file in ["vmlinux", "config", "symvers"]
return Path(self.get_data_dir(arch), "boot", f"{file}-{self.kname()}")
def get_repo(self):
if self.update == 0:
return "standard"
repo = f"SUSE_SLE-{self.sle}"
if self.sp != 0:
repo = f"{repo}-SP{self.sp}"
repo = f"{repo}_Update"
# On 15.5 the RT kernels and in the main codestreams
if not self.rt or (self.sle == 15 and self.sp == 5):
return repo
return f"{repo}_Products_SLERT_Update"
def set_archs(self, archs):
self.archs = archs
def set_files(self, files):
self.files = files
def kname(self):
return self.kernel + self.ktype
def name(self):
if self.rt:
return f"{self.sle}.{self.sp}rtu{self.update}"
return f"{self.sle}.{self.sp}u{self.update}"
def name_cs(self):
if self.rt:
return f"{self.sle}.{self.sp}rt"
return f"{self.sle}.{self.sp}"
# Parse 15.2u25 to SLE15-SP2_Update_25
def name_full(self):
buf = f"SLE{self.sle}"
if int(self.sp) > 0:
buf = f"{buf}-SP{self.sp}"
if self.rt:
buf = f"{buf}-RT"
return f"{buf}_Update_{self.update}"
# 15.4 onwards we don't have module_mutex, so template generates
# different code
def is_mod_mutex(self):
return self.sle < 15 or (self.sle == 15 and self.sp < 4)
def get_mod_path(self, arch):
return Path(self.get_data_dir(arch), "lib", "modules", f"{self.kname()}")
# Returns the path to the kernel-obj's build dir, used when build testing
# the generated module
def get_kernel_build_path(self, arch):
return Path(self.get_mod_path(arch), "build")
def get_all_configs(self, conf):
"""
Get the config value for all supported architectures of a codestream. If
the configuration is not set the return value will be an empty dict.
"""
configs = {}
for arch in self.archs:
kconf = self.get_boot_file("config", arch)
with open(kconf) as f:
match = re.search(rf"{conf}=([ym])", f.read())
if match:
configs[arch] = match.group(1)
return configs
def data(self):
return {
"sle" : self.sle,
"sp" : self.sp,
"update" : self.update,
"rt" : self.rt,
"project" : self.project,
"kernel" : self.kernel,
"archs" : self.archs,
"files" : self.files,
"modules" : self.modules,
"repo" : self.repo,
"data_path" : str(self.data_path),
}
| 5,416 | Python | .py | 133 | 30.984962 | 108 | 0.550048 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,633 | inline.py | SUSE_klp-build/klpbuild/inline.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
import shutil
from pathlib import Path
import subprocess
from klpbuild.config import Config
from klpbuild.utils import ARCH
class Inliner(Config):
def __init__(self, lp_name, lp_filter):
super().__init__(lp_name, lp_filter)
if not self.lp_path.exists():
raise ValueError(f"{self.lp_path} not created. Run the setup subcommand first")
self.ce_inline_path = shutil.which("ce-inline")
if not self.ce_inline_path:
raise RuntimeError("ce-inline not found. Aborting.")
def check_inline(self, fname, func):
ce_args = [ str(self.ce_inline_path), "-where-is-inlined" ]
filtered = self.filter_cs()
if not filtered:
raise RuntimeError(f"Codestream {self.lp_filter} not found. Aborting.")
assert len(filtered) == 1
cs = filtered[0]
mod = cs.files.get(fname, {}).get("module", None)
if not mod:
raise RuntimeError(f"File {fname} not in setup phase. Aborting.")
ce_args.extend(["-debuginfo", str(self.get_module_obj(ARCH, cs, mod))])
# clang-extract works without ipa-clones, so don't hard require it
ipa_f = cs.get_ipa_file(fname)
if ipa_f.exists():
ce_args.extend(["-ipa-files", str(ipa_f)])
ce_args.extend(["-symvers", str(cs.get_boot_file("symvers"))])
ce_args.extend([func])
print(" ".join(ce_args))
print(subprocess.check_output(ce_args).decode())
| 1,602 | Python | .py | 36 | 36.944444 | 91 | 0.638065 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,634 | setup.py | SUSE_klp-build/klpbuild/setup.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
import copy
import json
import logging
import re
from pathlib import Path
from natsort import natsorted
from klpbuild import utils
from klpbuild.config import Config
from klpbuild.ksrc import GitHelper
class Setup(Config):
def __init__(
self,
lp_name,
lp_filter,
data_dir,
cve,
file_funcs,
mod_file_funcs,
conf_mod_file_funcs,
mod_arg,
conf,
archs,
skips,
no_check,
):
super().__init__(lp_name, lp_filter, data_dir, skips=skips)
archs.sort()
if not lp_name.startswith("bsc"):
raise ValueError("Please use prefix 'bsc' when creating a livepatch for codestreams")
if conf and not conf.startswith("CONFIG_"):
raise ValueError("Please specify --conf with CONFIG_ prefix")
if self.lp_path.exists() and not self.lp_path.is_dir():
raise ValueError("--name needs to be a directory, or not to exist")
if not file_funcs and not mod_file_funcs and not conf_mod_file_funcs:
raise ValueError("You need to specify at least one of the file-funcs variants!")
self.conf["archs"] = archs
if cve:
self.conf["cve"] = re.search(r"([0-9]+\-[0-9]+)", cve).group(1)
self.no_check = no_check
self.file_funcs = {}
for f in file_funcs:
filepath = f[0]
funcs = f[1:]
self.file_funcs[filepath] = {"module": mod_arg, "conf": conf, "symbols": funcs}
for f in mod_file_funcs:
fmod = f[0]
filepath = f[1]
funcs = f[2:]
self.file_funcs[filepath] = {"module": fmod, "conf": conf, "symbols": funcs}
for f in conf_mod_file_funcs:
fconf = f[0]
fmod = f[1]
filepath = f[2]
funcs = f[3:]
self.file_funcs[filepath] = {"module": fmod, "conf": fconf, "symbols": funcs}
def setup_codestreams(self):
ksrc = GitHelper(self.lp_name, self.filter, skips=self.skips)
# Called at this point because codestreams is populated
commits, patched_cs, patched_kernels, codestreams = ksrc.scan(
self.conf.get("cve", ""),
"",
self.no_check)
self.conf["commits"] = commits
self.conf["patched_kernels"] = patched_kernels
# Add new codestreams to the already existing list, skipping duplicates
self.conf["patched_cs"] = natsorted(list(set(self.conf.get("patched_cs",
[]) + patched_cs)))
return codestreams
def setup_project_files(self):
self.lp_path.mkdir(exist_ok=True)
codestreams = self.setup_codestreams()
logging.info(f"Affected architectures:")
logging.info(f"\t{' '.join(self.conf['archs'])}")
logging.info("Checking files, symbols, modules...")
# Setup the missing codestream info needed
for cs in codestreams:
cs.set_files(copy.deepcopy(self.file_funcs))
# Check if the files exist in the respective codestream directories
mod_syms = {}
kernel = cs.kernel
for f, fdata in cs.files.items():
self.validate_config(cs, fdata["conf"], fdata["module"])
sdir = cs.get_sdir()
if not Path(sdir, f).is_file():
raise RuntimeError(f"{cs.name()} ({kernel}): File {f} not found on {str(sdir)}")
ipa_f = cs.get_ipa_file(f)
if not ipa_f.is_file():
msg = f"{cs.name()} ({kernel}): File {ipa_f} not found. Creating an empty file."
ipa_f.touch()
logging.warning(msg)
# If the config was enabled on all supported architectures,
# there is no point in leaving the conf being set, since the
# feature will be available everywhere.
if self.conf["archs"] == utils.ARCHS:
fdata["conf"] = ""
mod = fdata["module"]
if not cs.modules.get(mod, ""):
if utils.is_mod(mod):
mod_path = str(self.find_module_obj(utils.ARCH, cs, mod,
check_support=True))
else:
mod_path = str(cs.get_boot_file("vmlinux"))
cs.modules[mod] = mod_path
mod_syms.setdefault(mod, [])
mod_syms[mod].extend(fdata["symbols"])
# Verify if the functions exist in the specified object
for mod, syms in mod_syms.items():
arch_syms = self.check_symbol_archs(cs, mod, syms, False)
if arch_syms:
for arch, syms in arch_syms.items():
m_syms = ",".join(syms)
cs_ = f"{cs.name()}-{arch} ({cs.kernel})"
logging.warning(f"{cs_}: Symbols {m_syms} not found on {mod} object")
self.flush_cs_file(codestreams)
# cpp will use this data in the next step
with open(self.conf_file, "w") as f:
f.write(json.dumps(self.conf, indent=4))
logging.info("Done. Setup finished.")
| 5,603 | Python | .py | 122 | 32.303279 | 100 | 0.532794 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,635 | config.py | SUSE_klp-build/klpbuild/config.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
import configparser
import copy
import json
import logging
import os
import re
from collections import OrderedDict
from pathlib import Path, PurePath
from klpbuild.codestream import Codestream
from klpbuild.utils import ARCH, classify_codestreams, is_mod
from klpbuild.utils import get_all_symbols_from_object, get_elf_object, get_elf_modinfo_entry
class Config:
def __init__(self, lp_name, lp_filter, data_dir=None, skips=""):
# FIXME: Config is instantiated multiple times, meaning that the
# config file gets loaded and the logs are printed as many times.
logging.basicConfig(level=logging.INFO, format="%(message)s")
home = Path.home()
self.user_conf_file = Path(home, ".config/klp-build/config")
if not self.user_conf_file.is_file():
logging.warning(f"Warning: user configuration file not found")
# If there's no configuration file assume fresh install.
# Prepare the system with a default environment and conf.
self.setup_user_env(Path(home, "klp"))
self.load_user_conf()
work = self.get_user_path('work_dir')
self.lp_name = lp_name
self.lp_path = Path(work, self.lp_name)
self.filter = lp_filter
self.skips = skips
self.codestreams = OrderedDict()
self.codestreams_list = []
self.conf = OrderedDict(
{"name": str(self.lp_name), "work_dir": str(self.lp_path), "data":
str(data_dir), }
)
self.conf_file = Path(self.lp_path, "conf.json")
if self.conf_file.is_file():
with open(self.conf_file) as f:
self.conf = json.loads(f.read(), object_pairs_hook=OrderedDict)
self.data = Path(self.conf.get("data", "non-existent"))
if not self.data.exists():
self.data = self.get_user_path('data_dir')
self.cs_file = Path(self.lp_path, "codestreams.json")
if self.cs_file.is_file():
with open(self.cs_file) as f:
self.codestreams = json.loads(f.read(), object_pairs_hook=OrderedDict)
for _, data in self.codestreams.items():
self.codestreams_list.append(Codestream.from_data(self.data, data))
# will contain the symbols from the to be livepatched object
# cached by the codestream : object
self.obj_symbols = {}
def setup_user_env(self, basedir):
workdir = Path(basedir, "livepatches")
datadir = Path(basedir, "data")
config = configparser.ConfigParser(allow_no_value=True)
config['Paths'] = {'work_dir': workdir,
'data_dir': datadir,
'## SUSE internal use only ##': None,
'#kgr_patches_dir': 'kgraft-patches/',
'#kgr_patches_tests_dir': 'kgraft-patches_testscripts/',
'#kernel_src_dir': 'kernel-src/',
'#ccp_pol_dir': 'kgr-scripts/ccp-pol/'}
config['Settings'] = {'workers': 4}
logging.info(f"Creating default user configuration: '{self.user_conf_file}'")
os.makedirs(os.path.dirname(self.user_conf_file), exist_ok=True)
with open(self.user_conf_file, 'w') as f:
config.write(f)
os.makedirs(workdir, exist_ok=True)
os.makedirs(datadir, exist_ok=True)
def load_user_conf(self):
config = configparser.ConfigParser()
logging.info(f"Loading user configuration from '{self.user_conf_file}'")
config.read(self.user_conf_file)
# Check mandatory fields
for s in {'Paths', 'Settings'}:
if s not in config:
raise ValueError(f"config: '{s}' section not found")
self.user_conf = config
def get_user_path(self, entry, isdir=True, isopt=False):
if entry not in self.user_conf['Paths']:
if isopt:
return ""
raise ValueError(f"config: '{entry}' entry not found")
p = Path(self.user_conf['Paths'][entry])
if not p.exists():
raise ValueError(f"'{p}' file or directory not found")
if isdir and not p.is_dir():
raise ValueError("{p} should be a directory")
if not isdir and not p.is_file():
raise ValueError("{p} should be a file")
return p
def get_user_settings(self, entry, isopt=False):
if entry not in self.user_conf['Settings']:
if isopt:
return ""
raise ValueError(f"config: '{entry}' entry not found")
return self.user_conf['Settings'][entry]
def lp_out_file(self, fname):
fpath = f'{str(fname).replace("/", "_").replace("-", "_")}'
return f"{self.lp_name}_{fpath}"
def get_cs_dir(self, cs, app):
return Path(self.lp_path, app, cs.name())
def get_work_dir(self, cs, fname, app):
fpath = f'work_{str(fname).replace("/", "_")}'
return Path(self.get_cs_dir(cs, app), fpath)
# Return a Codestream object from the codestream name
def get_cs(self, cs):
return Codestream.from_data(self.data, self.codestreams[cs])
def validate_config(self, cs, conf, mod):
"""
Check if the CONFIG is enabled on the codestream. If the configuration
entry is set as M, check if a module was specified (different from
vmlinux).
"""
configs = {}
name = cs.name()
# Validate only the specified architectures, but check if the codestream
# is supported on that arch (like RT that is currently supported only on
# x86_64)
for arch, conf_entry in cs.get_all_configs(conf).items():
if conf_entry == "m" and mod == "vmlinux":
raise RuntimeError(f"{name}:{arch} ({cs.kernel}): Config {conf} is set as module, but no module was specified")
elif conf_entry == "y" and mod != "vmlinux":
raise RuntimeError(f"{name}:{arch} ({cs.kernel}): Config {conf} is set as builtin, but a module {mod} was specified")
configs.setdefault(conf_entry, [])
configs[conf_entry].append(f"{name}:{arch}")
if len(configs.keys()) > 1:
print(configs["y"])
print(configs["m"])
raise RuntimeError(f"Configuration mismtach between codestreams. Aborting.")
def get_tests_path(self):
self.kgraft_tests_path = self.get_user_path('kgr_patches_tests_dir')
test_sh = Path(self.kgraft_tests_path, f"{self.lp_name}_test_script.sh")
test_dir_sh = Path(self.kgraft_tests_path, f"{self.lp_name}/test_script.sh")
if test_sh.is_file():
test_src = test_sh
elif test_dir_sh.is_file():
# For more complex tests we support using a directory containing
# as much files as needed. A `test_script.sh` is still required
# as an entry point.
test_src = Path(os.path.dirname(test_dir_sh))
else:
raise RuntimeError(f"Couldn't find {test_sh} or {test_dir_sh}")
return test_src
# Update and save codestreams data
def flush_cs_file(self, working_cs):
for cs in working_cs:
self.codestreams[cs.name()] = cs.data()
with open(self.cs_file, "w") as f:
f.write(json.dumps(self.codestreams, indent=4))
# This function can be called to get the path to a module that has symbols
# that were externalized, so we need to find the path to the module as well.
def get_module_obj(self, arch, cs, module):
if not is_mod(module):
return cs.get_boot_file("vmlinux", arch)
obj = cs.modules.get(module, "")
if not obj:
obj = self.find_module_obj(arch, cs, module)
return Path(cs.get_mod_path(arch), obj)
# Return only the name of the module to be livepatched
def find_module_obj(self, arch, cs, mod, check_support=False):
assert mod != "vmlinux"
# Module name use underscores, but the final module object uses hyphens.
mod = mod.replace("_", "[-_]")
mod_path = cs.get_mod_path(arch)
with open(Path(mod_path, "modules.order")) as f:
obj_match = re.search(rf"([\w\/\-]+\/{mod}.k?o)", f.read())
if not obj_match:
raise RuntimeError(f"{cs.name()}-{arch} ({cs.kernel}): Module not found: {mod}")
# modules.order will show the module with suffix .o, so
# make sure the extension. Also check for multiple extensions since we
# can have modules being compressed using different algorithms.
for ext in [".ko", ".ko.zst", ".ko.gz"]:
obj = str(PurePath(obj_match.group(1)).with_suffix(ext))
if Path(mod_path, obj).exists():
break
if check_support:
# Validate if the module being livepatches is supported or not
elffile = get_elf_object(Path(mod_path, obj))
if "no" == get_elf_modinfo_entry(elffile, "supported"):
print(f"WARN: {cs.name()}-{arch} ({cs.kernel}): Module {mod} is not supported by SLE")
return obj
# Return the codestreams list but removing already patched codestreams,
# codestreams without file-funcs and not matching the filter
def filter_cs(self, cs_list=None, verbose=False):
if not cs_list:
cs_list = self.codestreams_list
full_cs = copy.deepcopy(cs_list)
if verbose:
logging.info("Checking filter and skips...")
result = []
filtered = []
for cs in full_cs:
name = cs.name()
if self.filter and not re.match(self.filter, name):
filtered.append(name)
continue
elif self.skips and re.match(self.skips, name):
filtered.append(name)
continue
result.append(cs)
if verbose:
if filtered:
logging.info("Skipping codestreams:")
logging.info(f'\t{" ".join(classify_codestreams(filtered))}')
return result
# Cache the symbols using the object path. It differs for each
# codestream and architecture
# Return all the symbols not found per arch/obj
def check_symbol(self, arch, cs, mod, symbols):
name = cs.name()
self.obj_symbols.setdefault(arch, {})
self.obj_symbols[arch].setdefault(name, {})
if not self.obj_symbols[arch][name].get(mod, ""):
obj = self.get_module_obj(arch, cs, mod)
self.obj_symbols[arch][name][mod] = get_all_symbols_from_object(obj, True)
ret = []
for symbol in symbols:
nsyms = self.obj_symbols[arch][name][mod].count(symbol)
if nsyms == 0:
ret.append(symbol)
elif nsyms > 1:
print(f"WARNING: {cs.name()}-{arch} ({cs.kernel}): symbol {symbol} duplicated on {mod}")
# If len(syms) == 1 means that we found a unique symbol, which is
# what we expect, and nothing need to be done.
return ret
# This functions is used to check if the symbols exist in the module they
# we will livepatch. In this case skip_on_host argument will be false,
# meaning that we want the symbol to checked against all supported
# architectures before creating the livepatches.
#
# It is also used when we want to check if a symbol externalized in one
# architecture exists in the other supported ones. In this case skip_on_host
# will be True, since we trust the decisions made by the extractor tool.
def check_symbol_archs(self, cs, mod, symbols, skip_on_host):
arch_sym = {}
# Validate only architectures supported by the codestream
for arch in cs.archs:
if arch == ARCH and skip_on_host:
continue
# Skip if the arch is not supported by the livepatch code
if not arch in self.conf.get("archs"):
continue
# Assign the not found symbols on arch
syms = self.check_symbol(arch, cs, mod, symbols)
if syms:
arch_sym[arch] = syms
return arch_sym
| 12,413 | Python | .py | 252 | 38.797619 | 133 | 0.603922 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,636 | ccp.py | SUSE_klp-build/klpbuild/ccp.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
import os
from pathlib import Path
import shutil
from klpbuild.config import Config
from klpbuild.utils import ARCH, is_mod
class CCP(Config):
def __init__(self, lp_name, lp_filter, avoid_ext):
super().__init__(lp_name, lp_filter)
self.env = os.environ
# List of symbols that are currently not resolvable for klp-ccp
avoid_syms = [
"__xadd_wrong_size",
"__bad_copy_from",
"__bad_copy_to",
"rcu_irq_enter_disabled",
"rcu_irq_enter_irqson",
"rcu_irq_exit_irqson",
"verbose",
"__write_overflow",
"__read_overflow",
"__read_overflow2",
"__real_strnlen",
"__real_strlcpy",
"twaddle",
"set_geometry",
"valid_floppy_drive_params",
"__real_memchr_inv",
"__real_kmemdup",
"lockdep_rtnl_is_held",
"lockdep_rht_mutex_is_held",
"debug_lockdep_rcu_enabled",
"lockdep_rcu_suspicious",
"rcu_read_lock_bh_held",
"lock_acquire",
"preempt_count_add",
"rcu_read_lock_any_held",
"preempt_count_sub",
"lock_release",
"trace_hardirqs_off",
"trace_hardirqs_on",
"debug_smp_processor_id",
"lock_is_held_type",
"mutex_lock_nested",
"rcu_read_lock_held",
"__bad_unaligned_access_size",
"__builtin_alloca",
"tls_validate_xmit_skb_sw",
]
# The backlist tells the klp-ccp to always copy the symbol code,
# instead of externalizing. This helps in cases where different archs
# have different inline decisions, optimizing and sometimes removing the
# symbols.
if avoid_ext:
avoid_syms.extend(avoid_ext)
self.env["KCP_EXT_BLACKLIST"] = ",".join(avoid_syms)
self.env["KCP_READELF"] = "readelf"
self.env["KCP_RENAME_PREFIX"] = "klp"
# Generate the list of exported symbols
def get_symbol_list(self, out_dir):
exts = []
for ext_file in ["fun_exts", "obj_exts"]:
ext_path = Path(out_dir, ext_file)
if not ext_path.exists():
continue
with open(ext_path) as f:
for l in f:
l = l.strip()
if not l.startswith("KALLSYMS") and not l.startswith("KLP_CONVERT"):
continue
_, sym, var, mod = l.split(" ")
if not is_mod(mod):
mod = "vmlinux"
exts.append((sym, var, mod))
exts.sort(key=lambda tup: tup[0])
# store the externalized symbols and module used in this codestream file
symbols = {}
for ext in exts:
sym, mod = ext[0], ext[2]
symbols.setdefault(mod, [])
symbols[mod].append(sym)
return symbols
def cmd_args(self, needs_ibt, cs, fname, funcs, out_dir, fdata, cmd):
lp_name = self.lp_out_file(fname)
lp_out = Path(out_dir, lp_name)
ccp_args = [str(shutil.which("klp-ccp")) , "-P", "suse.KlpPolicy",
"--compiler=x86_64-gcc-9.1.0", "-i", f"{funcs}", "-o",
f"{str(lp_out)}", "--"]
# -flive-patching and -fdump-ipa-clones are only present in upstream gcc
# 15.4u0 options
# -fno-allow-store-data-races and -Wno-zero-length-bounds
# 15.4u1 options
# -mindirect-branch-cs-prefix appear in 15.4u1
# more options to be removed
# -mharden-sls=all
# 15.6 options
# -fmin-function-alignment=16
for opt in [
"-flive-patching=inline-clone",
"-fdump-ipa-clones",
"-fno-allow-store-data-races",
"-Wno-zero-length-bounds",
"-mindirect-branch-cs-prefix",
"-mharden-sls=all",
"-fmin-function-alignment=16",
]:
cmd = cmd.replace(opt, "")
if cs.sle >= 15 and cs.sp >= 4:
cmd += " -D__has_attribute(x)=0"
ccp_args.extend(cmd.split(" "))
ccp_args = list(filter(None, ccp_args))
# Needed, otherwise threads would interfere with each other
env = self.env.copy()
env["KCP_KLP_CONVERT_EXTS"] = "1" if needs_ibt else "0"
env["KCP_MOD_SYMVERS"] = str(cs.get_boot_file("symvers"))
env["KCP_KBUILD_ODIR"] = str(cs.get_odir())
env["KCP_PATCHED_OBJ"] = self.get_module_obj(ARCH, cs, fdata["module"])
env["KCP_KBUILD_SDIR"] = str(cs.get_sdir())
env["KCP_IPA_CLONES_DUMP"] = str(cs.get_ipa_file(fname))
env["KCP_WORK_DIR"] = str(out_dir)
return ccp_args, env
| 4,970 | Python | .py | 124 | 28.919355 | 88 | 0.536085 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,637 | templ.py | SUSE_klp-build/klpbuild/templ.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
import shutil
from datetime import datetime
from pathlib import Path
from mako.lookup import TemplateLookup
from mako.template import Template
from klpbuild.config import Config
from klpbuild.utils import ARCH, ARCHS, is_mod
TEMPL_H = """\
#ifndef _${ fname.upper() }_H
#define _${ fname.upper() }_H
% if check_enabled:
#if IS_ENABLED(${ config })
% endif
int ${ fname }_init(void);
% if mod:
void ${ fname }_cleanup(void);
% else:
static inline void ${ fname }_cleanup(void) {}
% endif %
% for p in proto_files:
<%include file="${ p }"/>
% endfor
% if check_enabled:
#else /* !IS_ENABLED(${ config }) */
% endif
static inline int ${ fname }_init(void) { return 0; }
static inline void ${ fname }_cleanup(void) {}
% if check_enabled:
#endif /* IS_ENABLED(${ config }) */
% endif
#endif /* _${ fname.upper() }_H */
"""
TEMPL_SUSE_HEADER = """\
<%
def get_commits(cmts, cs):
if not cmts.get(cs, ''):
return ' * Not affected'
ret = []
for commit, msg in cmts[cs].items():
if not msg:
ret.append(' * Not affected')
else:
for m in msg:
ret.append(f' * {m}')
return "\\n".join(ret)
%>\
/*
* ${fname}
*
* Fix for CVE-${cve}, bsc#${lp_num}
*
% if include_header:
* Upstream commit:
${get_commits(commits, 'upstream')}
*
* SLE12-SP5 commit:
${get_commits(commits, '12.5')}
*
* SLE15-SP2 and -SP3 commit:
${get_commits(commits, 'cve-5.3')}
*
* SLE15-SP4 and -SP5 commit:
${get_commits(commits, '15.4')}
*
* SLE15-SP6 commit:
${get_commits(commits, '15.6')}
*
% endif
* Copyright (c) ${year} SUSE
* Author: ${ user } <${ email }>
*
* Based on the original Linux kernel code. Other copyrights apply.
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, see <http://www.gnu.org/licenses/>.
*/
"""
TEMPL_KLP_LONE_FILE = """\
<%include file="${ inc_src_file }"/>
#include <linux/livepatch.h>
% for obj, funcs in klp_objs.items():
static struct klp_func _${ obj }_funcs[] = {
% for func in funcs:
{
.old_name = "${ func }",
.new_func = klpp_${ func },
},
% endfor
% endfor
{}
};
static struct klp_object objs[] = {
% for obj, _ in klp_objs.items():
{
%if obj != "vmlinux":
.name = "${ obj }",
%endif
.funcs = _${ obj }_funcs
},
% endfor
{}
};
static struct klp_patch patch = {
.mod = THIS_MODULE,
.objs = objs,
};
static int ${ fname }_init(void)
{
return klp_enable_patch(&patch);
}
static void ${ fname }_cleanup(void)
{
}
module_init(${ fname }_init);
module_exit(${ fname }_cleanup);
MODULE_LICENSE("GPL");
MODULE_INFO(livepatch, "Y");
"""
TEMPL_GET_EXTS = """\
<%
def get_exts(app, ibt_mod, ext_vars):
# CE doesn't need any additional externalization
if ibt_mod and app == 'ce':
return ''
ext_list = []
for obj, syms in ext_vars.items():
if obj == 'vmlinux':
mod = ''
else:
mod = obj
# ibt_mod is only used with IBT
if not ibt_mod:
for sym in syms:
lsym = f'\\t{{ "{sym}",'
prefix_var = f'klpe_{sym}'
if not mod:
var = f' (void *)&{prefix_var} }},'
else:
var = f' (void *)&{prefix_var},'
mod = f' "{obj}" }},'
# 73 here is because a tab is 8 spaces, so 72 + 8 == 80, which is
# our goal when splitting these lines
if len(lsym + var + mod) < 73:
ext_list.append(lsym + var + mod)
elif len(lsym + var) < 73:
ext_list.append(lsym + var)
if mod:
ext_list.append('\\t ' + mod)
else:
ext_list.append(lsym)
if len(var + mod) < 73:
ext_list.append(f'\\t {var}{mod}')
else:
ext_list.append(f'\\t {var}')
if mod:
ext_list.append(f'\\t {mod}')
else:
for sym in syms:
start = f"extern typeof({sym})"
lsym = f"{sym}"
end = f"KLP_RELOC_SYMBOL({ibt_mod}, {obj}, {sym});"
if len(start + lsym + end) < 80:
ext_list.append(f"{start} {lsym} {end}")
elif len(start + lsym) < 80:
ext_list.append(f"{start} {lsym}")
ext_list.append(f"\\t {end}")
else:
ext_list.append(start)
if len(lsym + end) < 80:
ext_list.append(f"\\t {lsym} {end}")
else:
ext_list.append(f"\\t {lsym}")
ext_list.append(f"\\t {end}")
return '\\n#include <linux/livepatch.h>\\n\\n' + '\\n'.join(ext_list)
%>
"""
TEMPL_PATCH_VMLINUX = """\
% if check_enabled:
#if IS_ENABLED(${ config })
% endif # check_enabled
<%include file="${ inc_src_file }"/>
#include "livepatch_${ lp_name }.h"
% if ext_vars:
% if ibt:
${get_exts(app, "vmlinux", ext_vars)}
% else: # ibt
#include <linux/kernel.h>
#include "../kallsyms_relocs.h"
static struct klp_kallsyms_reloc klp_funcs[] = {
${get_exts(app, "", ext_vars)}
};
int ${ fname }_init(void)
{
% if mod_mutex:
return __klp_resolve_kallsyms_relocs(klp_funcs, ARRAY_SIZE(klp_funcs));
% else: # mod_mutex
return klp_resolve_kallsyms_relocs(klp_funcs, ARRAY_SIZE(klp_funcs));
% endif # mod_mutex
}
% endif # ibt
% endif # ext_vars
% if check_enabled:
#endif /* IS_ENABLED(${ config }) */
% endif # check_enabled
"""
TEMPL_PATCH_MODULE = """\
% if check_enabled:
#if IS_ENABLED(${ config })
#if !IS_MODULE(${ config })
#error "Live patch supports only CONFIG=m"
#endif
% endif # check_enabled
<%include file="${ inc_src_file }"/>
#include "livepatch_${ lp_name }.h"
% if ext_vars:
% if ibt:
${get_exts(app, mod, ext_vars)}
% else: # ibt
#include <linux/kernel.h>
#include <linux/module.h>
#include "../kallsyms_relocs.h"
#define LP_MODULE "${ mod }"
static struct klp_kallsyms_reloc klp_funcs[] = {
${get_exts(app, "", ext_vars)}
};
static int module_notify(struct notifier_block *nb,
unsigned long action, void *data)
{
struct module *mod = data;
int ret;
if (action != MODULE_STATE_COMING || strcmp(mod->name, LP_MODULE))
return 0;
% if mod_mutex:
mutex_lock(&module_mutex);
ret = __klp_resolve_kallsyms_relocs(klp_funcs, ARRAY_SIZE(klp_funcs));
mutex_unlock(&module_mutex);
% else: # mod_mutex
ret = klp_resolve_kallsyms_relocs(klp_funcs, ARRAY_SIZE(klp_funcs));
% endif # mod_mutex
WARN(ret, "%s: delayed kallsyms lookup failed. System is broken and can crash.\\n",
__func__);
return ret;
}
static struct notifier_block module_nb = {
.notifier_call = module_notify,
.priority = INT_MIN+1,
};
int ${ fname }_init(void)
{
int ret;
% if mod_mutex:
mutex_lock(&module_mutex);
if (find_module(LP_MODULE)) {
ret = __klp_resolve_kallsyms_relocs(klp_funcs,
ARRAY_SIZE(klp_funcs));
if (ret)
goto out;
}
ret = register_module_notifier(&module_nb);
out:
mutex_unlock(&module_mutex);
return ret;
% else: # mod_mutex
struct module *mod;
ret = klp_kallsyms_relocs_init();
if (ret)
return ret;
ret = register_module_notifier(&module_nb);
if (ret)
return ret;
rcu_read_lock_sched();
mod = (*klpe_find_module)(LP_MODULE);
if (!try_module_get(mod))
mod = NULL;
rcu_read_unlock_sched();
if (mod) {
ret = klp_resolve_kallsyms_relocs(klp_funcs,
ARRAY_SIZE(klp_funcs));
}
if (ret)
unregister_module_notifier(&module_nb);
module_put(mod);
return ret;
% endif # mod_mutex
}
void ${ fname }_cleanup(void)
{
unregister_module_notifier(&module_nb);
}
% endif # ibt
% endif # ext_vars
% if check_enabled:
#endif /* IS_ENABLED(${ config }) */
% endif # check_enabled
"""
TEMPL_HOLLOW = """\
% if check_enabled:
#if IS_ENABLED(${ config })
% endif # check_enabled
#include "livepatch_${ lp_name }.h"
int ${ fname }_init(void)
{
\treturn 0;
}
void ${ fname }_cleanup(void)
{
}
% if check_enabled:
#endif /* IS_ENABLED(${ config }) */
% endif # check_enabled
"""
TEMPL_COMMIT = """\
Fix for CVE-${cve} ("CHANGE ME!")
Live patch for CVE-${cve}. ${msg}:
% for cmsg in commits:
- ${cmsg}
% endfor
KLP: CVE-${cve}
References: bsc#${ lp_name } CVE-${cve}
Signed-off-by: ${user} <${email}>
"""
TEMPL_KBUILD = """\
<%
from pathlib import PurePath
def get_entries(lpdir, bsc, cs):
ret = []
for entry in lpdir.iterdir():
fname = entry.name
if not fname.endswith('.c'):
continue
# Add both the older and the new format to apply flags to objects
fname = PurePath(fname).with_suffix('.o')
ret.append(f'CFLAGS_{fname} += -Werror')
fname = f'{bsc}/{fname}'
ret.append(f'CFLAGS_{fname} += -Werror')
return "\\n".join(ret)
%>\
${get_entries(lpdir, bsc, cs)}
"""
TEMPL_PATCHED = """\
<%
def get_patched(cs_files, check_enabled):
ret = []
for ffile, fdata in cs_files.items():
conf = ''
if check_enabled and fdata['conf']:
conf = f' IS_ENABLED({fdata["conf"]})'
mod = fdata['module'].replace('-', '_')
for func in fdata['symbols']:
ret.append(f'{mod} {func} klpp_{func}{conf}')
return "\\n".join(ret)
%>\
${get_patched(cs_files, check_enabled)}
"""
TEMPL_MAKEFILE = """\
KDIR := ${ kdir }
MOD_PATH := ${ pwd }
obj-m := ${ obj }
CFLAGS_${ obj } = -Wno-missing-declarations -Wno-missing-prototypes
modules:
\tmake -C $(KDIR) modules M=$(MOD_PATH)
clean:
\tmake -C $(KDIR) clean M=$(MOD_PATH)
"""
class TemplateGen(Config):
def __init__(self, lp_name, lp_filter, app="ccp"):
super().__init__(lp_name, lp_filter)
# Require the IS_ENABLED ifdef guard whenever we have a livepatch that
# is not enabled on all architectures
self.check_enabled = self.conf["archs"] != ARCHS
self.app = app
try:
import git
git_data = git.GitConfigParser()
self.user = git_data.get_value("user", "name")
self.email = git_data.get_value("user", "email")
except:
# it couldn't find the default user and email
self.user = "Change me"
self.email = "change@me"
def preproc_slashes(text):
txt = r"<%! BS='\\' %>" + text.replace("\\", "${BS}")
return r"<%! HASH='##' %>" + txt.replace("##", "${HASH}")
def fix_mod_string(self, mod):
# Modules like snd-pcm needs to be replaced by snd_pcm in LP_MODULE
# and in kallsyms lookup
return mod.replace("-", "_")
def GeneratePatchedFuncs(self, lp_path, cs_files):
render_vars = {"cs_files": cs_files, "check_enabled": self.check_enabled}
with open(Path(lp_path, "patched_funcs.csv"), "w") as f:
f.write(Template(TEMPL_PATCHED).render(**render_vars))
def get_work_dirname(self, fname):
return f'work_{str(fname).replace("/", "_")}'
def __GenerateHeaderFile(self, lp_path, cs):
out_name = f"livepatch_{self.lp_name}.h"
lp_inc_dir = Path()
proto_files = []
configs = set()
config = ""
mod = ""
for f, data in cs.files.items():
configs.add(data["conf"])
# At this point we only care to know if we are livepatching a module
# or not, so we can overwrite the module.
mod = data["module"]
if self.app == "ce":
proto_files.append(str(Path(self.get_work_dirname(f), "proto.h")))
# Only add the inc_dir if CE is used, since it's the only backend that
# produces the proto.h headers
if len(proto_files) > 0:
lp_inc_dir = self.get_cs_dir(cs, self.app)
# Only populate the config check in the header if the livepatch is
# patching code under only one config. Otherwise let the developer to
# fill it.
if len(configs) == 1:
config = configs.pop()
render_vars = {
"fname": str(Path(out_name).with_suffix("")).replace("-", "_"),
"check_enabled": self.check_enabled,
"proto_files": proto_files,
"config": config,
"mod": mod,
}
with open(Path(lp_path, out_name), "w") as f:
lpdir = TemplateLookup(directories=[lp_inc_dir], preprocessor=TemplateGen.preproc_slashes)
f.write(Template(TEMPL_H, lookup=lpdir).render(**render_vars))
def __BuildKlpObjs(self, cs, src):
objs = {}
for src_file, fdata in cs.files.items():
if src and src != src_file:
continue
mod = fdata["module"].replace("-", "_")
objs.setdefault(mod, [])
objs[mod].extend(fdata["symbols"])
return objs
def __GenerateLivepatchFile(self, lp_path, cs, src_file, use_src_name=False):
if src_file:
lp_inc_dir = str(self.get_work_dir(cs, src_file, self.app))
lp_file = self.lp_out_file(src_file)
fdata = cs.files[str(src_file)]
mod = self.fix_mod_string(fdata["module"])
if not is_mod(mod):
mod = ""
fconf = fdata["conf"]
exts = fdata["ext_symbols"]
ibt = fdata.get("ibt", False)
else:
lp_inc_dir = Path("non-existent")
lp_file = None
mod = ""
fconf = ""
exts = {}
ibt = False
# if use_src_name is True, the final file will be:
# bscXXXXXXX_{src_name}.c
# else:
# livepatch_bscXXXXXXXX.c
if use_src_name:
out_name = lp_file
else:
out_name = f"livepatch_{self.lp_name}.c"
render_vars = {
"include_header": "livepatch_" in out_name,
"cve": self.conf.get("cve", "XXXX-XXXX"),
"lp_name": self.lp_name,
"lp_num": self.lp_name.replace("bsc", ""),
"fname": str(Path(out_name).with_suffix("")).replace("-", "_"),
"year": datetime.today().year,
"user": self.user,
"email": self.email,
"config": fconf,
"mod": mod,
"mod_mutex": cs.is_mod_mutex(),
"check_enabled": self.check_enabled,
"ext_vars": exts,
"inc_src_file": lp_file,
"ibt": ibt,
"app": self.app,
}
render_vars['commits'] = self.conf["commits"]
with open(Path(lp_path, out_name), "w") as f:
lpdir = TemplateLookup(directories=[lp_inc_dir], preprocessor=TemplateGen.preproc_slashes)
# For C files, first add the LICENSE header template to the file
f.write(Template(TEMPL_SUSE_HEADER, lookup=lpdir).render(**render_vars))
# If we have multiple source files for the same livepatch,
# create one hollow file to wire-up the multiple _init and
# _clean functions
#
# If we are patching a module, we should have the
# module_notifier armed to signal whenever the module comes on
# in order to do the symbol lookups. Otherwise only _init is
# needed, and only if there are externalized symbols being used.
if not lp_file:
temp_str = TEMPL_HOLLOW
elif mod:
temp_str = TEMPL_GET_EXTS + TEMPL_PATCH_MODULE
else:
temp_str = TEMPL_GET_EXTS + TEMPL_PATCH_VMLINUX
f.write(Template(temp_str, lookup=lpdir).render(**render_vars))
def get_cs_lp_dir(self, cs):
return Path(self.get_cs_dir(cs, self.app), "lp")
def CreateMakefile(self, cs, fname, final):
if not final:
work_dir = self.get_work_dir(cs, fname, self.app)
obj = "livepatch.o"
lp_path = Path(work_dir, "livepatch.c")
# Add more data to make it compile correctly
shutil.copy(Path(work_dir, self.lp_out_file(fname)), lp_path)
with open(lp_path, "a") as f:
f.write('#include <linux/module.h>\nMODULE_LICENSE("GPL");')
else:
work_dir = self.get_cs_lp_dir(cs)
obj = f"livepatch_{self.lp_name}.o"
render_vars = {"kdir": cs.get_kernel_build_path(ARCH), "pwd": work_dir, "obj": obj}
with open(Path(work_dir, "Makefile"), "w") as f:
f.write(Template(TEMPL_MAKEFILE).render(**render_vars))
def GenerateLivePatches(self, cs):
lp_path = self.get_cs_lp_dir(cs)
lp_path.mkdir(exist_ok=True)
files = cs.files
is_multi_files = len(files.keys()) > 1
self.GeneratePatchedFuncs(lp_path, files)
# If there are more then one source file, we cannot fully infer what are
# the correct configs and mods to be livepatched, so leave the mod and
# config entries empty
self.__GenerateHeaderFile(lp_path, cs)
# Run the template engine for each touched source file.
for src_file, _ in files.items():
self.__GenerateLivepatchFile(lp_path, cs, src_file, is_multi_files)
# One additional file to encapsulate the _init and _clenaup methods
# of the other source files
if is_multi_files:
self.__GenerateLivepatchFile(lp_path, cs, None, False)
# Create Kbuild.inc file adding an entry for all generated livepatch files.
def CreateKbuildFile(self, cs):
lpdir = self.get_cs_lp_dir(cs)
render_vars = {"bsc": self.lp_name, "cs": cs, "lpdir": lpdir}
with open(Path(lpdir, "Kbuild.inc"), "w") as f:
f.write(Template(TEMPL_KBUILD).render(**render_vars))
def generate_commit_msg_file(self):
cmts = self.conf["commits"].get("upstream", {})
if cmts:
cmts = cmts["commits"]
render_vars = {
"lp_name": self.lp_name.replace("bsc", ""),
"user": self.user,
"email": self.email,
"cve": self.conf.get("cve", "XXXX-XXXX"),
"commits": cmts,
"msg": "Upstream commits" if len(cmts) > 1 else "Upstream commit",
}
with open(Path(self.lp_path, "commit.msg"), "w") as f:
f.write(Template(TEMPL_COMMIT).render(**render_vars))
| 19,282 | Python | .py | 567 | 26.897707 | 102 | 0.570614 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,638 | ce.py | SUSE_klp-build/klpbuild/ce.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
import shutil
from pathlib import Path
from klpbuild.config import Config
from klpbuild.utils import ARCH
class CE(Config):
def __init__(self, lp_name, lp_filter, avoid_ext, ignore_errors):
super().__init__(lp_name, lp_filter)
self.app = "ce"
self.avoid_externalize = avoid_ext
self.ignore_errors = ignore_errors
self.ce_path = shutil.which("clang-extract")
if not self.ce_path:
raise RuntimeError("clang-extract not found. Aborting.")
# Check if the extract command line is compilable with gcc
# Generate the list of exported symbols
def get_symbol_list(self, out_dir):
exts = []
dsc_out = Path(out_dir, "lp.dsc")
with open(dsc_out) as f:
for l in f:
l = l.strip()
if l.startswith("#"):
mod = "vmlinux"
if l.count(":") == 2:
sym, _, mod = l.replace("#", "").split(":")
else:
sym, _ = l.replace("#", "").split(":")
exts.append((sym, mod))
exts.sort(key=lambda tup: tup[0])
# store the externalized symbols and module used in this codestream file
symbols = {}
for ext in exts:
sym, mod = ext
symbols.setdefault(mod, [])
symbols[mod].append(sym)
return symbols
def cmd_args(self, needs_ibt, cs, fname, funcs, out_dir, fdata, cmd):
ce_args = [self.ce_path]
ce_args.extend(cmd.split(" "))
if self.avoid_externalize:
funcs += "," + ",".join(self.avoid_externalize)
ce_args = list(filter(None, ce_args))
# Now add the macros to tell clang-extract what to do
ce_args.extend(
[
f'-DCE_DEBUGINFO_PATH={self.get_module_obj(ARCH, cs, fdata["module"])}',
f'-DCE_SYMVERS_PATH={cs.get_boot_file("symvers")}',
f"-DCE_OUTPUT_FILE={Path(out_dir, self.lp_out_file(fname))}",
f'-DCE_OUTPUT_FUNCTION_PROTOTYPE_HEADER={Path(out_dir, "proto.h")}',
f'-DCE_DSC_OUTPUT={Path(out_dir, "lp.dsc")}',
f"-DCE_EXTRACT_FUNCTIONS={funcs}",
]
)
if needs_ibt:
ce_args.extend(["-D__USE_IBT__"])
# clang-extract works without ipa-clones, so don't hard require it
ipa_f = cs.get_ipa_file(fname)
if ipa_f.exists():
ce_args.extend([f"-DCE_IPACLONES_PATH={ipa_f}"])
# Keep includes is necessary so don't end up expanding all headers,
# generating a huge amount of code. This only makes sense for the
# kernel so far.
ce_args.extend(["-DCE_KEEP_INCLUDES", "-DCE_RENAME_SYMBOLS", "-DCE_LATE_EXTERNALIZE"])
# For debug purposes. Uncomment for dumping clang-extract passes
# ce_args.extend(['-DCE_DUMP_PASSES'])
if self.ignore_errors:
ce_args.extend(["-DCE_IGNORE_CLANG_ERRORS"])
return ce_args, None
| 3,176 | Python | .py | 72 | 33.472222 | 94 | 0.565542 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,639 | utils.py | SUSE_klp-build/klpbuild/utils.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
import gzip
import io
import platform
from elftools.common.utils import bytes2str
from elftools.elf.elffile import ELFFile
from elftools.elf.sections import SymbolTableSection
import lzma
import zstandard
ARCH = platform.processor()
ARCHS = ["ppc64le", "s390x", "x86_64"]
# Group all codestreams that share code in a format like bellow:
# [15.2u10 15.2u11 15.3u10 15.3u12 ]
# Will be converted to:
# 15.2u10-11 15.3u10 15.3u12
# The returned value will be a list of lists, each internal list will
# contain all codestreams which share the same code
def classify_codestreams(cs_list):
# Group all codestreams that share the same codestream by a new dict
# divided by the SLE version alone, making it easier to process
# later
cs_group = {}
for cs in cs_list:
if not isinstance(cs, str):
cs = cs.name()
prefix, up = cs.split("u")
if not cs_group.get(prefix, ""):
cs_group[prefix] = [int(up)]
else:
cs_group[prefix].append(int(up))
ret_list = []
for cs, ups in cs_group.items():
if len(ups) == 1:
ret_list.append(f"{cs}u{ups[0]}")
continue
sim = []
while len(ups):
if not sim:
sim.append(ups.pop(0))
continue
cur = ups.pop(0)
last_item = sim[len(sim) - 1]
if last_item + 1 <= cur:
sim.append(cur)
continue
# they are different, print them
if len(sim) == 1:
ret_list.append(f"{cs}u{sim[0]}")
else:
ret_list.append(f"{cs}u{sim[0]}-{last_item}")
sim = [cur]
# Loop finished, check what's in similar list to print
if len(sim) == 1:
ret_list.append(f"{cs}u{sim[0]}")
elif len(sim) > 1:
last_item = sim[len(sim) - 1]
ret_list.append(f"{cs}u{sim[0]}-{last_item}")
return ret_list
def is_mod(mod):
return mod != "vmlinux"
def get_elf_modinfo_entry(elffile, conf):
sec = elffile.get_section_by_name(".modinfo")
if not sec:
return None
# Iterate over all info on modinfo section
for line in bytes2str(sec.data()).split("\0"):
if line.startswith(conf):
key, val = line.split("=")
return val.strip()
return ""
def get_elf_object(obj):
with open(obj, "rb") as f:
data = f.read()
# FIXME: use magic lib instead of checking the file extension
if str(obj).endswith(".gz"):
io_bytes = io.BytesIO(gzip.decompress(data))
elif str(obj).endswith(".zst"):
dctx = zstandard.ZstdDecompressor()
io_bytes = io.BytesIO(dctx.decompress(data))
elif str(obj).endswith(".xz"):
io_bytes = io.BytesIO(lzma.decompress(data))
else:
io_bytes = io.BytesIO(data)
return ELFFile(io_bytes)
# Load the ELF object and return all symbols
def get_all_symbols_from_object(obj, defined):
syms = []
for sec in get_elf_object(obj).iter_sections():
if not isinstance(sec, SymbolTableSection):
continue
if sec['sh_entsize'] == 0:
continue
for symbol in sec.iter_symbols():
# Somehow we end up receiving an empty symbol
if not symbol.name:
continue
if str(symbol["st_shndx"]) == "SHN_UNDEF" and not defined:
syms.append(symbol.name)
elif str(symbol["st_shndx"]) != "SHN_UNDEF" and defined:
syms.append(symbol.name)
return syms
| 3,730 | Python | .py | 104 | 27.875 | 72 | 0.596662 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,640 | ksrc.py | SUSE_klp-build/klpbuild/ksrc.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]
import logging
import re
import shutil
import subprocess
import sys
from datetime import datetime
from pathlib import Path
from pathlib import PurePath
import git
import requests
from natsort import natsorted
from klpbuild.codestream import Codestream
from klpbuild.config import Config
from klpbuild.ibs import IBS
from klpbuild import utils
class GitHelper(Config):
def __init__(self, lp_name, lp_filter, data_dir=None, skips=""):
super().__init__(lp_name, lp_filter, data_dir, skips)
self.kern_src = self.get_user_path('kernel_src_dir', isopt=True)
self.kernel_branches = {
"12.5": "SLE12-SP5",
"15.2": "SLE15-SP2-LTSS",
"15.3": "SLE15-SP3-LTSS",
"15.4": "SLE15-SP4-LTSS",
"15.5": "SLE15-SP5",
"15.5rt": "SLE15-SP5-RT",
"15.6": "SLE15-SP6",
"15.6rt": "SLE15-SP6-RT",
"cve-5.3": "cve/linux-5.3-LTSS",
"cve-5.14": "cve/linux-5.14-LTSS",
}
self.branches = []
self.kgr_patches = self.get_user_path('kgr_patches_dir', isopt=True)
if not self.kgr_patches:
logging.warning("kgr_patches_dir not found")
else:
# Filter only the branches related to this BSC
repo = git.Repo(self.kgr_patches).branches
for r in repo:
if r.name.startswith(self.lp_name):
self.branches.append(r.name)
def get_cs_branch(self, cs):
cs_sle, sp, cs_up, rt = cs.sle, cs.sp, cs.update, cs.rt
if not self.kgr_patches:
logging.warning("kgr_patches_dir not found")
return ""
branch_name = ""
for branch in self.branches:
# Check if the codestream is a rt one, and if yes, apply the correct
# separator later on
if rt and "rt" not in branch:
continue
separator = "u"
if rt:
separator = "rtu"
# First check if the branch has more than code stream sharing
# the same code
for b in branch.replace(self.lp_name + "_", "").split("_"):
# Only check the branches that are the same type of the branch
# being searched. Only check RT branches if the codestream is a
# RT one.
if rt and "rtu" not in b:
continue
if not rt and "rtu" in b:
continue
sle, u = b.split(separator)
if f"{cs_sle}.{sp}" != f"{sle}":
continue
# Get codestreams interval
up = u
down = u
if "-" in u:
down, up = u.split("-")
# Codestream between the branch codestream interval
if cs_up >= int(down) and cs_up <= int(up):
branch_name = branch
break
# At this point we found a match for our codestream in
# codestreams.json, but we may have a more specialized git
# branch later one, like:
# bsc1197597_12.4u21-25_15.0u25-28
# bsc1197597_15.0u25-28
# Since 15.0 SLE uses a different kgraft-patches branch to
# be built on. In this case, we continue to loop over the
# other branches.
return branch_name
def format_patches(self, version):
ver = f"v{version}"
# index 1 will be the test file
index = 2
if not self.kgr_patches:
logging.warning("kgr_patches_dir not found, patches will be incomplete")
# Remove dir to avoid leftover patches with different names
patches_dir = Path(self.lp_path, "patches")
shutil.rmtree(patches_dir, ignore_errors=True)
test_src = self.get_tests_path()
subprocess.check_output(
[
"/usr/bin/git",
"-C",
str(self.kgraft_tests_path),
"format-patch",
"-1",
f"{test_src}",
"--cover-letter",
"--start-number",
"1",
"--subject-prefix",
f"PATCH {ver}",
"--output-directory",
f"{patches_dir}",
]
)
# Filter only the branches related to this BSC
for branch in self.branches:
print(branch)
bname = branch.replace(self.lp_name + "_", "")
bs = " ".join(bname.split("_"))
bsc = self.lp_name.replace("bsc", "bsc#")
prefix = f"PATCH {ver} {bsc} {bs}"
subprocess.check_output(
[
"/usr/bin/git",
"-C",
str(self.kgr_patches),
"format-patch",
"-1",
branch,
"--start-number",
f"{index}",
"--subject-prefix",
f"{prefix}",
"--output-directory",
f"{patches_dir}",
]
)
index += 1
# Currently this function returns the date of the patch and it's subject
def get_commit_data(commit, savedir=None):
req = requests.get(f"https://git.kernel.org/pub/scm/linux/kernel/git/torvalds/linux.git/patch/?id={commit}")
req.raise_for_status()
# Save the upstream commit if requested
if savedir:
with open(Path(savedir, f"{commit}.patch"), "w") as f:
f.write(req.text)
# Search for Subject until a blank line, since commit messages can be
# seen in multiple lines.
msg = re.search(r"Subject: (.*?)(?:(\n\n))", req.text, re.DOTALL).group(1).replace("\n", "")
# Sometimes the MIME-Version string comes right after the commit
# message, so we should remove it as well
if 'MIME-Version:' in msg:
msg = re.sub(r"MIME-Version(.*)", "", msg)
dstr = re.search(r"Date: ([\w\s,:]+)", req.text).group(1)
d = datetime.strptime(dstr.strip(), "%a, %d %b %Y %H:%M:%S")
return d, msg
def get_commits(self, cve):
if not self.kern_src:
logging.info("kernel_src_dir not found, skip getting SUSE commits")
return {}
# ensure that the user informed the commits at least once per 'project'
if not cve:
logging.info(f"No CVE informed, skipping the processing of getting the patches.")
return {}
# Support CVEs from 2020 up to 2029
if not re.match(r"^202[0-9]-[0-9]{4,7}$", cve):
logging.info(f"Invalid CVE number {cve}, skipping the processing of getting the patches.")
return {}
print("Fetching changes from all supported branches...")
# Mount the command to fetch all branches for supported codestreams
subprocess.check_output(["/usr/bin/git", "-C", self.kern_src, "fetch",
"--quiet", "--tags", "origin"] +
list(self.kernel_branches.values()))
print("Getting SUSE fixes for upstream commits per CVE branch. It can take some time...")
# Store all commits from each branch and upstream
commits = {}
# List of upstream commits, in creation date order
ucommits = []
upatches = Path(self.lp_path, "upstream")
upatches.mkdir(exist_ok=True, parents=True)
# Get backported commits from all possible branches, in order to get
# different versions of the same backport done in the CVE branches.
# Since the CVE branch can be some patches "behind" the LTSS branch,
# it's good to have both backports code at hand by the livepatch author
for bc, mbranch in self.kernel_branches.items():
patches = []
commits[bc] = {"commits": []}
try:
patch_files = subprocess.check_output(
["/usr/bin/git", "-C", self.kern_src, "grep", "-l", f"CVE-{cve}", f"remotes/origin/{mbranch}"],
stderr=subprocess.STDOUT,
).decode(sys.stdout.encoding)
except subprocess.CalledProcessError:
patch_files = ""
# If we don't find any commits, add a note about it
if not patch_files:
continue
# Prepare command to extract correct ordering of patches
cmd = ["/usr/bin/git", "-C", self.kern_src, "grep", "-o", "-h"]
for patch in patch_files.splitlines():
_, fname = patch.split(":")
cmd.append("-e")
cmd.append(fname)
cmd += [f"remotes/origin/{mbranch}:series.conf"]
# Now execute the command
try:
patch_files = subprocess.check_output(cmd, stderr=subprocess.STDOUT).decode(sys.stdout.encoding)
except subprocess.CalledProcessError:
patch_files = ""
# The command above returns a list of strings in the format
# branch:file/path
idx = 0
for patch in patch_files.splitlines():
if patch.strip().startswith("#"):
continue
idx += 1
branch_path = Path(self.lp_path, "fixes", bc)
branch_path.mkdir(exist_ok=True, parents=True)
pfile = subprocess.check_output(
["/usr/bin/git", "-C", self.kern_src, "show", f"remotes/origin/{mbranch}:{patch}"],
stderr=subprocess.STDOUT,
).decode(sys.stdout.encoding)
# removing the patches.suse dir from the filepath
basename = PurePath(patch).name.replace(".patch", "")
# Save the patch for later review from the livepatch developer
with open(Path(branch_path, f"{idx:02d}-{basename}.patch"), "w") as f:
f.write(pfile)
# Get the upstream commit and save it. The Git-commit can be
# missing from the patch if the commit is not backporting the
# upstream fix, and is using a different way to mimic the fix.
# In this case add a note for the livepatch author to fill the
# blank when finishing the livepatch
ups = ""
m = re.search(r"Git-commit: ([\w]+)", pfile)
if m:
ups = m.group(1)[:12]
# Aggregate all upstream fixes found
if ups and ups not in ucommits:
ucommits.append(ups)
# Now get all commits related to that file on that branch,
# including the "Refresh" ones.
try:
phashes = subprocess.check_output(
[
"/usr/bin/git",
"-C",
self.kern_src,
"log",
"--no-merges",
"--pretty=oneline",
f"remotes/origin/{mbranch}",
"--",
patch,
],
stderr=subprocess.STDOUT,
).decode("ISO-8859-1")
except subprocess.CalledProcessError:
print(
f"File {fname} doesn't exists {mbranch}. It could "
" be removed, so the branch is not affected by the issue."
)
commits[bc]["commits"] = ["Not affected"]
continue
# Skip the Update commits, that only change the References tag
for hash_entry in phashes.splitlines():
if "Update" in hash_entry and "patches.suse" in hash_entry:
continue
# Sometimes we can have a commit that touches two files. In
# these cases we can have duplicated hash commits, since git
# history for each individual file will show the same hash.
# Skip if the same hash already exists.
hash_commit = hash_entry.split(" ")[0]
if hash_commit not in commits[bc]["commits"]:
commits[bc]["commits"].append(hash_commit)
# Grab each commits subject and date for each commit. The commit dates
# will be used to sort the patches in the order they were
# created/merged.
ucommits_sort = []
for c in ucommits:
d, msg = GitHelper.get_commit_data(c, upatches)
ucommits_sort.append((d, c, msg))
ucommits_sort.sort()
commits["upstream"] = {"commits": []}
for d, c, msg in ucommits_sort:
commits["upstream"]["commits"].append(f'{c} ("{msg}")')
print("")
for key, val in commits.items():
print(f"{key}")
branch_commits = val["commits"]
if not branch_commits:
print("None")
for c in branch_commits:
print(c)
print("")
return commits
def get_patched_tags(self, suse_commits):
tag_commits = {}
patched = []
total_commits = len(suse_commits)
# Grab only the first commit, since they would be put together
# in a release either way. The order of the array is backards, the
# first entry will be the last patch found.
for su in suse_commits:
tag_commits[su] = []
tags = subprocess.check_output(["/usr/bin/git", "-C", self.kern_src,
"tag", f"--contains={su}",
"rpm-*"])
for tag in tags.decode().splitlines():
# Remove noise around the kernel version, like
# rpm-5.3.18-150200.24.112--sle15-sp2-ltss-updates
if "--" in tag:
continue
tag = tag.replace("rpm-", "")
tag_commits.setdefault(tag, [])
tag_commits[tag].append(su)
# "patched branches" are those who contain all commits
for tag, b in tag_commits.items():
if len(b) == total_commits:
patched.append(tag)
# remove duplicates
return natsorted(list(set(patched)))
def is_kernel_patched(self, kernel, suse_commits, cve):
commits = []
ret = subprocess.check_output(["/usr/bin/git", "-C", self.kern_src, "log",
f"--grep=CVE-{cve}",
f"--tags=*rpm-{kernel}",
"--pretty=format:\"%H\""]);
for c in ret.decode().splitlines():
# Remove quotes for each commit hash
commits.append(c.replace("\"", ""))
# "patched kernels" are those who contain all commits.
return len(suse_commits) == len(commits), commits
def get_patched_kernels(self, codestreams, commits, cve):
if not commits:
return []
if not self.kern_src:
logging.info("kernel_src_dir not found, skip getting SUSE commits")
return []
if not cve:
logging.info("No CVE informed, skipping the processing of getting the patched kernels.")
return []
print("Searching for already patched codestreams...")
kernels = []
for bc, _ in self.kernel_branches.items():
suse_commits = commits[bc]["commits"]
if not suse_commits:
continue
# Get all the kernels/tags containing the commits in the main SLE
# branch. This information alone is not reliable enough to decide
# if a kernel is patched.
suse_tags = self.get_patched_tags(suse_commits)
# Proceed to analyse each codestream's kernel
for cs in codestreams:
if bc+'u' not in cs.name():
continue
kernel = cs.kernel
patched, kern_commits = self.is_kernel_patched(kernel, suse_commits, cve)
if not patched and kernel not in suse_tags:
continue
print(f"\n{cs.name()} ({kernel}):")
# If no patches/commits were found for this kernel, fallback to
# the commits in the main SLE branch. In either case, we can
# assume that this kernel is already patched.
for c in kern_commits if patched else suse_commits:
print(f"{c}")
kernels.append(kernel)
print("")
# remove duplicates
return natsorted(list(set(kernels)))
@staticmethod
def cs_is_affected(cs, cve, commits):
# We can only check if the cs is affected or not if the CVE was informed
# (so we can get all commits related to that specific CVE). Otherwise we
# consider all codestreams as affected.
if not cve:
return True
return len(commits[cs.name_cs()]["commits"]) > 0
@staticmethod
def download_supported_file(data_path):
logging.info("Downloading codestreams file")
cs_url = "https://gitlab.suse.de/live-patching/sle-live-patching-data/raw/master/supported.csv"
suse_cert = Path("/etc/ssl/certs/SUSE_Trust_Root.pem")
if suse_cert.exists():
req = requests.get(cs_url, verify=suse_cert)
else:
req = requests.get(cs_url)
# exit on error
req.raise_for_status()
first_line = True
codestreams = []
for line in req.iter_lines():
# skip empty lines
if not line:
continue
# skip file header
if first_line:
first_line = False
continue
# remove the last two columns, which are dates of the line
# and add a fifth field with the forth one + rpm- prefix, and
# remove the build counter number
full_cs, proj, kernel_full, _, _ = line.decode("utf-8").strip().split(",")
kernel = re.sub(r"\.\d+$", "", kernel_full)
codestreams.append(Codestream.from_codestream(data_path, full_cs, proj, kernel))
return codestreams
def scan(self, cve, conf, no_check):
# Always get the latest supported.csv file and check the content
# against the codestreams informed by the user
all_codestreams = GitHelper.download_supported_file(self.data)
if not cve:
commits = {}
patched_kernels = []
else:
commits = self.get_commits(cve)
patched_kernels = self.get_patched_kernels(all_codestreams, commits, cve)
# list of codestreams that matches the file-funcs argument
working_cs = []
patched_cs = []
unaffected_cs = []
data_missing = []
cs_missing = []
conf_not_set = []
if no_check:
logging.info("Option --no-check was specified, checking all codestreams that are not filtered out...")
for cs in all_codestreams:
# Skip patched codestreams
if not no_check:
if cs.kernel in patched_kernels:
patched_cs.append(cs.name())
continue
if not GitHelper.cs_is_affected(cs, cve, commits):
unaffected_cs.append(cs)
continue
# Set supported archs for the codestream
# RT is supported only on x86_64 at the moment
archs = ["x86_64"]
if not cs.rt:
archs.extend(["ppc64le", "s390x"])
cs.set_archs(archs)
if not cs.get_boot_file("config").exists():
data_missing.append(cs)
cs_missing.append(cs.name())
# recheck later if we can add the missing codestreams
continue
if conf and not cs.get_all_configs(conf):
conf_not_set.append(cs)
continue
working_cs.append(cs)
# Found missing cs data, downloading and extract
if data_missing:
logging.info("Download the necessary data from the following codestreams:")
logging.info(f'\t{" ".join(cs_missing)}\n')
IBS(self.lp_name, self.filter).download_cs_data(data_missing)
logging.info("Done.")
for cs in data_missing:
# Ok, the downloaded codestream has the configuration set
if cs.get_all_configs(conf):
working_cs.append(cs)
# Nope, the config is missing, so don't add it to working_cs
else:
conf_not_set.append(cs)
if conf_not_set:
cs_list = utils.classify_codestreams(conf_not_set)
logging.info(f"Skipping codestreams without {conf} set:")
logging.info(f'\t{" ".join(cs_list)}')
if patched_cs:
cs_list = utils.classify_codestreams(patched_cs)
logging.info("Skipping already patched codestreams:")
logging.info(f'\t{" ".join(cs_list)}')
if unaffected_cs:
cs_list = utils.classify_codestreams(unaffected_cs)
logging.info("Skipping unaffected codestreams (missing backports):")
logging.info(f'\t{" ".join(cs_list)}')
# working_cs will contain the final dict of codestreams that wast set
# by the user, avoid downloading missing codestreams that are not affected
working_cs = self.filter_cs(working_cs, verbose=True)
if not working_cs:
logging.info("All supported codestreams are already patched. Exiting klp-build")
sys.exit(0)
logging.info("All affected codestreams:")
cs_list = utils.classify_codestreams(working_cs)
logging.info(f'\t{" ".join(cs_list)}')
return commits, patched_cs, patched_kernels, working_cs
| 22,584 | Python | .py | 486 | 32.45679 | 116 | 0.535214 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,641 | ibs.py | SUSE_klp-build/klpbuild/ibs.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
import concurrent.futures
import errno
import logging
import os
import re
import shutil
import subprocess
import sys
import time
from operator import itemgetter
from pathlib import Path
import pkg_resources
import requests
from lxml import etree
from lxml.objectify import fromstring
from lxml.objectify import SubElement
from natsort import natsorted
from osctiny import Osc
from klpbuild.config import Config
from klpbuild.utils import ARCH, ARCHS, get_all_symbols_from_object, get_elf_object, get_elf_modinfo_entry
class IBS(Config):
def __init__(self, lp_name, lp_filter):
super().__init__(lp_name, lp_filter)
self.osc = Osc(url="https://api.suse.de")
self.ibs_user = self.osc.username
self.prj_prefix = f"home:{self.ibs_user}:{self.lp_name}-klp"
self.workers = int(self.get_user_settings("workers"))
# Total number of work items
self.total = 0
# Skip osctiny INFO messages
logging.getLogger("osctiny").setLevel(logging.WARNING)
def do_work(self, func, args):
if len(args) == 0:
return
with concurrent.futures.ThreadPoolExecutor(max_workers=self.workers) as executor:
results = executor.map(func, args)
for result in results:
if result:
logging.error(result)
# The projects has different format: 12_5u5 instead of 12.5u5
def get_projects(self):
prjs = []
projects = self.osc.search.project(f"starts-with(@name, '{self.prj_prefix}')")
for prj in projects.findall("project"):
prj_name = prj.get("name")
cs = self.convert_prj_to_cs(prj_name)
if self.filter and not re.match(self.filter, cs):
continue
prjs.append(prj)
return prjs
def get_project_names(self):
names = []
i = 1
for result in self.get_projects():
names.append((i, result.get("name")))
i += 1
return natsorted(names, key=itemgetter(1))
def delete_project(self, i, prj, verbose=True):
try:
ret = self.osc.projects.delete(prj, force=True)
if type(ret) is not bool:
logging.error(etree.tostring(ret))
raise ValueError(prj)
except requests.exceptions.HTTPError as e:
# project not found, no problem
if e.response.status_code == 404:
pass
if verbose:
logging.info(f"({i}/{self.total}) {prj} deleted")
def delete_projects(self, prjs, verbose=True):
for i, prj in prjs:
self.delete_project(i, prj, verbose)
def extract_rpms(self, args):
i, cs, arch, rpm, dest = args
# We don't need to extract the -extra packages for non x86_64 archs.
# These packages are only needed to be uploaded to the kgr-test
# repos, since they aren't published, but we need them for testing.
if arch != "x86_64" and "-extra" in rpm:
return
path_dest = cs.get_data_dir(arch)
path_dest.mkdir(exist_ok=True, parents=True)
rpm_file = Path(dest, rpm)
cmd = f"rpm2cpio {rpm_file} | cpio --quiet -uidm"
subprocess.check_output(cmd, shell=True, cwd=path_dest)
logging.info(f"({i}/{self.total}) extracted {cs.name()} {rpm}: ok")
def download_and_extract(self, args):
i, cs, _, _, arch, _, rpm, dest = args
self.download_binary_rpms(args)
# Do not extract kernel-macros rpm
if "kernel-macros" not in rpm:
self.extract_rpms((i, cs, arch, rpm, dest))
def download_cs_data(self, cs_list):
rpms = []
i = 1
cs_data = {
"kernel-default": r"(kernel-(default|rt)\-((livepatch|kgraft)?\-?devel)?\-?[\d\.\-]+.(s390x|x86_64|ppc64le).rpm)",
"kernel-source": r"(kernel-(source|devel)(\-rt)?\-?[\d\.\-]+.noarch.rpm)",
}
logging.info("Getting list of files...")
for cs in cs_list:
prj = cs.project
repo = cs.repo
path_dest = Path(self.data, "kernel-rpms")
path_dest.mkdir(exist_ok=True, parents=True)
for arch in cs.archs:
for pkg, regex in cs_data.items():
# RT kernels have different package names
if cs.rt:
if pkg == "kernel-default":
pkg = "kernel-rt"
elif pkg == "kernel-source":
pkg = "kernel-source-rt"
if repo != "standard":
pkg = f"{pkg}.{repo}"
ret = self.osc.build.get_binary_list(prj, repo, arch, pkg)
for file in re.findall(regex, str(etree.tostring(ret))):
# FIXME: adjust the regex to only deal with strings
if isinstance(file, str):
rpm = file
else:
rpm = file[0]
# Download all packages for the HOST arch
# For the others only download kernel-default
if arch != ARCH and not re.search("kernel-default-\d", rpm):
continue
# Extract the source and kernel-devel in the current
# machine arch to make it possible to run klp-build in
# different architectures
if "kernel-source" in rpm or "kernel-default-devel" in rpm:
if arch != ARCH:
continue
rpms.append((i, cs, prj, repo, arch, pkg, rpm, path_dest))
i += 1
logging.info(f"Downloading {len(rpms)} rpms...")
self.total = len(rpms)
self.do_work(self.download_and_extract, rpms)
# Create a list of paths pointing to lib/modules for each downloaded
# codestream
for cs in cs_list:
for arch in cs.archs:
# Extract modules and vmlinux files that are compressed
mod_path = Path(cs.get_data_dir(arch), "lib", "modules", cs.kname())
for fext, ecmd in [("zst", "unzstd -f -d"), ("xz", "xz --quiet -d -k")]:
cmd = rf'find {mod_path} -name "*ko.{fext}" -exec {ecmd} --quiet {{}} \;'
subprocess.check_output(cmd, shell=True)
# Extract gzipped files per arch
files = ["vmlinux", "symvers"]
for f in files:
f_path = Path(cs.get_data_dir(arch), "boot", f"{f}-{cs.kname()}.gz")
# ppc64le doesn't gzips vmlinux
if f_path.exists():
subprocess.check_output(rf'gzip -k -d -f {f_path}', shell=True)
# Use the SLE .config
shutil.copy(cs.get_boot_file("config"), Path(cs.get_odir(), ".config"))
# Recreate the build link to enable us to test the generated LP
mod_path = cs.get_kernel_build_path(ARCH)
mod_path.unlink()
os.symlink(cs.get_odir(), mod_path)
# Create symlink from lib to usr/lib so we can use virtme on the
# extracted kernels
usr_lib = Path(self.data, ARCH, "usr", "lib")
if not usr_lib.exists():
usr_lib.symlink_to(Path(self.data, ARCH, "lib"))
logging.info("Finished extract vmlinux and modules...")
def download_binary_rpms(self, args):
i, cs, prj, repo, arch, pkg, rpm, dest = args
try:
self.osc.build.download_binary(prj, repo, arch, pkg, rpm, dest)
logging.info(f"({i}/{self.total}) {cs.name()} {rpm}: ok")
except OSError as e:
if e.errno == errno.EEXIST:
logging.info(f"({i}/{self.total}) {cs.name()} {rpm}: already downloaded. skipping.")
else:
raise RuntimeError(f"download error on {prj}: {rpm}")
def convert_prj_to_cs(self, prj):
return prj.replace(f"{self.prj_prefix}-", "").replace("_", ".")
def find_missing_symbols(self, cs, arch, lp_mod_path):
vmlinux_path = cs.get_boot_file("vmlinux", arch)
vmlinux_syms = get_all_symbols_from_object(vmlinux_path, True)
# Get list of UNDEFINED symbols from the livepatch module
lp_und_symbols = get_all_symbols_from_object(lp_mod_path, False)
missing_syms = []
# Find all UNDEFINED symbols that exists in the livepatch module that
# aren't defined in the vmlinux
for sym in lp_und_symbols:
if sym not in vmlinux_syms:
missing_syms.append(sym)
return missing_syms
def validate_livepatch_module(self, cs, arch, rpm_dir, rpm):
match = re.search(r"(livepatch)-.*(default|rt)\-(\d+)\-(\d+)\.(\d+)\.(\d+)\.", rpm)
if match:
dir_path = match.group(1)
ktype = match.group(2)
lp_file = f"livepatch-{match.group(3)}-{match.group(4)}_{match.group(5)}_{match.group(6)}.ko"
else:
ktype = "default"
match = re.search(r"(kgraft)\-patch\-.*default\-(\d+)\-(\d+)\.(\d+)\.", rpm)
if match:
dir_path = match.group(1)
lp_file = f"kgraft-patch-{match.group(2)}-{match.group(3)}_{match.group(4)}.ko"
fdest = Path(rpm_dir, rpm)
# Extract the livepatch module for later inspection
cmd = f"rpm2cpio {fdest} | cpio --quiet -uidm"
subprocess.check_output(cmd, shell=True, cwd=rpm_dir)
# Check depends field
# At this point we found that our livepatch module depends on
# exported functions from other modules. List the modules here.
lp_mod_path = Path(rpm_dir, "lib", "modules", f"{cs.kernel}-{ktype}", dir_path, lp_file)
elffile = get_elf_object(lp_mod_path)
deps = get_elf_modinfo_entry(elffile, "depends")
if len(deps):
logging.warning(f"{cs.name()}:{arch} has dependencies: {deps}.")
funcs = self.find_missing_symbols(cs, arch, lp_mod_path)
if funcs:
logging.warning(f'{cs.name()}:{arch} Undefined functions: {" ".join(funcs)}')
shutil.rmtree(Path(rpm_dir, "lib"), ignore_errors=True)
def prepare_tests(self):
# Download all built rpms
self.download()
test_src = self.get_tests_path()
run_test = pkg_resources.resource_filename("scripts", "run-kgr-test.sh")
logging.info(f"Validating the downloaded RPMs...")
for arch in ARCHS:
tests_path = Path(self.lp_path, "tests", arch)
test_arch_path = Path(tests_path, self.lp_name)
# Remove previously created directory and archive
shutil.rmtree(test_arch_path, ignore_errors=True)
shutil.rmtree(f"{str(test_arch_path)}.tar.xz", ignore_errors=True)
test_arch_path.mkdir(exist_ok=True, parents=True)
shutil.copy(run_test, test_arch_path)
for d in ["built", "repro", "tests.out"]:
Path(test_arch_path, d).mkdir(exist_ok=True)
logging.info(f"Checking {arch} symbols...")
build_cs = []
for cs in self.filter_cs():
if arch not in cs.archs:
continue
rpm_dir = Path(self.lp_path, "ccp", cs.name(), arch, "rpm")
if not rpm_dir.exists():
logging.info(f"{cs.name()}/{arch}: rpm dir not found. Skipping.")
continue
# TODO: there will be only one rpm, format it directly
rpm = os.listdir(rpm_dir)
if len(rpm) > 1:
raise RuntimeError(f"ERROR: {cs.name()}/{arch}. {len(rpm)} rpms found. Excepting to find only one")
for rpm in os.listdir(rpm_dir):
# Check for dependencies
self.validate_livepatch_module(cs, arch, rpm_dir, rpm)
shutil.copy(Path(rpm_dir, rpm), Path(test_arch_path, "built"))
if cs.rt and arch != "x86_64":
continue
build_cs.append(cs.name_full())
logging.info("Done.")
# Prepare the config and test files used by kgr-test
test_dst = Path(test_arch_path, f"repro/{self.lp_name}")
if test_src.is_file():
shutil.copy(test_src, f"{test_dst}_test_script.sh")
config = f"{test_dst}_config.in"
else:
# Alternatively, we create test_dst as a directory containing
# at least a test_script.sh and a config.in
shutil.copytree(test_src, test_dst)
config = Path(test_dst, "config.in")
with open(config, "w") as f:
f.write("\n".join(natsorted(build_cs)))
logging.info(f"Creating {arch} tar file...")
subprocess.run(
["tar", "-cJf", f"{self.lp_name}.tar.xz", f"{self.lp_name}"],
cwd=tests_path,
stdout=sys.stdout,
stderr=subprocess.PIPE,
check=True,
)
logging.info("Done.")
# We can try delete a project that was removed, so don't bother with errors
def delete_rpms(self, cs):
try:
for arch in cs.archs:
shutil.rmtree(Path(self.lp_path, "ccp", cs.name(), arch, "rpm"), ignore_errors=True)
except KeyError:
pass
def download(self):
rpms = []
i = 1
for result in self.get_projects():
prj = result.get("name")
cs_name = self.convert_prj_to_cs(prj)
cs = self.get_cs(cs_name)
# Remove previously downloaded rpms
self.delete_rpms(cs)
archs = result.xpath("repository/arch")
for arch in archs:
ret = self.osc.build.get_binary_list(prj, "devbuild", arch, "klp")
rpm_name = f"{arch}.rpm"
for rpm in ret.xpath("binary/@filename"):
if not rpm.endswith(rpm_name):
continue
if "preempt" in rpm:
continue
# Create a directory for each arch supported
dest = Path(self.lp_path, "ccp", cs.name(), str(arch), "rpm")
dest.mkdir(exist_ok=True, parents=True)
rpms.append((i, cs, prj, "devbuild", arch, "klp", rpm, dest))
i += 1
logging.info(f"Downloading {len(rpms)} packages...")
self.total = len(rpms)
self.do_work(self.download_binary_rpms, rpms)
logging.info(f"Download finished.")
def status(self, wait=False):
finished_prj = []
while True:
prjs = {}
for _, prj in self.get_project_names():
if prj in finished_prj:
continue
prjs[prj] = {}
for res in self.osc.build.get(prj).findall("result"):
if not res.xpath("status/@code"):
continue
code = res.xpath("status/@code")[0]
prjs[prj][res.get("arch")] = code
print(f"{len(prjs)} codestreams to finish")
for prj, archs in prjs.items():
st = []
finished = False
# Save the status of all architecture build, and set to fail if
# an error happens in any of the supported architectures
for k, v in archs.items():
st.append(f"{k}: {v}")
if v in ["unresolvable", "failed"]:
finished = True
# Only set finished is all architectures supported by the
# codestreams built without issues
if not finished:
states = set(archs.values())
if len(states) == 1 and states.pop() == "succeeded":
finished = True
if finished:
finished_prj.append(prj)
logging.info("{}\t{}".format(prj, "\t".join(st)))
for p in finished_prj:
prjs.pop(p, None)
if not wait or not prjs:
break
# Wait 30 seconds before getting status again
time.sleep(30)
logging.info("")
def cleanup(self):
prjs = self.get_project_names()
self.total = len(prjs)
if self.total == 0:
logging.info("No projects found.")
return
logging.info(f"Deleting {self.total} projects...")
self.delete_projects(prjs, True)
def cs_to_project(self, cs):
return self.prj_prefix + "-" + cs.name().replace(".", "_")
def create_prj_meta(self, cs):
prj = fromstring(
"<project name=''><title></title><description></description>"
"<build><enable/></build><publish><disable/></publish>"
"<debuginfo><disable/></debuginfo>"
'<repository name="devbuild">'
f"<path project=\"{cs.project}\" repository=\"{cs.repo}\"/>"
"</repository>"
"</project>"
)
repo = prj.find("repository")
for arch in cs.archs:
ar = SubElement(repo, "arch")
ar._setText(arch)
return prj
def create_lp_package(self, i, cs):
# get the kgraft branch related to this codestream
from klpbuild.ksrc import GitHelper
branch = GitHelper(self.lp_name, self.filter).get_cs_branch(cs)
if not branch:
logging.info(f"Could not find git branch for {cs.name()}. Skipping.")
return
logging.info(f"({i}/{self.total}) pushing {cs.name()} using branch {branch}...")
# If the project exists, drop it first
prj = self.cs_to_project(cs)
self.delete_project(i, prj, verbose=False)
meta = self.create_prj_meta(cs)
prj_desc = f"Development of livepatches for {cs.name()}"
try:
self.osc.projects.set_meta(
prj, metafile=meta, title="", bugowner=self.ibs_user, maintainer=self.ibs_user, description=prj_desc
)
self.osc.packages.set_meta(prj, "klp", title="", description="Test livepatch")
except Exception as e:
logging.error(e, e.response.content)
raise RuntimeError("")
base_path = Path(self.lp_path, "ccp", cs.name())
# Remove previously created directories
prj_path = Path(base_path, "checkout")
if prj_path.exists():
shutil.rmtree(prj_path)
code_path = Path(base_path, "code")
if code_path.exists():
shutil.rmtree(code_path)
self.osc.packages.checkout(prj, "klp", prj_path)
kgraft_path = self.get_user_path('kgr_patches_dir')
# Get the code from codestream
subprocess.check_output(
["/usr/bin/git", "clone", "--single-branch", "-b", branch, str(kgraft_path), str(code_path)],
stderr=subprocess.STDOUT,
)
# Check if the directory related to this bsc exists.
# Otherwise only warn the caller about this fact.
# This scenario can occur in case of LPing function that is already
# part of different LP in which case we modify the existing one.
if self.lp_name not in os.listdir(code_path):
logging.warning(f"Warning: Directory {self.lp_name} not found on branch {branch}")
# Fix RELEASE version
with open(Path(code_path, "scripts", "release-version.sh"), "w") as f:
ver = cs.name_full().replace("EMBARGO", "")
f.write(f"RELEASE={ver}")
subprocess.check_output(
["bash", "./scripts/tar-up.sh", "-d", str(prj_path)], stderr=subprocess.STDOUT, cwd=code_path
)
shutil.rmtree(code_path)
# Add all files to the project, commit the changes and delete the directory.
for fname in prj_path.iterdir():
with open(fname, "rb") as fdata:
self.osc.packages.push_file(prj, "klp", fname.name, fdata.read())
self.osc.packages.cmd(prj, "klp", "commit", comment=f"Dump {branch}")
shutil.rmtree(prj_path)
logging.info(f"({i}/{self.total}) {cs.name()} done")
def log(self, cs, arch):
logging.info(self.osc.build.get_log(self.cs_to_project(cs), "devbuild", arch, "klp"))
def push(self, wait=False):
cs_list = self.filter_cs()
if not cs_list:
logging.error(f"push: No codestreams found for {self.lp_name}")
sys.exit(1)
logging.info(f"Preparing {len(cs_list)} projects on IBS...")
self.total = len(cs_list)
i = 1
# More threads makes OBS to return error 500
for cs in cs_list:
self.create_lp_package(i, cs)
i += 1
if wait:
# Give some time for IBS to start building the last pushed
# codestreams
time.sleep(30)
self.status(wait)
# One more status after everything finished, since we remove
# finished builds on each iteration
self.status(False)
| 21,600 | Python | .py | 455 | 34.736264 | 126 | 0.551658 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,642 | main.py | SUSE_klp-build/klpbuild/main.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
import sys
from klpbuild.cmd import main_func
def main():
main_func(sys.argv[1:])
if __name__ == "__main__":
main()
| 256 | Python | .py | 10 | 23.2 | 52 | 0.695833 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,643 | cmd.py | SUSE_klp-build/klpbuild/cmd.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
import argparse
from klpbuild.codestream import Codestream
from klpbuild.extractor import Extractor
from klpbuild.ibs import IBS
from klpbuild.inline import Inliner
from klpbuild.ksrc import GitHelper
from klpbuild.setup import Setup
from klpbuild.utils import ARCHS
def create_parser() -> argparse.ArgumentParser:
parentparser = argparse.ArgumentParser(add_help=False)
parentparser.add_argument(
"-n",
"--name",
type=str,
required=True,
help="The livepatch name. This will be the directory name of the "
"resulting livepatches.",
)
parentparser.add_argument("--filter", type=str, help=r"Filter out codestreams using a regex. Example: 15\.3u[0-9]+")
parser = argparse.ArgumentParser(add_help=False)
sub = parser.add_subparsers(dest="cmd")
setup = sub.add_parser("setup", parents=[parentparser])
setup.add_argument("--cve", type=str, help="SLE specific. The CVE assigned to this livepatch")
setup.add_argument("--conf", type=str, required=True, help="The kernel CONFIG used to be build the livepatch")
setup.add_argument(
"--no-check",
action="store_true",
help="SLE specific. Do not check for already patched codestreams, do the setup for all non filtered codestreams.",
)
setup.add_argument(
"--data-dir",
type=str,
required=False,
default=None,
help="The path where source files and modules will be found",
)
setup.add_argument(
"--file-funcs",
required=False,
action="append",
nargs="*",
default=[],
help="File and functions to be livepatched. Can be set "
"multiple times. The format is --file-funcs file/path.c func1 "
"func2 --file-func file/patch2 func1...",
)
setup.add_argument(
"--mod-file-funcs",
required=False,
action="append",
nargs="*",
default=[],
help="Module, file and functions to be livepatched. Can be set "
"multiple times. The format is --file-funcs module1 file/path.c func1 "
"func2 --file-func module2 file/patch2 func1...",
)
setup.add_argument(
"--conf-mod-file-funcs",
required=False,
action="append",
nargs="*",
default=[],
help="Conf, module, file and functions to be livepatched. Can be set "
"multiple times. The format is --file-funcs conf1 module1 file/path.c func1 "
"func2 --file-func conf2 module2 file/patch2 func1...",
)
setup.add_argument(
"--module", type=str, default="vmlinux", help="The module that will be livepatched for all files"
)
setup.add_argument(
"--archs",
default=ARCHS,
choices=ARCHS,
nargs="+",
help="SLE specific. Supported architectures for this livepatch",
)
setup.add_argument("--skips", help="List of codestreams to filter out")
check_inline = sub.add_parser("check-inline", parents=[parentparser])
check_inline.add_argument(
"--codestream",
type=str,
default="",
required=True,
help="SLE specific. Codestream to check the inlined symbol.",
)
check_inline.add_argument(
"--file",
type=str,
required=True,
help="File to be checked.",
)
check_inline.add_argument(
"--symbol",
type=str,
required=True,
help="Symbol to be found",
)
extract_opts = sub.add_parser("extract", parents=[parentparser])
extract_opts.add_argument(
"--avoid-ext",
nargs="+",
type=str,
default=[],
help="Functions to be copied into the LP instead of externalizing. "
"Useful to make sure to include symbols that are optimized in "
"different architectures",
)
extract_opts.add_argument(
"--apply-patches", action="store_true", help="Apply patches found by get-patches subcommand, if they exist"
)
extract_opts.add_argument(
"--ignore-errors", action="store_true", help="Don't exit clang-extract if an error is detected when "
"extracting the code. Should be used on cases like extracting tracepoints or other code that are "
"usually problematic.")
extract_opts.add_argument(
"--type", type=str, choices=["ccp", "ce"], default="ccp", help="Choose between ccp and ce"
)
diff_opts = sub.add_parser("cs-diff", parents=[parentparser])
diff_opts.add_argument(
"--cs", nargs=2, type=str, required=True, help="SLE specific. Apply diff on two different codestreams"
)
diff_opts.add_argument("--type", type=str, choices=["ccp", "ce"], default="ccp", help="Choose between ccp and ce")
fmt = sub.add_parser(
"format-patches", parents=[parentparser], help="SLE specific. Extract patches from kgraft-patches"
)
fmt.add_argument("-v", "--version", type=int, required=True, help="Version to be added, like vX")
patches = sub.add_parser("get-patches", parents=[parentparser])
patches.add_argument(
"--cve", required=True, help="SLE specific. CVE number to search for related backported patches"
)
scan = sub.add_parser("scan")
scan.add_argument(
"--cve", required=True, help="SLE specific. Shows which codestreams are vulnerable to the CVE"
)
scan.add_argument(
"--conf", required=False, help="SLE specific. Helps to check only the codestreams that have this config set."
)
sub.add_parser("cleanup", parents=[parentparser], help="SLE specific. Remove livepatch packages from IBS")
sub.add_parser(
"prepare-tests",
parents=[parentparser],
help="SLE specific. Download the built tests and check for LP dependencies",
)
push = sub.add_parser(
"push", parents=[parentparser], help="SLE specific. Push livepatch packages to IBS to be built"
)
push.add_argument("--wait", action="store_true", help="Wait until all codestreams builds are finished")
status = sub.add_parser("status", parents=[parentparser], help="SLE specific. Check livepatch build status on IBS")
status.add_argument("--wait", action="store_true", help="Wait until all codestreams builds are finished")
log = sub.add_parser("log", parents=[parentparser], help="SLE specific. Get build log from IBS")
log.add_argument("--cs", type=str, required=True, help="The codestream to get the log from")
log.add_argument("--arch", type=str, default="x86_64", choices=ARCHS, help="Build architecture")
return parser
def main_func(main_args):
args = create_parser().parse_args(main_args)
if args.cmd == "setup":
setup = Setup(
args.name,
args.filter,
args.data_dir,
args.cve,
args.file_funcs,
args.mod_file_funcs,
args.conf_mod_file_funcs,
args.module,
args.conf,
args.archs,
args.skips,
args.no_check,
)
setup.setup_project_files()
elif args.cmd == "extract":
Extractor(args.name, args.filter, args.apply_patches, args.type,
args.avoid_ext, args.ignore_errors).run()
elif args.cmd == "cs-diff":
lp_filter = args.cs[0] + "|" + args.cs[1]
Extractor(args.name, lp_filter, False, args.type, [], False).diff_cs()
elif args.cmd == "check-inline":
Inliner(args.name, args.codestream).check_inline(args.file, args.symbol)
elif args.cmd == "get-patches":
GitHelper(args.name, args.filter).get_commits(args.cve)
elif args.cmd == "scan":
GitHelper("bsc_check", "").scan(args.cve, args.conf, False)
elif args.cmd == "format-patches":
GitHelper(args.name, args.filter).format_patches(args.version)
elif args.cmd == "status":
IBS(args.name, args.filter).status(args.wait)
elif args.cmd == "push":
IBS(args.name, args.filter).push(args.wait)
elif args.cmd == "log":
IBS(args.name, args.filter).log(Codestream.from_cs("", args.cs), args.arch)
elif args.cmd == "cleanup":
IBS(args.name, args.filter).cleanup()
elif args.cmd == "prepare-tests":
IBS(args.name, args.filter).prepare_tests()
| 8,416 | Python | .py | 199 | 34.994975 | 122 | 0.643293 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,644 | extractor.py | SUSE_klp-build/klpbuild/extractor.py | # SPDX-License-Identifier: GPL-2.0-only
#
# Copyright (C) 2021-2024 SUSE
# Author: Marcos Paulo de Souza <[email protected]>
import concurrent.futures
import difflib as dl
import json
import logging
import os
import re
import shutil
import subprocess
import sys
from collections import OrderedDict
from pathlib import Path
from pathlib import PurePath
from threading import Lock
from filelock import FileLock
from natsort import natsorted
from klpbuild import utils
from klpbuild.ccp import CCP
from klpbuild.ce import CE
from klpbuild.config import Config
from klpbuild.templ import TemplateGen
class Extractor(Config):
def __init__(self, lp_name, lp_filter, apply_patches, app, avoid_ext, ignore_errors):
super().__init__(lp_name, lp_filter)
self.sdir_lock = FileLock(Path(self.data, utils.ARCH, "sdir.lock"))
self.sdir_lock.acquire()
if not self.lp_path.exists():
raise ValueError(f"{self.lp_path} not created. Run the setup subcommand first")
patches = self.get_patches_dir()
self.apply_patches = apply_patches
workers = self.get_user_settings('workers', True)
if workers == "":
self.workers = 4
else:
self.workers = int(workers)
if self.apply_patches and not patches.exists():
raise ValueError("--apply-patches specified without patches. Run get-patches!")
if patches.exists():
self.quilt_log = open(Path(patches, "quilt.log"), "w")
self.quilt_log.truncate()
else:
self.quilt_log = open("/dev/null", "w")
self.total = 0
self.make_lock = Lock()
if app == "ccp":
self.runner = CCP(lp_name, lp_filter, avoid_ext)
else:
self.runner = CE(lp_name, lp_filter, avoid_ext, ignore_errors)
self.app = app
self.tem = TemplateGen(self.lp_name, self.filter, self.app)
def __del__(self):
if self.sdir_lock:
self.sdir_lock.release()
os.remove(self.sdir_lock.lock_file)
@staticmethod
def unquote_output(matchobj):
return matchobj.group(0).replace('"', "")
@staticmethod
def process_make_output(output):
# some strings have single quotes around double quotes, so remove the
# outer quotes
output = output.replace("'", "")
# Remove the compiler name used to compile the object. TODO: resolve
# when clang is used, or other cross-compilers.
if output.startswith("gcc "):
output = output[4:]
# also remove double quotes from macros like -D"KBUILD....=.."
return re.sub(r'-D"KBUILD_([\w\#\_\=\(\)])+"', Extractor.unquote_output, output)
@staticmethod
def get_make_cmd(out_dir, cs, filename, odir, sdir):
filename = PurePath(filename)
file_ = str(filename.with_suffix(".o"))
log_path = Path(out_dir, "make.out.txt")
with open(log_path, "w") as f:
# Corner case for lib directory, that fails with the conventional
# way of grabbing the gcc args used to compile the file. If then
# need to ask the make to show the commands for all files inside the
# directory. Later process_make_output will take care of picking
# what is interesting for klp-build
if filename.parent == PurePath("arch/x86/lib") or filename.parent == PurePath("drivers/block/aoe"):
file_ = str(filename.parent) + "/"
gcc_ver = int(subprocess.check_output(["gcc", "-dumpversion"]).decode().strip())
# gcc12 and higher have a problem with kernel and xrealloc implementation
if gcc_ver < 12:
cc = "gcc"
# if gcc12 or higher is the default compiler, check if gcc7 is available
elif shutil.which("gcc-7"):
cc = "gcc-7"
else:
logging.error("Only gcc12 or higher are available, and it's problematic with kernel sources")
raise
make_args = [
"make",
"-sn",
f"CC={cc}",
f"KLP_CS={cs.name()}",
f"HOSTCC={cc}",
"WERROR=0",
"CFLAGS_REMOVE_objtool=-Werror",
file_,
]
f.write(f"Executing make on {odir}\n")
f.write(" ".join(make_args))
f.write("\n")
f.flush()
ofname = "." + filename.name.replace(".c", ".o.d")
ofname = Path(filename.parent, ofname)
completed = subprocess.check_output(make_args, cwd=odir, stderr=f).decode()
f.write("Full output of the make command:\n")
f.write(str(completed).strip())
f.write("\n")
f.flush()
# 15.4 onwards changes the regex a little: -MD -> -MMD
# 15.6 onwards we don't have -isystem.
# Also, it's more difficult to eliminate the objtool command
# line, so try to search until the fixdep script
for regex in [
rf"(-Wp,(\-MD|\-MMD),{ofname}\s+-nostdinc\s+-isystem.*{str(filename)});",
rf"(-Wp,(\-MD|\-MMD),{ofname}\s+-nostdinc\s+.*-c -o {file_} {sdir}/{filename})\s+;.*fixdep"
]:
f.write(f"Searching for the pattern: {regex}\n")
f.flush()
result = re.search(regex, str(completed).strip())
if result:
break
f.write(f"Not found\n")
f.flush()
if not result:
logging.error(f"Failed to get the kernel cmdline for file {str(ofname)} in {cs.name()}. "
f"Check file {str(log_path)} for more details.")
return None
ret = Extractor.process_make_output(result.group(1))
# WORKAROUND: tomoyo security module uses a generated file that is
# not part of kernel-source. For this reason, add a new option for
# the backend process to ignore the inclusion of the missing file
if "tomoyo" in file_:
ret += " -DCONFIG_SECURITY_TOMOYO_INSECURE_BUILTIN_SETTING"
# save the cmdline
f.write(ret)
if not " -pg " in ret:
logging.warning(f"{cs.name()}:{file_} is not compiled with livepatch support (-pg flag)")
return ret
return None
def get_patches_dir(self):
return Path(self.lp_path, "fixes")
def remove_patches(self, cs, fil):
sdir = cs.get_sdir()
# Check if there were patches applied previously
patches_dir = Path(sdir, "patches")
if not patches_dir.exists():
return
fil.write(f"\nRemoving patches from {cs.name()}({cs.kernel})\n")
fil.flush()
err = subprocess.run(["quilt", "pop", "-a"], cwd=sdir, stderr=fil, stdout=fil)
if err.returncode not in [0, 2]:
raise RuntimeError(f"{cs.name()}: quilt pop failed on {sdir}: ({err.returncode}) {err.stderr}")
shutil.rmtree(patches_dir, ignore_errors=True)
shutil.rmtree(Path(sdir, ".pc"), ignore_errors=True)
def apply_all_patches(self, cs, fil):
dirs = []
if cs.rt:
dirs.extend([f"{cs.sle}.{cs.sp}rtu{cs.update}", f"{cs.sle}.{cs.sp}rt"])
dirs.extend([f"{cs.sle}.{cs.sp}u{cs.update}", f"{cs.sle}.{cs.sp}"])
if cs.sle == 15 and cs.sp < 4:
dirs.append("cve-5.3")
elif cs.sle == 15 and cs.sp <= 5:
dirs.append("cve-5.14")
patch_dirs = []
for d in dirs:
patch_dirs.append(Path(self.get_patches_dir(), d))
patched = False
sdir = cs.get_sdir()
for pdir in patch_dirs:
if not pdir.exists():
fil.write(f"\nPatches dir {pdir} doesnt exists\n")
continue
fil.write(f"\nApplying patches on {cs.name()}({cs.kernel}) from {pdir}\n")
fil.flush()
for patch in sorted(pdir.iterdir(), reverse=True):
if not str(patch).endswith(".patch"):
continue
err = subprocess.run(["quilt", "import", str(patch)], cwd=sdir, stderr=fil, stdout=fil)
if err.returncode != 0:
fil.write("\nFailed to import patches, remove applied and try again\n")
self.remove_patches(cs, fil)
err = subprocess.run(["quilt", "push", "-a"], cwd=sdir, stderr=fil, stdout=fil)
if err.returncode != 0:
fil.write("\nFailed to apply patches, remove applied and try again\n")
self.remove_patches(cs, fil)
continue
patched = True
fil.flush()
# Stop the loop in the first dir that we find patches.
break
if not patched:
raise RuntimeError(f"{cs.name()}({cs.kernel}): Failed to apply patches. Aborting")
def get_cmd_from_json(self, cs, fname):
cc_file = Path(cs.get_odir(), "compile_commands.json")
# FIXME: compile_commands.json that is packaged with SLE/openSUSE
# doesn't quite work yet, so don't use it yet.
return None
with open(cc_file) as f:
buf = f.read()
data = json.loads(buf)
for d in data:
if fname in d["file"]:
output = d["command"]
return Extractor.process_make_output(output)
logging.error(f"Couldn't find cmdline for {fname}. Aborting")
return None
def process(self, args):
i, fname, cs, fdata = args
sdir = cs.get_sdir()
odir = cs.get_odir()
# The header text has two tabs
cs_info = cs.name().ljust(15, " ")
idx = f"({i}/{self.total})".rjust(15, " ")
logging.info(f"{idx} {cs_info} {fname}")
out_dir = self.get_work_dir(cs, fname, self.app)
out_dir.mkdir(parents=True, exist_ok=True)
# create symlink to the respective codestream file
os.symlink(Path(sdir, fname), Path(out_dir, Path(fname).name))
# Make can regenerate fixdep for each file being processed per
# codestream, so avoid the TXTBUSY error by serializing the 'make -sn'
# calls. Make is pretty fast, so there isn't a real slow down here.
with self.make_lock:
cmd = self.get_cmd_from_json(cs, fname)
if not cmd:
cmd = Extractor.get_make_cmd(out_dir, cs, fname, odir, sdir)
if not cmd:
raise
# SLE15-SP6 doesn't enabled CET, but we would like to start using
# klp-convert either way.
needs_ibt = cs.sle > 15 or (cs.sle == 15 and cs.sp >= 6)
args, lenv = self.runner.cmd_args(needs_ibt, cs, fname, ",".join(fdata["symbols"]), out_dir, fdata, cmd)
# Detect and set ibt information. It will be used in the TemplateGen
if '-fcf-protection' in cmd or needs_ibt:
cs.files[fname]["ibt"] = True
out_log = Path(out_dir, f"{self.app}.out.txt")
with open(out_log, "w") as f:
# Write the command line used
f.write(f"Executing {self.app} on {odir}\n")
f.write("\n".join(args) + "\n")
f.flush()
try:
subprocess.run(args, cwd=odir, stdout=f, stderr=f, env=lenv, check=True)
except:
logging.error(f"Error when processing {cs.name()}:{fname}. Check file {out_log} for details.")
raise
cs.files[fname]["ext_symbols"] = self.runner.get_symbol_list(out_dir)
lp_out = Path(out_dir, self.lp_out_file(fname))
# Remove the local path prefix of the klp-ccp generated comments
# Open the file, read, seek to the beginning, write the new data, and
# then truncate (which will use the current position in file as the
# size)
with open(str(lp_out), "r+") as f:
file_buf = f.read()
f.seek(0)
f.write(file_buf.replace(f"from {str(sdir)}/", "from "))
f.truncate()
self.tem.CreateMakefile(cs, fname, False)
def run(self):
logging.info(f"Work directory: {self.lp_path}")
working_cs = self.filter_cs(verbose=True)
if len(working_cs) == 0:
logging.error(f"No codestreams found")
sys.exit(1)
# Make it perform better by spawning a process function per
# cs/file/funcs tuple, instead of spawning a thread per codestream
args = []
i = 1
for cs in working_cs:
# remove any previously generated files and leftover patches
shutil.rmtree(self.get_cs_dir(cs, self.app), ignore_errors=True)
self.remove_patches(cs, self.quilt_log)
# Apply patches before the LPs were created
if self.apply_patches:
self.apply_all_patches(cs, self.quilt_log)
for fname, fdata in cs.files.items():
args.append((i, fname, cs, fdata))
i += 1
logging.info(f"Extracting code using {self.app}")
self.total = len(args)
logging.info(f"\nGenerating livepatches for {len(args)} file(s) using {self.workers} workers...")
logging.info("\t\tCodestream\tFile")
with concurrent.futures.ThreadPoolExecutor(max_workers=self.workers) as executor:
results = executor.map(self.process, args)
try:
for result in results:
if result:
logging.error(f"{cs}: {result}")
except:
executor.shutdown()
sys.exit(1)
# Save the ext_symbols set by execute
self.flush_cs_file(working_cs)
# TODO: change the templates so we generate a similar code than we
# already do for SUSE livepatches
# Create the livepatches per codestream
for cs in working_cs:
self.tem.GenerateLivePatches(cs)
self.group_equal_files(args)
self.tem.generate_commit_msg_file()
logging.info("Checking the externalized symbols in other architectures...")
missing_syms = OrderedDict()
# Iterate over each codestream, getting each file processed, and all
# externalized symbols of this file
for cs in working_cs:
# Cleanup patches after the LPs were created if they were applied
if self.apply_patches:
self.remove_patches(cs, self.quilt_log)
# Map all symbols related to each obj, to make it check the symbols
# only once per object
obj_syms = {}
for f, fdata in cs.files.items():
for obj, syms in fdata["ext_symbols"].items():
obj_syms.setdefault(obj, [])
obj_syms[obj].extend(syms)
for obj, syms in obj_syms.items():
missing = self.check_symbol_archs(cs, obj, syms, True)
if missing:
for arch, arch_syms in missing.items():
missing_syms.setdefault(arch, {})
missing_syms[arch].setdefault(obj, {})
missing_syms[arch][obj].setdefault(cs.name(), [])
missing_syms[arch][obj][cs.name()].extend(arch_syms)
self.tem.CreateKbuildFile(cs)
if missing_syms:
with open(Path(self.lp_path, "missing_syms"), "w") as f:
f.write(json.dumps(missing_syms, indent=4))
logging.warning("Symbols not found:")
logging.warn(json.dumps(missing_syms, indent=4))
def get_work_lp_file(self, cs, fname):
return Path(self.get_work_dir(cs, fname, self.app), self.lp_out_file(fname))
def get_cs_code(self, args):
cs_files = {}
# Mount the cs_files dict
for arg in args:
_, file, cs, _ = arg
cs_files.setdefault(cs.name(), [])
fpath = self.get_work_lp_file(cs, file)
with open(fpath, "r+") as fi:
src = fi.read()
src = re.sub(r'#include ".+kconfig\.h"', "", src)
# Since 15.4 klp-ccp includes a compiler-version.h header
src = re.sub(r'#include ".+compiler\-version\.h"', "", src)
# Since RT variants, there is now an definition for auto_type
src = src.replace(r"#define __auto_type int\n", "")
# We have problems with externalized symbols on macros. Ignore
# codestream names specified on paths that are placed on the
# expanded macros
src = re.sub(f"{cs.get_data_dir(utils.ARCH)}.+{file}", "", src)
# We can have more details that can differ for long expanded
# macros, like the patterns bellow
src = re.sub(rf"\.lineno = \d+,", "", src)
# Remove any mentions to klpr_trace, since it's currently
# buggy in klp-ccp
src = re.sub(r".+klpr_trace.+", "", src)
# Remove clang-extract comments
src = re.sub(r"clang-extract: .+", "", src)
# Reduce the noise from klp-ccp when expanding macros
src = re.sub(r"__compiletime_assert_\d+", "__compiletime_assert", src)
cs_files[cs.name()].append((file, src))
return cs_files
# cs_list should be only two entries
def diff_cs(self):
args = []
cs_cmp = []
for cs in self.filter_cs():
cs_cmp.append(cs.name())
for fname, _ in cs.files.items():
args.append((_, fname, cs, _))
assert len(cs_cmp) == 2
cs_code = self.get_cs_code(args)
f1 = cs_code.get(cs_cmp[0])
f2 = cs_code.get(cs_cmp[1])
assert len(f1) == len(f2)
for i in range(len(f1)):
content1 = f1[i][1].splitlines()
content2 = f2[i][1].splitlines()
for l in dl.unified_diff(content1, content2, fromfile=f1[i][0], tofile=f2[i][0]):
print(l)
# Get the code for each codestream, removing boilerplate code
def group_equal_files(self, args):
cs_equal = []
processed = []
cs_files = self.get_cs_code(args)
toprocess = list(cs_files.keys())
while len(toprocess):
current_cs_list = []
# Get an element, and check if it wasn't associated with a previous
# codestream
cs = toprocess.pop(0)
if cs in processed:
continue
# last element, it's different from all other codestreams, so add it
# to the cs_equal alone.
if not toprocess:
cs_equal.append([cs])
break
# start a new list with the current element to compare with others
current_cs_list.append(cs)
data_cs = cs_files[cs]
len_data = len(data_cs)
# Compare the file names, and file content between codestrams,
# trying to find ones that have the same files and contents
for cs_proc in toprocess:
data_proc = cs_files[cs_proc]
if len_data != len(data_proc):
continue
ok = True
for i in range(len_data):
file, src = data_cs[i]
file_proc, src_proc = data_proc[i]
if file != file_proc or src != src_proc:
ok = False
break
# cs is equal to cs_proc, with the same number of files, same
# file names, and the files have the same content. So we don't
# need to process cs_proc later in the process
if ok:
processed.append(cs_proc)
current_cs_list.append(cs_proc)
# Append the current list of equal codestreams to a global list to
# be grouped later
cs_equal.append(natsorted(current_cs_list))
# cs_equal will contain a list of lists with codestreams that share the
# same code
groups = []
for cs_list in cs_equal:
groups.append(" ".join(utils.classify_codestreams(cs_list)))
with open(Path(self.lp_path, self.app, "groups"), "w") as f:
f.write("\n".join(groups))
logging.info("\nGrouping codestreams that share the same content and files:")
for group in groups:
logging.info(f"\t{group}")
| 20,784 | Python | .py | 439 | 35.164009 | 112 | 0.562602 | SUSE/klp-build | 8 | 2 | 4 | GPL-2.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,645 | __init__.py | PaladinStudiosBVs_Blender-RigAssistant/Blender-RigAssistant/__init__.py | # Addon info
bl_info = {
"name": "Blender Rig Assistant",
"description":"Rig anything with ease",
"author": "Thomas Breuker",
"blender": (3, 4, 1),
"version": (0, 0, 2),
"category": "Rigging",
"location": "View3D > Sidebar > RigAssistant",
"warning": "",
"wiki_url": "",
"tracker_url": "",
}
import bpy
from mathutils import Vector
from .operators.rigshapes import OBJECT_OT_create_circle, OBJECT_OT_create_cube, OBJECT_OT_create_piramid, OBJECT_OT_create_sphere, OBJECT_OT_create_square
from .operators.ctrlbones import OBJECT_OT_suffix_l, OBJECT_OT_suffix_r, OBJECT_OT_create_control_bone, OBJECT_OT_create_local_offset_bone, OBJECT_OT_add_controls, OBJECT_OT_remove_controls
from .operators.cnstrbones import OBJECT_OT_remove_all_cnstr, OBJECT_OT_create_cnstr, OBJECT_OT_add_cnstr, OBJECT_OT_remove_cnstr_bone, OBJECT_OT_remove_selected_bone, OBJECT_OT_append_cnstr, OBJECT_OT_create_cnstr_ctrl
from .operators.deformbones import OBJECT_OT_create_armature, OBJECT_OT_disconnect_bones, OBJECT_OT_remove_roll, OBJECT_OT_chain_parent,OBJECT_OT_chain_rename
# Tells the which constraint to pick when using create constraint add constraint or append constraint.
class constraint_properties(bpy.types.PropertyGroup):
constraint_enum : bpy.props.EnumProperty(
name = "type",
description = "choose the type of constraint",
items = [('OP1',"TRANSFORMS",""),
('OP2',"LOCATION",""),
('OP3',"ROTATION",""),
('OP4',"SCALE",""),
('OP5',"IK",""),
('OP6',"NONE",""),
]
)
#switches between local or world space for control bones
class world_local_properties(bpy.types.PropertyGroup):
world_local_enum : bpy.props.EnumProperty(
name = "space",
description = "choose between world or local",
items = [('OP1',"LOCAL",""),
('OP2',"WORLD",""),
]
)
#UI window
class VIEW3D_PT_blender_rig_assistant(bpy.types.Panel):
bl_space_type = 'VIEW_3D'
bl_region_type = 'UI'
bl_category = "Rig Assistant"
bl_label = "Rig Assistant"
def draw(self, context):
coltop = self.layout.column(heading="Armature Creator")
coltop.label(text="Armature")
coltop.operator('object.create_armature',icon = 'ARMATURE_DATA')
coltop.operator('object.disconnect_bones', icon = 'BONE_DATA')
coltop.operator('object.remove_roll', icon ='OUTLINER_DATA_GREASEPENCIL')
coltop.operator('object.chain_parent',icon ='DECORATE_LINKED')
coltop.operator('object.chain_rename',icon ='FILE_TEXT')
self.layout.separator()
rowa=self.layout.row(align=True)
rowa.operator('object.prefix_l', icon ='EVENT_L')
rowa.operator('object.prefix_r', icon ='EVENT_R')
self.layout.separator()
col= self.layout.column()
col.label(text="Constraints")
col.prop(context.scene.type_constrain, "constraint_enum")
col.operator('object.create_cnstr', icon = 'CONSTRAINT_BONE')
col.operator('object.append_cnstr', icon = 'CONSTRAINT')
col.operator('object.add_cnstr', icon = 'GROUP_BONE')
self.layout.separator()
colb=self.layout.column()
colb.label(text="Removing Bones and Constraints")
colb.operator('object.remove_all_cnstr', icon = 'CANCEL')
colb.operator('object.remove_cnstr_bone', icon = 'CONSTRAINT_BONE')
colb.operator('object.remove_selected_bone', icon = 'BONE_DATA')
self.layout.separator()
colc= self.layout.column()
colc.label(text="Controls and Offsets")
colc.prop(context.scene.local_world_switch, "world_local_enum")
colc.operator('object.create_control_bone', icon = 'OUTLINER_DATA_ARMATURE')
colc.operator('object.create_local_offset_bone' , icon = 'CON_ARMATURE')
colc.operator('object.create_cnstr_ctrl',icon ='OUTLINER_OB_ARMATURE')
self.layout.separator()
cold=self.layout.column()
cold.label(text="Control Shapes")
cold.operator('object.add_controls', icon = 'MOD_SKIN')
cold.operator('object.remove_controls', icon ='MOD_PHYSICS')
self.layout.separator()
colf=self.layout.grid_flow(row_major=True, columns=2, align=True)
colf.operator('object.create_circle', icon ='MESH_CIRCLE')
colf.operator('object.create_cube', icon ='CUBE')
colf.operator('object.create_piramid', icon ='CONE')
colf.operator('object.create_sphere', icon ='SPHERE')
colf.operator('object.create_square', icon = 'MESH_PLANE')
blender_classes = [
constraint_properties,
world_local_properties,
OBJECT_OT_remove_all_cnstr,
OBJECT_OT_create_cnstr,
OBJECT_OT_add_cnstr,
OBJECT_OT_chain_parent,
OBJECT_OT_chain_rename,
OBJECT_OT_create_cnstr_ctrl,
VIEW3D_PT_blender_rig_assistant,
OBJECT_OT_remove_cnstr_bone,
OBJECT_OT_remove_selected_bone,
OBJECT_OT_create_control_bone,
OBJECT_OT_create_local_offset_bone,
OBJECT_OT_add_controls,
OBJECT_OT_remove_controls,
OBJECT_OT_remove_roll,
OBJECT_OT_append_cnstr,
OBJECT_OT_create_armature,
OBJECT_OT_disconnect_bones,
OBJECT_OT_suffix_l,
OBJECT_OT_suffix_r,
OBJECT_OT_create_circle,
OBJECT_OT_create_cube,
OBJECT_OT_create_piramid,
OBJECT_OT_create_sphere,
OBJECT_OT_create_square,
]
def register():
for blender_class in blender_classes:
bpy.utils.register_class(blender_class)
bpy.types.Scene.type_constrain = bpy.props.PointerProperty(type = constraint_properties)
bpy.types.Scene.local_world_switch = bpy.props.PointerProperty(type = world_local_properties)
def unregister():
for blender_class in blender_classes:
bpy.utils.unregister_class(blender_class)
del bpy.types.Scene.type_constrain
del bpy.types.Scene.local_world_switch
| 5,959 | Python | .py | 129 | 39.162791 | 219 | 0.677213 | PaladinStudiosBVs/Blender-RigAssistant | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,646 | deformbones.py | PaladinStudiosBVs_Blender-RigAssistant/Blender-RigAssistant/operators/deformbones.py | import bpy
from mathutils import Vector
# Handles everything related to deform bones parenting and naming
class OBJECT_OT_disconnect_bones(bpy.types.Operator):
bl_idname = 'object.disconnect_bones'
bl_label = "Disconnect Bones"
#Simple operator disconnects bones from eachother
def execute (self, context):
bpy.ops.armature.parent_clear(type='DISCONNECT')
return{'FINISHED'}
class OBJECT_OT_create_armature(bpy.types.Operator):
bl_idname = 'object.create_armature'
bl_label = "Create An Armature"
# Creates a starting armature with a zero-ed out bone the is called root
def execute (self, context):
if bpy.context.selected_objects:
bpy.ops.object.mode_set(mode = 'OBJECT')
bpy.ops.object.armature_add(enter_editmode=True, align='WORLD', location=(0, 0, 0), scale=(1, 1, 1))
bpy.context.active_bone.name = "root"
bpy.ops.transform.translate(value=(0, 1, -1), orient_type='GLOBAL')
bpy.context.object.data.collections.new('Deform')
bpy.ops.object.mode_set(mode='POSE')
bpy.context.object.data.collections['Deform'].assign(bpy.context.object.pose.bones['root'])
bpy.context.object.data.collections.remove(bpy.context.object.data.collections['Bones'])
bpy.context.object.data.collections.new('CNSTR')
bpy.context.object.data.collections.new('CTRL')
bpy.context.object.data.collections.new('LocOff')
bpy.ops.object.mode_set(mode='EDIT')
return{'FINISHED'}
class OBJECT_OT_chain_parent(bpy.types.Operator):
"""Select a bones to parent them"""
bl_idname = 'object.chain_parent'
bl_label = "Chain Parent"
# Activates a mode where every new bone you select is parented to the previous one
#enters this mode
def execute(self,context):
bpy.ops.object.mode_set(mode='EDIT')
bpy.ops.armature.select_all(action='DESELECT')
self.report({'INFO'}, "Shift click bones in the 3D view to Chain parent/Use control in the outliner")
def modal(self, context, event):
if event.type == 'LEFTMOUSE':
return {'PASS_THROUGH'}
elif event.type in {'WHEELUPMOUSE', 'WHEELDOWNMOUSE'}:
return {'PASS_THROUGH'}
if event.type == 'MOUSEMOVE':
selected_bones = bpy.context.selected_bones
if len(selected_bones)==2:
bpy.ops.armature.parent_set(type='OFFSET')
active_bone = bpy.context.object.data.edit_bones.active
bpy.ops.armature.select_all(action='DESELECT')
bpy.context.object.data.edit_bones[active_bone.name].select = True
bpy.context.object.data.edit_bones[active_bone.name].select_head = True
bpy.context.object.data.edit_bones[active_bone.name].select_tail = True
bpy.context.object.data.edit_bones.active = bpy.context.object.data.edit_bones[active_bone.name]
self.report({'INFO'}, "Bones Happily Parented! Press ENTER to stop")
# right mouse buttons stops the chain parent action
elif event.type in {'RIGHTMOUSE', 'RET'}:
bpy.ops.armature.select_all(action='DESELECT')
self.report({'INFO'}, "chain bone mode deactivated...")
return {'FINISHED'}
return {'RUNNING_MODAL'}
def invoke(self, context, event):
if context.object:
context.window_manager.modal_handler_add(self)
return {'RUNNING_MODAL'}
else:
self.report({'WARNING'}, "No active object, could not finish")
return {'CANCELLED'}
class OBJECT_OT_chain_rename(bpy.types.Operator):
"""Rename bones to chains"""
bl_idname = 'object.chain_rename'
bl_label = "Chain Rename"
text : bpy.props.StringProperty(name = "Enter Text", default="")
startat : bpy.props.IntProperty(name = "Start at", default = 1)
def execute(self, context):
number = self.startat
digits = len(str(len(bpy.context.selected_bones) + self.startat - 1)) # Determine the number of digits needed
for bone in bpy.context.selected_bones:
bone.name = f"{self.text}_{number:0{digits}d}" # Use format specifier for padding with leading zeros
number += 1
return {'FINISHED'}
def invoke(self, context, event):
return context.window_manager.invoke_props_dialog(self)
class OBJECT_OT_remove_roll(bpy.types.Operator):
bl_idname = 'object.remove_roll'
bl_label = "Remove Roll"
#Removes roll from the bone.
def execute (self, context):
current_mode = bpy.context.object.mode
bpy.ops.object.mode_set(mode='EDIT')
for b in bpy.context.selected_bones:
b.roll = 0
bpy.ops.object.mode_set(mode= current_mode)
return{'FINISHED'} | 4,936 | Python | .py | 94 | 42.659574 | 118 | 0.656883 | PaladinStudiosBVs/Blender-RigAssistant | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,647 | ctrlbones.py | PaladinStudiosBVs_Blender-RigAssistant/Blender-RigAssistant/operators/ctrlbones.py | import bpy
from mathutils import Vector
#Handles everything related to CTRL_, offset and location bones
class OBJECT_OT_create_control_bone(bpy.types.Operator):
"""creates a cnstr bone for selected bones"""
bl_idname = 'object.create_control_bone'
bl_label = "Create Control Bones"
# Creates a control bone and searches for the CNSTR_ bone to become it's parent
# Depending which space is selected CTRL_ bone is either created in world or local space
def execute (self, context):
boneCollections = bpy.context.object.data.collections_all;
visibilityCache = []
for i in boneCollections:
visibilityCache.append(i.is_visible)
for b in range(0,len(visibilityCache)):
boneCollections[b].is_visible = True
if bpy.context.selected_pose_bones is None and bpy.context.selected_bones is None :
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
self.report({"WARNING"}, "No Bones selected Check if they are visible")
return {'CANCELLED'}
# Collection stuff: Check if there's a collection CTRL if it's not, make it
if boneCollections.get('CTRL') is None:
bcoll = bpy.context.object.data.collections.new('CTRL')
current_mode = bpy.context.object.mode
if current_mode == 'EDIT' or current_mode == 'POSE':
bpy.ops.object.mode_set(mode='EDIT')
armanm = bpy.context.active_object
armature = bpy.context.object.data
bpy.ops.object.mode_set(mode='POSE')
pbones = bpy.context.selected_pose_bones
bpy.ops.object.mode_set(mode='EDIT')
current_bone = 0
if context.scene.local_world_switch.world_local_enum == 'OP1':
for b in bpy.context.selected_bones:
if bpy.context.object.data.edit_bones.get("CTRL_" + b.name):
bpy.context.object.data.edit_bones.remove(bpy.context.object.data.edit_bones.get("CTRL_" + b.name))
cb = bpy.context.object.data.edit_bones.new("CTRL_" + b.name)
cb.head = b.head
cb.tail = b.tail
cb.matrix = b.matrix
bpy.context.object.data.edit_bones.get("CTRL_" + b.name).use_deform = False
if bpy.context.object.data.edit_bones.get("CNSTR_" + b.name):
bpy.context.object.data.edit_bones["CNSTR_" + b.name].parent = bpy.context.object.data.edit_bones[cb.name]
if context.scene.local_world_switch.world_local_enum == 'OP2':
for b in bpy.context.selected_bones:
if bpy.context.object.data.edit_bones.get("CTRL_" + b.name):
bpy.context.object.data.edit_bones.remove(bpy.context.object.data.edit_bones.get("CTRL_" + b.name))
cb = bpy.context.object.data.edit_bones.new("CTRL_" + b.name)
world_vector=Vector((0,b.length,0))
cb.head = b.head
cb.tail = cb.head + world_vector
bpy.context.object.data.edit_bones.get("CTRL_" + b.name).use_deform = False
if bpy.context.object.data.edit_bones.get("CNSTR_" + b.name):
bpy.context.object.data.edit_bones["CNSTR_" + b.name].parent = bpy.context.object.data.edit_bones[cb.name]
bpy.ops.object.mode_set(mode='POSE')
bpy.ops.pose.select_all(action='DESELECT')
for pb in pbones:
#Put the bone into the right collection
bpy.context.object.data.collections['CTRL'].assign(bpy.context.object.pose.bones["CTRL_" + pbones[current_bone].name])
bpy.context.object.data.bones["CTRL_" + pbones[current_bone].name].select = True
current_bone += 1
current_bone=0
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
bpy.ops.object.mode_set(mode= current_mode)
return{'FINISHED'}
else:
self.report({"WARNING"}, "You gotta be in edit or pose mode")
return {'CANCELLED'}
class OBJECT_OT_create_local_offset_bone(bpy.types.Operator):
"""creates a local offset bone to the last selected parents the first selected under it"""
bl_idname = 'object.create_local_offset_bone'
bl_label = "Create Local Offset Bones"
# Creates a duplicate of the selected bone and parents the original bone under it
# When 2 bones are selected it duplicates the first selected bone and parents it under the active bone.
def execute (self, context):
boneCollections = bpy.context.object.data.collections_all;
visibilityCache = []
for i in boneCollections:
visibilityCache.append(i.is_visible)
for b in range(0,len(visibilityCache)):
boneCollections[b].is_visible = True
if bpy.context.selected_pose_bones is None and bpy.context.selected_bones is None :
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
self.report({"WARNING"}, "No Bones selected Check if they are visible")
return {'CANCELLED'}
current_mode = bpy.context.object.mode
if current_mode == 'EDIT' or current_mode == 'POSE':
bpy.ops.object.mode_set(mode='POSE')
pbones = bpy.context.selected_pose_bones
bpy.ops.object.mode_set(mode='EDIT')
armanm = bpy.context.active_object
armature = bpy.context.object.data
selected_bones = bpy.context.selected_bones
selected_active_bone = bpy.context.object.data.edit_bones.active
# Collection stuff: Check if there's a collection LocOff if it's not, make it
if boneCollections.get('LocOff') is None:
bcoll = bpy.context.object.data.collections.new('LocOff')
if len(selected_bones) == 2:
if selected_bones[0] == selected_active_bone:
active=1
else:
active=0
cb = bpy.context.object.data.edit_bones.new("LOC_" + selected_bones[active].name)
cb.head = selected_bones[active].head
cb.tail = selected_bones[active].tail
cb.matrix = selected_bones[active].matrix
bpy.context.object.data.edit_bones.get("LOC_" + selected_bones[active].name).use_deform = False
bpy.context.object.data.edit_bones[cb.name].parent = bpy.context.object.data.edit_bones[selected_active_bone.name]
bpy.ops.object.mode_set(mode='POSE')
bpy.context.object.data.collections['LocOff'].assign(bpy.context.object.pose.bones["LOC_" + pbones[active].name])
if len(selected_bones) == 1:
cb = bpy.context.object.data.edit_bones.new("OFF_" + selected_bones[0].name)
cb.head = selected_bones[0].head
cb.tail = selected_bones[0].tail
cb.matrix = selected_bones[0].matrix
bpy.context.object.data.edit_bones.get("OFF_" + selected_bones[0].name).use_deform = False
bpy.context.object.data.edit_bones[selected_active_bone.name].parent = bpy.context.object.data.edit_bones[cb.name]
bpy.ops.object.mode_set(mode='POSE')
bpy.context.object.data.collections['LocOff'].assign(bpy.context.object.pose.bones["OFF_" + pbones[0].name])
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
bpy.ops.object.mode_set(mode= current_mode)
return{'FINISHED'}
else:
self.report({"WARNING"}, "You gotta be in edit or pose mode")
return {'CANCELLED'}
class OBJECT_OT_add_controls(bpy.types.Operator):
"""creates custom shapes on selected pose bones"""
bl_idname = 'object.add_controls'
bl_label = "Add Control Shapes"
# Checks selected bones, checks if there's an object selected
# Makes the object the shape of the selected bones
def execute (self, context):
selected_objects = bpy.context.selected_objects
bpy.ops.object.mode_set(mode='POSE')
selected_pose_bones = bpy.context.selected_pose_bones
bpy.ops.object.mode_set(mode= 'OBJECT')
bpy.ops.object.select_all(action='DESELECT')
for meshes in selected_objects:
if meshes.type == 'MESH':
bpy.data.objects[meshes.name].select_set(state = True)
mesh_count = len(bpy.context.selected_objects)
if mesh_count > 1:
print ("Too many meshes selected, Im going to take the first one")
bpy.ops.object.mode_set(mode= 'POSE')
selected_mesh = bpy.context.selected_objects[0]
for bone in selected_pose_bones:
bpy.context.object.pose.bones[bone.name].custom_shape = bpy.data.objects[selected_mesh.name]
if mesh_count == 1:
bpy.ops.object.mode_set(mode= 'POSE')
selected_mesh = bpy.context.selected_objects[0]
for bone in selected_pose_bones:
bpy.context.object.pose.bones[bone.name].custom_shape = bpy.data.objects[selected_mesh.name]
if mesh_count == 0:
print ("No mesh selected, I can't work with that")
return{'FINISHED'}
class OBJECT_OT_remove_controls(bpy.types.Operator):
"""creates custom shapes on selected pose bones"""
bl_idname = 'object.remove_controls'
bl_label = "Remove Control Shapes"
# Removes any object shapes that the bones have currently on them
def execute (self, context):
selected_pose_bones = bpy.context.selected_pose_bones
for shapes in selected_pose_bones:
bpy.context.object.pose.bones[shapes.name].custom_shape = None
return{'FINISHED'}
class OBJECT_OT_suffix_l(bpy.types.Operator):
bl_idname = 'object.prefix_l'
bl_label = "Suffix .l"
# ends a bone name with .l making it suitable for mirroring and symetrization
def execute (self, context):
current_mode = bpy.context.object.mode
bpy.ops.object.mode_set(mode='EDIT')
for b in bpy.context.selected_bones:
b.name = b.name + ".l"
bpy.ops.object.mode_set(mode= current_mode)
return{'FINISHED'}
class OBJECT_OT_suffix_r(bpy.types.Operator):
bl_idname = 'object.prefix_r'
bl_label = "Suffix .r"
# ends a bone name with .r making it suitable for mirroring and symetrization
def execute (self, context):
current_mode = bpy.context.object.mode
bpy.ops.object.mode_set(mode='EDIT')
for b in bpy.context.selected_bones:
b.name = b.name + ".r"
bpy.ops.object.mode_set(mode= current_mode)
return{'FINISHED'}
| 11,449 | Python | .py | 195 | 45.097436 | 134 | 0.623228 | PaladinStudiosBVs/Blender-RigAssistant | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,648 | cnstrbones.py | PaladinStudiosBVs_Blender-RigAssistant/Blender-RigAssistant/operators/cnstrbones.py | import bpy
from mathutils import Vector
# Does everything with the CNSTR bones and creating constraints
class OBJECT_OT_create_cnstr(bpy.types.Operator):
"""creates a cnstr bone for selected bones"""
bl_idname = 'object.create_cnstr'
bl_label = "Create Constraint Bones"
#Creates a duplicate of the selected bone(s) with the prefix CNSTR_ and
#constraints the original bone to the newly created bone. The type of constraint is picked in the UI
def execute (self, context):
boneCollections = bpy.context.object.data.collections_all;
visibilityCache = []
for i in boneCollections:
visibilityCache.append(i.is_visible)
for b in range(0,len(visibilityCache)):
boneCollections[b].is_visible = True
if bpy.context.selected_pose_bones is None and bpy.context.selected_bones is None :
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
self.report({"WARNING"}, "No Bones selected Check if they are visible")
return {'CANCELLED'}
current_mode = bpy.context.object.mode
if current_mode == 'EDIT' or current_mode == 'POSE':
bpy.ops.object.mode_set(mode='EDIT')
armanm = bpy.context.active_object
armature = bpy.context.object.data
bpy.ops.object.mode_set(mode='POSE')
pbones = bpy.context.selected_pose_bones
bpy.ops.object.mode_set(mode='EDIT')
current_bone = 0
# Collection stuff: Check if there's a collection CNSTR if it's not, make it
if boneCollections.get('CNSTR') is None:
bcoll = bpy.context.object.data.collections.new('CNSTR')
# this part duplicates the bone. If the duplicate already exists it deletes the old one and creates a new one
# Also checks if there is a CTRL_ prefixed bone to parent under.
for b in bpy.context.selected_bones:
if bpy.context.object.data.edit_bones.get("CNSTR_" + b.name):
bpy.context.object.data.edit_bones.remove(bpy.context.object.data.edit_bones.get("CNSTR_" + b.name))
cb = armature.edit_bones.new("CNSTR_" + b.name)
cb.head = b.head
cb.tail = b.tail
cb.matrix = b.matrix
bpy.context.object.data.edit_bones.get("CNSTR_" + b.name).use_deform = False
if bpy.context.object.data.edit_bones.get("CTRL_" + b.name):
bpy.context.object.data.edit_bones["CNSTR_" + b.name].parent = bpy.context.object.data.edit_bones["CTRL_" + b.name]
#This part sets up the constraint
bpy.ops.object.mode_set(mode='POSE')
for pb in pbones:
for c in pb.constraints:
pb.constraints.remove(c)
#first put the bone into the right collection
bpy.context.object.data.collections['CNSTR'].assign(bpy.context.object.pose.bones["CNSTR_" + pbones[current_bone].name])
bpy.ops.pose.select_all(action='DESELECT')
bpy.context.object.data.bones[pbones[current_bone].name].select = True
bpy.context.object.data.bones["CNSTR_" + pbones[current_bone].name].select = True
bpy.context.object.data.bones.active = bpy.context.object.pose.bones[pbones[current_bone].name].bone
if context.scene.type_constrain.constraint_enum == 'OP1':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_TRANSFORMS')
if context.scene.type_constrain.constraint_enum == 'OP2':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_LOCATION')
if context.scene.type_constrain.constraint_enum == 'OP3':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_ROTATION')
if context.scene.type_constrain.constraint_enum == 'OP4':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_SCALE')
if context.scene.type_constrain.constraint_enum == 'OP5':
bpy.ops.pose.constraint_add_with_targets(type = 'IK')
constraint_count = 1-len(bpy.context.selected_pose_bones[0].constraints)
bpy.context.selected_pose_bones[0].constraints[constraint_count].use_tail = False
bpy.context.selected_pose_bones[0].constraints[constraint_count].chain_count= 2
bpy.ops.pose.select_all(action='DESELECT')
current_bone += 1
current_bone=0
for pb in pbones:
bpy.context.object.data.bones[pbones[current_bone].name].select = True
current_bone += 1
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
bpy.ops.object.mode_set(mode= current_mode)
return{'FINISHED'}
else:
self.report({"WARNING"}, "You gotta be in edit or pose mode")
return {'CANCELLED'}
class OBJECT_OT_remove_cnstr_bone(bpy.types.Operator):
bl_idname = 'object.remove_cnstr_bone'
bl_label = "Remove Constraint Bone"
#This cleanly removes a CNSTR_ bone also deleting the contraint on the deform bone
def execute (self, context):
boneCollections = bpy.context.object.data.collections_all;
visibilityCache = []
for i in boneCollections:
visibilityCache.append(i.is_visible)
for b in range(0,len(visibilityCache)):
boneCollections[b].is_visible = True
if bpy.context.selected_pose_bones is None and bpy.context.selected_bones is None :
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
self.report({"WARNING"}, "No Bones selected Check if they are visible")
return {'CANCELLED'}
current_mode = bpy.context.object.mode
bpy.ops.object.mode_set(mode='POSE')
pbones = bpy.context.selected_pose_bones
bpy.ops.object.mode_set(mode='EDIT')
for b in bpy.context.selected_bones:
if bpy.context.object.data.edit_bones.get("CNSTR_" + b.name):
bpy.context.object.data.edit_bones.remove(bpy.context.object.data.edit_bones.get("CNSTR_" + b.name))
for bone in pbones:
for c in bone.constraints:
bone.constraints.remove(c) # Remove constraint
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
bpy.ops.object.mode_set(mode= current_mode)
return{'FINISHED'}
class OBJECT_OT_remove_selected_bone(bpy.types.Operator):
bl_idname = 'object.remove_selected_bone'
bl_label = "Remove Selected Bones"
#This just deletes bones
def execute (self, context):
boneCollections = bpy.context.object.data.collections_all;
visibilityCache = []
for i in boneCollections:
visibilityCache.append(i.is_visible)
for b in range(0,len(visibilityCache)):
boneCollections[b].is_visible = True
if bpy.context.selected_pose_bones is None and bpy.context.selected_bones is None :
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
self.report({"WARNING"}, "No Bones selected Check if they are visible")
return {'CANCELLED'}
current_mode = bpy.context.object.mode
bpy.ops.object.mode_set(mode='EDIT')
for b in bpy.context.selected_bones:
bpy.context.object.data.edit_bones.remove(b)
bpy.ops.object.mode_set(mode='POSE')
bpy.ops.object.mode_set(mode= current_mode)
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
return{'FINISHED'}
class OBJECT_OT_remove_all_cnstr(bpy.types.Operator):
bl_idname = 'object.remove_all_cnstr'
bl_label = "Remove all constraints"
# removes all the constraints from a selected bone
# goes to pose mode, clocks the selected bones, clocks the constraints and deletes them all
# goes back to the previous selected mode
def execute (self, context):
boneCollections = bpy.context.object.data.collections_all;
visibilityCache = []
for i in boneCollections:
visibilityCache.append(i.is_visible)
for b in range(0,len(visibilityCache)):
boneCollections[b].is_visible = True
if bpy.context.selected_pose_bones is None and bpy.context.selected_bones is None :
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
self.report({"WARNING"}, "No Bones selected Check if they are visible")
return {'CANCELLED'}
current_mode = bpy.context.object.mode
bpy.ops.object.mode_set(mode='POSE')
for bone in bpy.context.selected_pose_bones:
for c in bone.constraints:
bone.constraints.remove(c) # Remove constraint
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
bpy.ops.object.mode_set(mode= current_mode)
return{'FINISHED'}
class OBJECT_OT_add_cnstr(bpy.types.Operator):
bl_idname = 'object.add_cnstr'
bl_label = "Constraint Between Selected Bones"
#Adds a constrain between selected bones
#Constrain type gets picked in the UI in __init__
#IK has already been set to most used config
def execute(self,context):
boneCollections = bpy.context.object.data.collections_all;
visibilityCache = []
for i in boneCollections:
visibilityCache.append(i.is_visible)
for b in range(0,len(visibilityCache)):
boneCollections[b].is_visible = True
if bpy.context.selected_pose_bones is None and bpy.context.selected_bones is None :
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
self.report({"WARNING"}, "No Bones selected Check if they are visible")
return {'CANCELLED'}
current_mode = bpy.context.object.mode
bpy.ops.object.mode_set(mode='POSE')
if context.scene.type_constrain.constraint_enum == 'OP1':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_TRANSFORMS')
if context.scene.type_constrain.constraint_enum == 'OP2':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_LOCATION')
if context.scene.type_constrain.constraint_enum == 'OP3':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_ROTATION')
if context.scene.type_constrain.constraint_enum == 'OP4':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_SCALE')
if context.scene.type_constrain.constraint_enum == 'OP5':
bpy.ops.pose.constraint_add_with_targets(type = 'IK')
constraint_count = 1-len(bpy.context.selected_pose_bones[0].constraints)
bpy.context.selected_pose_bones[0].constraints[constraint_count].use_tail = False
bpy.context.selected_pose_bones[0].constraints[constraint_count].chain_count= 2
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
bpy.ops.object.mode_set(mode= current_mode)
return{'FINISHED'}
class OBJECT_OT_append_cnstr(bpy.types.Operator):
bl_idname = 'object.append_cnstr'
bl_label = "Append Constraint To Bones"
#Will append a constraint to a bone that already has a CNSTR bone.
#Constrain type gets picked in the UI in __init__
#IK has already been set to most used config
def execute(self,context):
boneCollections = bpy.context.object.data.collections_all;
visibilityCache = []
for i in boneCollections:
visibilityCache.append(i.is_visible)
for b in range(0,len(visibilityCache)):
boneCollections[b].is_visible = True
if bpy.context.selected_pose_bones is None and bpy.context.selected_bones is None :
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
self.report({"WARNING"}, "No Bones selected Check if they are visible")
return {'CANCELLED'}
current_mode = bpy.context.object.mode
current_bone = 0
bpy.ops.object.mode_set(mode='POSE')
pbones = bpy.context.selected_pose_bones
for pb in pbones:
bpy.ops.pose.select_all(action='DESELECT')
bpy.context.object.data.bones[pbones[current_bone].name].select = True
bpy.context.object.data.bones["CNSTR_" + pbones[current_bone].name].select = True
bpy.context.object.data.bones.active = bpy.context.object.pose.bones[pbones[current_bone].name].bone
if context.scene.type_constrain.constraint_enum == 'OP1':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_TRANSFORMS')
if context.scene.type_constrain.constraint_enum == 'OP2':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_LOCATION')
if context.scene.type_constrain.constraint_enum == 'OP3':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_ROTATION')
if context.scene.type_constrain.constraint_enum == 'OP4':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_SCALE')
if context.scene.type_constrain.constraint_enum == 'OP5':
bpy.ops.pose.constraint_add_with_targets(type = 'IK')
constraint_count = 1-len(bpy.context.selected_pose_bones[0].constraints)
bpy.context.selected_pose_bones[0].constraints[constraint_count].use_tail = False
bpy.context.selected_pose_bones[0].constraints[constraint_count].chain_count= 2
bpy.ops.pose.select_all(action='DESELECT')
current_bone += 1
current_bone=0
for pb in pbones:
bpy.context.object.data.bones[pbones[current_bone].name].select = True
current_bone += 1
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
bpy.ops.object.mode_set(mode='EDIT')
bpy.ops.object.mode_set(mode= current_mode)
return{'FINISHED'}
class OBJECT_OT_create_cnstr_ctrl(bpy.types.Operator):
"""creates a cnstr bone for selected bones"""
bl_idname = 'object.create_cnstr_ctrl'
bl_label = "Constraint & Control"
#Creates a duplicate of the selected bone(s) with the prefix CNSTR_ and
#constraints the original bone to the newly created bone. The type of constraint is picked in the UI
def execute (self, context):
boneCollections = bpy.context.object.data.collections_all;
visibilityCache = []
for i in boneCollections:
visibilityCache.append(i.is_visible)
for b in range(0,len(visibilityCache)):
boneCollections[b].is_visible = True
if bpy.context.selected_pose_bones is None and bpy.context.selected_bones is None :
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
self.report({"WARNING"}, "No Bones selected Check if they are visible")
return {'CANCELLED'}
current_mode = bpy.context.object.mode
if current_mode == 'EDIT' or current_mode == 'POSE':
bpy.ops.object.mode_set(mode='EDIT')
armanm = bpy.context.active_object
armature = bpy.context.object.data
bpy.ops.object.mode_set(mode='POSE')
pbones = bpy.context.selected_pose_bones
bpy.ops.object.mode_set(mode='EDIT')
current_bone = 0
# Collection stuff: Check if there's a collection CNSTR if it's not, make it
if boneCollections.get('CNSTR') is None:
bcoll = bpy.context.object.data.collections.new('CNSTR')
# Collection stuff: Check if there's a collection CTRL if it's not, make it
if boneCollections.get('CTRL') is None:
bcoll = bpy.context.object.data.collections.new('CTRL')
# this part duplicates the bone. If the duplicate already exists it deletes the old one and creates a new one
# Also checks if there is a CTRL_ prefixed bone to parent under.
for b in bpy.context.selected_bones:
if bpy.context.object.data.edit_bones.get("CNSTR_" + b.name):
bpy.context.object.data.edit_bones.remove(bpy.context.object.data.edit_bones.get("CNSTR_" + b.name))
cb = armature.edit_bones.new("CNSTR_" + b.name)
cb.head = b.head
cb.tail = b.tail
cb.matrix = b.matrix
bpy.context.object.data.edit_bones.get("CNSTR_" + b.name).use_deform = False
if bpy.context.object.data.edit_bones.get("CTRL_" + b.name):
bpy.context.object.data.edit_bones["CNSTR_" + b.name].parent = bpy.context.object.data.edit_bones["CTRL_" + b.name]
#This part sets up the constraint
bpy.ops.object.mode_set(mode='POSE')
for pb in pbones:
for c in pb.constraints:
pb.constraints.remove(c)
#first put the bone into the right collection
bpy.context.object.data.collections['CNSTR'].assign(bpy.context.object.pose.bones["CNSTR_" + pbones[current_bone].name])
bpy.ops.pose.select_all(action='DESELECT')
bpy.context.object.data.bones[pbones[current_bone].name].select = True
bpy.context.object.data.bones["CNSTR_" + pbones[current_bone].name].select = True
bpy.context.object.data.bones.active = bpy.context.object.pose.bones[pbones[current_bone].name].bone
if context.scene.type_constrain.constraint_enum == 'OP1':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_TRANSFORMS')
if context.scene.type_constrain.constraint_enum == 'OP2':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_LOCATION')
if context.scene.type_constrain.constraint_enum == 'OP3':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_ROTATION')
if context.scene.type_constrain.constraint_enum == 'OP4':
bpy.ops.pose.constraint_add_with_targets(type = 'COPY_SCALE')
if context.scene.type_constrain.constraint_enum == 'OP5':
bpy.ops.pose.constraint_add_with_targets(type = 'IK')
constraint_count = 1-len(bpy.context.selected_pose_bones[0].constraints)
bpy.context.selected_pose_bones[0].constraints[constraint_count].use_tail = False
bpy.context.selected_pose_bones[0].constraints[constraint_count].chain_count= 2
bpy.ops.pose.select_all(action='DESELECT')
current_bone += 1
current_bone=0
for pb in pbones:
bpy.context.object.data.bones[pbones[current_bone].name].select = True
current_bone += 1
bpy.ops.object.mode_set(mode='EDIT')
current_bone=0
if context.scene.local_world_switch.world_local_enum == 'OP1':
for b in bpy.context.selected_bones:
if bpy.context.object.data.edit_bones.get("CTRL_" + b.name):
bpy.context.object.data.edit_bones.remove(bpy.context.object.data.edit_bones.get("CTRL_" + b.name))
cb = bpy.context.object.data.edit_bones.new("CTRL_" + b.name)
cb.head = b.head
cb.tail = b.tail
cb.matrix = b.matrix
bpy.context.object.data.edit_bones.get("CTRL_" + b.name).use_deform = False
if bpy.context.object.data.edit_bones.get("CNSTR_" + b.name):
bpy.context.object.data.edit_bones["CNSTR_" + b.name].parent = bpy.context.object.data.edit_bones[cb.name]
if context.scene.local_world_switch.world_local_enum == 'OP2':
for b in bpy.context.selected_bones:
if bpy.context.object.data.edit_bones.get("CTRL_" + b.name):
bpy.context.object.data.edit_bones.remove(bpy.context.object.data.edit_bones.get("CTRL_" + b.name))
cb = bpy.context.object.data.edit_bones.new("CTRL_" + b.name)
world_vector=Vector((0,b.length,0))
cb.head = b.head
cb.tail = cb.head + world_vector
bpy.context.object.data.edit_bones.get("CTRL_" + b.name).use_deform = False
if bpy.context.object.data.edit_bones.get("CNSTR_" + b.name):
bpy.context.object.data.edit_bones["CNSTR_" + b.name].parent = bpy.context.object.data.edit_bones[cb.name]
bpy.ops.object.mode_set(mode='POSE')
bpy.ops.pose.select_all(action='DESELECT')
for pb in pbones:
#Put the bone into the right collection
bpy.context.object.data.collections['CTRL'].assign(bpy.context.object.pose.bones["CTRL_" + pbones[current_bone].name])
bpy.context.object.data.bones["CTRL_" + pbones[current_bone].name].select = True
current_bone += 1
current_bone=0
current_bone=0
for i in range(0,len(visibilityCache)):
boneCollections[i].is_visible = visibilityCache[i]
visibilityCache.clear
bpy.ops.object.mode_set(mode= current_mode)
return{'FINISHED'}
else:
self.report({"WARNING"}, "You gotta be in edit or pose mode")
return {'CANCELLED'}
| 23,267 | Python | .py | 381 | 46.464567 | 138 | 0.624921 | PaladinStudiosBVs/Blender-RigAssistant | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,649 | rigshapes.py | PaladinStudiosBVs_Blender-RigAssistant/Blender-RigAssistant/operators/rigshapes.py | import bpy
from mathutils import Vector
# Create different shapes that can be used as bone shapes
class OBJECT_OT_create_circle(bpy.types.Operator):
bl_idname = 'object.create_circle'
bl_label = "Circle"
def execute (self, context):
if bpy.context.selected_objects:
bpy.ops.object.mode_set(mode = 'OBJECT')
bpy.ops.mesh.primitive_circle_add()
bpy.context.object.name = "circle_shpctrl"
return{'FINISHED'}
class OBJECT_OT_create_cube(bpy.types.Operator):
bl_idname = 'object.create_cube'
bl_label = "Cube"
def execute (self, context):
if bpy.context.selected_objects:
bpy.ops.object.mode_set(mode = 'OBJECT')
bpy.ops.mesh.primitive_cube_add()
bpy.context.object.name = "cube_shpctrl"
bpy.ops.object.mode_set(mode = 'EDIT')
bpy.ops.mesh.delete(type='ONLY_FACE')
bpy.ops.object.mode_set(mode = 'OBJECT')
bpy.context.object.show_wire = True
return{'FINISHED'}
class OBJECT_OT_create_piramid(bpy.types.Operator):
bl_idname = 'object.create_piramid'
bl_label = "Piramid"
def execute (self, context):
if bpy.context.selected_objects:
bpy.ops.object.mode_set(mode = 'OBJECT')
bpy.ops.mesh.primitive_cone_add(vertices=4)
bpy.context.object.name = "piramid_shpctrl"
bpy.ops.object.mode_set(mode = 'EDIT')
bpy.ops.transform.rotate(value=0.785398, orient_axis='Z', orient_type='GLOBAL')
bpy.ops.mesh.delete(type='ONLY_FACE')
bpy.ops.object.mode_set(mode = 'OBJECT')
bpy.context.object.show_wire = True
return{'FINISHED'}
class OBJECT_OT_create_sphere(bpy.types.Operator):
bl_idname = 'object.create_sphere'
bl_label = "Sphere"
def execute (self, context):
if bpy.context.selected_objects:
bpy.ops.object.mode_set(mode = 'OBJECT')
bpy.ops.mesh.primitive_circle_add(enter_editmode=True)
bpy.ops.mesh.primitive_circle_add(rotation = (1.5707963267948966, 0, 0))
bpy.ops.mesh.primitive_circle_add(rotation = (0, 1.5707963267948966, 0))
bpy.ops.object.mode_set(mode = 'OBJECT')
return{'FINISHED'}
class OBJECT_OT_create_square(bpy.types.Operator):
bl_idname = 'object.create_square'
bl_label = "Square"
def execute (self, context):
if bpy.context.selected_objects:
bpy.ops.object.mode_set(mode = 'OBJECT')
bpy.ops.mesh.primitive_plane_add()
bpy.context.object.name = "square_shpctrl"
bpy.ops.object.mode_set(mode = 'EDIT')
bpy.ops.mesh.delete(type='ONLY_FACE')
bpy.ops.object.mode_set(mode = 'OBJECT')
bpy.context.object.show_wire = True
return{'FINISHED'}
| 2,760 | Python | .py | 63 | 36.126984 | 87 | 0.656098 | PaladinStudiosBVs/Blender-RigAssistant | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,650 | config.py | tinaarobot_XSPAM/config.py |
import logging
from telethon import TelegramClient
from os import getenv
from ROYEDITX.data import AVISHA
logging.basicConfig(format='[%(levelname) 5s/%(asctime)s] %(name)s: %(message)s', level=logging.WARNING)
# VALUES REQUIRED FOR XBOTS
API_ID = 18136872
API_HASH = "312d861b78efcd1b02183b2ab52a83a4"
CMD_HNDLR = getenv("CMD_HNDLR", default=".")
HEROKU_APP_NAME = getenv("HEROKU_APP_NAME", None)
HEROKU_API_KEY = getenv("HEROKU_API_KEY", None)
BOT_TOKEN = getenv("BOT_TOKEN", default=None)
SUDO_USERS = list(map(lambda x: int(x), getenv("SUDO_USERS", default="6922271843").split()))
for x in AVISHA:
SUDO_USERS.append(x)
OWNER_ID = int(getenv("OWNER_ID", default="6922271843"))
SUDO_USERS.append(OWNER_ID)
# ------------- CLIENTS -------------
X1 = TelegramClient('X1', API_ID, API_HASH).start(bot_token=BOT_TOKEN)
| 868 | Python | .py | 19 | 42 | 105 | 0.711328 | tinaarobot/XSPAM | 8 | 22 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,651 | main.py | tinaarobot_XSPAM/main.py | import sys
import glob
import asyncio
import logging
import importlib
import urllib3
from pathlib import Path
from config import X1
logging.basicConfig(format='[%(levelname) 5s/%(asctime)s] %(name)s: %(message)s', level=logging.WARNING)
urllib3.disable_warnings(urllib3.exceptions.InsecureRequestWarning)
def load_plugins(plugin_name):
path = Path(f"ROYEDITX/modules/{plugin_name}.py")
spec = importlib.util.spec_from_file_location(f"ROYEDITX.modules.{plugin_name}", path)
load = importlib.util.module_from_spec(spec)
load.logger = logging.getLogger(plugin_name)
spec.loader.exec_module(load)
sys.modules["ROYEDITX.modules." + plugin_name] = load
print("♥︎ Xspam has Imported " + plugin_name)
files = glob.glob("ROYEDITX/modules/*.py")
for name in files:
with open(name) as a:
patt = Path(a.name)
plugin_name = patt.stem
load_plugins(plugin_name.replace(".py", ""))
print("♥︎ Bot Deployed Successfully.")
async def main():
await X1.run_until_disconnected()
loop = asyncio.get_event_loop()
loop.run_until_complete(main())
| 1,108 | Python | .py | 29 | 34.206897 | 104 | 0.735741 | tinaarobot/XSPAM | 8 | 22 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,652 | data.py | tinaarobot_XSPAM/ROYEDITX/data.py |
RAID = [
"ЁЭЧаЁЭЧФ╠ВЁЭЧФ╠ВЁЭЧЧЁЭЧФЁЭЧеЁЭЧЦЁЭЧЫ├ШЁЭЧЧ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШ ЁЭЧЪЁЭЧЫЁЭЧиЁЭЧзЁЭЧЮЁЭЧФ ЁЭЧЮЁЭЧЫЁЭЧФЁЭЧФЁЭЧЮЁЭЧШ ЁЭЧзЁЭЧЫЁЭЧвЁЭЧвЁЭЧЮ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЯдгЁЯдг",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧШ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧЮЁЭЧи ЁЭЧЧЁЭЧФЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧФЁЭЧе ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧЮЁЭЧФ ЁЭЧЮЁЭЧЫЁЭЧвЁЭЧвЁЭЧб ЁЭЧЮЁЭЧФЁЭЧе ЁЭЧЧЁЭЧиЁЭЧЪЁЭЧФ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧйЁЭЧФЁЭЧЫЁЭЧШЁЭЧШЁЭЧб ЁЭЧбЁЭЧЫЁЭЧЬ ЁЭЧЫЁЭЧФЁЭЧЬ ЁЭЧЮЁЭЧмЁЭЧФ? 9 ЁЭЧаЁЭЧФЁЭЧЫЁЭЧЬЁЭЧбЁЭЧШ ЁЭЧеЁЭЧиЁЭЧЮ ЁЭЧжЁЭЧФЁЭЧЪЁЭЧЬ ЁЭЧйЁЭЧФЁЭЧЫЁЭЧШЁЭЧШЁЭЧб ЁЭЧЧЁЭЧШЁЭЧзЁЭЧФ ЁЭЧЫЁЭЧи ЁЯдгЁЯдгЁЯдй",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧШ ЁЭЧаЁЭЧШ ЁЭЧФЁЭЧШЁЭЧеЁЭЧвЁЭЧгЁЭЧЯЁЭЧФЁЭЧбЁЭЧШЁЭЧгЁЭЧФЁЭЧеЁЭЧЮ ЁЭЧЮЁЭЧФЁЭЧеЁЭЧЮЁЭЧШ ЁЭЧиЁЭЧЧЁЭЧФЁЭЧФЁЭЧб ЁЭЧХЁЭЧЫЁЭЧФЁЭЧе ЁЭЧЧЁЭЧиЁЭЧЪЁЭЧФ тЬИя╕ПЁЯЫл",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШ ЁЭЧжЁЭЧиЁЭЧзЁЭЧЯЁЭЧЬ ЁЭЧХЁЭЧвЁЭЧаЁЭЧХ ЁЭЧЩЁЭЧвЁЭЧЧ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЭЁЭЧЫЁЭЧФЁЭЧФЁЭЧзЁЭЧШ ЁЭЧЭЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШ ЁЭЧЮЁЭЧЫЁЭЧФЁЭЧФЁЭЧЮ ЁЭЧЫЁЭЧв ЁЭЧЭЁЭЧФЁЭЧмЁЭЧШЁЭЧЪЁЭЧЬЁЯТг",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШ ЁЭЧжЁЭЧЦЁЭЧвЁЭЧвЁЭЧзЁЭЧШЁЭЧе ЁЭЧЧЁЭЧФЁЭЧФЁЭЧЯ ЁЭЧЧЁЭЧиЁЭЧЪЁЭЧФЁЯСЕ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧЮЁЭЧФЁЭЧЮЁЭЧзЁЭЧШ ЁЯд▒ ЁЭЧЪЁЭЧФЁЭЧЯЁЭЧЬ ЁЭЧЮЁЭЧШ ЁЭЧЮЁЭЧиЁЭЧзЁЭЧзЁЭЧв ЁЯжо ЁЭЧаЁЭЧШ ЁЭЧХЁЭЧФЁЭЧФЁЭЧз ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧгЁЭЧЫЁЭЧЬЁЭЧе ЁЯНЮ ЁЭЧХЁЭЧеЁЭЧШЁЭЧФЁЭЧЧ ЁЭЧЮЁЭЧЬ ЁЭЧзЁЭЧФЁЭЧеЁЭЧЫ ЁЭЧЮЁЭЧЫЁЭЧФЁЭЧмЁЭЧШЁЭЧбЁЭЧЪЁЭЧШ ЁЭЧкЁЭЧв ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз",
"ЁЭЧЧЁЭЧиЁЭЧЧЁЭЧЫ ЁЭЧЫЁЭЧЬЁЭЧЯЁЭЧФЁЭЧФЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧйЁЭЧФЁЭЧЫЁЭЧШЁЭЧШЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧиЁЭЧгЁЭЧе ЁЭЧбЁЭЧЬЁЭЧЦЁЭЧЫЁЭЧШ ЁЯЖЩЁЯЖТЁЯШЩ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШЁЭЧЫЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШ ЁЭЧЮЁЭЧШЁЭЧЯЁЭЧШ ЁЭЧЮЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧЬЁЭЧЯЁЭЧЮЁЭЧШ ЁЯНМЁЯНМЁЯШН",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧйЁЭЧФЁЭЧЫЁЭЧШЁЭЧШЁЭЧб ЁЭЧЧЁЭЧЫЁЭЧФЁЭЧбЁЭЧЧЁЭЧЫЁЭЧШ ЁЭЧйЁЭЧФЁЭЧФЁЭЧЯЁЭЧЬ ЁЯШЛЁЯШЫ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧШ ЁЭЧаЁЭЧШ ЁЭЧФЁЭЧЦ ЁЭЧЯЁЭЧФЁЭЧЪЁЭЧФ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧжЁЭЧФЁЭЧФЁЭЧеЁЭЧЬ ЁЭЧЪЁЭЧФЁЭЧеЁЭЧаЁЭЧЬ ЁЭЧбЁЭЧЬЁЭЧЮЁЭЧФЁЭЧЯ ЁЭЧЭЁЭЧФЁЭЧФЁЭЧмЁЭЧШЁЭЧЪЁЭЧЬ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧйЁЭЧФЁЭЧЫЁЭЧШЁЭЧШЁЭЧб ЁЭЧЮЁЭЧв ЁЭЧЫЁЭЧвЁЭЧеЁЭЧЯЁЭЧЬЁЭЧЦЁЭЧЮЁЭЧж ЁЭЧгЁЭЧШЁЭЧШЁЭЧЯЁЭЧФЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧаЁЭЧФ╠ВЁЭЧФ╠ВЁЭЧЧЁЭЧФЁЭЧеЁЭЧЦЁЭЧЫ├ШЁЭЧЧЁЯШЪ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧв ЁЭЧЮЁЭЧвЁЭЧЯЁЭЧЮЁЭЧФЁЭЧзЁЭЧФ ЁЭЧйЁЭЧФЁЭЧФЁЭЧЯЁЭЧШ ЁЭЧЭЁЭЧЬЁЭЧзЁЭЧи ЁЭЧХЁЭЧЫЁЭЧФЁЭЧЬЁЭЧмЁЭЧФ ЁЭЧЮЁЭЧФ ЁЭЧЯЁЭЧиЁЭЧбЁЭЧЧ ЁЭЧаЁЭЧиЁЭЧХЁЭЧФЁЭЧеЁЭЧФЁЭЧЮ ЁЯдйЁЯдй",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧиЁЭЧаЁЭЧаЁЭЧм ЁЭЧЮЁЭЧЬ ЁЭЧЩЁЭЧФЁЭЧбЁЭЧзЁЭЧФЁЭЧжЁЭЧм ЁЭЧЫЁЭЧи ЁЭЧЯЁЭЧФЁЭЧкЁЭЧЧЁЭЧШ, ЁЭЧзЁЭЧи ЁЭЧФЁЭЧгЁЭЧбЁЭЧЬ ЁЭЧХЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧв ЁЭЧжЁЭЧаЁЭЧХЁЭЧЫЁЭЧФЁЭЧФЁЭЧЯ ЁЯШИЁЯШИ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧФ ЁЭЧгЁЭЧШЁЭЧЫЁЭЧЯЁЭЧФ ЁЭЧХЁЭЧФЁЭЧФЁЭЧг ЁЭЧЫЁЭЧи ЁЭЧаЁЭЧФ╠ВЁЭЧФ╠ВЁЭЧЧЁЭЧФЁЭЧеЁЭЧЦЁЭЧЫ├ШЁЭЧЧ ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧйЁЭЧФЁЭЧЫЁЭЧШЁЭЧШЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧШ ЁЭЧаЁЭЧШ ЁЭЧлЁЭЧйЁЭЧЬЁЭЧЧЁЭЧШЁЭЧвЁЭЧж.ЁЭЧЦЁЭЧвЁЭЧа ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧЯЁЭЧФ ЁЭЧЮЁЭЧШ ЁЭЧаЁЭЧиЁЭЧзЁЭЧЫ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧеЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЯдбЁЯШ╣",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧФ ЁЭЧЪЁЭЧеЁЭЧвЁЭЧиЁЭЧг ЁЭЧйЁЭЧФЁЭЧФЁЭЧЯЁЭЧвЁЭЧб ЁЭЧжЁЭЧФЁЭЧФЁЭЧзЁЭЧЫ ЁЭЧаЁЭЧЬЁЭЧЯЁЭЧЮЁЭЧШ ЁЭЧЪЁЭЧФЁЭЧбЁЭЧЪ ЁЭЧХЁЭЧФЁЭЧбЁЭЧЪ ЁЭЧЮЁЭЧеЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЯЩМЁЯП╗тШая╕П ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧЬЁЭЧзЁЭЧШЁЭЧа ЁЭЧЮЁЭЧЬ ЁЭЧЪЁЭЧФЁЭЧФЁЭЧбЁЭЧЧ ЁЭЧаЁЭЧШ ЁЭЧЯЁЭЧиЁЭЧбЁЭЧЧ ЁЭЧЧЁЭЧФЁЭЧФЁЭЧЯЁЭЧЮЁЭЧШ,ЁЭЧзЁЭЧШЁЭЧеЁЭЧШ ЁЭЧЭЁЭЧФЁЭЧЬЁЭЧжЁЭЧФ ЁЭЧШЁЭЧЮ ЁЭЧвЁЭЧе ЁЭЧбЁЭЧЬЁЭЧЮЁЭЧФЁЭЧФЁЭЧЯ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧаЁЭЧФ╠ВЁЭЧФ╠ВЁЭЧЧЁЭЧФЁЭЧеЁЭЧЦЁЭЧЫ├ШЁЭЧЧЁЯдШЁЯП╗ЁЯЩМЁЯП╗тШая╕П ",
"ЁЭЧФЁЭЧиЁЭЧЮЁЭЧФЁЭЧФЁЭЧз ЁЭЧаЁЭЧШ ЁЭЧеЁЭЧШЁЭЧЫ ЁЭЧйЁЭЧеЁЭЧбЁЭЧФ ЁЭЧЪЁЭЧФЁЭЧФЁЭЧбЁЭЧЧ ЁЭЧаЁЭЧШ ЁЭЧЧЁЭЧФЁЭЧбЁЭЧЧЁЭЧФ ЁЭЧЧЁЭЧФЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШ ЁЭЧаЁЭЧиЁЭЧЫ ЁЭЧжЁЭЧШ ЁЭЧбЁЭЧЬЁЭЧЮЁЭЧФЁЭЧФЁЭЧЯ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧжЁЭЧЫЁЭЧФЁЭЧеЁЭЧЬЁЭЧе ЁЭЧХЁЭЧЫЁЭЧЬ ЁЭЧЧЁЭЧФЁЭЧбЁЭЧЧЁЭЧШ ЁЭЧЭЁЭЧШЁЭЧжЁЭЧФ ЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧЫЁЭЧШЁЭЧЪЁЭЧФ ЁЯЩДЁЯднЁЯдн",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧиЁЭЧаЁЭЧаЁЭЧм ЁЭЧЮЁЭЧШ ЁЭЧжЁЭЧФЁЭЧФЁЭЧзЁЭЧЫ ЁЭЧЯЁЭЧиЁЭЧЧЁЭЧв ЁЭЧЮЁЭЧЫЁЭЧШЁЭЧЯЁЭЧзЁЭЧШ ЁЭЧЮЁЭЧЫЁЭЧШЁЭЧЯЁЭЧзЁЭЧШ ЁЭЧиЁЭЧжЁЭЧЮЁЭЧШ ЁЭЧаЁЭЧиЁЭЧЫ ЁЭЧаЁЭЧШ ЁЭЧФЁЭЧгЁЭЧбЁЭЧФ ЁЭЧЯЁЭЧвЁЭЧЧЁЭЧФ ЁЭЧЧЁЭЧШ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФтШЭЁЯП╗тШЭЁЯП╗ЁЯШм",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧйЁЭЧФЁЭЧЫЁЭЧШЁЭЧШЁЭЧб ЁЭЧЮЁЭЧв ЁЭЧФЁЭЧгЁЭЧбЁЭЧШ ЁЭЧЯЁЭЧиЁЭЧбЁЭЧЧ ЁЭЧгЁЭЧе ЁЭЧЬЁЭЧзЁЭЧбЁЭЧФ ЁЭЧЭЁЭЧЫЁЭЧиЁЭЧЯЁЭЧФЁЭЧФЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧЮЁЭЧЬ ЁЭЧЭЁЭЧЫЁЭЧиЁЭЧЯЁЭЧзЁЭЧШ ЁЭЧЭЁЭЧЫЁЭЧиЁЭЧЯЁЭЧзЁЭЧШ ЁЭЧЫЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЦЁЭЧЫЁЭЧФ ЁЭЧгЁЭЧФЁЭЧЬЁЭЧЧЁЭЧФ ЁЭЧЮЁЭЧе ЁЭЧЧЁЭЧШЁЭЧЪЁЭЧЬЁЯСАЁЯСп ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧзЁЭЧзЁЭЧШЁЭЧеЁЭЧм ЁЭЧЯЁЭЧФЁЭЧЪЁЭЧФ ЁЭЧЮЁЭЧШ ЁЭЧгЁЭЧвЁЭЧкЁЭЧШЁЭЧеЁЭЧХЁЭЧФЁЭЧбЁЭЧЮ ЁЭЧХЁЭЧФЁЭЧбЁЭЧФ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЯФЛ ЁЯФеЁЯдй",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧЦ++ ЁЭЧжЁЭЧзЁЭЧеЁЭЧЬЁЭЧбЁЭЧЪ ЁЭЧШЁЭЧбЁЭЧЦЁЭЧеЁЭЧмЁЭЧгЁЭЧзЁЭЧЬЁЭЧвЁЭЧб ЁЭЧЯЁЭЧФЁЭЧЪЁЭЧФ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧзЁЭЧЬ ЁЭЧЫЁЭЧиЁЭЧмЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧеЁЭЧиЁЭЧЮ ЁЭЧЭЁЭЧФЁЭЧмЁЭЧШЁЭЧЪЁЭЧЬЁЭЧЬЁЭЧЬЁЭЧЬЁЯШИЁЯФеЁЯШН",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧШ ЁЭЧЪЁЭЧФЁЭЧФЁЭЧбЁЭЧЧ ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧЭЁЭЧЫЁЭЧФЁЭЧФЁЭЧЧЁЭЧи ЁЭЧЧЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШ ЁЭЧаЁЭЧвЁЭЧе ЁЯжЪ ЁЭЧХЁЭЧФЁЭЧбЁЭЧФ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФ ЁЯдйЁЯе╡ЁЯШ▒",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧжЁЭЧЫЁЭЧвЁЭЧиЁЭЧЯЁЭЧЧЁЭЧШЁЭЧеЁЭЧЬЁЭЧбЁЭЧЪ ЁЭЧЮЁЭЧФЁЭЧе ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФ ЁЭЧЫЁЭЧЬЁЭЧЯЁЭЧФЁЭЧзЁЭЧШ ЁЭЧЫЁЭЧиЁЭЧмЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧЬ ЁЭЧЧЁЭЧФЁЭЧеЁЭЧЧ ЁЭЧЫЁЭЧвЁЭЧЪЁЭЧФЁЭЧФЁЭЧФЁЯШ▒ЁЯдоЁЯС║",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧв ЁЭЧеЁЭЧШЁЭЧЧЁЭЧЬ ЁЭЧгЁЭЧШ ЁЭЧХЁЭЧФЁЭЧЬЁЭЧзЁЭЧЫЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШ ЁЭЧиЁЭЧжЁЭЧжЁЭЧШ ЁЭЧиЁЭЧжЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧХЁЭЧЬЁЭЧЯЁЭЧкЁЭЧФЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФ ЁЯТ░ ЁЯШ╡ЁЯдй",
"ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ 4 ЁЭЧЫЁЭЧвЁЭЧЯЁЭЧШ ЁЭЧЫЁЭЧФЁЭЧЬ ЁЭЧиЁЭЧбЁЭЧаЁЭЧШ ЁЭЧаЁЭЧжЁЭЧШЁЭЧФЁЭЧЯ ЁЭЧЯЁЭЧФЁЭЧЪЁЭЧФ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧиЁЭЧз ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧзЁЭЧЬ ЁЭЧЫЁЭЧФЁЭЧЬ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧЩЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШЁЯСКЁЯдоЁЯдвЁЯдв",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧеЁЭЧЪЁЭЧФЁЭЧЧ ЁЭЧЮЁЭЧФ ЁЭЧгЁЭЧШЁЭЧЧ ЁЭЧиЁЭЧЪЁЭЧФ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФ ЁЭЧЦЁЭЧвЁЭЧеЁЭЧвЁЭЧбЁЭЧФ ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧжЁЭЧФЁЭЧХ ЁЭЧвЁЭЧлЁЭЧмЁЭЧЪЁЭЧШЁЭЧб ЁЭЧЯЁЭЧШЁЭЧЮЁЭЧФЁЭЧе ЁЭЧЭЁЭЧФЁЭЧмЁЭЧШЁЭЧбЁЭЧЪЁЭЧШЁЯдвЁЯдйЁЯе│",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧжЁЭЧиЁЭЧЧЁЭЧв ЁЭЧЯЁЭЧФЁЭЧЪЁЭЧФ ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧЬЁЭЧЪЁЭЧжЁЭЧгЁЭЧФЁЭЧа ЁЭЧЯЁЭЧФЁЭЧЪЁЭЧФ ЁЭЧЮЁЭЧШ 9999 ЁЭЧЩЁЭЧиЁЭЧЦЁЭЧЮ ЁЭЧЯЁЭЧФЁЭЧЪЁЭЧФЁЭЧФ ЁЭЧЧЁЭЧи ЁЯдйЁЯе│ЁЯФе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧйЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШ ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧХЁЭЧШЁЭЧжЁЭЧФЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧЯЁЭЧФЁЭЧЧЁЭЧЧЁЭЧи ЁЭЧХЁЭЧЫЁЭЧФЁЭЧе ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЯдйЁЯе│ЁЯФеЁЯШИ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧЮЁЭЧЫЁЭЧвЁЭЧЧ ЁЭЧЮЁЭЧШ ЁЭЧиЁЭЧжЁЭЧаЁЭЧШ ЁЭЧЦЁЭЧмЁЭЧЯЁЭЧЬЁЭЧбЁЭЧЧЁЭЧШЁЭЧе тЫ╜я╕П ЁЭЧЩЁЭЧЬЁЭЧз ЁЭЧЮЁЭЧФЁЭЧеЁЭЧЮЁЭЧШ ЁЭЧиЁЭЧжЁЭЧаЁЭЧШЁЭЧШ ЁЭЧЧЁЭЧФЁЭЧЯ ЁЭЧаЁЭЧФЁЭЧЮЁЭЧЫЁЭЧФЁЭЧбЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧбЁЭЧФЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФЁЭЧФЁЯдйЁЯСКЁЯФе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧжЁЭЧЫЁЭЧШЁЭЧШЁЭЧжЁЭЧЫЁЭЧФ ЁЭЧЧЁЭЧФЁЭЧЯ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФЁЭЧФ ЁЭЧФЁЭЧиЁЭЧе ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧиЁЭЧеЁЭЧФЁЭЧЫЁЭЧШ ЁЭЧгЁЭЧШ ЁЭЧзЁЭЧФЁЭЧФЁЭЧбЁЭЧЪ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШЁЯШИЁЯШ▒ЁЯдй",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧЦЁЭЧеЁЭЧШЁЭЧЧЁЭЧЬЁЭЧз ЁЭЧЦЁЭЧФЁЭЧеЁЭЧЧ ЁЭЧЧЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШ ЁЭЧФЁЭЧЪЁЭЧШ ЁЭЧжЁЭЧШ 500 ЁЭЧЮЁЭЧШ ЁЭЧЮЁЭЧФЁЭЧФЁЭЧеЁЭЧШ ЁЭЧЮЁЭЧФЁЭЧФЁЭЧеЁЭЧШ ЁЭЧбЁЭЧвЁЭЧзЁЭЧШ ЁЭЧбЁЭЧЬЁЭЧЮЁЭЧФЁЭЧЯЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШЁЯТ░ЁЯТ░ЁЯдй",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧШ ЁЭЧжЁЭЧФЁЭЧзЁЭЧЫ ЁЭЧжЁЭЧиЁЭЧФЁЭЧе ЁЭЧЮЁЭЧФ ЁЭЧжЁЭЧШЁЭЧл ЁЭЧЮЁЭЧФЁЭЧеЁЭЧкЁЭЧФ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФ ЁЭЧШЁЭЧЮ ЁЭЧжЁЭЧФЁЭЧзЁЭЧЫ 6-6 ЁЭЧХЁЭЧФЁЭЧЦЁЭЧЫЁЭЧШ ЁЭЧЧЁЭЧШЁЭЧЪЁЭЧЬЁЯТ░ЁЯФеЁЯШ▒",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧФЁЭЧгЁЭЧгЁЭЧЯЁЭЧШ ЁЭЧЮЁЭЧФ 18ЁЭЧк ЁЭЧкЁЭЧФЁЭЧЯЁЭЧФ ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧеЁЭЧЪЁЭЧШЁЭЧе ЁЯФеЁЯдй",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЪЁЭЧФЁЭЧФЁЭЧбЁЭЧЧ ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧвЁЭЧбЁЭЧШЁЭЧгЁЭЧЯЁЭЧиЁЭЧж ЁЭЧЮЁЭЧФ ЁЭЧкЁЭЧеЁЭЧФЁЭЧг ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧеЁЭЧЪЁЭЧШЁЭЧе 30ЁЭЧк ЁЭЧЫЁЭЧЬЁЭЧЪЁЭЧЫ ЁЭЧгЁЭЧвЁЭЧкЁЭЧШЁЭЧе ЁЯТеЁЯШВЁЯШО",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧЮЁЭЧв ЁЭЧФЁЭЧаЁЭЧФЁЭЧнЁЭЧвЁЭЧб ЁЭЧжЁЭЧШ ЁЭЧвЁЭЧеЁЭЧЧЁЭЧШЁЭЧе ЁЭЧЮЁЭЧФЁЭЧеЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ 10 ЁЭЧ┐ЁЭША ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧФЁЭЧиЁЭЧе ЁЭЧЩЁЭЧЯЁЭЧЬЁЭЧгЁЭЧЮЁЭЧФЁЭЧеЁЭЧз ЁЭЧгЁЭЧШ 20 ЁЭЧеЁЭЧж ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧХЁЭЧШЁЭЧЦЁЭЧЫ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЯдоЁЯС┐ЁЯШИЁЯдЦ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЧЁЭЧЬ ЁЭЧХЁЭЧЫЁЭЧиЁЭЧбЁЭЧЧ ЁЭЧаЁЭЧШ ЁЭЧнЁЭЧвЁЭЧаЁЭЧФЁЭЧзЁЭЧв ЁЭЧЧЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШ ЁЭЧжЁЭЧиЁЭЧХЁЭЧкЁЭЧФЁЭЧм ЁЭЧЮЁЭЧФ ЁЭЧХЁЭЧЩЁЭЧЩ ЁЭЧйЁЭЧШЁЭЧЪ ЁЭЧжЁЭЧиЁЭЧХ ЁЭЧЦЁЭЧвЁЭЧаЁЭЧХЁЭЧв [15ЁЭЧ░ЁЭЧ║ , 16 ЁЭЧ╢ЁЭЧ╗ЁЭЧ░ЁЭЧ╡ЁЭЧ▓ЁЭША ] ЁЭЧвЁЭЧеЁЭЧЧЁЭЧШЁЭЧе ЁЭЧЦЁЭЧвЁЭЧЧ ЁЭЧЮЁЭЧеЁЭЧйЁЭЧФЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧвЁЭЧе ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЭЁЭЧФЁЭЧХ ЁЭЧЧЁЭЧЬЁЭЧЯЁЭЧЬЁЭЧйЁЭЧШЁЭЧеЁЭЧм ЁЭЧЧЁЭЧШЁЭЧбЁЭЧШ ЁЭЧФЁЭЧмЁЭЧШЁЭЧЪЁЭЧЬ ЁЭЧзЁЭЧФЁЭЧХ ЁЭЧиЁЭЧжЁЭЧгЁЭЧШ ЁЭЧЭЁЭЧФЁЭЧФЁЭЧЧЁЭЧи ЁЭЧЮЁЭЧеЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧвЁЭЧе ЁЭЧЩЁЭЧЬЁЭЧе 9 ЁЭЧаЁЭЧвЁЭЧбЁЭЧзЁЭЧЫ ЁЭЧХЁЭЧФЁЭЧФЁЭЧЧ ЁЭЧйЁЭЧв ЁЭЧШЁЭЧЮ ЁЭЧвЁЭЧе ЁЭЧЩЁЭЧеЁЭЧШЁЭЧШ ЁЭЧЧЁЭЧЬЁЭЧЯЁЭЧЬЁЭЧйЁЭЧШЁЭЧеЁЭЧм ЁЭЧЧЁЭЧШЁЭЧЪЁЭЧЬЁЯЩАЁЯСНЁЯе│ЁЯФе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧЮЁЭЧФЁЭЧФЁЭЧЯЁЭЧЬЁЯЩБЁЯдгЁЯТе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧбЁЭЧЪЁЭЧШЁЭЧж ЁЭЧЦЁЭЧвЁЭЧаЁЭЧаЁЭЧЬЁЭЧз ЁЭЧЮЁЭЧеЁЭЧиЁЭЧЪЁЭЧФ ЁЭЧЩЁЭЧЬЁЭЧе ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧЫЁЭЧШЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧФЁЭЧиЁЭЧзЁЭЧвЁЭЧаЁЭЧФЁЭЧзЁЭЧЬЁЭЧЦЁЭЧФЁЭЧЯЁЭЧЯЁЭЧм ЁЭЧиЁЭЧгЁЭЧЧЁЭЧФЁЭЧзЁЭЧШ ЁЭЧЫЁЭЧвЁЭЧЭЁЭЧФЁЭЧФЁЭЧмЁЭЧШЁЭЧЪЁЭЧЬЁЯдЦЁЯЩПЁЯдФ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФЁЭЧиЁЭЧжЁЭЧЬ ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧШ ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧЬЁЭЧбЁЭЧЧЁЭЧЬЁЭЧФЁЭЧб ЁЭЧеЁЭЧФЁЭЧЬЁЭЧЯЁЭЧкЁЭЧФЁЭЧм ЁЯЪВЁЯТеЁЯШВ",
"ЁЭЧзЁЭЧи ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧзЁЭЧШЁЭЧеЁЭЧФ ЁЭЧЮЁЭЧЫЁЭЧФЁЭЧбЁЭЧЧЁЭЧФЁЭЧб ЁЭЧжЁЭЧФЁЭЧХ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧЯЁЭЧФЁЭЧкЁЭЧЧЁЭЧШ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЭЧЫЁЭЧФЁЭЧЬ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЯдвтЬЕЁЯФе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧЬЁЭЧвЁЭЧбЁЭЧЬЁЭЧЦ ЁЭЧХЁЭЧвЁЭЧбЁЭЧЧ ЁЭЧХЁЭЧФЁЭЧбЁЭЧФ ЁЭЧЮЁЭЧШ ЁЭЧйЁЭЧЬЁЭЧеЁЭЧЪЁЭЧЬЁЭЧбЁЭЧЬЁЭЧзЁЭЧм ЁЭЧЯЁЭЧвЁЭЧвЁЭЧжЁЭЧШ ЁЭЧЮЁЭЧФЁЭЧеЁЭЧкЁЭЧФ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧиЁЭЧжЁЭЧЮЁЭЧЬ ЁЯУЪ ЁЯШОЁЯдй",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧжЁЭЧШ ЁЭЧгЁЭЧиЁЭЧЦЁЭЧЫЁЭЧбЁЭЧФ ЁЭЧХЁЭЧФЁЭЧФЁЭЧг ЁЭЧЮЁЭЧФ ЁЭЧбЁЭЧФЁЭЧФЁЭЧа ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧЯЁЭЧвЁЭЧЧЁЭЧШЁЭЧШЁЭЧШЁЭЧШЁЭЧШ ЁЯдйЁЯе│ЁЯШ│",
"ЁЭЧзЁЭЧи ЁЭЧФЁЭЧиЁЭЧе ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЧЁЭЧвЁЭЧбЁЭЧв ЁЭЧЮЁЭЧЬ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧШ ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧаЁЭЧШЁЭЧзЁЭЧеЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧЯЁЭЧкЁЭЧФ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧаЁЭЧФЁЭЧЧЁЭЧФЁЭЧеЁЭЧлЁЭЧЫЁЭЧвЁЭЧЧ ЁЯЪЗЁЯдйЁЯШ▒ЁЯе╢",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧв ЁЭЧЬЁЭЧзЁЭЧбЁЭЧФ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧзЁЭЧШЁЭЧеЁЭЧФ ЁЭЧХЁЭЧФЁЭЧФЁЭЧг ЁЭЧХЁЭЧЫЁЭЧЬ ЁЭЧиЁЭЧжЁЭЧЮЁЭЧв ЁЭЧгЁЭЧФЁЭЧЫЁЭЧЦЁЭЧЫЁЭЧФЁЭЧбЁЭЧФЁЭЧбЁЭЧШ ЁЭЧжЁЭЧШ ЁЭЧаЁЭЧФЁЭЧбЁЭЧФ ЁЭЧЮЁЭЧФЁЭЧе ЁЭЧЧЁЭЧШЁЭЧЪЁЭЧФЁЯШВЁЯС┐ЁЯдй",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧШ ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧЫЁЭЧФЁЭЧЬЁЭЧе ЁЭЧЧЁЭЧеЁЭЧмЁЭЧШЁЭЧе ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧЯЁЭЧФ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФЁЯТеЁЯФеЁЯФе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧзЁЭЧШЁЭЧЯЁЭЧШЁЭЧЪЁЭЧеЁЭЧФЁЭЧа ЁЭЧЮЁЭЧЬ ЁЭЧжЁЭЧФЁЭЧеЁЭЧЬ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬЁЭЧмЁЭЧвЁЭЧб ЁЭЧЮЁЭЧФ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЭЧЮЁЭЧЫЁЭЧФЁЭЧбЁЭЧФ ЁЭЧЮЁЭЧЫЁЭЧвЁЭЧЯ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФЁЯС┐ЁЯдоЁЯШО",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧФЁЭЧЯЁЭЧШЁЭЧлЁЭЧФ ЁЭЧЧЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШЁЭЧШ ЁЭЧЧЁЭЧЭ ЁЭЧХЁЭЧФЁЭЧЭЁЭЧФЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФЁЭЧФ ЁЯО╢ тмЖя╕ПЁЯдйЁЯТе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧШ ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧЪЁЭЧЬЁЭЧзЁЭЧЫЁЭЧиЁЭЧХ ЁЭЧЧЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШ ЁЭЧФЁЭЧгЁЭЧбЁЭЧФ ЁЭЧХЁЭЧвЁЭЧз ЁЭЧЫЁЭЧвЁЭЧжЁЭЧз ЁЭЧЮЁЭЧФЁЭЧеЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФ ЁЯдйЁЯСКЁЯСдЁЯШН",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧФ ЁЭЧйЁЭЧгЁЭЧж ЁЭЧХЁЭЧФЁЭЧбЁЭЧФ ЁЭЧЮЁЭЧШ 24*7 ЁЭЧХЁЭЧФЁЭЧжЁЭЧЫ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧЧЁЭЧФЁЭЧЬ ЁЭЧЦЁЭЧвЁЭЧаЁЭЧаЁЭЧФЁЭЧбЁЭЧЧ ЁЭЧЧЁЭЧШ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФ ЁЯдйЁЯТеЁЯФеЁЯФе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧиЁЭЧаЁЭЧаЁЭЧм ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧзЁЭЧШЁЭЧеЁЭЧШ ЁЭЧЯЁЭЧФЁЭЧбЁЭЧЧ ЁЭЧЮЁЭЧв ЁЭЧЧЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШ ЁЭЧЮЁЭЧФЁЭЧФЁЭЧз ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧаЁЭЧФ╠ВЁЭЧФ╠ВЁЭЧЧЁЭЧФЁЭЧеЁЭЧЦЁЭЧЫ├ШЁЭЧЧ ЁЯФкЁЯШВЁЯФе",
"ЁЭЧжЁЭЧиЁЭЧб ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧФ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧФ ЁЭЧФЁЭЧиЁЭЧе ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧФ ЁЭЧХЁЭЧЫЁЭЧЬ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧФ ЁЯС┐ЁЯШОЁЯСК",
"ЁЭЧзЁЭЧиЁЭЧЭЁЭЧЫЁЭЧШ ЁЭЧЧЁЭЧШЁЭЧЮЁЭЧЫ ЁЭЧЮЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧгЁЭЧШ ЁЭЧзЁЭЧФЁЭЧеЁЭЧФЁЭЧж ЁЭЧФЁЭЧзЁЭЧФ ЁЭЧЫЁЭЧФЁЭЧЬ ЁЭЧаЁЭЧиЁЭЧЭЁЭЧЫЁЭЧШ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧЯЁЭЧвЁЭЧЧЁЭЧШЁЭЧШЁЭЧШЁЭЧШ ЁЯС┐ЁЯТеЁЯдйЁЯФе",
"ЁЭЧжЁЭЧиЁЭЧб ЁЭЧаЁЭЧФ╠ВЁЭЧФ╠ВЁЭЧЧЁЭЧФЁЭЧеЁЭЧЦЁЭЧЫ├ШЁЭЧЧ ЁЭЧЭЁЭЧмЁЭЧФЁЭЧЧЁЭЧФ ЁЭЧбЁЭЧФ ЁЭЧиЁЭЧЦЁЭЧЫЁЭЧФЁЭЧЯ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧ ЁЭЧЧЁЭЧШЁЭЧбЁЭЧЪЁЭЧШ ЁЭЧШЁЭЧЮ ЁЭЧаЁЭЧЬЁЭЧб ЁЭЧаЁЭЧШЁЭЧЬ тЬЕЁЯдгЁЯФеЁЯдй",
"ЁЭЧФЁЭЧгЁЭЧбЁЭЧЬ ЁЭЧФЁЭЧаЁЭЧаЁЭЧФ ЁЭЧжЁЭЧШ ЁЭЧгЁЭЧиЁЭЧЦЁЭЧЫЁЭЧбЁЭЧФ ЁЭЧиЁЭЧжЁЭЧЮЁЭЧв ЁЭЧиЁЭЧж ЁЭЧЮЁЭЧФЁЭЧФЁЭЧЯЁЭЧЬ ЁЭЧеЁЭЧФЁЭЧФЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧЮЁЭЧФЁЭЧиЁЭЧб ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧбЁЭЧШЁЭЧШ ЁЭЧФЁЭЧмЁЭЧФ ЁЭЧзЁЭЧЫЁЭЧФЁЭЧФЁЭЧФ! ЁЭЧзЁЭЧШЁЭЧеЁЭЧШ ЁЭЧЬЁЭЧж ЁЭЧгЁЭЧФЁЭЧгЁЭЧФ ЁЭЧЮЁЭЧФ ЁЭЧбЁЭЧФЁЭЧФЁЭЧа ЁЭЧЯЁЭЧШЁЭЧЪЁЭЧЬ ЁЯШВЁЯС┐ЁЯШ│",
"ЁЭЧзЁЭЧвЁЭЧЫЁЭЧФЁЭЧе ЁЭЧХЁЭЧФЁЭЧЫЁЭЧЬЁЭЧб ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧи ЁЭЧХЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧЯЁЭЧФЁЭЧкЁЭЧЧЁЭЧШ ЁЭЧиЁЭЧжЁЭЧаЁЭЧШ ЁЭЧаЁЭЧЬЁЭЧзЁЭЧзЁЭЧЬ ЁЭЧЧЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШ ЁЭЧЦЁЭЧШЁЭЧаЁЭЧШЁЭЧбЁЭЧз ЁЭЧжЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧФЁЭЧе ЁЭЧЧЁЭЧи ЁЯПаЁЯдвЁЯдйЁЯТе",
"ЁЭЧзЁЭЧиЁЭЧЭЁЭЧЫЁЭЧШ ЁЭЧФЁЭЧХ ЁЭЧзЁЭЧФЁЭЧЮ ЁЭЧбЁЭЧФЁЭЧЫЁЭЧЬ ЁЭЧжЁЭЧаЁЭЧЭЁЭЧЫ ЁЭЧФЁЭЧмЁЭЧФ ЁЭЧЮЁЭЧЬ ЁЭЧаЁЭЧФЁЭЧЬ ЁЭЧЫЁЭЧЬ ЁЭЧЫЁЭЧи ЁЭЧзЁЭЧиЁЭЧЭЁЭЧЫЁЭЧШ ЁЭЧгЁЭЧФЁЭЧЬЁЭЧЧЁЭЧФ ЁЭЧЮЁЭЧФЁЭЧеЁЭЧбЁЭЧШ ЁЭЧкЁЭЧФЁЭЧЯЁЭЧФ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШЁЭЧШ ЁЭЧФЁЭЧгЁЭЧбЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧжЁЭЧШ ЁЭЧгЁЭЧиЁЭЧЦЁЭЧЫ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧФЁЭЧЦЁЭЧЫЁЭЧШЁЭЧШЁЭЧШЁЭЧШ ЁЯдйЁЯСКЁЯСдЁЯШН",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧШ ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧжЁЭЧгЁЭЧвЁЭЧзЁЭЧЬЁЭЧЩЁЭЧм ЁЭЧЧЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШ ЁЭЧЯЁЭЧвЁЭЧЩЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЭЁЭЧФЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧЧЁЭЧЬЁЭЧб ЁЭЧХЁЭЧЫЁЭЧФЁЭЧе ЁЯШНЁЯО╢ЁЯО╢ЁЯТе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧФ ЁЭЧбЁЭЧФЁЭЧмЁЭЧФ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЭЧЮЁЭЧЫЁЭЧФЁЭЧбЁЭЧФ ЁЭЧЮЁЭЧЫЁЭЧвЁЭЧЯЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧЦЁЭЧЫЁЭЧЬЁЭЧбЁЭЧзЁЭЧФ ЁЭЧаЁЭЧФЁЭЧз ЁЭЧЮЁЭЧФЁЭЧе ЁЯСКЁЯдгЁЯдгЁЯШ│",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧФ ЁЭЧХЁЭЧФЁЭЧФЁЭЧг ЁЭЧЫЁЭЧи ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧв ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЭЧЮЁЭЧЫЁЭЧФЁЭЧбЁЭЧШ ЁЭЧгЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧЧЁЭЧкЁЭЧФ ЁЭЧЮЁЭЧШ ЁЭЧиЁЭЧж ЁЭЧгЁЭЧФЁЭЧЬЁЭЧжЁЭЧШ ЁЭЧЮЁЭЧЬ ЁЭЧЧЁЭЧФЁЭЧФЁЭЧеЁЭЧи ЁЭЧгЁЭЧШЁЭЧШЁЭЧзЁЭЧФ ЁЭЧЫЁЭЧи ЁЯН╖ЁЯдйЁЯФе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧФЁЭЧгЁЭЧбЁЭЧФ ЁЭЧХЁЭЧФЁЭЧЧЁЭЧФ ЁЭЧжЁЭЧФ ЁЭЧЯЁЭЧвЁЭЧЧЁЭЧФ ЁЭЧЪЁЭЧЫЁЭЧиЁЭЧжЁЭЧжЁЭЧФ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФЁЭЧФ ЁЭЧЮЁЭЧФЁЭЧЯЁЭЧЯЁЭЧФЁЭЧФЁЭЧг ЁЭЧЮЁЭЧШ ЁЭЧаЁЭЧФЁЭЧе ЁЭЧЭЁЭЧФЁЭЧмЁЭЧШЁЭЧЪЁЭЧЬ ЁЯдйЁЯШ│ЁЯШ│ЁЯФе",
"ЁЭЧзЁЭЧвЁЭЧЫЁЭЧФЁЭЧе ЁЭЧаЁЭЧиЁЭЧаЁЭЧаЁЭЧм ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧгЁЭЧиЁЭЧеЁЭЧЬ ЁЭЧЮЁЭЧЬ ЁЭЧгЁЭЧиЁЭЧеЁЭЧЬ ЁЭЧЮЁЭЧЬЁЭЧбЁЭЧЪЁЭЧЩЁЭЧЬЁЭЧжЁЭЧЫЁЭЧШЁЭЧе ЁЭЧЮЁЭЧЬ ЁЭЧХЁЭЧвЁЭЧзЁЭЧзЁЭЧЯЁЭЧШ ЁЭЧЧЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШ ЁЭЧзЁЭЧвЁЭЧЧ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧФЁЭЧбЁЭЧЧЁЭЧШЁЭЧе ЁЭЧЫЁЭЧЬ ЁЯШ▒ЁЯШВЁЯдй",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧв ЁЭЧЬЁЭЧзЁЭЧбЁЭЧФ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧЮЁЭЧЬ ЁЭЧжЁЭЧФЁЭЧгЁЭЧбЁЭЧШ ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧХЁЭЧЫЁЭЧЬ ЁЭЧаЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧЧЁЭЧФЁЭЧЬ ЁЭЧмЁЭЧФЁЭЧФЁЭЧЧ ЁЭЧЮЁЭЧФЁЭЧеЁЭЧШЁЭЧЪЁЭЧЬ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЯе│ЁЯШНЁЯСКЁЯТе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧиЁЭЧаЁЭЧаЁЭЧм ЁЭЧФЁЭЧиЁЭЧе ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧв ЁЭЧЧЁЭЧФЁЭЧиЁЭЧЧЁЭЧФ ЁЭЧЧЁЭЧФЁЭЧиЁЭЧЧЁЭЧФ ЁЭЧбЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧиЁЭЧбЁЭЧЮЁЭЧШ ЁЭЧбЁЭЧв ЁЭЧХЁЭЧвЁЭЧЯЁЭЧбЁЭЧШ ЁЭЧгЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧЬ ЁЭЧЯЁЭЧФЁЭЧбЁЭЧЧ ЁЭЧЪЁЭЧЫЁЭЧиЁЭЧжЁЭЧФ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧФЁЭЧбЁЭЧЧЁЭЧШЁЭЧе ЁЭЧзЁЭЧФЁЭЧЮ ЁЯШОЁЯШОЁЯдгЁЯФе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧиЁЭЧаЁЭЧаЁЭЧм ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧЮЁЭЧв ЁЭЧвЁЭЧбЁЭЧЯЁЭЧЬЁЭЧбЁЭЧШ ЁЭЧвЁЭЧЯЁЭЧл ЁЭЧгЁЭЧШ ЁЭЧХЁЭЧШЁЭЧЦЁЭЧЫЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧФЁЭЧиЁЭЧе ЁЭЧгЁЭЧФЁЭЧЬЁЭЧжЁЭЧШ ЁЭЧжЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧФ ЁЭЧЮЁЭЧвЁЭЧзЁЭЧЫЁЭЧФ ЁЭЧЮЁЭЧЫЁЭЧвЁЭЧЯ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЯШОЁЯдйЁЯШЭЁЯШН",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧФ ЁЭЧЬЁЭЧзЁЭЧбЁЭЧФ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧЮЁЭЧЬ ЁЭЧзЁЭЧи ЁЭЧЦЁЭЧФЁЭЧЫ ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧЬ ЁЭЧкЁЭЧв ЁЭЧаЁЭЧФЁЭЧжЁЭЧз ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧЧЁЭЧФЁЭЧЬ ЁЭЧжЁЭЧШ ЁЭЧЧЁЭЧиЁЭЧе ЁЭЧбЁЭЧЫЁЭЧЬ ЁЭЧЭЁЭЧФ ЁЭЧгЁЭЧФЁЭЧмЁЭЧШЁЭЧЪЁЭЧФЁЭЧФ ЁЯШПЁЯШПЁЯдйЁЯШН",
"ЁЭЧжЁЭЧиЁЭЧб ЁЭЧХЁЭЧШ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЭЧЮЁЭЧЬ ЁЭЧФЁЭЧиЁЭЧЯЁЭЧФЁЭЧФЁЭЧЧ ЁЭЧзЁЭЧи ЁЭЧФЁЭЧгЁЭЧбЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧжЁЭЧШ ЁЭЧжЁЭЧШЁЭЧШЁЭЧЮЁЭЧЫ ЁЭЧЮЁЭЧиЁЭЧЦЁЭЧЫ ЁЭЧЮЁЭЧФЁЭЧЬЁЭЧжЁЭЧШ ЁЭЧЪЁЭЧФЁЭЧФЁЭЧбЁЭЧЧ ЁЭЧаЁЭЧФЁЭЧеЁЭЧкЁЭЧФЁЭЧзЁЭЧШ ЁЭЧЫЁЭЧФЁЭЧЬЁЯШПЁЯдмЁЯФеЁЯТе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧФ ЁЭЧмЁЭЧФЁЭЧФЁЭЧе ЁЭЧЫЁЭЧи ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧФЁЭЧиЁЭЧе ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧФ ЁЭЧгЁЭЧмЁЭЧФЁЭЧФЁЭЧе ЁЭЧЫЁЭЧи ЁЭЧаЁЭЧШЁЭЧЬ ЁЭЧФЁЭЧЭЁЭЧФ ЁЭЧаЁЭЧШЁЭЧеЁЭЧФ ЁЭЧЯЁЭЧФЁЭЧбЁЭЧЧ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧвЁЭЧж ЁЭЧЯЁЭЧШ ЁЯдйЁЯдгЁЯТе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШ ЁЭЧиЁЭЧжЁЭЧШЁЭЧеЁЭЧХЁЭЧвЁЭЧз ЁЭЧЯЁЭЧФЁЭЧЪЁЭЧФЁЭЧФЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧжЁЭЧФЁЭЧжЁЭЧзЁЭЧШ ЁЭЧжЁЭЧгЁЭЧФЁЭЧа ЁЭЧЮЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧШ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЪЁЭЧФЁЭЧФЁЭЧбЁЭЧЧ ЁЭЧаЁЭЧШ ЁЭЧжЁЭЧФЁЭЧеЁЭЧЬЁЭЧмЁЭЧФ ЁЭЧЧЁЭЧФЁЭЧФЁЭЧЯ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧаЁЭЧФ╠ВЁЭЧФ╠ВЁЭЧЧЁЭЧФЁЭЧеЁЭЧЦЁЭЧЫ├ШЁЭЧЧ ЁЭЧиЁЭЧжЁЭЧЬ ЁЭЧжЁЭЧФЁЭЧеЁЭЧЬЁЭЧмЁЭЧШ ЁЭЧгЁЭЧе ЁЭЧзЁЭЧФЁЭЧбЁЭЧЪ ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧФЁЭЧЦЁЭЧЫЁЭЧШ ЁЭЧгЁЭЧФЁЭЧЬЁЭЧЧЁЭЧФ ЁЭЧЫЁЭЧвЁЭЧбЁЭЧЪЁЭЧШ ЁЯШ▒ЁЯШ▒",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШ тЬЛ ЁЭЧЫЁЭЧФЁЭЧзЁЭЧзЁЭЧЫ ЁЭЧЧЁЭЧФЁЭЧЯЁЭЧЮЁЭЧШ ЁЯС╢ ЁЭЧХЁЭЧФЁЭЧЦЁЭЧЦЁЭЧЫЁЭЧШ ЁЭЧбЁЭЧЬЁЭЧЮЁЭЧФЁЭЧЯ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЯШН",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШЁЭЧЫЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШ ЁЭЧЮЁЭЧШЁЭЧЯЁЭЧШ ЁЭЧЮЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧЬЁЭЧЯЁЭЧЮЁЭЧШ ЁЯддЁЯдд",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧз ЁЭЧаЁЭЧШ ЁЭЧжЁЭЧиЁЭЧзЁЭЧЯЁЭЧЬ ЁЭЧХЁЭЧвЁЭЧаЁЭЧХ ЁЭЧЩЁЭЧвЁЭЧЧ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧЮЁЭЧЬ ЁЭЧЭЁЭЧЫЁЭЧФЁЭЧФЁЭЧзЁЭЧШ ЁЭЧЭЁЭЧФЁЭЧЯ ЁЭЧЮЁЭЧШ ЁЭЧЮЁЭЧЫЁЭЧФЁЭЧФЁЭЧЮ ЁЭЧЫЁЭЧв ЁЭЧЭЁЭЧФЁЭЧмЁЭЧШЁЭЧЪЁЭЧЬЁЯТгЁЯТЛ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧйЁЭЧФЁЭЧЫЁЭЧШЁЭЧШЁЭЧб ЁЭЧЮЁЭЧв ЁЭЧЫЁЭЧвЁЭЧеЁЭЧЯЁЭЧЬЁЭЧЦЁЭЧЮЁЭЧж ЁЭЧгЁЭЧШЁЭЧШЁЭЧЯЁЭЧФЁЭЧЮЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧаЁЭЧФ╠ВЁЭЧФ╠ВЁЭЧЧЁЭЧФЁЭЧеЁЭЧЦЁЭЧЫ├ШЁЭЧЧЁЯШЪ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧЬЁЭЧзЁЭЧШЁЭЧа ЁЭЧЮЁЭЧЬ ЁЭЧЪЁЭЧФЁЭЧФЁЭЧбЁЭЧЧ ЁЭЧаЁЭЧШ ЁЭЧЯЁЭЧиЁЭЧбЁЭЧЧ ЁЭЧЧЁЭЧФЁЭЧФЁЭЧЯЁЭЧЮЁЭЧШ,ЁЭЧзЁЭЧШЁЭЧеЁЭЧШ ЁЭЧЭЁЭЧФЁЭЧЬЁЭЧжЁЭЧФ ЁЭЧШЁЭЧЮ ЁЭЧвЁЭЧе ЁЭЧбЁЭЧЬЁЭЧЮЁЭЧФЁЭЧФЁЭЧЯ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧаЁЭЧФ╠ВЁЭЧФ╠ВЁЭЧЧЁЭЧФЁЭЧеЁЭЧЦЁЭЧЫ├ШЁЭЧЧЁЯШЖЁЯддЁЯТЛ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧйЁЭЧФЁЭЧЫЁЭЧШЁЭЧШЁЭЧб ЁЭЧЮЁЭЧв ЁЭЧФЁЭЧгЁЭЧбЁЭЧШ ЁЭЧЯЁЭЧиЁЭЧбЁЭЧЧ ЁЭЧгЁЭЧе ЁЭЧЬЁЭЧзЁЭЧбЁЭЧФ ЁЭЧЭЁЭЧЫЁЭЧиЁЭЧЯЁЭЧФЁЭЧФЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧЮЁЭЧЬ ЁЭЧЭЁЭЧЫЁЭЧиЁЭЧЯЁЭЧзЁЭЧШ ЁЭЧЭЁЭЧЫЁЭЧиЁЭЧЯЁЭЧзЁЭЧШ ЁЭЧЫЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧЦЁЭЧЫЁЭЧФ ЁЭЧгЁЭЧФЁЭЧЬЁЭЧЧЁЭЧФ ЁЭЧЮЁЭЧе ЁЭЧЧЁЭЧШЁЭЧЪЁЭЧЬ ЁЯТжЁЯТЛ",
"ЁЭЧжЁЭЧиЁЭЧФЁЭЧе ЁЭЧЮЁЭЧШ ЁЭЧгЁЭЧЬЁЭЧЯЁЭЧЯЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧв ЁЭЧжЁЭЧФЁЭЧЧЁЭЧФЁЭЧЮ ЁЭЧгЁЭЧе ЁЭЧЯЁЭЧЬЁЭЧзЁЭЧФЁЭЧЮЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЯШВЁЯШЖЁЯдд",
"ЁЭЧФЁЭЧХЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧФ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧФ ЁЭЧаЁЭЧФЁЭЧЧЁЭЧШЁЭЧеЁЭЧЦЁЭЧЫЁЭЧвЁЭЧвЁЭЧЧ ЁЭЧЮЁЭЧе ЁЭЧгЁЭЧЬЁЭЧЯЁЭЧЯЁЭЧШ ЁЭЧгЁЭЧФЁЭЧгЁЭЧФ ЁЭЧжЁЭЧШ ЁЭЧЯЁЭЧФЁЭЧЧЁЭЧШЁЭЧЪЁЭЧФ ЁЭЧзЁЭЧи ЁЯШ╝ЁЯШВЁЯдд",
"ЁЭЧЪЁЭЧФЁЭЧЯЁЭЧЬ ЁЭЧЪЁЭЧФЁЭЧЯЁЭЧЬ ЁЭЧбЁЭЧШ ЁЭЧжЁЭЧЫЁЭЧвЁЭЧе ЁЭЧЫЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠А ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧе ЁЭЧЫЁЭЧШ ЁЯТЛЁЯТЛЁЯТж",
"ЁЭЧФЁЭЧХЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧи ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШ ЁЭЧгЁЭЧЬЁЭЧЯЁЭЧЯЁЭЧШ ЁЭЧЮЁЭЧиЁЭЧзЁЭЧзЁЭЧШ ЁЭЧЮЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧШ ЁЯШВЁЯС╗ЁЯФе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧв ЁЭЧФЁЭЧЬЁЭЧжЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧФ ЁЭЧФЁЭЧЬЁЭЧжЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧФ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧФ ЁЭЧХЁЭЧШЁЭЧЧ ЁЭЧгЁЭЧШЁЭЧЫЁЭЧЬ ЁЭЧаЁЭЧиЁЭЧзЁЭЧЫ ЁЭЧЧЁЭЧЬЁЭЧФ ЁЯТжЁЯТжЁЯТжЁЯТж",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧШ ЁЭЧаЁЭЧШ ЁЭЧФЁЭЧФЁЭЧФЁЭЧЪ ЁЭЧЯЁЭЧФЁЭЧЪЁЭЧФЁЭЧЧЁЭЧЬЁЭЧФ ЁЭЧаЁЭЧШЁЭЧеЁЭЧФ ЁЭЧаЁЭЧвЁЭЧзЁЭЧФ ЁЭЧЯЁЭЧиЁЭЧбЁЭЧЧ ЁЭЧЧЁЭЧФЁЭЧЯЁЭЧЮЁЭЧШ ЁЯФеЁЯФеЁЯТжЁЯШЖЁЯШЖ",
"ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧФЁЭЧЦЁЭЧЫЁЭЧЫЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧи ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧЯ ЁЭЧбЁЭЧЬЁЭЧЮЁЭЧФЁЭЧЯ",
"ЁЭЧЮЁЭЧЬЁЭЧзЁЭЧбЁЭЧФ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧи ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧзЁЭЧЫ ЁЭЧФЁЭЧХЁЭЧХ ЁЭЧФЁЭЧгЁЭЧбЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧв ЁЭЧХЁЭЧЫЁЭЧШЁЭЧЭ ЁЯШЖЁЯС╗ЁЯдд",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧвЁЭЧзЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧЮЁЭЧШ ЁЭЧгЁЭЧиЁЭЧеЁЭЧФ ЁЭЧЩЁЭЧФЁЭЧФЁЭЧЧ ЁЭЧЧЁЭЧЬЁЭЧФ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧзЁЭЧЫ ЁЭЧФЁЭЧХЁЭЧХ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧЪЁЭЧЩ ЁЭЧЮЁЭЧв ЁЭЧХЁЭЧЫЁЭЧШЁЭЧЭ ЁЯШЖЁЯТжЁЯдд",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧЪЁЭЧЩ ЁЭЧЮЁЭЧв ЁЭЧШЁЭЧзЁЭЧбЁЭЧФ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧФ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧЯЁЭЧвЁЭЧЧЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧЪЁЭЧЩ ЁЭЧзЁЭЧв ЁЭЧаЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧбЁЭЧЪЁЭЧФЁЭЧмЁЭЧЬ ЁЭЧФЁЭЧХЁЭЧХ ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧЯ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧзЁЭЧФ ЁЭЧЩЁЭЧЬЁЭЧеЁЭЧжЁЭЧШ тЩея╕ПЁЯТжЁЯШЖЁЯШЖЁЯШЖЁЯШЖ",
"ЁЭЧЫЁЭЧФЁЭЧеЁЭЧЬ ЁЭЧЫЁЭЧФЁЭЧеЁЭЧЬ ЁЭЧЪЁЭЧЫЁЭЧФЁЭЧФЁЭЧж ЁЭЧаЁЭЧШ ЁЭЧЭЁЭЧЫЁЭЧвЁЭЧгЁЭЧЧЁЭЧФ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧФ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧФ ЁЯдгЁЯдгЁЯТЛЁЯТж",
"ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧЯ ЁЭЧзЁЭЧШЁЭЧеЁЭЧШ ЁЭЧХЁЭЧФЁЭЧФЁЭЧг ЁЭЧЮЁЭЧв ЁЭЧХЁЭЧЫЁЭЧШЁЭЧЭ ЁЭЧзЁЭЧШЁЭЧеЁЭЧФ ЁЭЧХЁЭЧФЁЭЧжЁЭЧЮЁЭЧФ ЁЭЧбЁЭЧЫЁЭЧЬ ЁЭЧЫЁЭЧШ ЁЭЧгЁЭЧФЁЭЧгЁЭЧФ ЁЭЧжЁЭЧШ ЁЭЧЯЁЭЧФЁЭЧЧЁЭЧШЁЭЧЪЁЭЧФ ЁЭЧзЁЭЧи",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧзЁЭЧЫ ЁЭЧаЁЭЧШ ЁЭЧХЁЭЧвЁЭЧаЁЭЧХ ЁЭЧЧЁЭЧФЁЭЧЯЁЭЧЮЁЭЧШ ЁЭЧиЁЭЧЧЁЭЧФ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧШ ЁЭЧЯЁЭЧФЁЭЧкЁЭЧЧЁЭЧШ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧв ЁЭЧзЁЭЧеЁЭЧФЁЭЧЬЁЭЧб ЁЭЧаЁЭЧШ ЁЭЧЯЁЭЧШЁЭЧЭЁЭЧФЁЭЧЮЁЭЧШ ЁЭЧзЁЭЧвЁЭЧг ЁЭЧХЁЭЧШЁЭЧЧ ЁЭЧгЁЭЧШ ЁЭЧЯЁЭЧЬЁЭЧзЁЭЧФЁЭЧЮЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧжЁЭЧиЁЭЧФЁЭЧе ЁЭЧЮЁЭЧШ ЁЭЧгЁЭЧЬЁЭЧЯЁЭЧЯЁЭЧШ ЁЯдгЁЯдгЁЯТЛЁЯТЛ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧФЁЭЧЮЁЭЧШ ЁЭЧбЁЭЧиЁЭЧЧЁЭЧШЁЭЧж ЁЭЧЪЁЭЧвЁЭЧвЁЭЧЪЁЭЧЯЁЭЧШ ЁЭЧгЁЭЧШ ЁЭЧиЁЭЧгЁЭЧЯЁЭЧвЁЭЧФЁЭЧЧ ЁЭЧЮЁЭЧФЁЭЧеЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧЯЁЭЧФЁЭЧШЁЭЧкЁЭЧЧЁЭЧШ ЁЯС╗ЁЯФе",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧЮЁЭЧШ ЁЭЧйЁЭЧЬЁЭЧЧЁЭЧШЁЭЧв ЁЭЧХЁЭЧФЁЭЧбЁЭЧФЁЭЧЮЁЭЧШ ЁЭЧлЁЭЧбЁЭЧлЁЭЧл.ЁЭЧЦЁЭЧвЁЭЧа ЁЭЧгЁЭЧШ ЁЭЧбЁЭЧШЁЭЧШЁЭЧЯЁЭЧФЁЭЧа ЁЭЧЮЁЭЧФЁЭЧеЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧЮЁЭЧиЁЭЧзЁЭЧзЁЭЧШ ЁЭЧЮЁЭЧШ ЁЭЧгЁЭЧЬЁЭЧЯЁЭЧЯЁЭЧШ ЁЯТжЁЯТЛ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧФЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧЧЁЭЧФЁЭЧЬ ЁЭЧЮЁЭЧв ЁЭЧгЁЭЧвЁЭЧеЁЭЧбЁЭЧЫЁЭЧиЁЭЧХ.ЁЭЧЦЁЭЧвЁЭЧа ЁЭЧгЁЭЧШ ЁЭЧиЁЭЧгЁЭЧЯЁЭЧвЁЭЧФЁЭЧЧ ЁЭЧЮЁЭЧФЁЭЧеЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧжЁЭЧиЁЭЧФЁЭЧе ЁЭЧЮЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧШ ЁЯдгЁЯТЛЁЯТж",
"ЁЭЧФЁЭЧХЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧи ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧФЁЭЧЦЁЭЧЫЁЭЧЫЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧШЁЭЧЮЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧЮЁЭЧЮЁЭЧв ЁЭЧжЁЭЧШ ЁЭЧгЁЭЧЬЁЭЧЯЁЭЧкЁЭЧФЁЭЧйЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧФЁЭЧЦЁЭЧЫЁЭЧЫЁЭЧШ ЁЯдгЁЯдг",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧзЁЭЧЫ ЁЭЧЩЁЭЧФЁЭЧФЁЭЧЧЁЭЧЮЁЭЧШ ЁЭЧеЁЭЧФЁЭЧЮЁЭЧЧЁЭЧЬЁЭЧФ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧШ ЁЭЧЯЁЭЧвЁЭЧЧЁЭЧШ ЁЭЧЭЁЭЧФЁЭЧФ ЁЭЧФЁЭЧХЁЭЧХ ЁЭЧжЁЭЧЬЁЭЧЯЁЭЧкЁЭЧФЁЭЧЯЁЭЧШ ЁЯСДЁЯСД",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧзЁЭЧЫ ЁЭЧаЁЭЧШ ЁЭЧаЁЭЧШЁЭЧеЁЭЧФ ЁЭЧЯЁЭЧиЁЭЧбЁЭЧЧ ЁЭЧЮЁЭЧФЁЭЧФЁЭЧЯЁЭЧФ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЯЁЭЧШЁЭЧзЁЭЧЬ ЁЭЧаЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧЯЁЭЧиЁЭЧбЁЭЧЧ ЁЭЧХЁЭЧФЁЭЧЧЁЭЧШ ЁЭЧаЁЭЧФЁЭЧжЁЭЧзЁЭЧЬ ЁЭЧжЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧв ЁЭЧаЁЭЧШЁЭЧбЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧ ЁЭЧЧЁЭЧФЁЭЧЯЁЭЧФ ЁЭЧХЁЭЧвЁЭЧЫЁЭЧвЁЭЧз ЁЭЧжЁЭЧФЁЭЧжЁЭЧзЁЭЧШ ЁЭЧжЁЭЧШ",
"ЁЭЧХЁЭЧШЁЭЧзЁЭЧШ ЁЭЧзЁЭЧи ЁЭЧХЁЭЧФЁЭЧФЁЭЧг ЁЭЧжЁЭЧШ ЁЭЧЯЁЭЧШЁЭЧЪЁЭЧФ ЁЭЧгЁЭЧФЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧФ ЁЭЧЮЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧЮЁЭЧФЁЭЧеЁЭЧЮЁЭЧШ ЁЭЧбЁЭЧФЁЭЧбЁЭЧЪЁЭЧФ ЁЯТжЁЯТЛ",
"ЁЭЧЫЁЭЧФЁЭЧЫЁЭЧФЁЭЧЫЁЭЧФЁЭЧЫ ЁЭЧаЁЭЧШЁЭЧеЁЭЧШ ЁЭЧХЁЭЧШЁЭЧзЁЭЧШ ЁЭЧФЁЭЧЪЁЭЧЯЁЭЧЬ ЁЭЧХЁЭЧФЁЭЧФЁЭЧе ЁЭЧФЁЭЧгЁЭЧбЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧв ЁЭЧЯЁЭЧШЁЭЧЮЁЭЧШ ЁЭЧФЁЭЧФЁЭЧмЁЭЧФ ЁЭЧаЁЭЧФЁЭЧзЁЭЧЫ ЁЭЧЮЁЭЧФЁЭЧз ЁЭЧвЁЭЧе ЁЭЧаЁЭЧШЁЭЧеЁЭЧШ ЁЭЧаЁЭЧвЁЭЧзЁЭЧШ ЁЭЧЯЁЭЧиЁЭЧбЁЭЧЧ ЁЭЧжЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧЧЁЭЧкЁЭЧФЁЭЧмЁЭЧФ ЁЭЧаЁЭЧФЁЭЧзЁЭЧЫ ЁЭЧЮЁЭЧФЁЭЧе",
"ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧЯ ЁЭЧХЁЭЧШЁЭЧзЁЭЧФ ЁЭЧзЁЭЧиЁЭЧЭЁЭЧЫЁЭЧШ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЩ ЁЭЧЮЁЭЧЬЁЭЧФ ЁЯдг ЁЭЧФЁЭЧХЁЭЧХ ЁЭЧФЁЭЧгЁЭЧбЁЭЧЬ ЁЭЧЪЁЭЧЩ ЁЭЧЮЁЭЧв ЁЭЧХЁЭЧЫЁЭЧШЁЭЧЭ",
"ЁЭЧжЁЭЧЫЁЭЧФЁЭЧеЁЭЧФЁЭЧа ЁЭЧЮЁЭЧФЁЭЧе ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧФ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧФ ЁЭЧЮЁЭЧЬЁЭЧзЁЭЧбЁЭЧФ ЁЭЧЪЁЭЧФЁЭЧФЁЭЧЯЁЭЧЬЁЭЧФ ЁЭЧжЁЭЧиЁЭЧбЁЭЧкЁЭЧФЁЭЧмЁЭЧШЁЭЧЪЁЭЧФ ЁЭЧФЁЭЧгЁЭЧбЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧФ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧШ ЁЭЧиЁЭЧгЁЭЧШЁЭЧе",
"ЁЭЧФЁЭЧХЁЭЧШ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШ ЁЭЧХЁЭЧФЁЭЧЦЁЭЧЫЁЭЧЫЁЭЧШ ЁЭЧФЁЭЧиЁЭЧЮЁЭЧФЁЭЧз ЁЭЧбЁЭЧЫЁЭЧЬ ЁЭЧЫЁЭЧШЁЭЧзЁЭЧв ЁЭЧФЁЭЧгЁЭЧбЁЭЧЬ ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧв ЁЭЧЯЁЭЧШЁЭЧЮЁЭЧШ ЁЭЧФЁЭЧФЁЭЧмЁЭЧФ ЁЭЧаЁЭЧФЁЭЧзЁЭЧЫ ЁЭЧЮЁЭЧФЁЭЧе ЁЭЧЫЁЭЧФЁЭЧЫЁЭЧФЁЭЧЫЁЭЧФЁЭЧЫЁЭЧФ",
"ЁЭЧЮЁЭЧЬЁЭЧЧЁЭЧн ЁЭЧаЁЭЧФ╠ВЁЭЧФ╠ВЁЭЧЧЁЭЧФЁЭЧеЁЭЧЦЁЭЧЫ├ШЁЭЧЧ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧЮЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧе ЁЭЧЯЁЭЧЬЁЭЧмЁЭЧШ ЁЭЧХЁЭЧЫЁЭЧФЁЭЧЬ ЁЭЧЧЁЭЧШЁЭЧЧЁЭЧЬЁЭЧмЁЭЧФ",
"ЁЭЧЭЁЭЧиЁЭЧбЁЭЧЪЁЭЧЯЁЭЧШ ЁЭЧаЁЭЧШ ЁЭЧбЁЭЧФЁЭЧЦЁЭЧЫЁЭЧзЁЭЧФ ЁЭЧЫЁЭЧШ ЁЭЧаЁЭЧвЁЭЧеЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧЧЁЭЧФЁЭЧЬ ЁЭЧЧЁЭЧШЁЭЧЮЁЭЧЮЁЭЧШ ЁЭЧжЁЭЧФЁЭЧХ ЁЭЧХЁЭЧвЁЭЧЯЁЭЧзЁЭЧШ ЁЭЧвЁЭЧбЁЭЧЦЁЭЧШ ЁЭЧаЁЭЧвЁЭЧеЁЭЧШ ЁЭЧвЁЭЧбЁЭЧЦЁЭЧШ ЁЭЧаЁЭЧвЁЭЧеЁЭЧШ ЁЯдгЁЯдгЁЯТжЁЯТЛ",
"ЁЭЧЪЁЭЧФЁЭЧЯЁЭЧЬ ЁЭЧЪЁЭЧФЁЭЧЯЁЭЧЬ ЁЭЧаЁЭЧШ ЁЭЧеЁЭЧШЁЭЧЫЁЭЧзЁЭЧФ ЁЭЧЫЁЭЧШ ЁЭЧжЁЭЧФЁЭЧбЁЭЧЧ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧ ЁЭЧЧЁЭЧФЁЭЧЯЁЭЧФ ЁЭЧвЁЭЧе ЁЭЧХЁЭЧФЁЭЧбЁЭЧФ ЁЭЧЧЁЭЧЬЁЭЧФ ЁЭЧеЁЭЧФЁЭЧбЁЭЧЧ ЁЯддЁЯдг",
"ЁЭЧжЁЭЧФЁЭЧХ ЁЭЧХЁЭЧвЁЭЧЯЁЭЧзЁЭЧШ ЁЭЧаЁЭЧиЁЭЧЭЁЭЧЫЁЭЧЮЁЭЧв ЁЭЧгЁЭЧФЁЭЧгЁЭЧФ ЁЭЧЮЁЭЧмЁЭЧвЁЭЧиЁЭЧбЁЭЧЮЁЭЧЬ ЁЭЧаЁЭЧШЁЭЧбЁЭЧШ ЁЭЧХЁЭЧФЁЭЧбЁЭЧФЁЭЧЧЁЭЧЬЁЭЧФ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧв ЁЭЧгЁЭЧеЁЭЧШЁЭЧЪЁЭЧбЁЭЧШЁЭЧбЁЭЧз ЁЯдгЁЯдг",
"ЁЭЧжЁЭЧиЁЭЧФЁЭЧе ЁЭЧЮЁЭЧШ ЁЭЧгЁЭЧЬЁЭЧЯЁЭЧЯЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧзЁЭЧЫ ЁЭЧаЁЭЧШ ЁЭЧжЁЭЧиЁЭЧФЁЭЧе ЁЭЧЮЁЭЧФ ЁЭЧЯЁЭЧвЁЭЧиЁЭЧЧЁЭЧФ ЁЭЧвЁЭЧе ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧзЁЭЧЫ ЁЭЧаЁЭЧШ ЁЭЧаЁЭЧШЁЭЧеЁЭЧФ ЁЭЧЯЁЭЧвЁЭЧЧЁЭЧФ",
"ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧЯ ЁЭЧЦЁЭЧЫЁЭЧФЁЭЧЯ ЁЭЧФЁЭЧгЁЭЧбЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧЦЁЭЧЫЁЭЧЬЁЭЧмЁЭЧФ ЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧФ",
"ЁЭЧЫЁЭЧФЁЭЧЫЁЭЧФЁЭЧЫЁЭЧФЁЭЧЫЁЭЧФ ЁЭЧХЁЭЧФЁЭЧЦЁЭЧЫЁЭЧЫЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧФЁЭЧЮЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧ ЁЭЧЧЁЭЧЬЁЭЧФ ЁЭЧбЁЭЧФЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧЮЁЭЧФЁЭЧеЁЭЧЮЁЭЧШ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧЪЁЭЧЩ ЁЭЧЫЁЭЧШ ЁЭЧХЁЭЧФЁЭЧЧЁЭЧЬ ЁЭЧжЁЭЧШЁЭЧлЁЭЧм ЁЭЧиЁЭЧжЁЭЧЮЁЭЧв ЁЭЧгЁЭЧЬЁЭЧЯЁЭЧФЁЭЧЮЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧвЁЭЧЧЁЭЧШЁЭЧбЁЭЧЪЁЭЧШ ЁЭЧгЁЭЧШЁЭЧгЁЭЧжЁЭЧЬ",
"2 ЁЭЧеЁЭЧиЁЭЧгЁЭЧФЁЭЧм ЁЭЧЮЁЭЧЬ ЁЭЧгЁЭЧШЁЭЧгЁЭЧжЁЭЧЬ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧиЁЭЧаЁЭЧаЁЭЧм ЁЭЧжЁЭЧФЁЭЧХЁЭЧжЁЭЧШ ЁЭЧжЁЭЧШЁЭЧлЁЭЧм ЁЯТЛЁЯТж",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧв ЁЭЧЦЁЭЧЫЁЭЧШЁЭЧШЁЭЧаЁЭЧж ЁЭЧжЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧЧЁЭЧкЁЭЧФЁЭЧйЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧаЁЭЧФЁЭЧЧЁЭЧШЁЭЧеЁЭЧЦЁЭЧЫЁЭЧвЁЭЧвЁЭЧЧ ЁЭЧЮЁЭЧШ ЁЭЧгЁЭЧЬЁЭЧЯЁЭЧЯЁЭЧШ ЁЯТжЁЯдг",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧЬ ЁЭЧЦЁЭЧЫЁЭЧиЁЭЧи╠БЁЭЧзЁЭЧЫ ЁЭЧаЁЭЧШ ЁЭЧаЁЭЧиЁЭЧзЁЭЧЫЁЭЧЮЁЭЧШ ЁЭЧЩЁЭЧФЁЭЧеЁЭЧФЁЭЧе ЁЭЧЫЁЭЧвЁЭЧЭЁЭЧФЁЭЧйЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ ЁЭЧЫЁЭЧиЁЭЧЬ ЁЭЧЫЁЭЧиЁЭЧЬ ЁЭЧЫЁЭЧиЁЭЧЬ",
"ЁЭЧжЁЭЧгЁЭЧШЁЭЧШЁЭЧЧ ЁЭЧЯЁЭЧФЁЭЧФЁЭЧФ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧЁЭЧи ЁЭЧе├ЖЁЭЧбЁЭЧЧЁЭЧЬЁЭЧЮЁЭЧШ ЁЭЧгЁЭЧЬЁЭЧЯЁЭЧЯЁЭЧШ ЁЯТЛЁЯТжЁЯдг",
"ЁЭЧФЁЭЧеЁЭЧШ ЁЭЧеЁЭЧШ ЁЭЧаЁЭЧШЁЭЧеЁЭЧШ ЁЭЧХЁЭЧШЁЭЧзЁЭЧШ ЁЭЧЮЁЭЧмЁЭЧвЁЭЧиЁЭЧб ЁЭЧжЁЭЧгЁЭЧШЁЭЧШЁЭЧЧ ЁЭЧгЁЭЧФЁЭЧЮЁЭЧФЁЭЧЧ ЁЭЧбЁЭЧФ ЁЭЧгЁЭЧФЁЭЧФЁЭЧФ ЁЭЧеЁЭЧФЁЭЧЫЁЭЧФ ЁЭЧФЁЭЧгЁЭЧбЁЭЧШ ЁЭЧХЁЭЧФЁЭЧФЁЭЧг ЁЭЧЮЁЭЧФ ЁЭЧЫЁЭЧФЁЭЧЫЁЭЧФЁЭЧЫЁЯдгЁЯдг",
"ЁЭЧжЁЭЧиЁЭЧб ЁЭЧжЁЭЧиЁЭЧб ЁЭЧжЁЭЧиЁЭЧФЁЭЧе ЁЭЧЮЁЭЧШ ЁЭЧгЁЭЧЬЁЭЧЯЁЭЧЯЁЭЧШ ЁЭЧЭЁЭЧЫЁЭЧФЁЭЧбЁЭЧзЁЭЧв ЁЭЧЮЁЭЧШ ЁЭЧжЁЭЧвЁЭЧиЁЭЧЧЁЭЧФЁЭЧЪЁЭЧФЁЭЧе ЁЭЧФЁЭЧгЁЭЧбЁЭЧЬ ЁЭЧаЁЭЧиЁЭЧаЁЭЧаЁЭЧм ЁЭЧЮЁЭЧЬ ЁЭЧбЁЭЧиЁЭЧЧЁЭЧШЁЭЧж ЁЭЧХЁЭЧЫЁЭЧШЁЭЧЭ",
"ЁЭЧФЁЭЧХЁЭЧШ ЁЭЧжЁЭЧиЁЭЧб ЁЭЧЯЁЭЧвЁЭЧЧЁЭЧШ ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧХЁЭЧШ╠БЁЭЧЫЁЭЧШЁЭЧб ЁЭЧЮЁЭЧФ ЁЭЧХЁЭЧЫЁЭЧвЁЭЧжЁЭЧЧЁЭЧФ ЁЭЧЩЁЭЧФЁЭЧФЁЭЧЧ ЁЭЧЧЁЭЧиЁЭЧбЁЭЧЪЁЭЧФ",
"ЁЭЧзЁЭЧШЁЭЧеЁЭЧЬ ЁЭЧаЁЭЧФ╠БЁЭЧФ╠АЁЭЧЮЁЭЧв ЁЭЧЮЁЭЧЫЁЭЧиЁЭЧЯЁЭЧШ ЁЭЧХЁЭЧФЁЭЧЭЁЭЧФЁЭЧе ЁЭЧаЁЭЧШ ЁЭЧЦЁЭЧЫЁЭЧвЁЭЧЧ ЁЭЧЧЁЭЧФЁЭЧЯЁЭЧФ ЁЯдгЁЯдгЁЯТЛ",
"ЁЭЧжЁЭЧЫЁЭЧФЁЭЧеЁЭЧФЁЭЧа ЁЭЧФЁЭЧФ ЁЭЧЪЁЭЧмЁЭЧЬ ЁЭЧЫЁЭЧФЁЭЧЬ ЁЭЧзЁЭЧв ЁЭЧбЁЭЧФЁЭЧнЁЭЧеЁЭЧШЁЭЧб ЁЭЧЭЁЭЧЫЁЭЧиЁЭЧЮЁЭЧФ ЁЭЧЯЁЭЧЬЁЭЧЭЁЭЧЬЁЭЧмЁЭЧШ ЁЭЧвЁЭЧе ЁЭЧФЁЭЧЪЁЭЧФЁЭЧе ЁЭЧЯЁЭЧиЁЭЧбЁЭЧЧ ЁЭЧаЁЭЧШ ЁЭЧЧЁЭЧФЁЭЧа ЁЭЧбЁЭЧЫЁЭЧЬ ЁЭЧзЁЭЧв ЁЭЧжЁЭЧЫЁЭЧЬЁЭЧЯЁЭЧФЁЭЧЭЁЭЧШЁЭЧШЁЭЧз ЁЭЧЮЁЭЧЫЁЭЧФ ЁЭЧЯЁЭЧЬЁЭЧЭЁЭЧЬЁЭЧмЁЭЧШ...ЁЯдгЁЯШВЁЯШВ"
]
AVISHA = [6922271843]
REPLYRAID = [
"MADARCHOD",
"BHOSDIKE",
"LAAAWEEE KE BAAAAAL",
"MAAAAR KI JHAAAAT KE BBBBBAAAAALLLLL",
"MADRCHOD..",
"TERI MA KI CHUT..",
"LWDE KE BAAALLL.",
"MACHAR KI JHAAT KE BAAALLLL",
"TERI MA KI CHUT M DU TAPA TAP?",
"TERI MA KA BHOSDAA",
"TERI BHN SBSBE BDI RANDI.",
"TERI MA OSSE BADI RANDDDDD",
"TERA BAAP CHKAAAA",
"KITNI CHODU TERI MA AB OR..",
"TERI MA CHOD DI HM NE",
"MIGHTY !! BAAP BOLTE",
"TERI MA KE STH REELS BNEGA ROAD PEE",
"TERI MA KI CHUT EK DAM TOP SEXY",
"MALUM NA PHR KESE LETA HU M TERI MA KI CHUT TAPA TAPPPPP",
"LUND KE CHODE TU KEREGA TYPIN",
"SPEED PKD LWDEEEE",
"BAAP KI SPEED MTCH KRRR",
"LWDEEE",
"PAPA KI SPEED MTCH NHI HO RHI KYA",
"ALE ALE MELA BCHAAAA",
"[RYAN](t.me/PYTH0NXD) TERA BAAP !!",
"CHUD GYA PAPA SEEE",
"KISAN KO KHODNA OR",
"SALE RAPEKL KRDKA TERA",
"HAHAHAAAAA",
"KIDSSSS",
"BACHHE TERI MAA KI CHUTT",
"TERI BHEN KI CHUTT BHOSDIWALE",
"TERI MA CHUD GYI AB FRAR MT HONA",
"YE LDNGE BAPP SE",
"KIDSSS FRAR HAHAHH",
"BHEN KE LWDE SHRM KR",
"KITNI GLIYA PDWEGA APNI MA KO",
"NALLEE",
"SUAR KE PILLE TERI MAAKO SADAK PR LITAKE CHOD DUNGA ЁЯШВЁЯШЖЁЯдд",
"ABE TERI MAAKA BHOSDA MADERCHOOD KR PILLE PAPA SE LADEGA TU ЁЯШ╝ЁЯШВЁЯдд",
"GALI GALI NE SHOR HE TERI MAA RANDI CHOR HE ЁЯТЛЁЯТЛЁЯТж",
"ABE TERI BEHEN KO CHODU RANDIKE PILLE KUTTE KE CHODE ЁЯШВЁЯС╗ЁЯФе",
"TERI MAAKO AISE CHODA AISE CHODA TERI MAAA BED PEHI MUTH DIA ЁЯТжЁЯТжЁЯТжЁЯТж",
"TERI BEHEN KE BHOSDE ME AAAG LAGADIA MERA MOTA LUND DALKE ЁЯФеЁЯФеЁЯТжЁЯШЖЁЯШЖ",
"RANDIKE BACHHE TERI MAAKO CHODU CHAL NIKAL",
"KITNA CHODU TERI RANDI MAAKI CHUTH ABB APNI BEHEN KO BHEJ ЁЯШЖЁЯС╗ЁЯдд",
"TERI BEHEN KOTO CHOD CHODKE PURA FAAD DIA CHUTH ABB TERI GF KO BHEJ ЁЯШЖЁЯТжЁЯдд",
"TERI GF KO ETNA CHODA BEHEN KE LODE TERI GF TO MERI RANDI BANGAYI ABB CHAL TERI MAAKO CHODTA FIRSE тЩея╕ПЁЯТжЁЯШЖЁЯШЖЁЯШЖЁЯШЖ",
"HARI HARI GHAAS ME JHOPDA TERI MAAKA BHOSDA ЁЯдгЁЯдгЁЯТЛЁЯТж",
"CHAL TERE BAAP KO BHEJ TERA BASKA NHI HE PAPA SE LADEGA TU",
"TERI BEHEN KI CHUTH ME BOMB DALKE UDA DUNGA MAAKE LAWDE",
"TERI MAAKO TRAIN ME LEJAKE TOP BED PE LITAKE CHOD DUNGA SUAR KE PILLE ЁЯдгЁЯдгЁЯТЛЁЯТЛ",
"TERI MAAAKE NUDES GOOGLE PE UPLOAD KARDUNGA BEHEN KE LAEWDE ЁЯС╗ЁЯФе",
"TERI MAAAKE NUDES GOOGLE PE UPLOAD KARDUNGA BEHEN KE LAEWDE ЁЯС╗ЁЯФе",
"TERI BEHEN KO CHOD CHODKE VIDEO BANAKE XNXX.COM PE NEELAM KARDUNGA KUTTE KE PILLE ЁЯТжЁЯТЛ",
"TERI MAAAKI CHUDAI KO PORNHUB.COM PE UPLOAD KARDUNGA SUAR KE CHODE ЁЯдгЁЯТЛЁЯТж",
"ABE TERI BEHEN KO CHODU RANDIKE BACHHE TEREKO CHAKKO SE PILWAVUNGA RANDIKE BACHHE ЁЯдгЁЯдг",
"TERI MAAKI CHUTH FAADKE RAKDIA MAAKE LODE JAA ABB SILWALE ЁЯСДЁЯСД",
"TERI BEHEN KI CHUTH ME MERA LUND KAALA",
"TERI BEHEN LETI MERI LUND BADE MASTI SE TERI BEHEN KO MENE CHOD DALA BOHOT SASTE SE",
"BETE TU BAAP SE LEGA PANGA TERI MAAA KO CHOD DUNGA KARKE NANGA ЁЯТжЁЯТЛ",
"HAHAHAH MERE BETE AGLI BAAR APNI MAAKO LEKE AAYA MATH KAT OR MERE MOTE LUND SE CHUDWAYA MATH KAR",
"CHAL BETA TUJHE MAAF KIA ЁЯдг ABB APNI GF KO BHEJ",
"SHARAM KAR TERI BEHEN KA BHOSDA KITNA GAALIA SUNWAYEGA APNI MAAA BEHEN KE UPER",
"ABE RANDIKE BACHHE AUKAT NHI HETO APNI RANDI MAAKO LEKE AAYA MATH KAR HAHAHAHA",
"KIDZ MADARCHOD TERI MAAKO CHOD CHODKE TERR LIYE BHAI DEDIYA",
"JUNGLE ME NACHTA HE MORE TERI MAAKI CHUDAI DEKKE SAB BOLTE ONCE MORE ONCE MORE ЁЯдгЁЯдгЁЯТжЁЯТЛ",
"GALI GALI ME REHTA HE SAND TERI MAAKO CHOD DALA OR BANA DIA RAND ЁЯддЁЯдг",
"SAB BOLTE MUJHKO PAPA KYOUNKI MENE BANADIA TERI MAAKO PREGNENT ЁЯдгЁЯдг",
"SUAR KE PILLE TERI MAAKI CHUTH ME SUAR KA LOUDA OR TERI BEHEN KI CHUTH ME MERA LODA",
"CHAL CHAL APNI MAAKI CHUCHIYA DIKA",
"HAHAHAHA BACHHE TERI MAAAKO CHOD DIA NANGA KARKE",
"TERI GF HE BADI SEXY USKO PILAKE CHOODENGE PEPSI",
"2 RUPAY KI PEPSI TERI MUMMY SABSE SEXY ЁЯТЛЁЯТж",
"TERI MAAKO CHEEMS SE CHUDWAVUNGA MADERCHOOD KE PILLE ЁЯТжЁЯдг",
"TERI BEHEN KI CHUTH ME MUTHKE FARAR HOJAVUNGA HUI HUI HUI",
"SPEED LAAA TERI BEHEN CHODU RANDIKE PILLE ЁЯТЛЁЯТжЁЯдг",
"ARE RE MERE BETE KYOUN SPEED PAKAD NA PAAA RAHA APNE BAAP KA HAHAHЁЯдгЁЯдг",
"SUN SUN SUAR KE PILLE JHANTO KE SOUDAGAR APNI MUMMY KI NUDES BHEJ",
"ABE SUN LODE TERI BEHEN KA BHOSDA FAAD DUNGA",
"TERI MAAKO KHULE BAJAR ME CHOD DALA ЁЯдгЁЯдгЁЯТЛ",
"SHRM KR",
"MERE LUND KE BAAAAALLLLL",
"KITNI GLIYA PDWYGA APNI MA BHEN KO",
"RNDI KE LDKEEEEEEEEE",
"KIDSSSSSSSSSSSS",
"Apni gaand mein muthi daal",
"Apni lund choos",
"Apni ma ko ja choos",
"Bhen ke laude",
"Bhen ke takke",
"Abla TERA KHAN DAN CHODNE KI BARIII",
"BETE TERI MA SBSE BDI RAND",
"LUND KE BAAAL JHAT KE PISSSUUUUUUU",
"LUND PE LTKIT MAAALLLL KI BOND H TUUU",
"KASH OS DIN MUTH MRKE SOJTA M TUN PAIDA NA HOTAA",
"GLTI KRDI TUJW PAIDA KRKE",
"SPEED PKDDD",
"Gaand main LWDA DAL LE APNI MERAAA",
"Gaand mein bambu DEDUNGAAAAAA",
"GAND FTI KE BALKKK",
"Gote kitne bhi bade ho, lund ke niche hi rehte hai",
"Hazaar lund teri gaand main",
"Jhaant ke pissu-",
"TERI MA KI KALI CHUT",
"Khotey ki aulad",
"Kutte ka awlad",
"Kutte ki jat",
"Kutte ke tatte",
"TETI MA KI.CHUT , tERI MA RNDIIIIIIIIIIIIIIIIIIII",
"Lavde ke bal",
"muh mei lele",
"Lund Ke Pasine",
"MERE LWDE KE BAAAAALLL",
"HAHAHAAAAAA",
"CHUD GYAAAAA",
"Randi khanE KI ULADDD",
"Sadi hui gaand",
"Teri gaand main kute ka lund",
"Teri maa ka bhosda",
"Teri maa ki chut",
"Tere gaand mein keede paday",
"Ullu ke pathe",
"SUNN MADERCHOD",
"TERI MAA KA BHOSDA",
"BEHEN K LUND",
"TERI MAA KA CHUT KI CHTNIIII",
"MERA LAWDA LELE TU AGAR CHAIYE TOH",
"GAANDU",
"CHUTIYA",
"TERI MAA KI CHUT PE JCB CHADHAA DUNGA",
"SAMJHAA LAWDE",
"YA DU TERE GAAND ME TAPAA TAPя┐╜я┐╜",
"TERI BEHEN MERA ROZ LETI HAI",
"TERI GF K SAATH MMS BANAA CHUKA HUя┐╜я┐╜я┐╜ф╕Ня┐╜ф╕Н",
"TU CHUTIYA TERA KHANDAAN CHUTIYA",
"AUR KITNA BOLU BEY MANN BHAR GAYA MERAя┐╜ф╕Н",
"TERIIIIII MAAAA KI CHUTTT ME ABCD LIKH DUNGA MAA KE LODE",
"TERI MAA KO LEKAR MAI FARAR",
"RANIDIII",
"BACHEE",
"CHODU",
"RANDI",
"RANDI KE PILLE",
"TERIIIII MAAA KO BHEJJJ",
"TERAA BAAAAP HU",
"teri MAA KI CHUT ME HAAT DAALLKE BHAAG JAANUGA",
"Teri maa KO SARAK PE LETAA DUNGA",
"TERI MAA KO GB ROAD PE LEJAKE BECH DUNGA",
"Teri maa KI CHUT M├Й KAALI MITCH",
"TERI MAA SASTI RANDI HAI",
"TERI MAA KI CHUT ME KABUTAR DAAL KE SOUP BANAUNGA MADARCHOD",
"TERI MAAA RANDI HAI",
"TERI MAAA KI CHUT ME DETOL DAAL DUNGA MADARCHOD",
"TERI MAA KAAA BHOSDAA",
"TERI MAA KI CHUT ME LAPTOP",
"Teri maa RANDI HAI",
"TERI MAA KO BISTAR PE LETAAKE CHODUNGA",
"TERI MAA KO AMERICA GHUMAAUNGA MADARCHOD",
"TERI MAA KI CHUT ME NAARIYAL PHOR DUNGA",
"TERI MAA KE GAND ME DETOL DAAL DUNGA",
"TERI MAAA KO HORLICKS PILAUNGA MADARCHOD",
"TERI MAA KO SARAK PE LETAAA DUNGAAA",
"TERI MAA KAA BHOSDA",
"MERAAA LUND PAKAD LE MADARCHOD",
"CHUP TERI MAA AKAA BHOSDAA",
"TERIII MAA CHUF GEYII KYAAA LAWDEEE",
"TERIII MAA KAA BJSODAAA",
"MADARXHODDD",
"TERIUUI MAAA KAA BHSODAAA",
"TERIIIIII BEHENNNN KO CHODDDUUUU MADARXHODDDD",
"NIKAL MADARCHOD",
"RANDI KE BACHE",
"TERA MAA MERI FAN",
"TERI SEXY BAHEN KI CHUT OP"
]
GROUP = [-1002010924139]
PORMS = [
"https://te.legra.ph/file/a66008b78909b431fc92b.mp4",
"https://te.legra.ph/file/0ab82f535e1193d09c0e4.mp4",
"https://te.legra.ph/file/1ab9cde9388117db9d26c.mp4",
"https://te.legra.ph/file/75e49339469dbf9ad1dd2.mp4",
"https://telegra.ph/file/9bcc076fd81dfe3feb291.mp4",
"https://telegra.ph/file/b7a1a42429a65f64e67af.mp4",
"https://telegra.ph/file/dc3da5a3eb77ae20fa21d.mp4",
"https://telegra.ph/file/7b15fbca08ae1e73e559c.mp4",
"https://telegra.ph/file/a9c1dea3f34925bb60686.mp4",
"https://telegra.ph/file/913b4e567b7f435b7f0db.mp4",
"https://telegra.ph/file/5a5d1a919a97af2314955.mp4",
"https://telegra.ph/file/0f8b903669600d304cbe4.mp4",
"https://telegra.ph/file/f3816b54c9eb7617356b6.mp4",
"https://telegra.ph/file/516dbaa03fde1aaa70633.mp4",
"https://telegra.ph/file/07bba6ead0f1e381b1bd1.mp4",
"https://telegra.ph/file/0a4f7935df9b4ab8d62ed.mp4",
"https://telegra.ph/file/40966bf68c0e4dbe18058.mp4",
"https://telegra.ph/file/50637aa9c04d136687523.mp4",
"https://telegra.ph/file/b81c0b0e491da73e64260.mp4",
"https://telegra.ph/file/4ddf5f29783d92ae03804.mp4",
"https://telegra.ph/file/4037dc2517b702cc208b1.mp4",
"https://telegra.ph/file/33cebe2798c15d52a2547.mp4",
"https://telegra.ph/file/4dc3c8b03616da516104a.mp4",
"https://telegra.ph/file/6b148dace4d987fae8f3e.mp4",
"https://telegra.ph/file/8cb081db4eeed88767635.mp4",
"https://telegra.ph/file/98d3eb94e6f00ed56ef91.mp4",
"https://telegra.ph/file/1fb387cf99e057b62d75d.mp4",
"https://telegra.ph/file/6e1161f63879c07a1f213.mp4",
"https://telegra.ph/file/0bf4defb9540d2fa6d277.mp4",
"https://telegra.ph/file/d5f8280754d9aa5dffa6a.mp4",
"https://telegra.ph/file/0f23807ed1930704e2bef.jpg",
"https://telegra.ph/file/c49280b8f1dcecaf86c00.jpg",
"https://telegra.ph/file/f483400ff141de73767ca.jpg",
"https://telegra.ph/file/1543bbea4e3c1abb6764a.jpg",
"https://telegra.ph/file/a0d77be0d769c7cd334ab.jpg",
"https://telegra.ph/file/6c6e93860527d2f577df8.jpg",
"https://telegra.ph/file/d987b0e72eb3bb4801f01.jpg",
"https://telegra.ph/file/b434999287d3580250960.jpg",
"https://telegra.ph/file/0729cc082bf97347988f7.jpg",
"https://telegra.ph/file/bb96d25df82178a2892e7.jpg",
"https://telegra.ph/file/be73515791ea33be92a7d.jpg",
"https://telegra.ph/file/fe234d6273093282d2dcc.jpg",
"https://telegra.ph/file/66254bb72aa8094d38250.jpg",
"https://telegra.ph/file/44bdaf37e5f7bdfc53ac6.jpg",
"https://telegra.ph/file/e561ee1e1ca88db7e8038.jpg",
"https://telegra.ph/file/f1960ccfc866b29ea5ad2.jpg",
"https://telegra.ph/file/97622cad291472fb3c4aa.jpg",
"https://telegra.ph/file/a46e316b413e9dc43e91b.jpg",
"https://telegra.ph/file/497580fc3bddc21e0e162.jpg",
"https://telegra.ph/file/3e86cc6cab06a6e2bde82.jpg",
"https://telegra.ph/file/83140e2c57ddd95f310e6.jpg",
"https://telegra.ph/file/2b20f8509d9437e94fed5.jpg",
"https://telegra.ph/file/571960dcee4fce56698a4.jpg",
"https://telegra.ph/file/25929a0b49452d8946c14.mp4",
"https://telegra.ph/file/f5c9ceded3ee6e76a5931.jpg",
"https://telegra.ph/file/a8bf6c6df8a48e4a306ca.jpg",
"https://telegra.ph/file/af9e3f98da0bd937adf6e.jpg",
"https://telegra.ph/file/2fcccbc72c57b6892d23a.jpg",
"https://telegra.ph/file/843109296a90b8a6c5f68.jpg"
]
MRAID = [
"Tere naalo challiye haseen koyi NA ЁЯШБЁЯШБ",
"Taare chann ambar zameen koyi nA",
"Main Jado Tere Mode Utte Sir RakheyaЁЯзРЁЯзР",
"Eh Ton Sachi Sama Vi Haseen Koi NaЁЯШЦЁЯШЦ",
"Sohniyan Vi Laggan Giyan Fer WalianЁЯШНЁЯШН",
"Galan Nal Jado Takraiyan WaliyanЁЯе░ЁЯе░",
"Tare Dekhi Labh Labh Kiven HardeЁЯШБЁЯШБ",
"Tu Bala Ch Lakoiyan Jado Ratan KaliyanЁЯШТЁЯШТ",
"Main Sab Kuj Har Tere Utton DeтАЩungaЁЯШМЁЯШМ",
"Sab Kuj War Tere Utton DeтАЩungaЁЯШЙЁЯШЙ",
"Akhir Ch Jan Tainu DeтАЩun ApniЁЯШОЁЯШО",
"Chala Tainu Bhavein Pehli War DeтАЩungaЁЯШЪЁЯШЪ",
"Han Main Cheti Cheti LawanЁЯШлЁЯШл",
"Tere Nal Laini anЁЯШгЁЯШг",
"Samay Da Tan Bhora Vi Yakeen Koi NaЁЯе║ЁЯе║",
"Tere Nalo Jhaliye Haseen Koi NaЁЯе░ЁЯе░",
"Tare Chann Ambar Zameen Koi NaЁЯШШЁЯШШ",
"Tu Yar Mera Tu Hi Ae Sahara AdiyE",
"Main Pani Tera Mera Tu Kinara Adiye",
"Phul Ban Jai Main Khushboo Bann Ju",
"Deevan Bani Mera Teri Lau Ban Ju",
"Haye Ujadiyan Thawan Te Banate Bag Ne",
"Teriyan Ankhan Ne Kitte Jadu Yad Ne",
"Jado Wang Kolon Phadi Vi Ni KassKe",
"Totte Sambh Rakhe Tutte Hoye Kach De",
"Han Ki Dil Yadan Rakhda Ae, Sambh Sambh Ke",
"Hor Dil Sajjna Machine Koi Na",
"Tere Nalo Jhaliye Haseen Koi Na",
"Tare Chann Ambar Zameen Koi Na",
"Main Jado Tere Mode Utte Sir Rakheya",
"Eh Ton Sachi Sama Vi Haseen Koi Na",
"Kine Din Hogye Meri Akh Soi Na",
"Tere Ton Bagair Mera Aithe Koi Na",
"Tu Bhukh Vi Ae Tu Hi Ae Guzara Adiye",
"Mannu Sab Kari Tu Ishara Adiye",
"Ho Khaure Kinni War Seene Vich Khubiyan",
"Surme De Vich Dovein Ankhan Dubbiyan",
"Kini Sohni Lagge Jadon Chup Kar Je",
"Jandi Jandi Shaman Nu Vi Dhup Kar Je",
"Haye Main Paun Farmaishi Rang Tere Sohniye",
"Unj Bahotan Gifty Shaukeen Koi Na",
"Tare Chann Ambar Zameen Koi NaЁЯе░ЁЯе░",
"Tere Nalo Jhaliye Haseen Koi NaЁЯШНЁЯШН",
"Main Jado Tere Mode Utte Sir RakheyaЁЯШБЁЯШБ",
"Eh Ton Sachi Sama Vi Haseen Koi NaЁЯШТЁЯШТ",
"Kanna Wich JhumkaЁЯСАЁЯСА",
"Akhan Wich SurmaЁЯЩИЁЯЩИ",
"Ho Jaise Strawberry CandyЁЯШЛЁЯШЛ",
"Nakk Utte KokaЁЯдиЁЯди",
"Jeena Kare AukhaЁЯднЁЯдн",
"Haye Meri Jaan Kadd LaindiЁЯШМЁЯШМ",
"Tere Nakhre Haye Tauba Sanu MaardeЁЯдлЁЯдл",
"Ho Gaya Hai Mera Baby Bura HaaLЁЯШКЁЯШК",
"Sachi Lut Gaye Hum Tere Is Pyar MeinЁЯШПЁЯШП",
"Jeeni Zindagi Hai Bas Tere NaalЁЯШЪЁЯШЪ",
"I Love YoU SO MUCH ЁЯШНЁЯШН",
"cause I Love You ЁЯШШЁЯШШ",
"Sapno Mein Mere AayIЁЯШЭЁЯШЭ",
"Baby! Lage Sohna Kitna PyarAЁЯШЪЁЯШЪ",
"Sapno Mein Mere AayiЁЯШЭЁЯШЭ",
"Uff Oh Phir Neendein Hi ChurayiЁЯШЬЁЯШЬ",
"Oh No! Tera Husan NazaraЁЯе░ЁЯе░",
"Tainu Diamond Mundri PehnawaЁЯШОЁЯШО",
"Naale Duniya Sari GhumawaЁЯЩИЁЯЩИ",
"Chhoti-Chhoti Gallan Utte Main HasavaanЁЯТЩЁЯТЩ",
"Yaara Kade Vi Na Tainu Main RulawaanЁЯЩКЁЯЩК",
"cause I Love You ЁЯЩИЁЯЩИ",
"I Love You тЭдя╕ПтЭдя╕П",
"cause I Love YouЁЯЩИЁЯЩИ",
"Yaari Laawan Sachi YaarIЁЯТлЁЯТл",
"Tu Jaan Ton Vi PyariЁЯШБЁЯШБ",
"Will Love You To The Moon And BackЁЯШЖЁЯШЖ",
"Hogi Saza Na Koyi HogiЁЯШЩЁЯШЩ",
"Chahe Karun Chori Chaand TaareЁЯШЙЁЯШЙ",
"Imma Give You ThemЁЯШЕЁЯШЕ",
"Yaari Laavan Sachi YaarIЁЯШШЁЯШШ",
"Tu Jaan Ton Vi PyarIЁЯШЖЁЯШЖ",
"Will Love You To The Moon And BackЁЯТХЁЯТХ",
"Hogee Sazaa Na Koyi HogiЁЯТУЁЯТУ",
"Chahe Karun Chori Chaand TaareЁЯе║ЁЯе║",
"Imma Give You ThemЁЯе╡ЁЯе╡",
"Puri Karunga Main Teri Sari KhahisheinЁЯШБЁЯШБ",
"Tera Rakhanga Main Rajj Ke KhayalЁЯШШЁЯШШ",
"Kitni Khoobiyan Hai Tere Is Yaar MeinЁЯе░ЁЯе░",
"Aaja Bahon Mein Tu Bahein Bas DaalЁЯШВЁЯШВ",
"Aur Hota Nahi Ab IntezarЁЯдйЁЯдй",
"Aur Hota Nahee Ab IntezaarЁЯШШЁЯШШ",
"cause I Love You ЁЯШНЁЯШН",
"I Love YoU ЁЯШЩЁЯШЩ",
"cause I Love You",
"I Love YoU SOOOOOOOOOOOOOOOOOO MUCHHHHHHHHHHHHHHHHHHHHH ЁЯШШЁЯШШ",
"WILL U BE MINE FOREVER??ЁЯдФЁЯдФ",
"Je tu akh te main aan kaajal veЁЯШМЁЯШМ",
"Tu baarish te main baadal veЁЯдлЁЯдл",
"Tu deewana main aan paagal veЁЯдкЁЯдк",
"Sohneya sohneyaтШ║я╕ПтШ║я╕П",
"Je tu chann te main aan taara veЁЯдЧЁЯдЧ",
"Main lehar te tu kinara veЁЯШ╢ЁЯШ╢",
"Main aadha te tu saara veЁЯдЧЁЯдЧ",
"Sohneya sohneyaЁЯШЧЁЯШЧ",
"Tu jahan hai main wahanЁЯШШЁЯШШ",
"Tere bin main hoon hi kyaЁЯе▓ЁЯе▓",
"Tere bin chehre se mereЁЯдФЁЯдФ",
"Udd jaaye rang veЁЯШЕЁЯШЕ",
"Tujhko paane ke liye huMЁЯШБЁЯШБ",
"Roz mangein mannat veЁЯЩИЁЯЩИ",
"Duniya to kya cheez hai yaaraЁЯЩЙЁЯЩЙ",
"Tujhko paane ke liye humЁЯШМЁЯШМ",
"Roz mangein mannat veЁЯдлЁЯдл",
"Duniya to kya cheez hai yaaraЁЯдФЁЯдФ",
"Na parwah mainu apni aaЁЯШБЁЯШБ",
"Na parwah mainu duniya diЁЯСЕЁЯСЕ",
"Na parwah mainu apni aaЁЯШЕЁЯШЕ",
"Tere ton juda nahi kar sakdiЁЯдмЁЯдм",
"Koyi taakat mainu duniya diЁЯШИЁЯШИ",
"Dooron aa jaave teri khushbuЁЯШОЁЯШО",
"Akhan hun band taan vi vekh lawanЁЯШНЁЯШН",
"Teri gali vich mera auna har rozЁЯШЛЁЯШЛ",
"Tera ghar jadon aave matha tek lawanЁЯШМЁЯШМ",
"Nirmaan tujhko dekh keЁЯШПЁЯШП",
"Aa jaave himmat veЁЯШЙЁЯШЙ",
"Tujhko paane ke liye humЁЯШКЁЯШК",
"Roz mangein mannat veЁЯШЙЁЯШЙ",
"Duniya to kya cheez hai yaaraЁЯШМЁЯШМ",
"Thukra denge jannat veЁЯШНЁЯШН",
"Tujhko paane ke liye humЁЯдлЁЯдл",
"Roz mangein mannat veЁЯШБЁЯШБ",
"Duniya to kya cheez hai yaaraЁЯШПЁЯШП",
"Thukra denge jannat veЁЯШМЁЯШМ",
"SO MISS ЁЯШ╢ЁЯШ╢",
"KYA SOCHA APNE BAARE MAINЁЯШЖЁЯШЖ",
"BADI MUSHKIL SE YEH SAB KARA H REЁЯе╡ЁЯе╡",
"PAHLE PURA BOT HI KANG MAAR DIYA BUTЁЯдлЁЯдл",
"WAHI ERROR AAYE JO AATE THEЁЯе▓ЁЯе▓",
"BUT TUMHARA HO CHUKA WALA BFЁЯШОЁЯШО",
"AND FUTURE HUSBAND JO BANNE WALA THA WO BHOT SMART H REЁЯШМЁЯШМ",
"ISS BAAR BOT BANAYA AND CHOTA SA EDIT KARA BASЁЯШБЁЯШБ",
"AUR DEKO ABHI TUM USSI BOT SE YEH PADH PAA RHIЁЯШВЁЯШВ",
"HEHE BTW YEH CHORO MEKO NA TUMSEЁЯШ╢ЁЯШ╢",
"KUCH PUCHNA THA KI MEЁЯдФЁЯдФ",
"TUMHARE KABIL HU YA",
"TUMHARE KABIL NHIЁЯШВЁЯТУ",
"AND EK AUR BAAT BOLNI THI KIЁЯШЩЁЯШЩ",
"I REALLY REALLY DEEPLYЁЯШЩЁЯШЩ",
"LOVE YOU FROM MY HEART TO YOUR HEAT AND MY SOUL ATTACHED BY YOUR SOUL CAN YOU BE MINE FOREVERЁЯШМЁЯШМтЭдя╕П"
]
SRAID = [
"рдЗрд╢реНреШ рд╣реИ рдпрд╛ рдХреБрдЫ рдФрд░ рдпреЗ рдкрддрд╛ рдирд╣реАрдВ, рдкрд░ рдЬреЛ рддреБрдорд╕реЗ рд╣реИ рдХрд┐рд╕реА рдФрд░ рд╕реЗ рдирд╣реАрдВ ЁЯШБЁЯШБ",
"рдореИ рдХреИрд╕реЗ рдХрд╣реВ рдХреА рдЙрд╕рдХрд╛ рд╕рд╛рде рдХреИрд╕рд╛ рд╣реИ, рд╡реЛ рдПрдХ рд╢рдЦреНрд╕ рдкреБрд░реЗ рдХрд╛рдпрдирд╛рдд рдЬреИрд╕рд╛ рд╣реИ ",
" рддреЗрд░рд╛ рд╣реЛрдирд╛ рд╣реА рдореЗрд░реЗ рд▓рд┐рдпреЗ рдЦрд╛рд╕ рд╣реИ, рддреВ рджреВрд░ рд╣реА рд╕рд╣реА рдордЧрд░ рдореЗрд░реЗ рджрд┐рд▓ рдХреЗ рдкрд╛рд╕ рд╣реИ ",
"рдореБрдЭреЗ рддреЗрд░рд╛ рд╕рд╛рде рдЬрд╝рд┐рдиреНрджрдЧреА рднрд░ рдирд╣реАрдВ рдЪрд╛рд╣рд┐рдпреЗ, рдмрд▓реНрдХрд┐ рдЬрдм рддрдХ рддреВ рд╕рд╛рде рд╣реИ рддрдмрддрдХ рдЬрд╝рд┐рдиреНрджрдЧреА рдЪрд╛рд╣рд┐рдП ЁЯШЦЁЯШЦ",
"рддреБрдЭрд╕реЗ рдореЛрд╣рдмреНрдмрдд рдХреБрдЫ рдЕрд▓рдЧ рд╕реА рд╣реИ рдореЗрд░реА, рддреБрдЭреЗ рдЦрдпрд╛рд▓реЛ рдореЗрдВ рдирд╣реАрдВ рджреБрдЖрдУ рдореЗрдВ рдпрд╛рдж рдХрд░рддреЗ рд╣реИЁЯШНЁЯШН",
"рддреВ рд╣реЫрд╛рд░ рдмрд╛рд░ рднреА рд░реВрдареЗ рддреЛ рдордирд╛ рд▓реВрдБрдЧрд╛ рддреБрдЭреЗ",
"рдордЧрд░ рджреЗрдЦ рдореЛрд╣рдмреНрдмрдд рдореЗрдВ рд╢рд╛рдорд┐рд▓ рдХреЛрдИ рджреВрд╕рд░рд╛ рдирд╛ рд╣реЛЁЯШБЁЯШБ",
"рдХрд┐рд╕реНрдордд рдпрд╣ рдореЗрд░рд╛ рдЗрдореНрддреЗрд╣рд╛рди рд▓реЗ рд░рд╣реА рд╣реИЁЯШТЁЯШТ",
"рддреЬрдк рдХрд░ рдпрд╣ рдореБрдЭреЗ рджрд░реНрдж рджреЗ рд░рд╣реА рд╣реИЁЯШМЁЯШМ",
"рджрд┐рд▓ рд╕реЗ рдХрднреА рднреА рдореИрдВрдиреЗ рдЙрд╕реЗ рджреВрд░ рдирд╣реАрдВ рдХрд┐рдпрд╛ЁЯШЙЁЯШЙ",
"рдлрд┐рд░ рдХреНрдпреЛрдВ рдмреЗрд╡рдлрд╛рдИ рдХрд╛ рд╡рд╣ рдЗрд▓реЫрд╛рдо рджреЗ рд░рд╣реА рд╣реИЁЯШОЁЯШО",
"рдорд░реЗ рддреЛ рд▓рд╛рдЦреЛрдВ рд╣реЛрдВрдЧреЗ рддреБрдЭ рдкрд░ЁЯШЪЁЯШЪ",
"рдореИрдВ рддреЛ рддреЗрд░реЗ рд╕рд╛рде рдЬреАрдирд╛ рдЪрд╛рд╣рддрд╛ рд╣реВрдБЁЯШлЁЯШл",
"рд╡рд╛рдкрд╕ рд▓реМрдЯ рдЖрдпрд╛ рд╣реИ рд╣рд╡рд╛рдУрдВ рдХрд╛ рд░реБрдЦ рдореЛреЬрдиреЗ рд╡рд╛рд▓рд╛ЁЯШгЁЯШг",
"рджрд┐рд▓ рдореЗрдВ рдлрд┐рд░ рдЙрддрд░ рд░рд╣рд╛ рд╣реИ рджрд┐рд▓ рддреЛреЬрдиреЗ рд╡рд╛рд▓рд╛ЁЯе║ЁЯе║",
"рдЕрдкрдиреЛрдВ рдХреЗ рдмреАрдЪ рдмреЗрдЧрд╛рдиреЗ рд╣реЛ рдЧрдП рд╣реИрдВЁЯе░ЁЯе░",
"рдкреНрдпрд╛рд░ рдХреЗ рд▓рдореНрд╣реЗ рдЕрдирдЬрд╛рдиреЗ рд╣реЛ рдЧрдП рд╣реИрдВЁЯШШЁЯШШ",
"рдЬрд╣рд╛рдБ рдкрд░ рдлреВрд▓ рдЦрд┐рд▓рддреЗ рдереЗ рдХрднреАЁЯШНЁЯШН",
"рдЖрдЬ рд╡рд╣рд╛рдВ рдкрд░ рд╡реАрд░рд╛рди рд╣реЛ рдЧрдП рд╣реИрдВЁЯе░ЁЯе░",
"рдЬреЛ рд╢рдЦреНрд╕ рддреЗрд░реЗ рддрд╕рд╡реНрд╡реБрд░ рд╕реЗ рд╣реЗ рдорд╣рдХ рдЬрд╛рдпреЗЁЯШБЁЯШБ",
"рд╕реЛрдЪреЛ рддреБрдореНрд╣рд╛рд░реЗ рджреАрджрд╛рд░ рдореЗрдВ рдЙрд╕рдХрд╛ рдХреНрдпрд╛ рд╣реЛрдЧрд╛ЁЯШТЁЯШТ",
"рдореЛрд╣рдмреНрдмрдд рдХрд╛ рдПрд╣рд╕рд╛рд╕ рддреЛ рд╣рдо рджреЛрдиреЛрдВ рдХреЛ рд╣реБрдЖ рдерд╛",
"рдлрд░реНрдХ рд╕рд┐рд░реНрдл рдЗрддрдирд╛ рдерд╛ рдХреА рдЙрд╕рдиреЗ рдХрд┐рдпрд╛ рдерд╛ рдФрд░ рдореБрдЭреЗ рд╣реБрдЖ рдерд╛",
"рд╕рд╛рдВрд╕реЛрдВ рдХреА рдбреЛрд░ рдЫреВрдЯрддреА рдЬрд╛ рд░рд╣реА рд╣реИ",
"рдХрд┐рд╕реНрдордд рднреА рд╣рдореЗ рджрд░реНрдж рджреЗрддреА рдЬрд╛ рд░рд╣реА рд╣реИ",
"рдореМрдд рдХреА рддрд░рдл рд╣реИрдВ рдХрджрдо рд╣рдорд╛рд░реЗ",
"рдореЛрд╣рдмреНрдмрдд рднреА рд╣рдо рд╕реЗ рдЫреВрдЯрддреА рдЬрд╛ рд░рд╣реА рд╣реИ",
"рд╕рдордЭрддрд╛ рд╣реА рдирд╣реАрдВ рд╡реЛ рдореЗрд░реЗ рдЕрд▓реЮрд╛реЫ рдХреА рдЧрд╣рд░рд╛рдИ",
"рдореИрдВрдиреЗ рд╣рд░ рд▓рдлреНреЫ рдХрд╣ рджрд┐рдпрд╛ рдЬрд┐рд╕реЗ рдореЛрд╣рдмреНрдмрдд рдХрд╣рддреЗ рд╣реИ",
"рд╕рдордВрджрд░ рди рд╕рд╣реА рдкрд░ рдПрдХ рдирджреА рддреЛ рд╣реЛрдиреА рдЪрд╛рд╣рд┐рдП",
"рддреЗрд░реЗ рд╢рд╣рд░ рдореЗрдВ реЫрд┐рдиреНрджрдЧреА рдХрд╣реА рддреЛ рд╣реЛрдиреА рдЪрд╛рд╣рд┐рдП",
"рдиреЫрд░реЛрдВ рд╕реЗ рджреЗрдЦреЛ рддреЛрд╣ рдЖрдмрд╛рдж рд╣рдо рд╣реИрдВ",
"рджрд┐рд▓ рд╕реЗ рджреЗрдЦреЛ рддреЛрд╣ рдмрд░реНрдмрд╛рдж рд╣рдо рд╣реИрдВ",
"рдЬреАрд╡рди рдХрд╛ рд╣рд░ рд▓рдореНрд╣рд╛ рджрд░реНрдж рд╕реЗ рднрд░ рдЧрдпрд╛",
"рдлрд┐рд░ рдХреИрд╕реЗ рдХрд╣ рджреЗрдВ рдЖреЫрд╛рдж рд╣рдо рд╣реИрдВ",
"рдореБрдЭреЗ рдирд╣реАрдВ рдорд╛рд▓реВрдо рд╡реЛ рдкрд╣рд▓реА рдмрд╛рд░ рдХрдм рдЕрдЪреНрдЫрд╛ рд▓рдЧрд╛",
"рдордЧрд░ рдЙрд╕рдХреЗ рдмрд╛рдж рдХрднреА рдмреБрд░рд╛ рднреА рдирд╣реАрдВ",
"рд╕рдЪреНрдЪреА рдореЛрд╣рдмреНрдмрдд рдХрднреА рдЦрддреНрдо рдирд╣реАрдВ рд╣реЛрддреА",
"рд╡реШреНрдд рдХреЗ рд╕рд╛рде рдЦрд╛рдореЛрд╢ рд╣реЛ рдЬрд╛рддреА рд╣реИ",
"реЫрд┐рдиреНрджрдЧреА рдХреЗ рд╕реЮрд░ рдореЗрдВ рдЖрдкрдХрд╛ рд╕рд╣рд╛рд░рд╛ рдЪрд╛рд╣рд┐рдП",
"рдЖрдкрдХреЗ рдЪрд░рдгреЛрдВ рдХрд╛ рдмрд╕ рдЖрд╕рд░рд╛ рдЪрд╛рд╣рд┐рдП",
"рд╣рд░ рдореБрд╢реНрдХрд┐рд▓реЛрдВ рдХрд╛ рд╣рдБрд╕рддреЗ рд╣реБрдП рд╕рд╛рдордирд╛ рдХрд░реЗрдВрдЧреЗ",
"рдмрд╕ рдард╛рдХреБрд░ рдЬреА рдЖрдкрдХрд╛ рдПрдХ рдЗрд╢рд╛рд░рд╛ рдЪрд╛рд╣рд┐рдП",
"рдЬрд┐рд╕ рджрд┐рд▓ рдореЗрдВ рдмрд╕рд╛ рдерд╛ рдирд╛рдо рддреЗрд░рд╛ рд╣рдордиреЗ рд╡реЛ рддреЛреЬ рджрд┐рдпрд╛",
"рди рд╣реЛрдиреЗ рджрд┐рдпрд╛ рддреБрдЭреЗ рдмрджрдирд╛рдо рдмрд╕ рддреЗрд░реЗ рдирд╛рдо рд▓реЗрдирд╛ рдЫреЛреЬ рджрд┐рдпрд╛",
"рдкреНрдпрд╛рд░ рд╡реЛ рдирд╣реАрдВ рдЬреЛ рд╣рд╛рд╕рд┐рд▓ рдХрд░рдиреЗ рдХреЗ рд▓рд┐рдП рдХреБрдЫ рднреА рдХрд░рд╡ рджреЗ",
"рдкреНрдпрд╛рд░ рд╡реЛ рд╣реИ рдЬреЛ рдЙрд╕рдХреА рдЦреБрд╢реА рдХреЗ рд▓рд┐рдП рдЕрдкрдиреЗ рдЕрд░рдорд╛рди рдЪреЛрд░ рджреЗ",
"рдЖрд╢рд┐рдХ рдХреЗ рдирд╛рдо рд╕реЗ рд╕рднреА рдЬрд╛рдирддреЗ рд╣реИрдВЁЯШНЁЯШН",
"рдЗрддрдирд╛ рдмрджрдирд╛рдо рд╣реЛ рдЧрдП рд╣рдо рдордпрдЦрд╛рдиреЗ рдореЗрдВЁЯе░ЁЯе░",
"рдЬрдм рднреА рддреЗрд░реА рдпрд╛рдж рдЖрддреА рд╣реИ рдмреЗрджрд░реНрдж рдореБрдЭреЗЁЯШНЁЯШН",
"рддреЛрд╣ рдкреАрддреЗ рд╣реИрдВ рд╣рдо рджрд░реНрдж рдкреИрдорд╛рдиреЗ рдореЗрдВЁЯе░ЁЯе░",
"рд╣рдо рдЗрд╢реНреШ рдХреЗ рд╡реЛ рдореБрдХрд╛рдо рдкрд░ рдЦреЬреЗ рд╣реИЁЯШБЁЯШБ",
"рдЬрд╣рд╛рдБ рджрд┐рд▓ рдХрд┐рд╕реА рдФрд░ рдХреЛ рдЪрд╛рд╣реЗ рддреЛ рдЧреБрдиреНрд╣рд╛ рд▓рдЧрддрд╛ рд╣реИЁЯШТЁЯШТ",
"рд╕рдЪреНрдЪреЗ рдкреНрдпрд╛рд░ рд╡рд╛рд▓реЛрдВ рдХреЛ рд╣рдореЗрд╢рд╛ рд▓реЛрдЧ рдЧрд▓рдд рд╣реА рд╕рдордЭрддреЗ рд╣реИЁЯСАЁЯСА",
"рдЬрдмрдХрд┐ рдЯрд╛рдЗрдо рдкрд╛рд╕ рд╡рд╛рд▓реЛ рд╕реЗ рд▓реЛрдЧ рдЦреБрд╢ рд░рд╣рддреЗ рд╣реИ рдЖрдЬ рдХрд▓ЁЯЩИЁЯЩИ",
"рдЧрд┐рд▓рд╛рд╕ рдкрд░ рдЧрд┐рд▓рд╛рд╕ рдмрд╣реБрдд рдЯреВрдЯ рд░рд╣реЗ рд╣реИрдВЁЯШЛЁЯШЛ",
"рдЦреБрд╕реА рдХреЗ рдкреНрдпрд╛рд▓реЗ рджрд░реНрдж рд╕реЗ рднрд░ рд░рд╣реЗ рд╣реИрдВЁЯдиЁЯди",
"рдорд╢рд╛рд▓реЛрдВ рдХреА рддрд░рд╣ рджрд┐рд▓ рдЬрд▓ рд░рд╣реЗ рд╣реИрдВЁЯднЁЯдн",
"рдЬреИрд╕реЗ реЫрд┐рдиреНрджрдЧреА рдореЗрдВ рдмрджрдХрд┐рд╕реНрдорддреА рд╕реЗ рдорд┐рд▓ рд░рд╣реЗ рд╣реИрдВЁЯШМЁЯШМ",
"рд╕рд┐рд░реНрдл рд╡реШреНрдд рдЧреБрдЬрд░рдирд╛ рд╣реЛ рддреЛ рдХрд┐рд╕реА рдФрд░ рдХреЛ рдЕрдкрдирд╛ рдмрдирд╛ рд▓реЗрдирд╛ЁЯдлЁЯдл",
"рд╣рдо рджреЛрд╕реНрддреА рднреА рдХрд░рддреЗ рд╣реИ рддреЛ рдкреНрдпрд╛рд░ рдХреА рддрд░рд╣ЁЯШКЁЯШК",
"рдЬрд░реВрд░реА рдирд╣реАрдВ рдЗрд╢реНреШ рдореЗрдВ рдмрдирд╣реВрдБ рдХреЗ рд╕рд╣рд╛рд░реЗ рд╣реА рдорд┐рд▓реЗЁЯШПЁЯШП",
"рдХрд┐рд╕реА рдХреЛ рдЬреА рднрд░ рдХреЗ рдорд╣рд╕реВрд╕ рдХрд░рдирд╛ рднреА рдореЛрд╣рдмреНрдмрдд рд╣реИЁЯШЪЁЯШЪ",
"рдирд╢реЗ рдореЗрдВ рднреА рддреЗрд░рд╛ рдирд╛рдо рд▓рдм рдкрд░ рдЖрддрд╛ рд╣реИЁЯШШЁЯШШ",
"рдЪрд▓рддреЗ рд╣реБрдП рдореЗрд░реЗ рдкрд╛рдБрд╡ рд▓реЬрдЦреЬрд╛рддреЗ рд╣реИрдВЁЯШНЁЯШН",
"рджрд░реНрдж рд╕рд╛ рджрд┐рд▓ рдореЗрдВ рдЙрдарддрд╛ рд╣реИ рдореЗрд░реЗЁЯШШЁЯШШ",
"рд╣рд╕реАрдВ рдЪреЗрд╣рд░реЗ рдкрд░ рднреА рджрд╛рдЧ рдирдЬрд░ рдЖрддрд╛ рд╣реИЁЯШНЁЯШН",
"рд╣рдордиреЗ рднреА рдПрдХ рдРрд╕реЗ рд╢рдЦреНрд╕ рдХреЛ рдЪрд╛рд╣рд╛ЁЯШЭЁЯШЭ",
"рдЬрд┐рд╕рдХреЛ рднреБрд▓рд╛ рди рд╕рдХреЗ рдФрд░ рд╡реЛ рдХрд┐рд╕реНрдордд рдореИрдВ рднреА рдирд╣реАрдВЁЯШЬЁЯШЬ",
"рд╕рдЪреНрдЪрд╛ рдкреНрдпрд╛рд░ рдХрд┐рд╕реА рднреВрдд рдХреА рддрд░рд╣ рд╣реЛрддрд╛ рд╣реИЁЯе░ЁЯе░",
"рдмрд╛рддреЗрдВ рддреЛ рд╕рдм рдХрд░рддреЗ рд╣реИ рджреЗрдЦрд╛ рдХрд┐рд╕реА рдиреЗ рдирд╣реАрдВЁЯШЪЁЯШЪ",
"рдордд рдкреВрдЫ рдпреЗ рдХреА рдореИрдВ рддреБрдЭреЗ рднреБрд▓рд╛ рдирд╣реАрдВ рд╕рдХрддрд╛ЁЯШЭЁЯШЭ",
"рддреЗрд░реА рдпрд╛рджреЛрдВ рдХреЗ рдкрдиреНрдиреЗ рдХреЛ рдореИрдВ рдЬрд▓рд╛ рдирд╣реАрдВ рд╕рдХрддрд╛ЁЯШЬЁЯШЬ",
"рд╕рдВрдШрд░реНрд╖ рдпрд╣ рд╣реИ рдХрд┐ рдЦреБрдж рдХреЛ рдорд╛рд░рдирд╛ рд╣реЛрдЧрд╛ЁЯе░ЁЯе░",
"рдФрд░ рдЕрдкрдиреЗ рд╕реБрдХреВрди рдХреА рдЦрд╛рддрд┐рд░ рддреБрдЭреЗ рд░реБрд▓рд╛ рдирд╣реАрдВ рд╕рдХрддрд╛ЁЯШЪЁЯШЪ",
"рджреБрдирд┐рдпрд╛ рдХреЛ рдЖрдЧ рд▓рдЧрд╛рдиреЗ рдХреА реЫрд░реВрд░рдд рдирд╣реАрдВЁЯШОЁЯШО",
"Naale Duniya Sari GhumawaЁЯЩИЁЯЩИ",
"рддреЛ рдореЗрд░реЗ рд╕рд╛рде рдЪрд╕рд▓ рдЖрдЧ рдЦреБрдж рд▓рдЧ рдЬрд╛рдПрдЧреАЁЯТЩЁЯТЩ",
"рддрд░рд╕ рдЧрдпреЗ рд╣реИ рд╣рдо рддреЗрд░реЗ рдореБрдВрд╣ рд╕реЗ рдХреБрдЫ рд╕реБрдирдиреЗ рдХреЛ рд╣рдоЁЯЩКЁЯЩК",
"рдкреНрдпрд╛рд░ рдХреА рдмрд╛рдд рди рд╕рд╣реА рдХреЛрдИ рд╢рд┐рдХрд╛рдпрдд рд╣реА рдХрд░ рджреЗ ЁЯЩИЁЯЩИ",
"рддреБрдо рдирд╣реАрдВ рд╣реЛ рдкрд╛рд╕ рдордЧрд░ рддрдиреНрд╣рд╛рдБ рд░рд╛рдд рд╡рд╣реА рд╣реИ тЭдя╕ПтЭдя╕П",
"рд╡рд╣реА рд╣реИ рдЪрд╛рд╣рдд рдпрд╛рджреЛрдВ рдХреА рдмрд░рд╕рд╛рдд рд╡рд╣реА рд╣реИЁЯЩИЁЯЩИ",
"рд╣рд░ рдЦреБрд╢реА рднреА рджреВрд░ рд╣реИ рдореЗрд░реЗ рдЖрд╢рд┐рдпрд╛рдиреЗ рд╕реЗ тЭдя╕ПтЭдя╕П",
"рдЦрд╛рдореЛрд╢ рд▓рдореНрд╣реЛрдВ рдореЗрдВ рджрд░реНрдж-рдП-рд╣рд╛рд▓рд╛рдд рд╡рд╣реА рд╣реИЁЯТлЁЯТл",
"рдХрд░рдиреЗ рд▓рдЧреЗ рдЬрдм рд╢рд┐рдХрд╡рд╛ рдЙрд╕рд╕реЗ рдЙрд╕рдХреА рдмреЗрд╡рдлрд╛рдИ рдХрд╛ЁЯШБЁЯШБ",
"рд░рдЦ рдХрд░ рд╣реЛрдВрдЯ рдХреЛ рд╣реЛрдВрдЯ рд╕реЗ рдЦрд╛рдореЛрд╢ рдХрд░ рджрд┐рдпрд╛ЁЯШЖЁЯШЖ",
"рд░рд╛рд╣ рдореЗрдВ рдорд┐рд▓реЗ рдереЗ рд╣рдо, рд░рд╛рд╣реЗрдВ рдирд╕реАрдм рдмрди рдЧрдИрдВЁЯШЩЁЯШЩ",
"рдирд╛ рддреВ рдЕрдкрдиреЗ рдШрд░ рдЧрдпрд╛, рдирд╛ рд╣рдо рдЕрдкрдиреЗ рдШрд░ рдЧрдпреЗЁЯШЙЁЯШЙ",
"рддреБрдореНрд╣реЗрдВ рдиреАрдВрдж рдирд╣реАрдВ рдЖрддреА рддреЛ рдХреЛрдИ рдФрд░ рд╡рдЬрд╣ рд╣реЛрдЧреАЁЯШЕЁЯШЕ",
"рдЕрдм рд╣рд░ рдРрдм рдХреЗ рд▓рд┐рдП рдХрд╕реВрд░рд╡рд╛рд░ рдЗрд╢реНрдХ рддреЛ рдирд╣реАрдВЁЯШШЁЯШШ",
"рдЕрдирд╛ рдХрд╣рддреА рд╣реИ рдЗрд▓реНрддреЗрдЬрд╛ рдХреНрдпрд╛ рдХрд░рдиреАЁЯШЖЁЯШЖ",
"рд╡реЛ рдореЛрд╣рдмреНрдмрдд рд╣реА рдХреНрдпрд╛ рдЬреЛ рдорд┐рдиреНрдирддреЛрдВ рд╕реЗ рдорд┐рд▓реЗЁЯТХЁЯТХ",
"рди рдЬрд╛рд╣рд┐рд░ рд╣реБрдИ рддреБрдорд╕реЗ рдФрд░ рди рд╣реА рдмрдпрд╛рди рд╣реБрдИ рд╣рдорд╕реЗЁЯТУЁЯТУ",
"рдмрд╕ рд╕реБрд▓рдЭреА рд╣реБрдИ рдЖрдБрдЦреЛ рдореЗрдВ рдЙрд▓рдЭреА рд░рд╣реА рдореЛрд╣рдмреНрдмрддЁЯе║ЁЯе║",
"рдЧреБрдлреНрддрдЧреВ рдмрдВрдж рди рд╣реЛ рдмрд╛рдд рд╕реЗ рдмрд╛рдд рдЪрд▓реЗЁЯе╡ЁЯе╡",
"рдирдЬрд░реЛрдВ рдореЗрдВ рд░рд╣реЛ рдХреИрдж рджрд┐рд▓ рд╕реЗ рджрд┐рд▓ рдорд┐рд▓реЗЁЯШБЁЯШБ",
"рд╣реИ рдЗрд╢реНреШ рдХреА рдордВреЫрд┐рд▓ рдореЗрдВ рд╣рд╛рд▓ рдХрд┐ рдЬреИрд╕реЗЁЯШШЁЯШШ",
"рд▓реБрдЯ рдЬрд╛рдП рдХрд╣реАрдВ рд░рд╛рд╣ рдореЗрдВ рд╕рд╛рдорд╛рди рдХрд┐рд╕реА рдХрд╛ЁЯе░",
"рдореБрдХрдореНрдорд▓ рдирд╛ рд╕рд╣реА рдЕрдзреВрд░рд╛ рд╣реА рд░рд╣рдиреЗ рджреЛЁЯШВЁЯШВ",
"рдпреЗ рдЗрд╢реНреШ рд╣реИ рдХреЛрдИ рдореШрд╕рдж рддреЛ рдирд╣реАрдВ рд╣реИЁЯдйЁЯдй",
"рд╡рдЬрд╣ рдирдлрд░рддреЛрдВ рдХреА рддрд▓рд╛рд╢реА рдЬрд╛рддреА рд╣реИЁЯШШЁЯШШ",
"рдореЛрд╣рдмреНрдмрдд рддреЛ рдмрд┐рди рд╡рдЬрд╣ рд╣реА рд╣реЛ рдЬрд╛рддреА рд╣реИ ЁЯШНЁЯШН",
"рд╕рд┐рд░реНрдл рдорд░реА рд╣реБрдИ рдордЫрд▓реА рдХреЛ рд╣реА рдкрд╛рдиреА рдХрд╛ рдмрд╣рд╛рд╡ рдЪрд▓рд╛рддреА рд╣реИ ЁЯШЩЁЯШЩ",
"рдЬрд┐рд╕ рдордЫрд▓реА рдореЗрдВ рдЬрд╛рди рд╣реЛрддреА рд╣реИ рд╡реЛ рдЕрдкрдирд╛ рд░рд╛рд╕реНрддрд╛ рдЦреБрдж рддрдп рдХрд░рддреА рд╣реИ",
"рдХрд╛рдордпрд╛рдм рд▓реЛрдЧреЛрдВ рдХреЗ рдЪреЗрд╣рд░реЛрдВ рдкрд░ рджреЛ рдЪреАрдЬреЗрдВ рд╣реЛрддреА рд╣реИ ЁЯШШЁЯШШ",
"рдПрдХ рд╕рд╛рдЗрд▓реЗрдВрд╕ рдФрд░ рджреВрд╕рд░рд╛ рд╕реНрдорд╛рдЗрд▓ЁЯдФЁЯдФ",
"рдореЗрд░реА рдЪрд╛рд╣рдд рджреЗрдЦрдиреА рд╣реИ рддреЛ рдореЗрд░реЗ рджрд┐рд▓ рдкрд░ рдЕрдкрдирд╛ рджрд┐рд▓ рд░рдЦрдХрд░ рджреЗрдЦeЁЯШМЁЯШМ",
"рддреЗрд░реА рдзреЬрдХрди рдирд╛ рднрдбреНрдЬрд╛рдпреЗ рддреЛ рдореЗрд░реА рдореЛрд╣рдмреНрдмрдд рдареБрдХрд░рд╛ рджреЗрдирд╛ЁЯдлЁЯдл",
"рдЧрд▓рддрдлрд╣рдореА рдХреА рдЧреБрдВрдЬрд╛рдИрд╢ рдирд╣реАрдВ рд╕рдЪреНрдЪреА рдореЛрд╣рдмреНрдмрдд рдореЗрдВЁЯдкЁЯдк",
"рдЬрд╣рд╛рдБ рдХрд┐рд░рджрд╛рд░ рд╣рд▓реНрдХрд╛ рд╣реЛ рдХрд╣рд╛рдиреА рдбреВрдм рдЬрд╛рддреА рд╣реИтШ║я╕ПтШ║я╕П",
"рд╣реЛрдиреЗ рджреЛ рдореБреЩрд╛рддрд┐рдм рдореБрдЭреЗ рдЖрдЬ рдЗрди рд╣реЛрдВрдЯреЛ рд╕реЗ рдЕрдмреНрдмрд╛рд╕ЁЯдЧЁЯдЧ",
"рдмрд╛рдд рди рддреЛ рдпреЗ рд╕рдордЭ рд░рд╣реЗ рд╣реИ рдкрд░ рдЧреБреЮреНрддрдЧреВ рдЬрд╛рд░реА рд╣реИЁЯШ╢ЁЯШ╢",
"рдЙрджрд╛рд╕рд┐рдпрд╛рдБ рдЗрд╢реНреШ рдХреА рдкрд╣рдЪрд╛рди рд╣реИЁЯдЧЁЯдЧ",
"рдореБрд╕реНрдХреБрд░рд╛ рджрд┐рдП рддреЛ рдЗрд╢реНреШ рдмреБрд░рд╛ рдорд╛рди рдЬрд╛рдпреЗрдЧрд╛ЁЯШЧЁЯШЧ",
"рдХреБрдЫ рдЗрд╕ рдЕрджрд╛ рд╕реЗ рд╣рд╛рд▓ рд╕реБрдирд╛рдирд╛ рд╣рдорд╛рд░реЗ рджрд┐рд▓ЁЯШШЁЯШШ",
"рд╡реЛ рдЦреБрдж рд╣реА рдХрд╣ рджреЗ рдХрд┐рджреА рднреВрд▓ рдЬрд╛рдирд╛ рдмреБрд░реА рдмрд╛рдд рд╣реИЁЯе▓",
"рдорд╛рдирд╛ рдХреА рдЙрд╕рд╕реЗ рдмрд┐рдЫрдбрд╝рдХрд░ рд╣рдо рдЙрдорд░ рднрд░ рд░реЛрддреЗ рд░рд╣реЗЁЯдФЁЯдФ",
"рдкрд░ рдореЗрд░реЗ рдорд╛рд░ рдЬрд╛рдиреЗ рдХреЗ рдмрд╛рдж рдЙрдорд░ рднрд░ рд░реЛрдПрдЧрд╛ рд╡реЛЁЯШЕЁЯШЕ",
"рджрд┐рд▓ рдореЗрдВ рддреБрдореНрд╣рд╛рд░реА рдЕрдкрдиреА рдХрднреА рдЪреЛрд░ рдЬрд╛рдпреЗрдВрдЧреЗЁЯШБЁЯШБ",
"рдЖрдБрдЦреЛрдВ рдореЗрдВ рдЗрдВрддреЫрд╛рд░ рдХреА рд▓рдХреАрд░ рдЫреЛреЬ рдЬрд╛рдпреЗрдВрдЧреЗЁЯЩИЁЯЩИ",
"рдХрд┐рд╕реА рдорд╛рд╕реВрдо рд▓рдореНрд╣реЗ рдореИрдВ рдХрд┐рд╕реА рдорд╛рд╕реВрдо рдЪреЗрд╣рд░реЗ рд╕реЗЁЯЩЙЁЯЩЙ",
"рдореЛрд╣рдмреНрдмрдд рдХреА рдирд╣реАрдВ рдЬрд╛рддреА рдореЛрд╣рдмреНрдмрдд рд╣реЛ рдЬрд╛рддреА рд╣реИЁЯШМЁЯШМ",
"рдХрд░реАрдм рдЖрдУ рддреЛ рд╢рд╛рдпрдж рд╣рдо рд╕рдордЭ рд▓реЛрдЧреЗЁЯШМЁЯШМ",
"рдпреЗ рджреВрд░рд┐рдпрд╛ рддреЛ рдХреЗрд╡рд▓ рдлрд╕рд▓реЗ рдмрдврд╝рддреА рд╣реИЁЯдлЁЯдл",
"рддреЗрд░реЗ рдЗрд╢реНреШ рдореЗрдВ рдЗрд╕ рддрд░рд╣ рдореИрдВ рдиреАрд▓рд╛рдо рд╣реЛ рдЬрд╛рдУЁЯдФЁЯдФ",
"рдЖрдЦрд░реА рд╣реЛ рдореЗрд░реА рдмреЛрд▓реА рдФрд░ рдореИрдВ рддреЗрд░реЗ рдирд╛рдо рд╣реЛ рдЬрд╛рдКЁЯШМЁЯШМ",
"рдЖрдк рдЬрдм рддрдХ рд░рд╣реЗрдВрдЧреЗ рдЖрдВрдЦреЛрдВ рдореЗрдВ рдирдЬрд╛рд░рд╛ рдмрдирдХрд░ЁЯШБЁЯШБ",
"рд░реЛрдЬ рдЖрдПрдВрдЧреЗ рдореЗрд░реА рджреБрдирд┐рдпрд╛ рдореЗрдВ рдЙрдЬрд╛рд▓рд╛ рдмрдирдХрд░ЁЯСЕЁЯСЕ",
"рдЙрд╕реЗ рдЬрдм рд╕реЗ рдмреЗрд╡рдлрд╛рдИ рдХреА рд╣реИ рдореИрдВ рдкреНрдпрд╛рд░ рдХреА рд░рд╛рд╣ рдореЗрдВ рдЪрд▓ рдирд╛ рд╕рдХрд╛ЁЯШЕЁЯШЕ",
"рдЙрд╕реЗ рддреЛ рдХрд┐рд╕реА рдФрд░ рдХрд╛ рд╣рд╛рде рдерд╛рдо рд▓рд┐рдпрд╛рдмрд╕ рдлрд┐рд░ рдХрднреА рд╕рдореНрднрд▓ рдирд╣реАрдВ рд╕рдХрд╛ЁЯСЕЁЯСЕ",
"рдПрдХ рд╣реА реЩреНрд╡рд╛рдм рджреЗрдЦрд╛ рд╣реИ рдХрдИ рдмрд╛рд░ рдореИрдВрдиреЗЁЯдмЁЯдм",
"рддреЗрд░реА рд╢рд╛рджреА рдореЗрдВ рдЙрд▓рдЭреА рд╣реИ рдЪрд╛рд╣рд┐рдП рдореЗрд░реЗ рдШрд░ рдХреАЁЯШИЁЯШИ",
"рддреБрдореНрд╣реЗ рдореЗрд░реА рдореЛрд╣рдмреНрдмрдд рдХреА рдХрд╕рдо рд╕рдЪ рдмрддрд╛рдирд╛ЁЯШОЁЯШО",
"рдЧрд▓реЗ рдореЗрдВ рдбрд╛рд▓ рдХрд░ рдмрд╛рд╣реЗрдВ рдХрд┐рд╕рд╕реЗ рд╕реАрдЦрд╛рдпрд╛ рд╣реИЁЯШНЁЯШН",
"рдирд╣реАрдВ рдкрддрд╛ рдХреА рд╡реЛ рдХрднреА рдореЗрд░реА рдереА рднреА рдпрд╛ рдирд╣реАрдВЁЯШЛЁЯШЛ",
"рдореБрдЭреЗ рдпреЗ рдкрддрд╛ рд╣реИ рдмрд╕ рдХреА рдорд╛рдИ рддреЛ рдерд╛ рдЙрдорд░ рдмрд╕ рдЙрд╕реА рдХрд╛ рд░рд╣рд╛ЁЯШМЁЯШМ",
"рддреБрдордиреЗ рджреЗрдЦрд╛ рдХрднреА рдЪрд╛рдБрдж рд╕реЗ рдкрд╛рдиреА рдЧрд┐рд░рддреЗ рд╣реБрдПeЁЯШПЁЯШП",
"рдореИрдВрдиреЗ рджреЗрдЦрд╛ рдпреЗ рдордВреЫрд░ рддреВ рдореЗрдВ рдЪреЗрд╣рд░рд╛ рдзреЛрддреЗ рд╣реБрдПЁЯШЙЁЯШЙ",
"рдареБрдХрд░рд╛ рджреЗ рдХреЛрдИ рдЪрд╛рд╣рдд рдХреЛ рддреВ рд╣рд╕ рдХреЗ рд╕рд╣ рд▓реЗрдирд╛ЁЯШКЁЯШК",
"рдкреНрдпрд╛рд░ рдХреА рддрдмрд┐рдпрдд рдореЗрдВ реЫрдмрд░ рдЬрд╕реНрддреА рдирд╣реАрдВ рд╣реЛрддреАЁЯШЙЁЯШЙ",
"рддреЗрд░рд╛ рдкрддрд╛ рдирд╣реАрдВ рдкрд░ рдореЗрд░рд╛ рджрд┐рд▓ рдХрднреА рддреИрдпрд╛рд░ рдирд╣реАрдВ рд╣реЛрдЧрд╛ЁЯШМЁЯШМ",
"рдореБрдЭреЗ рддреЗрд░реЗ рдЕрд▓рд╛рд╡рд╛ рдХрднреА рдХрд┐рд╕реА рдФрд░ рд╕реЗ рдкреНрдпрд╛рд░ рдирд╣реАрдВ рд╣реЛрдЧрд╛ЁЯШНЁЯШН",
"рджрд┐рд▓ рдореЗрдВ рдЖрд╣рдЯ рд╕реА рд╣реБрдИ рд░реВрд╣ рдореЗрдВ рджрд╕реНрддрдХ рдЧреВрдБрдЬреАЁЯдлЁЯдл",
"рдХрд┐рд╕ рдХреА рдЦреБрд╢рдмреВ рдпреЗ рдореБрдЭреЗ рдореЗрд░реЗ рд╕рд┐рд░рд╣рд╛рдиреЗ рдЖрдИЁЯШБЁЯШБ",
"рдЙрдореНрд░ рднрд░ рд▓рд┐рдЦрддреЗ рд░рд╣реЗ рдлрд┐рд░ рднреА рд╡рд╛рд░рдХ рд╕рджрд╛ рд░рд╣рд╛ЁЯШПЁЯШП",
"рдЬрд╛рдиреЗ рдХрд┐рдпрд╛ рд▓рдлреНреЫ рдереЗ рдЬреЛ рд╣рдо рд▓рд┐рдЦ рдирд╣реАрдВ рдкрд╛рдпреЗЁЯШМЁЯШМ",
"рд▓рдЧрд╛ рдХреЗ рдлреВрд▓ рд╣рд╛рдереЛрдВ рд╕реЗ рдЙрд╕рдиреЗ рдХрд╣рд╛ рдЪреБрдкрдХреЗ рд╕реЗЁЯШ╢ЁЯШ╢",
"рдЕрдЧрд░ рдпрд╣рд╛рдБ рдХреЛрдИ рдирд╣реАрдВ рд╣реЛрддрд╛ рддреЛ рдлреВрд▓ рдХреА рдЬрдЧрд╣ рддреБрдо рд╣реЛрддреЗЁЯШЖЁЯШЖ",
"рдЬрд╛рди рдЬрдм рдкреНрдпрд╛рд░реА рдереА рдорд░рдиреЗ рдХрд╛ рд╢реМрдХ рдерд╛ЁЯе╡ЁЯе╡",
"рдЕрдм рдорд░рдиреЗ рдХрд╛ рд╢реМрдХ рд╣реИ рддреЛ рдХрд╛рддрд┐рд▓ рдирд╣реАрдВ рдорд┐рд▓ рд░рд╣рд╛ЁЯдлЁЯдл",
"рд╕рд┐рд░реНрдл рдпрд╛рдж рдмрдирдХрд░ рди рд░рд╣ рдЬрд╛рдпреЗ рдкреНрдпрд╛рд░ рдореЗрд░рд╛ЁЯе▓ЁЯе▓",
"рдХрднреА рдХрднреА рдХреБрдЫ рд╡реШреНрдд рдХреЗ рд▓рд┐рдП рдЖрдпрд╛ рдХрд░реЛЁЯШОЁЯШО",
"рдореБрдЭ рдХреЛ рд╕рдордЭрд╛рдпрд╛ рдирд╛ рдХрд░реЛ рдЕрдм рддреЛ рд╣реЛ рдЪреБрдХреА рд╣реВрдБ рдореБрдЭ рдореИрдВЁЯШМЁЯШМ",
"рдореЛрд╣рдмреНрдмрдд рдорд╢рд╡рд░рд╛ рд╣реЛрддреА рддреЛ рддреБрдо рд╕реЗ рдкреВрдЫ рд▓реЗрддрд╛ЁЯШБЁЯШБ",
"рдЙрдиреНрд╣реЛрдВ рдиреЗ рдХрд╣рд╛ рдмрд╣реБрдд рдмреЛрд▓рддреЗ рд╣реЛ рдЕрдм рдХреНрдпрд╛ рдмрд░рд╕ рдЬрд╛рдУрдЧреЗЁЯШВЁЯШВ",
"рд╣рдордиреЗ рдХрд╣рд╛ рдЬрд┐рд╕ рджрд┐рди рдЪреБрдк рд╣реЛ рдЧрдпрд╛ рддреБрдо рддрд░рд╕ рдЬрд╛рдУ рдЧрдПЁЯШ╢ЁЯШ╢",
"рдХреБрдЫ рдРрд╕реЗ рд╣рд╕реНрджреЗ реЫрд┐рдиреНрджрдЧреА рдореИрдВ рд╣реЛрддреЗ рд╣реИЁЯдФЁЯдФ",
"рдХреЗ рдЗрдВрд╕рд╛рди рддреЛ рдмрдЪ рдЬрд╛рддрд╛ рд╣реИ рдордЧрд░ реЫрд┐рдВрджрд╛ рдирд╣реАрдВ рд░рд╣рддрд╛ЁЯШВЁЯТУ"
]
CRAID = [
'AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA',
'BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB',
'CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC',
'DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD',
'EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE',
'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF',
'GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG',
'HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH',
'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII',
'JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ',
'KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK',
'LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL',
'MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM',
'NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN',
'OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO',
'PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP',
'QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ',
'RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR',
'SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS',
'TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT',
'UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU',
'VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV',
'WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW',
'XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX',
'YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY',
'ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ'
]
| 68,217 | Python | .py | 698 | 92.45702 | 723 | 0.824063 | tinaarobot/XSPAM | 8 | 22 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,653 | help.py | tinaarobot_XSPAM/ROYEDITX/modules/help.py | from telethon import events, Button
from config import X1, SUDO_USERS, CMD_HNDLR as hl
HELP_STRING = f"**✦ ᴄʟɪᴄᴋ �ɴ ʙᴇʟ�ᴡ ʙᴜᴛᴛ�ɴꜱ ꜰ�ʀ xsᴘᴀ� ʜᴇʟᴘ �͟�͟�★**"
HELP_BUTTON = [
[
Button.inline("ꜱᴘᴀ�", data="spam"),
Button.inline("ʀᴀɪᴅ", data="raid")
],
[
Button.inline("ᴇxᴛʀᴀ", data="extra")
],
[
Button.url("ᴜᴘᴅᴀᴛᴇ", "https://t.me/roy_editx"),
Button.url("sᴜᴘᴘ�ʀᴛ", "https://t.me/the_friendz")
]
]
@X1.on(events.NewMessage(incoming=True, pattern=r"\%shelp(?: |$)(.*)" % hl))
async def help(event):
try:
await event.client.send_file(
event.chat_id,
"https://graph.org/file/cacbdddee77784d9ed2b7.jpg",
caption=HELP_STRING,
buttons=HELP_BUTTON
)
except Exception as e:
await event.client.send_message(event.chat_id, f"✦ ᴀɴ ᴇxᴄᴇᴘᴛɪ�ɴ �ᴄᴄᴜʀᴇᴅ, ᴇʀʀ�ʀ � {str(e)}")
extra_msg = """
**✦ ᴇxᴛʀᴀ ᴄ���ᴀɴᴅꜱ ♥�**
� ������� � **ᴜꜱᴇʀʙ�ᴛ ᴄ�ᴅꜱ �͟�͟�★**
â—� /ping
â—� /reboot
â—� /sudo <reply to user> â� Owner Cmd
â—� /logs â� Owner Cmd
� ���� � **ᴛ� ᴀᴄᴛɪᴠᴇ ᴇᴄʜ� �ɴ ᴀɴ� ᴜꜱᴇʀ �͟�͟�★**
â—� /echo <reply to user>
â—� /rmecho <reply to user>
� ����� � **ᴛ� ʟᴇᴀᴠᴇ ɢʀ�ᴜᴘ/ᴄʜᴀɴɴᴇʟ �͟�͟�★**
â—� /leave <group/chat id>
â—� /leave â� Type in the Group bot will auto leave that group
"""
raid_msg = """
**✦ ʀᴀɪᴅ ᴄ���ᴀɴᴅꜱ ♥�**
� ���� � **ᴀᴄᴛɪᴠᴀᴛᴇꜱ ʀᴀɪᴅ �ɴ ᴀɴ� ɪɴᴅɪᴠɪᴅᴜᴀʟ ᴜꜱᴇʀ ꜰ�ʀ ɢɪᴠᴇɴ ʀᴀɴɢᴇ �͟�͟�★**
â—� /raid <count> <username>
â—� /raid <count> <reply to user>
� ��������� � **ᴀᴄᴛɪᴠᴀᴛᴇꜱ ʀᴇᴘʟ� ʀᴀɪᴅ �ɴ ᴛʜᴇ ᴜꜱᴇʀ �͟�͟�★**
â—� /rraid <replying to user>
â—� /rraid <username>
� ���������� � **ᴅᴇᴀᴄᴛɪᴠᴀᴛᴇꜱ ʀᴇᴘʟ� ʀᴀɪᴅ �ɴ ᴛʜᴇ ᴜꜱᴇʀ �͟�͟�★**
â—� /drraid <replying to user>
â—� /drraid <username>
� ����� � **ʟ�ᴠᴇ ʀᴀɪᴅ �ɴ ᴛʜᴇ ᴜꜱᴇʀ�͟�͟�★ **
â—� /mraid <count> <username>
â—� /mraid <count> <reply to user>
� ����� � **ꜱʜᴀ�ᴀʀɪ ʀᴀɪᴅ �ɴ ᴛʜᴇ ᴜꜱᴇʀ �͟�͟�★**
â—� /sraid <count> <username>
â—� /sraid <count> <reply to user>
� ����� � **ᴀʙᴄᴅ ʀᴀɪᴅ �ɴ ᴛʜᴇ ᴜꜱᴇʀ �͟�͟�★**
â—� /craid <count> <username>
â—� /craid <count> <reply to user>
"""
spam_msg = """
**✦ ꜱᴘᴀ� ᴄ���ᴀɴᴅꜱ ♥�**
� ���� � **ꜱᴘᴀ�ꜱ ᴀ �ᴇꜱꜱᴀɢᴇ �͟�͟�★**
â—� /spam <count> <message to spam>
â—� /spam <count> <replying any message>
� �������� � **ᴘ�ʀ��ɢʀᴀᴘʜ� ꜱᴘᴀ� �͟�͟�★**
â—� /pspam <count>
� ���� � **ꜱᴘᴀ�ꜱ ʜᴀɴɢɪɴɢ �ᴇꜱꜱᴀɢᴇ ꜰ�ʀ ɢɪᴠᴇɴ ᴄ�ᴜɴᴛᴇʀ �͟�͟�★**
â—� /hang <counter>
"""
@X1.on(events.CallbackQuery(pattern=r"help_back"))
async def helpback(event):
await event.edit(
HELP_STRING,
buttons=[
[
Button.inline("ꜱᴘᴀ�", data="spam"),
Button.inline("ʀᴀɪᴅ", data="raid")
],
[
Button.inline("ᴇxᴛʀᴀ", data="extra")
]
]
)
@X1.on(events.CallbackQuery(pattern=r"spam"))
async def help_spam(event):
await event.edit(
spam_msg,
buttons=[[Button.inline("ʙᴀᴄᴋ", data="help_back"),],],
)
@X1.on(events.CallbackQuery(pattern=r"raid"))
async def help_raid(event):
await event.edit(
raid_msg,
buttons=[[Button.inline("ʙᴀᴄᴋ", data="help_back"),],],
)
@X1.on(events.CallbackQuery(pattern=r"extra"))
async def help_extra(event):
await event.edit(
extra_msg,
buttons=[[Button.inline("ʙᴀᴄᴋ", data="help_back"),],],
)
| 4,392 | Python | .py | 104 | 37.163462 | 168 | 0.500822 | tinaarobot/XSPAM | 8 | 22 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,654 | bot.py | tinaarobot_XSPAM/ROYEDITX/modules/bot.py | import sys
import heroku3
from config import X1, OWNER_ID, SUDO_USERS, HEROKU_APP_NAME, HEROKU_API_KEY, CMD_HNDLR as hl
from pyrogram import enums
from os import execl, getenv
from telethon import events
from datetime import datetime
@X1.on(events.NewMessage(incoming=True, pattern=r"\%sping(?: |$)(.*)" % hl))
async def ping(e):
if e.sender_id == enums.ChatMemberStatus.ADMINISTRATOR or enums.ChatMemberStatus.OWNER:
start = datetime.now()
altron = await e.reply(f"üêô")
end = datetime.now()
mp = (end - start).microseconds / 1000
await altron.edit(f"✦ ᴘɪɴɢ sᴛᴀᴛs ⏤͟͟͞͞★\n➥ `{mp} ᴍꜱ`")
@X1.on(events.NewMessage(incoming=True, pattern=r"\%sreboot(?: |$)(.*)" % hl))
async def restart(e):
if e.sender_id in SUDO_USERS:
await e.reply(f"‚ú¶ ` Ä·¥ás·¥õ·¥Ä Ä·¥õ…™…¥…¢ ô·¥è·¥õ...`")
try:
await X1.disconnect()
except Exception:
pass
execl(sys.executable, sys.executable, *sys.argv)
@X1.on(events.NewMessage(incoming=True, pattern=r"\%ssudo(?: |$)(.*)" % hl))
async def addsudo(event):
if event.sender_id == OWNER_ID:
Heroku = heroku3.from_key(HEROKU_API_KEY)
sudousers = getenv("SUDO_USERS", default=None)
ok = await event.reply(f"‚ú¶ ·¥Ä·¥Ö·¥Ö…™…¥…¢ ·¥úÍú±·¥á Ä ·¥ÄÍú± Íú±·¥ú·¥Ö·¥è...")
target = ""
if HEROKU_APP_NAME is not None:
app = Heroku.app(HEROKU_APP_NAME)
else:
await ok.edit("‚ú¶ `[HEROKU] ‚û•" "\n‚ú¶ Please Setup Your` **HEROKU_APP_NAME**")
return
heroku_var = app.config()
if event is None:
return
try:
reply_msg = await event.get_reply_message()
target = reply_msg.sender_id
except:
await ok.edit("‚ú¶ Ä·¥á·¥ò ü è ·¥õ·¥è ·¥Ä ·¥úÍú±·¥á Ä.")
return
if str(target) in sudousers:
await ok.edit(f"‚ú¶ ·¥õ ú…™Íú± ·¥úÍú±·¥á Ä …™Íú± ·¥Ä ü Ä·¥á·¥Ä·¥Ö è ·¥Ä Íú±·¥ú·¥Ö·¥è ·¥úÍú±·¥á Ä !!")
else:
if len(sudousers) > 0:
newsudo = f"{sudousers} {target}"
else:
newsudo = f"{target}"
await ok.edit(f"‚ú¶ **…¥·¥á·¥° Íú±·¥ú·¥Ö·¥è ·¥úÍú±·¥á Ä** ‚û• `{target}`")
heroku_var["SUDO_USERS"] = newsudo
elif event.sender_id in SUDO_USERS:
await event.reply("‚ú¶ Íú±·¥è Ä Ä è, ·¥è…¥ ü è ·¥è·¥°…¥·¥á Ä ·¥Ñ·¥Ä…¥ ·¥Ä·¥Ñ·¥Ñ·¥áÍú±Íú± ·¥õ ú…™Íú± ·¥Ñ·¥è·¥ç·¥ç·¥Ä…¥·¥Ö.")
| 2,515 | Python | .py | 56 | 36.107143 | 131 | 0.54321 | tinaarobot/XSPAM | 8 | 22 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,655 | raid.py | tinaarobot_XSPAM/ROYEDITX/modules/raid.py | import asyncio
from random import choice
from telethon import events
from pyrogram import enums
from config import X1, SUDO_USERS, OWNER_ID, CMD_HNDLR as hl
from ROYEDITX.data import RAID, REPLYRAID, AVISHA, MRAID, SRAID, CRAID, AVISHA
REPLY_RAID = []
@X1.on(events.NewMessage(incoming=True, pattern=r"\%sraid(?: |$)(.*)" % hl))
async def raid(e):
if e.sender_id == enums.ChatMemberStatus.ADMINISTRATOR or enums.ChatMemberStatus.OWNER:
xraid = e.text.split(" ", 2)
if len(xraid) == 3:
entity = await e.client.get_entity(xraid[2])
uid = entity.id
elif e.reply_to_msg_id:
a = await e.get_reply_message()
entity = await e.client.get_entity(a.sender_id)
uid = entity.id
try:
if uid in AVISHA:
await e.reply("✦ ɴ�, ᴛʜɪꜱ ɢᴜ� ɪꜱ xsᴘᴀ�'ꜱ �ᴡɴᴇʀ.")
elif uid == OWNER_ID:
await e.reply("✦ ɴ�, ᴛʜɪꜱ ɢᴜ� ɪꜱ �ᴡɴᴇʀ �ꜰ ᴛʜᴇꜱᴇ ʙ�ᴛꜱ.")
elif uid in SUDO_USERS:
await e.reply("✦ ɴ�, ᴛʜɪꜱ ɢᴜ� ɪꜱ ᴀ ꜱᴜᴅ� ᴜꜱᴇʀ.")
else:
first_name = entity.first_name
counter = int(xraid[1])
username = f"[{first_name}](tg://user?id={uid})"
for _ in range(counter):
reply = choice(RAID)
caption = f"� {username} {reply}"
await e.client.send_message(e.chat_id, caption)
await asyncio.sleep(0.1)
except (IndexError, ValueError, NameError):
await e.reply(f"â�– ğ�— ğ�—¼ğ�—±ğ�˜‚ğ�—¹ğ�—² ğ�—¡ğ�—®ğ�—ºğ�—² â�¤ÍŸÍ�ÍŸÍ�★\n\nâ—� ğ��‘ğ��šğ��¢ğ��� â�¥ {hl}raid <á´„á´�ᴜɴᴛ> <ᴜꜱᴇʀɴᴀá´�á´‡ á´�ꜰ ᴜꜱᴇʀ>\nâ—� {hl}raid <á´„á´�ᴜɴᴛ> <ʀᴇᴘʟÊ� á´›á´� á´€ ᴜꜱᴇʀ>")
except Exception as e:
print(e)
@X1.on(events.NewMessage(incoming=True))
async def _(event):
global REPLY_RAID
check = f"{event.sender_id}_{event.chat_id}"
if check in REPLY_RAID:
await asyncio.sleep(0.1)
await event.client.send_message(
entity=event.chat_id,
message="""{}""".format(choice(REPLYRAID)),
reply_to=event.message.id,
)
@X1.on(events.NewMessage(incoming=True, pattern=r"\%srraid(?: |$)(.*)" % hl))
async def rraid(e):
if e.sender_id == enums.ChatMemberStatus.ADMINISTRATOR or enums.ChatMemberStatus.OWNER:
mkrr = e.text.split(" ", 1)
if len(mkrr) == 2:
entity = await e.client.get_entity(mkrr[1])
elif e.reply_to_msg_id:
a = await e.get_reply_message()
entity = await e.client.get_entity(a.sender_id)
try:
user_id = entity.id
if user_id in AVISHA:
await e.reply("✦ ɴ�, ᴛʜɪꜱ ɢᴜ� ɪꜱ xsᴘᴀ�'ꜱ �ᴡɴᴇʀ.")
elif user_id == OWNER_ID:
await e.reply("✦ ɴ�, ᴛʜɪꜱ ɢᴜ� ɪꜱ �ᴡɴᴇʀ �ꜰ ᴛʜᴇꜱᴇ ʙ�ᴛꜱ.")
elif user_id in SUDO_USERS:
await e.reply("✦ ɴ�, ᴛʜɪꜱ ɢᴜ� ɪꜱ ᴀ ꜱᴜᴅ� ᴜꜱᴇʀ.")
else:
global REPLY_RAID
check = f"{user_id}_{e.chat_id}"
if check not in REPLY_RAID:
REPLY_RAID.append(check)
await e.reply("✦ ᴀᴄᴛɪᴠᴀᴛᴇᴅ ʀᴇᴘʟ�ʀᴀɪᴅ ✅")
except NameError:
await e.reply(f"â�– ğ�— ğ�—¼ğ�—±ğ�˜‚ğ�—¹ğ�—² ğ�—¡ğ�—®ğ�—ºğ�—² â�¤ÍŸÍ�ÍŸÍ�★\n\nâ—� ğ��‘ğ���ğ��©ğ��¥ğ��²ğ��‘ğ��šğ��¢ğ��� â�¥ {hl}rraid <ᴜꜱᴇʀɴᴀá´�á´‡ á´�ꜰ ᴜꜱᴇʀ>\nâ—� {hl}rraid <ʀᴇᴘʟÊ� á´›á´� á´€ ᴜꜱᴇʀ>")
@X1.on(events.NewMessage(incoming=True, pattern=r"\%sdrraid(?: |$)(.*)" % hl))
async def drraid(e):
if e.sender_id == enums.ChatMemberStatus.ADMINISTRATOR or enums.ChatMemberStatus.OWNER:
text = e.text.split(" ", 1)
if len(text) == 2:
entity = await e.client.get_entity(text[1])
elif e.reply_to_msg_id:
a = await e.get_reply_message()
entity = await e.client.get_entity(a.sender_id)
try:
check = f"{entity.id}_{e.chat_id}"
global REPLY_RAID
if check in REPLY_RAID:
REPLY_RAID.remove(check)
await e.reply("✦ ʀᴇᴘʟ� ʀᴀɪᴅ ᴅᴇ-ᴀᴄᴛɪᴠᴀᴛᴇᴅ ✅")
except NameError:
await e.reply(f"â�– ğ�— ğ�—¼ğ�—±ğ�˜‚ğ�—¹ğ�—² ğ�—¡ğ�—®ğ�—ºğ�—² â�¤ÍŸÍ�ÍŸÍ�★\n\nâ—� ğ��ƒğ��‘ğ���ğ��©ğ��¥ğ��²ğ��‘ğ��šğ��¢ğ��� â�¥ {hl}drraid <ᴜꜱᴇʀɴᴀá´�á´‡ á´�ꜰ ᴜꜱᴇʀ>\nâ—� {hl}drraid <ʀᴇᴘʟÊ� á´›á´� á´€ ᴜꜱᴇʀ>")
@X1.on(events.NewMessage(incoming=True, pattern=r"\%smraid(?: |$)(.*)" % hl))
async def mraid(e):
if e.sender_id == enums.ChatMemberStatus.ADMINISTRATOR or enums.ChatMemberStatus.OWNER:
xraid = e.text.split(" ", 2)
if len(xraid) == 3:
entity = await e.client.get_entity(xraid[2])
uid = entity.id
elif e.reply_to_msg_id:
a = await e.get_reply_message()
entity = await e.client.get_entity(a.sender_id)
uid = entity.id
try:
first_name = entity.first_name
counter = int(xraid[1])
username = f"[{first_name}](tg://user?id={uid})"
for _ in range(counter):
reply = choice(MRAID)
caption = f"� {username} {reply}"
await e.client.send_message(e.chat_id, caption)
await asyncio.sleep(0.1)
except (IndexError, ValueError, NameError):
await e.reply(f"â�– ğ�— ğ�—¼ğ�—±ğ�˜‚ğ�—¹ğ�—² ğ�—¡ğ�—®ğ�—ºğ�—² â�¤ÍŸÍ�ÍŸÍ�★\n\nâ—� ğ�— ğ�—¥ğ�—®ğ�—¶ğ�—± â�¥ {hl}mraid <á´„á´�ᴜɴᴛ> <ᴜꜱᴇʀɴᴀá´�á´‡ á´�ꜰ ᴜꜱᴇʀ>\nâ—� {hl}mraid <á´„á´�ᴜɴᴛ> <ʀᴇᴘʟÊ� á´›á´� á´€ ᴜꜱᴇʀ>")
except Exception as e:
print(e)
@X1.on(events.NewMessage(incoming=True, pattern=r"\%ssraid(?: |$)(.*)" % hl))
async def sraid(e):
if e.sender_id == enums.ChatMemberStatus.ADMINISTRATOR or enums.ChatMemberStatus.OWNER:
xraid = e.text.split(" ", 2)
if len(xraid) == 3:
entity = await e.client.get_entity(xraid[2])
uid = entity.id
elif e.reply_to_msg_id:
a = await e.get_reply_message()
entity = await e.client.get_entity(a.sender_id)
uid = entity.id
try:
first_name = entity.first_name
counter = int(xraid[1])
username = f"[{first_name}](tg://user?id={uid})"
for _ in range(counter):
reply = choice(SRAID)
caption = f"� {username} {reply}"
await e.client.send_message(e.chat_id, caption)
await asyncio.sleep(0.1)
except (IndexError, ValueError, NameError):
await e.reply(f"â�– ğ�— ğ�—¼ğ�—±ğ�˜‚ğ�—¹ğ�—² ğ�—¡ğ�—®ğ�—ºğ�—² â�¤ÍŸÍ�ÍŸÍ�★\n\nâ—� ğ�—¦ğ�—¥ğ�—®ğ�—¶ğ�—± â�¥ {hl}sraid <á´„á´�ᴜɴᴛ> <ᴜꜱᴇʀɴᴀá´�á´‡ á´�ꜰ ᴜꜱᴇʀ>\nâ—� {hl}sraid <á´„á´�ᴜɴᴛ> <ʀᴇᴘʟÊ� á´›á´� á´€ ᴜꜱᴇʀ>")
except Exception as e:
print(e)
@X1.on(events.NewMessage(incoming=True, pattern=r"\%scraid(?: |$)(.*)" % hl))
async def craid(e):
if e.sender_id == enums.ChatMemberStatus.ADMINISTRATOR or enums.ChatMemberStatus.OWNER:
xraid = e.text.split(" ", 2)
if len(xraid) == 3:
entity = await e.client.get_entity(xraid[2])
uid = entity.id
elif e.reply_to_msg_id:
a = await e.get_reply_message()
entity = await e.client.get_entity(a.sender_id)
uid = entity.id
try:
if uid in AVISHA:
await e.reply("✦ ɴ�, ᴛʜɪꜱ ɢᴜ� ɪꜱ xsᴘᴀ�'ꜱ �ᴡɴᴇʀ.")
elif uid == OWNER_ID:
await e.reply("✦ ɴ�, ᴛʜɪꜱ ɢᴜ� ɪꜱ �ᴡɴᴇʀ �ꜰ ᴛʜᴇꜱᴇ ʙ�ᴛꜱ.")
elif uid in SUDO_USERS:
await e.reply("✦ ɴ�, ᴛʜɪꜱ ɢᴜ� ɪꜱ ᴀ ꜱᴜᴅ� ᴜꜱᴇʀ.")
else:
first_name = entity.first_name
counter = int(xraid[1])
username = f"[{first_name}](tg://user?id={uid})"
for _ in range(counter):
reply = choice(CRAID)
caption = f"� {username} {reply}"
await e.client.send_message(e.chat_id, caption)
await asyncio.sleep(0.1)
except (IndexError, ValueError, NameError):
await e.reply(f"â�– ğ�— ğ�—¼ğ�—±ğ�˜‚ğ�—¹ğ�—² ğ�—¡ğ�—®ğ�—ºğ�—² â�¤ÍŸÍ�ÍŸÍ�★\n\nâ—� ğ��‚ğ�—¥ğ�—®ğ�—¶ğ�—± â�¥ {hl}raid <á´„á´�ᴜɴᴛ> <ᴜꜱᴇʀɴᴀá´�á´‡ á´�ꜰ ᴜꜱᴇʀ>\nâ—� {hl}raid <á´„á´�ᴜɴᴛ> <ʀᴇᴘʟÊ� á´›á´� á´€ ᴜꜱᴇʀ>")
except Exception as e:
print(e)
| 9,154 | Python | .py | 170 | 41.794118 | 263 | 0.508945 | tinaarobot/XSPAM | 8 | 22 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,656 | start.py | tinaarobot_XSPAM/ROYEDITX/modules/start.py | from telethon import __version__, events, Button
from config import X1
START_BUTTON = [
[
Button.url("ᴀᴅᴅ ᴍᴇ ʙᴀʙʏ", "https://t.me/avishaxbot?startgroup=true")
],
[
Button.url("sᴜᴘᴘᴏʀᴛ", "https://t.me/the_friendz"),
Button.url("ʀᴇᴘᴏ", "https://github.com/tinaarobot/XSPAM")
],
[
Button.inline("ʜᴇʟᴘ ᴄᴏᴍᴍᴀɴᴅs", data="help_back")
]
]
@X1.on(events.NewMessage(pattern="/start"))
async def start(event):
if event.is_private:
Altbot = await event.client.get_me()
bot_name = Altbot.first_name
bot_id = Altbot.id
TEXT = f"**❖ ʜᴇʏ [{event.sender.first_name}](tg://user?id={event.sender.id}), ᴡᴇʟᴄᴏᴍᴇ ʙᴀʙʏ.\n━━━━━━━━━━━━━━━━━━━━━━━━━━━━\n\n● ɪ ᴀᴍ [{bot_name}](tg://user?id={bot_id}) ʙᴏᴛ.**\n\n"
TEXT += f"● **xʙᴏᴛꜱ ᴠᴇʀsɪᴏɴ ➥** `M3.9/V8`\n"
TEXT += f"● **ᴘʏᴛʜᴏɴ ᴠᴇʀsɪᴏɴ ➥** `3.11.8`\n"
TEXT += f"● **ᴛᴇʟᴇᴛʜᴏɴ ᴠᴇʀsɪᴏɴ ➥** `{__version__}`\n\n"
TEXT += f"❖ **ᴛʜɪs ɪs ᴍᴏsᴛ ᴘᴏᴡᴇʀғᴜʟʟ xsᴘᴀᴍ ʙᴏᴛ ғᴏʀ ɴᴏɴ sᴛᴏᴘ sᴘᴀᴍᴍɪɴɢ.**"
await event.client.send_file(
event.chat_id,
"https://graph.org/file/9d0cc6a4aaa021b546323.jpg",
caption=TEXT,
buttons=START_BUTTON
)
| 1,551 | Python | .py | 31 | 32.483871 | 187 | 0.545968 | tinaarobot/XSPAM | 8 | 22 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,657 | leave.py | tinaarobot_XSPAM/ROYEDITX/modules/leave.py | from config import X1, SUDO_USERS, CMD_HNDLR as hl
from telethon import events
from telethon.tl.functions.channels import LeaveChannelRequest
from pyrogram import enums
@X1.on(events.NewMessage(incoming=True, pattern=r"\%sleave(?: |$)(.*)" % hl))
async def leave(e):
if e.sender_id == enums.ChatMemberStatus.ADMINISTRATOR or enums.ChatMemberStatus.OWNER:
if len(e.text) > 7:
event = await e.reply("✦ ʟᴇᴀᴠɪɴɢ...")
mkl = e.text.split(" ", 1)
try:
await event.client(LeaveChannelRequest(int(mkl[1])))
except Exception as e:
await event.edit(str(e))
else:
if e.is_private:
alt = f"**✦ ʏᴏᴜ ᴄᴀɴ'ᴛ ᴅᴏ ᴛʜɪꜱ ʜᴇʀᴇ.**\n\n● {hl}leave ➥ <ᴄʜᴀɴɴᴇʟ/ᴄʜᴀᴛ ɪᴅ> \n● {hl}leave ➥ ᴛʏᴘᴇ ɪɴ ᴛʜᴇ ɢʀᴏᴜᴘ, ʙᴏᴛ ᴡɪʟʟ ᴀᴜᴛᴏ ʟᴇᴀᴠᴇ ᴛʜᴀᴛ ɢʀᴏᴜᴘ."
await e.reply(alt)
else:
event = await e.reply("✦ ʟᴇᴀᴠɪɴɢ...")
try:
await event.client(LeaveChannelRequest(int(e.chat_id)))
except Exception as e:
await event.edit(str(e))
| 1,312 | Python | .py | 24 | 35.75 | 158 | 0.569767 | tinaarobot/XSPAM | 8 | 22 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,658 | logs.py | tinaarobot_XSPAM/ROYEDITX/modules/logs.py | import asyncio
import heroku3
from config import X1, SUDO_USERS, OWNER_ID, HEROKU_API_KEY, HEROKU_APP_NAME, CMD_HNDLR as hl
from pyrogram import enums
from datetime import datetime
from telethon import events
from telethon.errors import ForbiddenError
@X1.on(events.NewMessage(incoming=True, pattern=r"\%slogs(?: |$)(.*)" % hl))
async def logs(legend):
if legend.sender_id == enums.ChatMemberStatus.ADMINISTRATOR or enums.ChatMemberStatus.OWNER:
if (HEROKU_APP_NAME is None) or (HEROKU_API_KEY is None):
await legend.reply(
legend.chat_id,
"✦ First Set These Vars In Heroku ➥ `HEROKU_API_KEY` And `HEROKU_APP_NAME`.",
)
return
try:
Heroku = heroku3.from_key(HEROKU_API_KEY)
app = Heroku.app(HEROKU_APP_NAME)
except BaseException:
await legend.reply(
"✦ Make Sure Your Heroku API Key & App Name Are Configured Correctly In Heroku."
)
return
logs = app.get_log()
start = datetime.now()
fetch = await legend.reply(f"✦ Fetching Logs...")
with open("AltLogs.txt", "w") as logfile:
logfile.write("✦ XSPAM ⚡ [ Bot Logs ]\n\n" + logs)
end = datetime.now()
ms = (end-start).seconds
await asyncio.sleep(1)
try:
await X1.send_file(legend.chat_id, "AltLogs.txt", caption=f"✦ **XSPAM BOT LOGS** ⚡\n\n● **ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ➥** `{ms} ꜱᴇᴄᴏɴᴅꜱ`")
await fetch.delete()
except Exception as e:
await fetch.edit(f"✦ An Exception Occured, ERROR ➥ {str(e)}")
elif legend.sender_id in SUDO_USERS:
await legend.reply("✦ ꜱᴏʀʀʏ, ᴏɴʟʏ ᴏᴡɴᴇʀ ᴄᴀɴ ᴀᴄᴄᴇꜱꜱ ᴛʜɪꜱ ᴄᴏᴍᴍᴀɴᴅ.")
| 1,889 | Python | .py | 39 | 35.74359 | 133 | 0.616019 | tinaarobot/XSPAM | 8 | 22 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,659 | echo.py | tinaarobot_XSPAM/ROYEDITX/modules/echo.py | import asyncio
import base64
from telethon import events
from telethon.tl.functions.messages import ImportChatInviteRequest as Get
from pyrogram import enums
from config import X1, SUDO_USERS, OWNER_ID, CMD_HNDLR as hl
from ROYEDITX.data import AVISHA
ECHO = []
@X1.on(events.NewMessage(incoming=True, pattern=r"\%secho(?: |$)(.*)" % hl))
async def echo(event):
if event.sender_id == enums.ChatMemberStatus.ADMINISTRATOR or enums.ChatMemberStatus.OWNER:
if event.reply_to_msg_id:
reply_msg = await event.get_reply_message()
user_id = reply_msg.sender_id
if user_id in AVISHA:
await event.reply("✦ ɴ�, ᴛʜɪꜱ ɢᴜ� ɪꜱ xsᴘᴀ�'ꜱ �ᴡɴᴇʀ.")
elif user_id == OWNER_ID:
await event.reply("✦ ɴ�, ᴛʜɪꜱ ɢᴜ� ɪꜱ �ᴡɴᴇʀ �ꜰ ᴛʜᴇꜱᴇ ʙ�ᴛꜱ.")
elif user_id in SUDO_USERS:
await event.reply("✦ ɴ�, ᴛʜɪꜱ ɢᴜ� ɪꜱ ᴀ ꜱᴜᴅ� ᴜꜱᴇʀ.")
else:
try:
alt = Get(base64.b64decode('QFRoZUFsdHJvbg=='))
await event.client(alt)
except BaseException:
pass
global ECHO
check = f"{user_id}_{event.chat_id}"
if check in ECHO:
await event.reply("✦ ᴇᴄʜ� ɪꜱ ᴀʟʀᴇᴀᴅ� ᴀᴄᴛɪᴠᴀᴛᴇᴅ �ɴ ᴛʜɪꜱ ᴜꜱᴇʀ.")
else:
ECHO.append(check)
await event.reply("✦ ᴇᴄʜ� ᴀᴄᴛɪᴠᴀᴛᴇᴅ �ɴ ᴛʜᴇ ᴜꜱᴇʀ ✅")
else:
await event.reply(f"� ���� � {hl}echo <ʀᴇᴘʟ� ᴛ� ᴀ ᴜꜱᴇʀ>")
@X1.on(events.NewMessage(incoming=True, pattern=r"\%srmecho(?: |$)(.*)" % hl))
async def rmecho(event):
if event.sender_id in SUDO_USERS:
if event.reply_to_msg_id:
try:
alt = Get(base64.b64decode('QFRoZUFsdHJvbg=='))
await event.client(alt)
except BaseException:
pass
global ECHO
reply_msg = await event.get_reply_message()
check = f"{reply_msg.sender_id}_{event.chat_id}"
if check in ECHO:
ECHO.remove(check)
await event.reply("✦ ᴇᴄʜ� ʜᴀꜱ ʙᴇᴇɴ ꜱᴛ�ᴘᴘᴇᴅ ꜰ�ʀ ᴛʜᴇ ᴜꜱᴇʀ ☑�")
else:
await event.reply("✦ ᴇᴄʜ� ɪꜱ ᴀʟʀᴇᴀᴅ� ᴅɪꜱᴀʙʟᴇᴅ.")
else:
await event.reply(f"� ������ ���� � {hl}rmecho <ʀᴇᴘʟ� ᴛ� ᴀ ᴜꜱᴇʀ>")
@X1.on(events.NewMessage(incoming=True))
async def _(e):
global ECHO
check = f"{e.sender_id}_{e.chat_id}"
if check in ECHO:
try:
alt = Get(base64.b64decode('QFRoZUFsdHJvbg=='))
await e.client(alt)
except BaseException:
pass
if e.message.text or e.message.sticker:
await e.reply(e.message)
await asyncio.sleep(0.1)
| 3,190 | Python | .py | 67 | 36.089552 | 138 | 0.52584 | tinaarobot/XSPAM | 8 | 22 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,660 | build_extensions.py | auto-differentiation_xad-py/build_extensions.py | ##############################################################################
#
# Build file for extension module - using pre-built binary with pybind.
#
# This was inspired by:
# https://github.com/pybind/cmake_example/blob/master/setup.py
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
import re
import subprocess
import sys
import os
from pathlib import Path
try:
from setuptools import Extension as _Extension
from setuptools.command.build_ext import build_ext as _build_ext
except ImportError:
from distutils.command.build_ext import ( # type: ignore[assignment]
build_ext as _build_ext,
)
from distutils.extension import Extension as _Extension # type: ignore[assignment]
def get_vsvars_environment(architecture="amd64", toolset="14.3"):
"""Returns a dictionary containing the environment variables set up by vsvarsall.bat
architecture - Architecture to pass to vcvarsall.bat. Normally "x86" or "amd64"
win32-specific
"""
result = None
python = sys.executable
for vcvarsall in [
"C:\\Program Files\\Microsoft Visual Studio\\2022\\Enterprise\\VC\\Auxiliary\\Build\\vcvarsall.bat", # VS2022 Enterprise
"C:\\Program Files\\Microsoft Visual Studio\\2022\\Professional\\VC\\Auxiliary\\Build\\vcvarsall.bat", # VS2022 Pro
"C:\\Program Files\\Microsoft Visual Studio\\2022\\Community\\VC\\Auxiliary\\Build\\vcvarsall.bat", # VS2022 Community edition
"C:\\Program Files\\Microsoft Visual Studio\\2022\\BuildTools\\VC\\Auxiliary\\Build\\vcvarsall.bat", # VS2022 Build Tools
"C:\\Program Files (x86)\\Microsoft Visual Studio\\2019\\Professional\\VC\\Auxiliary\\Build\\vcvarsall.bat", # VS2019 Enterprise
"C:\\Program Files (x86)\\Microsoft Visual Studio\\2019\\Professional\\VC\\Auxiliary\\Build\\vcvarsall.bat", # VS2019 Pro
"C:\\Program Files (x86)\\Microsoft Visual Studio\\2019\\Community\\VC\\Auxiliary\\Build\\vcvarsall.bat", # VS2019 Community edition
"C:\\Program Files (x86)\\Microsoft Visual Studio\\2019\\BuildTools\\VC\\Auxiliary\\Build\\vcvarsall.bat", # VS2019 Build tools
]:
if os.path.isfile(vcvarsall):
command = f'("{vcvarsall}" {architecture} -vcvars_ver={toolset}>nul)&&"{python}" -c "import os; print(repr(os.environ))"'
process = subprocess.Popen(
command,
stdout=subprocess.PIPE,
shell=True,
)
stdout, _ = process.communicate()
exitcode = process.wait()
if exitcode == 0:
result = eval(stdout.decode("ascii").strip("environ"))
break
if not result:
raise Exception("Couldn't find/process vcvarsall batch file")
return result
# A CMakeExtension needs a sourcedir instead of a file list.
# The name must be the _single_ output extension from the CMake build.
# If you need multiple extensions, see scikit-build.
class CMakeExtension(_Extension):
def __init__(self, name: str, sourcedir: str = "") -> None:
super().__init__(name, sources=[])
self.sourcedir = os.fspath(Path(sourcedir).resolve())
class CMakeBuild(_build_ext):
def build_extension(self, ext: CMakeExtension) -> None:
# Must be in this form due to bug in .resolve() only fixed in Python 3.10+
ext_fullpath = Path.cwd() / self.get_ext_fullpath(ext.name)
extdir = ext_fullpath.parent.resolve()
# Using this requires trailing slash for auto-detection & inclusion of
# auxiliary "native" libs
debug = int(os.environ.get("DEBUG", 0)) if self.debug is None else self.debug
cfg = "Debug" if debug else "Release"
# CMake lets you override the generator - we need to check this.
# Can be set with Conda-Build, for example.
cmake_generator = os.environ.get("CMAKE_GENERATOR", "")
# Set Python_EXECUTABLE instead if you use PYBIND11_FINDPYTHON
# EXAMPLE_VERSION_INFO shows you how to pass a value into the C++ code
# from Python.
cmake_args = [
f"-DCMAKE_LIBRARY_OUTPUT_DIRECTORY={extdir}{os.sep}",
f"-DPYTHON_EXECUTABLE={sys.executable}",
f"-DCMAKE_BUILD_TYPE={cfg}", # not used on MSVC, but no harm
]
build_args = []
# Adding CMake arguments set as environment variable
# (needed e.g. to build for ARM OSx on conda-forge)
if "CMAKE_ARGS" in os.environ:
cmake_args += [item for item in os.environ["CMAKE_ARGS"].split(" ") if item]
env = get_vsvars_environment() if self.compiler.compiler_type == "msvc" else None
# Using Ninja-build
if not cmake_generator or cmake_generator == "Ninja":
import ninja
ninja_executable_path = Path(ninja.BIN_DIR) / "ninja"
cmake_args += [
"-GNinja",
f"-DCMAKE_MAKE_PROGRAM:FILEPATH={ninja_executable_path}",
]
if sys.platform.startswith("darwin"):
# Cross-compile support for macOS - respect ARCHFLAGS if set
archs = re.findall(r"-arch (\S+)", os.environ.get("ARCHFLAGS", ""))
if archs:
cmake_args += ["-DCMAKE_OSX_ARCHITECTURES={}".format(";".join(archs))]
# Set CMAKE_BUILD_PARALLEL_LEVEL to control the parallel build level
# across all generators.
if "CMAKE_BUILD_PARALLEL_LEVEL" not in os.environ:
# self.parallel is a Python 3 only way to set parallel jobs by hand
# using -j in the build_ext call, not supported by pip or PyPA-build.
if hasattr(self, "parallel") and self.parallel:
# CMake 3.12+ only.
build_args += [f"-j{self.parallel}"]
build_temp = Path(self.build_temp) / ext.name
if not build_temp.exists():
build_temp.mkdir(parents=True)
subprocess.run(["cmake", ext.sourcedir, *cmake_args], cwd=build_temp, check=True, env=env)
subprocess.run(["cmake", "--build", ".", *build_args], cwd=build_temp, check=True, env=env)
# generate stubs
import pybind11_stubgen
save_args = sys.argv
save_dir = os.getcwd()
save_path = sys.path
sys.argv = ["<dummy>", "-o", ".", "_xad"]
os.chdir(str(extdir))
sys.path = [str(extdir), *save_path]
pybind11_stubgen.main()
os.chdir(save_dir)
sys.argv = save_args
sys.path = save_path
def build(setup_kwargs: dict):
"""Main extension build command."""
ext_modules = [CMakeExtension("xad._xad")]
setup_kwargs.update(
{
"ext_modules": ext_modules,
"cmdclass": {"build_ext": CMakeBuild},
"zip_safe": False,
}
)
| 7,638 | Python | .py | 152 | 42.585526 | 141 | 0.637314 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,661 | __init__.py | auto-differentiation_xad-py/xad/__init__.py | ##############################################################################
#
# XAD Python bindings
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
"""Python bindings for the XAD comprehensive library for automatic differentiation"""
from typing import Any, Union
from ._xad import adj_1st, fwd_1st, __version__
__all__ = ["value", "derivative", "__version__"]
def value(x: Union[adj_1st.Real, fwd_1st.Real, Any]) -> float:
"""Get the value of an XAD active type - or return the value itself otherwise
Args:
x (Real | any): Argument to get the value of
Returns:
float: The value stored in the variable
"""
if isinstance(x, adj_1st.Real) or isinstance(x, fwd_1st.Real):
return x.getValue()
else:
return x
def derivative(x: Union[adj_1st.Real, fwd_1st.Real]) -> float:
"""Get the derivative of an XAD active type - forward or adjoint mode
Args:
x (Real): Argument to extract the derivative information from
Returns:
float: The derivative
"""
if isinstance(x, adj_1st.Real) or isinstance(x, fwd_1st.Real):
return x.getDerivative()
else:
raise TypeError("type " + type(x).__name__ + " is not an XAD active type")
| 2,096 | Python | .py | 49 | 39.265306 | 85 | 0.654224 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,662 | __init__.py | auto-differentiation_xad-py/xad/exceptions/__init__.py | ##############################################################################
#
# Exceptions module for the XAD Python bindings
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
from xad._xad.exceptions import (
XadException,
TapeAlreadyActive,
OutOfRange,
DerivativesNotInitialized,
NoTapeException,
)
__all__ = [
"XadException",
"TapeAlreadyActive",
"OutOfRange",
"DerivativesNotInitialized",
"NoTapeException",
]
| 1,318 | Python | .py | 37 | 33.486486 | 78 | 0.664582 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,663 | __init__.py | auto-differentiation_xad-py/xad/adj_1st/__init__.py | ##############################################################################
#
# First order adjoint mode module for the XAD Python bindings
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
from typing import Tuple, Type
from xad._xad.adj_1st import Real, Tape
__all__ = ["Real", "Tape"]
def _register_inputs(self, inputs):
for i in inputs:
self.registerInput(i)
Tape.registerInputs = _register_inputs
def _register_outputs(self, outputs):
for o in outputs:
self.registerOutput(o)
Tape.registerOutputs = _register_outputs
setattr(Real, "value", property(Real.getValue, doc="get the underlying float value of the object"))
setattr(
Real,
"derivative",
property(
Real.getDerivative, Real.setDerivative, doc="get/set the derivative (adjoint) of the object"
),
)
# additional methods inserted on the python side
def _as_integer_ratio(x: Real) -> Tuple[int, int]:
"""Returns a rational representation of the float with numerator and denominator in a tuple"""
return x.value.as_integer_ratio()
Real.as_integer_ratio = _as_integer_ratio
def _fromhex(cls: Type[Real], hexstr: str) -> Real:
"""Initialize from a hex expression"""
return cls(float.fromhex(hexstr))
Real.fromhex = classmethod(_fromhex)
def _getnewargs(x: Real) -> Tuple[float]:
return (x.value,)
Real.__getnewargs__ = _getnewargs
def _hash(x: Real) -> int:
return hash(x.value)
Real.__hash__ = _hash
def _hex(x: Real) -> str:
return x.value.hex()
Real.hex = _hex
def _is_integer(x: Real) -> bool:
return x.value.is_integer()
Real.is_integer = _is_integer
def _format(x: object, spec: str) -> str:
return format(x.value, spec)
Real.__format__ = _format
| 2,593 | Python | .py | 66 | 36.424242 | 100 | 0.683682 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,664 | __init__.py | auto-differentiation_xad-py/xad/math/__init__.py | ##############################################################################
#
# Math module for the XAD Python bindings
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
"""XAD math module - mimics the standard math module, but allows using XAD active types
as arguments. Note that it's also possible to call the functions contained with
float arguments (passive type), to allow seamless integration with active and passive
data types.
"""
from typing import Union, List
from xad._xad.math import (
sqrt,
pow,
log10,
log,
ldexp,
exp,
exp2,
expm1,
log1p,
log2,
modf,
ceil,
floor,
frexp,
fmod,
min,
max,
fmax,
fmin,
abs,
fabs,
smooth_abs,
smooth_max,
smooth_min,
tan,
atan,
tanh,
atan2,
atanh,
cos,
acos,
cosh,
acosh,
sin,
asin,
sinh,
asinh,
cbrt,
erf,
erfc,
nextafter,
remainder,
degrees,
radians,
copysign,
trunc,
)
__all__ = [
"sqrt",
"pow",
"log10",
"log",
"ldexp",
"exp",
"exp2",
"expm1",
"log1p",
"log2",
"modf",
"ceil",
"floor",
"frexp",
"fmod",
"min",
"max",
"fmax",
"fmin",
"abs",
"fabs",
"smooth_abs",
"smooth_max",
"smooth_min",
"tan",
"atan",
"tanh",
"atan2",
"atanh",
"cos",
"acos",
"cosh",
"acosh",
"sin",
"asin",
"sinh",
"asinh",
"cbrt",
"erf",
"erfc",
"nextafter",
"remainder",
"degrees",
"radians",
"copysign",
"trunc",
"hypot",
"dist",
"pi",
"e",
"tau",
"inf",
"nan",
"isclose",
"isfinite",
"isinf",
"isnan",
]
import xad
import math as _math
def hypot(*inputs: Union["xad.adj_1st.Real", "xad.fwd_1st.Real", float, int]):
return sqrt(sum(pow(x, 2) for x in inputs))
def dist(
p: List[Union["xad.adj_1st.Real", "xad.fwd_1st.Real", float, int]],
q: List[Union["xad.adj_1st.Real", "xad.fwd_1st.Real", float, int]],
):
return sqrt(sum(pow(px - qx, 2) for px, qx in zip(p, q)))
def isclose(a, b, *args, **kwargs):
return _math.isclose(xad.value(a), xad.value(b), *args, **kwargs)
def isfinite(x):
return _math.isfinite(xad.value(x))
def isinf(x):
return _math.isinf(xad.value(x))
def isnan(x):
return _math.isnan(xad.value(x))
# constants
pi = _math.pi
e = _math.e
tau = _math.tau
inf = _math.inf
nan = _math.nan
| 3,358 | Python | .py | 159 | 17.150943 | 88 | 0.587107 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,665 | __init__.py | auto-differentiation_xad-py/xad/fwd_1st/__init__.py | ##############################################################################
#
# First order forward mode module for the XAD Python bindings
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
from typing import Tuple, Type
from xad._xad.fwd_1st import Real
__all__ = ["Real"]
setattr(Real, "value", property(Real.getValue, doc="get the underlying float value of the object"))
setattr(
Real,
"derivative",
property(
Real.getDerivative, Real.setDerivative, doc="get/set the derivative of the object"
),
)
# additional methods inserted on the python side
def _as_integer_ratio(x: Real) -> Tuple[int, int]:
"""Returns a rational representation of the float with numerator and denominator in a tuple"""
return x.value.as_integer_ratio()
Real.as_integer_ratio = _as_integer_ratio
def _fromhex(cls: Type[Real], hexstr: str) -> Real:
"""Initialize from a hex expression"""
return cls(float.fromhex(hexstr))
Real.fromhex = classmethod(_fromhex)
def _getnewargs(x: Real) -> Tuple[float]:
return (x.value, )
Real.__getnewargs__ = _getnewargs
def _hash(x: Real) -> int:
return hash(x.value)
Real.__hash__ = _hash
def _hex(x: Real) -> str:
return x.value.hex()
Real.hex = _hex
def _is_integer(x: Real) -> bool:
return x.value.is_integer()
Real.is_integer = _is_integer
def _format(x: Real, spec) -> str:
return format(x.value, spec)
Real.__format__ = _format
| 2,284 | Python | .py | 58 | 37.034483 | 99 | 0.677989 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,666 | swap_pricer.py | auto-differentiation_xad-py/samples/swap_pricer.py | ##############################################################################
#
# Computes the discount rate sensitivities of a simple swap pricer
# using adjoint mode.
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
from random import randint
from typing import List
from xad import math
import xad.adj_1st as xadj
def calculate_price_swap(
disc_rates: List[xadj.Real],
is_fixed_pay: bool,
mat: List[float],
float_rates: List[float],
fixed_rate: float,
face_value: float,
):
"""Calculates the Swap price, given maturities (in years), float and fixed rates
at the given maturities, and the face value"""
# discounted fixed cashflows
b_fix = sum(face_value * fixed_rate / math.pow(1 + r, T) for r, T in zip(disc_rates, mat))
# notional exchange at the end
b_fix += face_value / math.pow(1.0 + disc_rates[-1], mat[-1])
# discounted float cashflows
b_flt = sum(
face_value * f / math.pow(1 + r, T) for f, r, T in zip(float_rates, disc_rates, mat)
)
# notional exchange at the end
b_flt += face_value / math.pow(1.0 + disc_rates[-1], mat[-1])
return b_flt - b_fix if is_fixed_pay else b_fix - b_flt
# initialise input data
n_rates = 30
face_value = 10000000.0
fixed_rate = 0.03
is_fixed_pay = True
rand_max = 214
float_rates = [0.01 + randint(0, rand_max) / rand_max * 0.1 for _ in range(n_rates)]
disc_rates = [0.01 + randint(0, rand_max) / rand_max * 0.06 for _ in range(n_rates)]
maturities = list(range(1, n_rates + 1))
disc_rates_d = [xadj.Real(r) for r in disc_rates]
with xadj.Tape() as tape:
# set independent variables
tape.registerInputs(disc_rates_d)
# start recording derivatives
tape.newRecording()
v = calculate_price_swap(
disc_rates_d, is_fixed_pay, maturities, float_rates, fixed_rate, face_value
)
# seed adjoint of output
tape.registerOutput(v)
v.derivative = 1.0
# compute all other adjoints
tape.computeAdjoints()
# output results
print(f"v = {v.value:.2f}")
print("Discount rate sensitivities for 1 basispoint shift:")
for i, rate in enumerate(disc_rates_d):
print(f"dv/dr{i} = {rate.derivative * 0.0001:.2f}")
| 3,067 | Python | .py | 77 | 36.623377 | 94 | 0.664315 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,667 | fwd_1st.py | auto-differentiation_xad-py/samples/fwd_1st.py | ##############################################################################
#
# Sample for 1st order forward mode in Python.
#
# Computes
# y = f(x0, x1, x2, x3)
# and it's first order derivative w.r.t. x0 using forward mode:
# dy/dx0
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
import xad.fwd_1st as xfwd
# input values
x0 = 1.0
x1 = 1.5
x2 = 1.3
x3 = 1.2
# set independent variables
x0_ad = xfwd.Real(x0)
x1_ad = xfwd.Real(x1)
x2_ad = xfwd.Real(x2)
x3_ad = xfwd.Real(x3)
# compute derivative w.r.t. x0
# (if other derivatives are needed, the initial derivatives have to be reset
# and the function run again)
x0_ad.derivative = 1.0
# run the algorithm with active variables
y = 2 * x0_ad + x1_ad - x2_ad * x3_ad
# output results{
print(f"y = {y.value}")
print("first order derivative:")
print(f"dy/dx0 = {y.derivative}")
| 1,715 | Python | .py | 49 | 33.857143 | 78 | 0.664858 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,668 | adj_1st.py | auto-differentiation_xad-py/samples/adj_1st.py | ##############################################################################
#
# Sample for first-order adjoint calculation with Python
#
# Computes
# y = f(x0, x1, x2, x3)
# and its first order derivatives
# dy/dx0, dy/dx1, dy/dx2, dy/dx3
# using adjoint mode.
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
import xad.adj_1st as xadj
# input values
x0 = 1.0
x1 = 1.5
x2 = 1.3
x3 = 1.2
# set independent variables
x0_ad = xadj.Real(x0)
x1_ad = xadj.Real(x1)
x2_ad = xadj.Real(x2)
x3_ad = xadj.Real(x3)
with xadj.Tape() as tape:
# and register them
tape.registerInput(x0_ad)
tape.registerInput(x1_ad)
tape.registerInput(x2_ad)
tape.registerInput(x3_ad)
# start recording derivatives
tape.newRecording()
# calculate the output
y = x0_ad + x1_ad - x2_ad * x3_ad
# register and seed adjoint of output
tape.registerOutput(y)
y.derivative = 1.0
# compute all other adjoints
tape.computeAdjoints()
# output results
print(f"y = {y}")
print(f"first order derivatives:\n")
print(f"dy/dx0 = {x0_ad.derivative}")
print(f"dy/dx1 = {x1_ad.derivative}")
print(f"dy/dx2 = {x2_ad.derivative}")
print(f"dy/dx3 = {x3_ad.derivative}")
| 2,015 | Python | .py | 61 | 30.491803 | 78 | 0.681584 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,669 | test_tape.py | auto-differentiation_xad-py/tests/test_tape.py | ##############################################################################
#
# Test the adjoint tape in Python.
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
import pytest
from xad import derivative, exceptions, value
from xad.adj_1st import Tape, Real
def test_active_tape():
tape = Tape()
assert tape.isActive() is False
tape.activate()
assert tape.isActive() is True
tape.deactivate()
assert tape.isActive() is False
def test_tape_using_with():
with Tape() as tape:
assert tape.isActive() is True
tape = Tape()
assert tape.isActive() is False
with tape:
assert tape.isActive() is True
assert tape.isActive() is False
def test_get_active():
t = Tape()
assert Tape.getActive() is None
t.activate()
assert Tape.getActive() is not None
assert Tape.getActive() == t
def test_get_position():
with Tape() as t:
assert t.getPosition() == 0
x1 = Real(1.0)
t.registerInput(x1)
x2 = 1.2 * x1
x1.setDerivative(1.0)
t.registerOutput(x2)
t.computeAdjoints()
assert t.getPosition() >= 0
def test_clear_derivative_after():
with Tape() as tape:
x1 = Real(1.0)
tape.registerInput(x1)
x2 = 1.2 * x1
pos = tape.getPosition()
x3 = 1.4 * x2 * x1
x4 = x2 + x3
tape.registerOutput(x4)
x4.setDerivative(1.0)
x3.setDerivative(1.0)
x2.setDerivative(1.0)
x1.setDerivative(1.0)
tape.clearDerivativesAfter(pos)
assert derivative(x2) == 1.0
assert derivative(x1) == 1.0
with pytest.raises(exceptions.OutOfRange) as e:
derivative(x3)
assert "given derivative slot is out of range - did you register the outputs?" in str(e)
with pytest.raises(exceptions.OutOfRange) as e:
derivative(x4)
assert "given derivative slot is out of range - did you register the outputs?" in str(e)
def test_reset_to_and_compute_adjoints_to_usage():
i = Real(2.0)
with Tape() as tape:
tape.registerInput(i)
tape.newRecording()
pos = tape.getPosition()
values = []
deriv = []
for p in range(1, 10):
v = p * i
tape.registerOutput(v)
v.setDerivative(1.0)
tape.computeAdjointsTo(pos)
values.append(value(v))
deriv.append(derivative(i))
tape.resetTo(pos)
tape.clearDerivatives()
assert values == [2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0]
assert deriv == [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0]
def test_derivative():
with Tape() as t:
x = Real(1.0)
t.registerInput(x)
assert t.derivative(x) == 0.0
def test_get_derivative():
with Tape() as t:
x = Real(1.0)
t.registerInput(x)
assert t.getDerivative(x) == 0.0
def test_set_derivative_value():
with Tape() as t:
x = Real(1.0)
t.registerInput(x)
t.setDerivative(x, 1.0)
assert t.derivative(x) == 1.0
with pytest.raises(exceptions.OutOfRange):
derivative(t.setDerivative(1231, 0.0))
def test_set_derivative_slot():
with Tape() as t:
x = Real(1.0)
t.registerInput(x)
slot = x.getSlot()
assert isinstance(slot, int)
t.setDerivative(slot, 1.0)
assert t.derivative(x) == 1.0
assert t.getDerivative(slot) == 1.0
| 4,361 | Python | .py | 125 | 28.416 | 96 | 0.605413 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,670 | test_package.py | auto-differentiation_xad-py/tests/test_package.py | ##############################################################################
#
# Pytests for the overall package interface
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
import xad
def test_version_info():
assert isinstance(xad.__version__, str)
| 1,116 | Python | .py | 26 | 41.692308 | 78 | 0.658088 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,671 | test_exceptions.py | auto-differentiation_xad-py/tests/test_exceptions.py | ##############################################################################
#
# Test exceptions bindings.
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
import pytest
from xad.adj_1st import Real, Tape
from xad.exceptions import (
XadException,
TapeAlreadyActive,
OutOfRange,
DerivativesNotInitialized,
NoTapeException,
)
@pytest.mark.parametrize("exception", [TapeAlreadyActive, XadException])
def test_exceptions_tape_active(exception):
with Tape() as t:
with pytest.raises(exception) as e:
# when it's already active
t.activate()
assert "A tape is already active for the current thread" in str(e)
@pytest.mark.parametrize("exception", [OutOfRange, XadException])
def test_exceptions_outofrange(exception):
with Tape() as t:
x = Real(1.0)
t.registerInput(x)
assert t.derivative(x) == 0.0
with pytest.raises(exception) as e:
t.derivative(12312)
assert "given derivative slot is out of range - did you register the outputs?" in str(e)
@pytest.mark.parametrize("exception", [DerivativesNotInitialized, XadException])
def test_exceptions_adjoints_not_initialized(exception):
with Tape() as t:
with pytest.raises(exception) as e:
x = Real(1.0)
t.registerInput(x)
t.newRecording()
y = x * x
t.registerOutput(y)
t.computeAdjoints()
assert "At least one derivative must be set before computing adjoint" in str(e)
@pytest.mark.parametrize("exception", [NoTapeException, XadException])
def test_exceptions_no_tape_exception(exception):
with pytest.raises(exception) as e:
x = Real(1.0)
x.setDerivative(1.0)
assert "No active tape for the current thread" in str(e)
| 2,666 | Python | .py | 65 | 36.246154 | 96 | 0.66821 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,672 | test_math_functions_derivatives.py | auto-differentiation_xad-py/tests/test_math_functions_derivatives.py | ##############################################################################
#
# Pytests for math functions and their derivatives
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
import sys
import pytest
from xad.adj_1st import Tape, Real as Areal
from xad.fwd_1st import Real as Freal
from xad import math as ad_math
import math
# This is a list of math functions with their expected outcomes and derivatives,
# used in parametrised tests, for unary functions.
#
# The format is a list of tuples, where each tuple has the following entries:
# - XAD math function: Callable
# - parameter value for the function: float
# - expected result: float
# - expected derivative value: float
#
PARAMETERS_FOR_UNARY_FUNC = [
(ad_math.sin, math.pi / 4, math.sin(math.pi / 4), math.cos(math.pi / 4)),
(ad_math.cos, math.pi / 4, math.cos(math.pi / 4), -1 * math.sin(math.pi / 4)),
(ad_math.tan, 0.5, math.tan(0.5), 2 / (1 + math.cos(2 * 0.5))),
(ad_math.atan, 0.5, math.atan(0.5), 1 / (1 + math.pow(0.5, 2))),
(ad_math.acos, 0.5, math.acos(0.5), -1 / math.sqrt(1 - math.pow(0.5, 2))),
(ad_math.asin, 0.5, math.asin(0.5), 1 / math.sqrt(1 - math.pow(0.5, 2))),
(ad_math.tanh, 0.5, math.tanh(0.5), 1 - math.pow(math.tanh(0.5), 2)),
(ad_math.cosh, 0.5, math.cosh(0.5), math.sinh(0.5)),
(ad_math.sinh, 0.5, math.sinh(0.5), math.cosh(0.5)),
(ad_math.atanh, 0.5, math.atanh(0.5), 1 / (1 - math.pow(0.5, 2))),
(ad_math.asinh, 0.5, math.asinh(0.5), 1 / math.sqrt(1 + math.pow(0.5, 2))),
(ad_math.acosh, 1.5, math.acosh(1.5), 1 / math.sqrt(math.pow(1.5, 2) - 1)),
(ad_math.sqrt, 4, math.sqrt(4), 1 / (2 * math.sqrt(4))),
(ad_math.log10, 4, math.log10(4), 1 / (4 * math.log(10))),
(ad_math.log, 4, math.log(4), 1 / 4),
(ad_math.exp, 4, math.exp(4), math.exp(4)),
(ad_math.expm1, 4, math.expm1(4), math.exp(4)),
(ad_math.log1p, 4, math.log1p(4), 1 / (5)),
(ad_math.log2, 4, math.log2(4), 1 / (4 * math.log(2))),
(ad_math.abs, -4, abs(-4), -1),
(ad_math.fabs, -4.4, 4.4, -1),
(ad_math.smooth_abs, -4.4, 4.4, -1),
(
ad_math.erf,
-1.4,
math.erf(-1.4),
(2 / math.sqrt(math.pi)) * math.exp(-1 * math.pow(-1.4, 2)),
),
(
ad_math.erfc,
-1.4,
math.erfc(-1.4),
(-2 / math.sqrt(math.pi)) * math.exp(-1 * math.pow(-1.4, 2)),
),
(ad_math.cbrt, 8, 2.0, (1 / 3) * (math.pow(8, (-2 / 3)))),
(ad_math.trunc, 8.1, math.trunc(8.1), 0),
(ad_math.ceil, 3.7, math.ceil(3.7), 0),
(ad_math.floor, 3.7, math.floor(3.7), 0),
]
# This is a list of math functions with their expected outcomes and derivatives,
# used in parametrised tests, for binary functions.
#
# The format is a list of tuples, where each tuple has the following entries:
# - XAD math function: Callable
# - parameter1 value for the function: float
# - parameter2 value for the function: float
# - expected result: float
# - expected derivative1 value: float
# - expected derivative2 value: float
#
PARAMETERS_FOR_BINARY_FUNC = [
(ad_math.min, 3, 4, 3, 1, 0),
(ad_math.min, 4, 3, 3, 0, 1),
(ad_math.max, 3, 4, 4, 0, 1),
(ad_math.max, 4, 3, 4, 1, 0),
(ad_math.fmin, 3.5, 4.3, 3.5, 1, 0),
(ad_math.fmin, 4.3, 3.5, 3.5, 0, 1),
(ad_math.fmax, 3.5, 4.3, 4.3, 0, 1),
(ad_math.fmax, 4.3, 3.5, 4.3, 1, 0),
(ad_math.smooth_min, 3.5, 4.3, 3.5, 1, 0),
(ad_math.smooth_min, 4.3, 3.5, 3.5, 0, 1),
(ad_math.smooth_max, 3.5, 4.3, 4.3, 0, 1),
(ad_math.smooth_max, 4.3, 3.5, 4.3, 1, 0),
(ad_math.remainder, 5, 2, math.remainder(5, 2), 1, -2),
(ad_math.fmod, 6, 2, math.fmod(6, 3), 1, -3),
]
_binary_with_scalar_funcs = [
(ad_math.pow, math.pow),
(ad_math.min, min),
(ad_math.max, max),
(ad_math.fmin, min),
(ad_math.fmax, max),
(ad_math.atan2, math.atan2),
(ad_math.remainder, math.remainder),
(ad_math.copysign, math.copysign),
]
if sys.version_info.major > 3 or (sys.version_info.major == 3 and sys.version_info.minor >= 9):
# introduced in Python 3.9
PARAMETERS_FOR_BINARY_FUNC.append((ad_math.nextafter, 3.5, 4.3, math.nextafter(3.5, 4.3), 1, 0))
_binary_with_scalar_funcs.append((ad_math.nextafter, math.nextafter))
@pytest.mark.parametrize("func,x,y,xd", PARAMETERS_FOR_UNARY_FUNC)
def test_unary_math_functions_for_adj(func, x, y, xd):
assert func(x) == pytest.approx(y)
x_ad = Areal(x)
with Tape() as tape:
tape.registerInput(x_ad)
tape.newRecording()
y_ad = func(x_ad)
tape.registerOutput(y_ad)
y_ad.setDerivative(1.0)
tape.computeAdjoints()
assert y_ad == pytest.approx(y)
assert x_ad.getDerivative() == pytest.approx(xd)
@pytest.mark.parametrize("func,x,y,yd", PARAMETERS_FOR_UNARY_FUNC)
def test_unary_math_functions_for_fwd(func, x, y, yd):
x_ad = Freal(x)
x_ad.setDerivative(1.0)
y_ad = func(x_ad)
assert y_ad == pytest.approx(y)
assert y_ad.getDerivative() == pytest.approx(yd)
@pytest.mark.parametrize("ad_func, func", _binary_with_scalar_funcs)
@pytest.mark.parametrize("value", [3, 3.1])
def test_binary_function_with_scalar_param(value, ad_func, func):
assert ad_func(4.1, value) == pytest.approx(func(4.1, value))
assert ad_func(4, value) == pytest.approx(func(4, value))
assert ad_func(Freal(4.1), value) == pytest.approx(func(4.1, value))
assert ad_func(Freal(4), value) == pytest.approx(func(4, value))
assert ad_func(value, Freal(4.1)) == pytest.approx(func(value, 4.1))
assert ad_func(value, Freal(4)) == pytest.approx(func(value, 4))
@pytest.mark.parametrize(
"func, y, derv",
[
(0, math.pow(4, 3), pytest.approx(3 * math.pow(4, 3 - 1))),
(1, math.pow(3, 4), pytest.approx(math.log(3) * math.pow(3, 4))),
],
)
def test_pow_for_adj(func, y, derv):
x_ad = Areal(4.0)
with Tape() as tape:
tape.registerInput(x_ad)
tape.newRecording()
if func == 0:
y_ad = ad_math.pow(x_ad, 3)
else:
y_ad = ad_math.pow(3, x_ad)
tape.registerOutput(y_ad)
y_ad.setDerivative(1.0)
tape.computeAdjoints()
assert y_ad == pytest.approx(y)
assert x_ad.getDerivative() == pytest.approx(derv)
@pytest.mark.parametrize(
"func, y, derv",
[
(0, math.pow(4, 3), pytest.approx(3 * math.pow(4, 3 - 1))),
(1, math.pow(3, 4), pytest.approx(math.log(3) * math.pow(3, 4))),
],
)
def test_pow_for_fwd(func, y, derv):
x_ad = Freal(4.0)
x_ad.setDerivative(1.0)
if func == 0:
y_ad = ad_math.pow(x_ad, 3)
else:
y_ad = ad_math.pow(3, x_ad)
assert y_ad == y
assert y_ad.getDerivative() == pytest.approx(derv)
@pytest.mark.parametrize("func,x1, x2,y,xd1, xd2", PARAMETERS_FOR_BINARY_FUNC)
def test_binary_math_functions_for_adj(func, x1, x2, y, xd1, xd2):
x1_ad = Areal(x1)
x2_ad = Areal(x2)
with Tape() as tape:
tape.registerInput(x1_ad)
tape.registerInput(x2_ad)
tape.newRecording()
y_ad = func(x1_ad, x2_ad)
tape.registerOutput(y_ad)
y_ad.setDerivative(1.0)
tape.computeAdjoints()
assert y_ad == pytest.approx(y)
assert x1_ad.getDerivative() == pytest.approx(xd1)
assert x2_ad.getDerivative() == pytest.approx(xd2)
@pytest.mark.parametrize("func,x1, x2,y,xd1, xd2", PARAMETERS_FOR_BINARY_FUNC)
@pytest.mark.parametrize("deriv", [1, 2])
def test_binary_math_functions_for_fwd(func, x1, x2, y, xd1, xd2, deriv):
x1_ad = Freal(x1)
x2_ad = Freal(x2)
if deriv == 1:
x1_ad.setDerivative(1.0)
else:
x2_ad.setDerivative(1.0)
y_ad = func(x1_ad, x2_ad)
assert y_ad == pytest.approx(y)
if deriv == 1:
assert y_ad.getDerivative() == pytest.approx(xd1)
else:
assert y_ad.getDerivative() == pytest.approx(xd2)
@pytest.mark.parametrize(
"func,x,y,xd",
[
(ad_math.modf, 3.23, math.modf(3.23), 1),
(ad_math.frexp, 3, math.frexp(3), 1 / math.pow(2, 2)),
],
)
def test_modf_frexp_functions_for_adj(func, x, y, xd):
x_ad = Areal(x)
with Tape() as tape:
tape.registerInput(x_ad)
tape.newRecording()
y_ad = func(x_ad)
tape.registerOutput(y_ad[0])
y_ad[0].setDerivative(1.0)
tape.computeAdjoints()
assert y_ad == pytest.approx(y)
assert x_ad.getDerivative() == pytest.approx(xd)
@pytest.mark.parametrize(
"func,x,y,xd",
[
(ad_math.modf, 3.23, math.modf(3.23), 1),
(ad_math.frexp, 3, math.frexp(3), 1 / math.pow(2, 2)),
],
)
def test_modf_frexp_functions_for_fwd(func, x, y, xd):
x_ad = Freal(x)
x_ad.setDerivative(1.0)
y_ad = func(x_ad)
assert y_ad == pytest.approx(y)
assert y_ad[0].getDerivative() == pytest.approx(xd)
@pytest.mark.parametrize(
"func, y, xd",
[
(ad_math.degrees, math.degrees(3), 180 / math.pi),
(ad_math.radians, math.radians(3), math.pi / 180),
],
)
def test_degrees_radians_adj(func, y, xd):
with Tape() as tape:
x_ad = Areal(3.0)
tape.registerInput(x_ad)
tape.newRecording()
y_ad = func(x_ad)
tape.registerOutput(y_ad)
y_ad.setDerivative(1.0)
tape.computeAdjoints()
assert y_ad.getValue() == pytest.approx(y)
assert x_ad.getDerivative() == pytest.approx(xd)
@pytest.mark.parametrize(
"func, y, xd",
[
(ad_math.degrees, math.degrees(3), 180 / math.pi),
(ad_math.radians, math.radians(3), math.pi / 180),
],
)
def test_degrees_radians_fwd(func, y, xd):
x_ad = Freal(3)
x_ad.setDerivative(1.0)
y_ad = func(x_ad)
assert y_ad.getValue() == pytest.approx(y)
assert y_ad.getDerivative() == pytest.approx(xd)
@pytest.mark.parametrize("Real", [Areal, Freal])
def test_copysign(Real):
assert ad_math.copysign(Real(-3.1), 4) == pytest.approx(math.copysign(-3.1, 4))
assert ad_math.copysign(Real(4), -3.1) == pytest.approx(math.copysign(4, -3.1))
assert ad_math.copysign(Real(-3.1), Real(4)) == pytest.approx(math.copysign(-3.1, 4))
def test_copysign_derivative_for_adj():
with Tape() as tape:
x1_ad = Areal(-3.1)
x2_ad = Areal(4)
tape.registerInput(x1_ad)
tape.registerInput(x2_ad)
tape.newRecording()
y_ad = ad_math.copysign(x1_ad, x2_ad)
tape.registerOutput(y_ad)
y_ad.setDerivative(1.0)
tape.computeAdjoints()
assert y_ad == pytest.approx(math.copysign(-3.1, 4))
assert x1_ad.getDerivative() == pytest.approx(-1)
assert x2_ad.getDerivative() == pytest.approx(0)
@pytest.mark.parametrize("deriv", [1, 2])
def test_copysign_derivative_for_fwd(deriv):
x1_ad = Freal(-3.1)
x2_ad = Freal(4)
if deriv == 1:
x1_ad.setDerivative(1.0)
else:
x2_ad.setDerivative(1.0)
y_ad = ad_math.copysign(x1_ad, x2_ad)
assert y_ad == pytest.approx(math.copysign(-3.1, 4))
if deriv == 1:
assert y_ad.getDerivative() == pytest.approx(-1)
else:
assert y_ad.getDerivative() == pytest.approx(0)
def test_sum_adj():
with Tape() as tape:
x1_ad = Areal(-3.1)
x2_ad = Areal(4)
x3_ad = Areal(2.4)
tape.registerInput(x1_ad)
tape.registerInput(x2_ad)
tape.registerInput(x3_ad)
tape.newRecording()
y_ad = sum([x1_ad, x2_ad, x3_ad])
tape.registerOutput(y_ad)
y_ad.setDerivative(1.0)
tape.computeAdjoints()
assert y_ad == pytest.approx(3.3)
assert x1_ad.getDerivative() == pytest.approx(1)
assert x2_ad.getDerivative() == pytest.approx(1)
assert x3_ad.getDerivative() == pytest.approx(1)
@pytest.mark.parametrize("deriv", [1, 2])
def test_sum_for_fwd(deriv):
x1_ad = Freal(-3.1)
x2_ad = Freal(4)
if deriv == 1:
x1_ad.setDerivative(1.0)
else:
x2_ad.setDerivative(1.0)
y_ad = sum([x1_ad, x2_ad])
assert y_ad == pytest.approx(sum([-3.1, 4]))
assert y_ad.getDerivative() == pytest.approx(1)
def test_hypot_adj():
with Tape() as tape:
x1_ad = Areal(-3.1)
x2_ad = Areal(4)
tape.registerInput(x1_ad)
tape.registerInput(x2_ad)
tape.newRecording()
y_ad = ad_math.hypot(x1_ad, x2_ad)
tape.registerOutput(y_ad)
y_ad.setDerivative(1.0)
tape.computeAdjoints()
assert y_ad == pytest.approx(math.hypot(-3.1, 4))
assert x1_ad.getDerivative() == pytest.approx(-3.1 / math.hypot(-3.1, 4))
assert x2_ad.getDerivative() == pytest.approx(4 / math.hypot(-3.1, 4))
@pytest.mark.parametrize("deriv", [1, 2])
def test_hypot_for_fwd(deriv):
x1_ad = Freal(-3.1)
x2_ad = Freal(4)
if deriv == 1:
x1_ad.setDerivative(1.0)
else:
x2_ad.setDerivative(1.0)
y_ad = ad_math.hypot(x1_ad, x2_ad)
assert y_ad == pytest.approx(math.hypot(-3.1, 4))
if deriv == 1:
assert y_ad.getDerivative() == pytest.approx(-3.1 / math.hypot(-3.1, 4))
else:
assert y_ad.getDerivative() == pytest.approx(4 / math.hypot(-3.1, 4))
def test_dist_for_adj():
with Tape() as tape:
x1_ad = Areal(-3.1)
x2_ad = Areal(4)
x3_ad = Areal(2.4)
x4_ad = Areal(1)
tape.registerInput(x1_ad)
tape.registerInput(x2_ad)
tape.registerInput(x3_ad)
tape.registerInput(x4_ad)
tape.newRecording()
y_ad = ad_math.dist([x1_ad, x2_ad], [x3_ad, x4_ad])
tape.registerOutput(y_ad)
y_ad.setDerivative(1.0)
tape.computeAdjoints()
assert y_ad == pytest.approx(math.dist([-3.1, 4], [2.4, 1]))
assert x1_ad.getDerivative() == pytest.approx(-5.5 / math.dist([-3.1, 4], [2.4, 1]))
assert x2_ad.getDerivative() == pytest.approx(3 / math.dist([-3.1, 4], [2.4, 1]))
assert x3_ad.getDerivative() == pytest.approx(5.5 / math.dist([-3.1, 4], [2.4, 1]))
assert x4_ad.getDerivative() == pytest.approx(-3 / math.dist([-3.1, 4], [2.4, 1]))
@pytest.mark.parametrize("deriv", [1, 2, 3, 4])
def test_dist_for_fwd(deriv):
x1_ad = Freal(-3.1)
x2_ad = Freal(4)
x3_ad = Freal(2.4)
x4_ad = Freal(1)
if deriv == 1:
x1_ad.setDerivative(1.0)
elif deriv == 2:
x2_ad.setDerivative(1.0)
elif deriv == 3:
x3_ad.setDerivative(1.0)
else:
x4_ad.setDerivative(1.0)
y_ad = ad_math.dist([x1_ad, x2_ad], [x3_ad, x4_ad])
assert y_ad == pytest.approx(math.dist([-3.1, 4], [2.4, 1]))
if deriv == 1:
assert y_ad.getDerivative() == pytest.approx(-5.5 / math.dist([-3.1, 4], [2.4, 1]))
elif deriv == 2:
assert y_ad.getDerivative() == pytest.approx(3 / math.dist([-3.1, 4], [2.4, 1]))
elif deriv == 3:
assert y_ad.getDerivative() == pytest.approx(5.5 / math.dist([-3.1, 4], [2.4, 1]))
else:
assert y_ad.getDerivative() == pytest.approx(-3 / math.dist([-3.1, 4], [2.4, 1]))
| 15,863 | Python | .py | 410 | 32.987805 | 100 | 0.599766 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,673 | test_real_operations.py | auto-differentiation_xad-py/tests/test_real_operations.py | ##############################################################################
#
# Pytests for operations and derivatives on the active types
#
# This file is part of XAD's Python bindings, a comprehensive library for
# automatic differentiation.
#
# Copyright (C) 2010-2024 Xcelerit Computing Ltd.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
from pytest import approx, raises
import pytest
from xad.adj_1st import Real as AReal, Tape
from xad.fwd_1st import Real as FReal
from xad import value, derivative
import math as m
# This is a list of math functions with their expected outcomes and derivatives,
# used in parametrised tests, for binary arithmetic functions with one active operand.
#
# The format is a list of tuples, where each tuple has the following entries:
# - math function: Callable (lambda), with one parameter
# - parameter1 value for the function: float
# - expected result: float
# - expected derivative1 value: float
#
PARAMETERS_FOR_BINARY_ARITHMETICS_1_ACTIVE_OPERAND = [
(lambda a: 2 * a, 3, 6, 2),
(lambda a: 2 + a, 3, 5, 1),
(lambda a: 2 - a, 3, -1, -1),
(lambda a: 2 / a, 3, 2 / 3, -2 / 9),
(lambda a: a * 3.6, 3, 10.8, 3.6),
(lambda a: a + 3.9, 3, 6.9, 1),
(lambda a: a - 4.3, 3, -1.3, 1),
(lambda a: a / 2, 3, 1.5, 1 / 2),
]
# This is a list of math functions with their expected outcomes and derivatives,
# used in parametrised tests, for unary arithmetic functions (+x, -x).
#
# The format is a list of tuples, where each tuple has the following entries:
# - math function: Callable (lambda), with one parameter
# - parameter1 value for the function: float
# - expected result: float
# - expected derivative1 value: float
#
PARAMETERS_FOR_UNARY_ARITHMETICS = [(lambda a: +a, 3, 3, 1), (lambda a: -a, 3, -3, -1)]
# This is a list of math functions with their expected outcomes and derivatives,
# used in parametrised tests, for binary arithmetic functions with two active operands.
#
# The format is a list of tuples, where each tuple has the following entries:
# - math function: Callable (lambda, 2 parameters)
# - parameter1 value for the function: float
# - parameter2 value for the function: float
# - expected result: float
# - expected derivative1 value: float
# - expected derivative2 value: float
#
PARAMETERS_FOR_BINARY_ARITHMETICS_2_ACTIVE_OPERANDS = [
(lambda a, b: a * b, 5.0, 2.0, 10, 2, 5),
(lambda a, b: a + b, 5.0, 2.0, 7, 1, 1),
(lambda a, b: a - b, 5.0, 2.0, 3, 1, -1),
(lambda a, b: a / b, 5.0, 2.0, 2.5, 0.5, -1.25),
]
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_initialize_from_float(ad_type):
assert ad_type(0.3).getValue() == approx(0.3)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_initialize_from_int(ad_type):
assert ad_type(1).getValue() == 1
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_add_float(ad_type):
real = ad_type(0.4) + 0.3
assert real.getValue() == approx(0.7)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_add_int(ad_type):
real = ad_type(1) + 2
assert real.getValue() == 3
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_sub_float(ad_type):
real = ad_type(0.3) - 0.4
assert real.getValue() == approx(-0.1)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_sub_int(ad_type):
real = ad_type(1) - 2
assert real.getValue() == -1
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_add_to_float(ad_type):
real = 0.3 + ad_type(0.4)
assert real.getValue() == approx(0.7)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_sub_to_float(ad_type):
real = 2.5 - ad_type(2.0)
assert real.getValue() == approx(0.5)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_add_to_int(ad_type):
real = 2 + ad_type(1)
assert real.getValue() == 3
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_sub_to_int(ad_type):
real = 2 - ad_type(1)
assert real.getValue() == 1
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_add_real(ad_type):
real = ad_type(2) + ad_type(1)
assert real.getValue() == 3
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_sub_real(ad_type):
real = ad_type(2) - ad_type(1)
assert real.getValue() == 1
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_mul_float(ad_type):
real = ad_type(0.2) * 0.5
assert real.getValue() == approx(0.1)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_mul_int(ad_type):
real = ad_type(1) * 2
assert real.getValue() == 2
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_mul_to_float(ad_type):
real = 0.5 * ad_type(0.2)
assert real.getValue() == approx(0.1)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_mul_to_int(ad_type):
real = 2 * ad_type(1)
assert real.getValue() == 2
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_mul_real(ad_type):
real = ad_type(0.2) * ad_type(0.5)
assert real.getValue() == approx(0.1)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_div_float(ad_type):
real = ad_type(0.2) / 0.5
assert real.getValue() == approx(0.4)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_div_int(ad_type):
real = ad_type(1) / 2
assert real.getValue() == approx(0.5)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_div_to_float(ad_type):
real = 0.5 / ad_type(0.2)
assert real.getValue() == approx(2.5)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_div_to_int(ad_type):
real = 2 / ad_type(1)
assert real.getValue() == 2
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_div_real(ad_type):
real = ad_type(0.2) / ad_type(0.5)
assert real.getValue() == approx(0.4)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_addition_assignment_int(ad_type):
real = ad_type(0.2)
real += 1
assert real.getValue() == approx(1.2)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_addition_assignment_float(ad_type):
real = ad_type(0.2)
real += 1.9
assert real.getValue() == approx(2.1)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_addition_assignment_real(ad_type):
real = ad_type(0.2)
real += ad_type(0.5)
assert real.getValue() == approx(0.7)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_sub_assignment_int(ad_type):
real = ad_type(0.2)
real -= 1
assert real.getValue() == approx(-0.8)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_sub_assignment_float(ad_type):
real = ad_type(0.2)
real -= 1.9
assert real.getValue() == approx(-1.7)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_sub_assignment_real(ad_type):
real = ad_type(0.2)
real -= ad_type(0.5)
assert real.getValue() == approx(-0.3)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_comparison_real_to_real(ad_type):
a = ad_type(0.2)
b = ad_type(0.5)
assert (b > a) is True
assert (a > b) is False
assert (b >= a) is True
assert (a >= b) is False
assert (b < a) is False
assert (a < b) is True
assert (b <= a) is False
assert (a <= b) is True
c = ad_type(0.2)
assert (a != b) is True
assert (a != c) is False
assert (a == c) is True
assert (b == c) is False
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_comparison_real_to_float(ad_type):
a = ad_type(0.2)
b = 0.5
assert (b > a) is True
assert (a > b) is False
assert (b >= a) is True
assert (a >= b) is False
assert (b < a) is False
assert (a < b) is True
assert (b <= a) is False
assert (a <= b) is True
c = 0.2
assert (a != b) is True
assert (a != c) is False
assert (a == c) is True
assert (b == c) is False
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_comparison_real_to_int(ad_type):
a = ad_type(2)
b = 5
assert (b > a) is True
assert (a > b) is False
assert (b >= a) is True
assert (a >= b) is False
assert (b < a) is False
assert (a < b) is True
assert (b <= a) is False
assert (a <= b) is True
c = 2
assert (a != b) is True
assert (a != c) is False
assert (a == c) is True
assert (b == c) is False
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_rounding(ad_type):
assert round(ad_type(2.345), 2) == pytest.approx(2.35)
assert round(ad_type(2.345), 1) == pytest.approx(2.3)
assert round(ad_type(2.345), 0) == pytest.approx(2.0)
assert round(ad_type(2.345)) == pytest.approx(2.0)
assert type(round(ad_type(2.3))) == type(round(2.3))
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
@pytest.mark.parametrize(
"func", [m.ceil, m.floor, m.trunc, int], ids=["ceil", "floor", "trunc", "int"]
)
def test_truncation_funcs(ad_type, func):
assert func(ad_type(2.345)) == func(2.345)
assert func(ad_type(2.845)) == func(2.845)
assert func(ad_type(-2.845)) == func(-2.845)
assert func(ad_type(0.0)) == func(0.0)
assert isinstance(func(ad_type(1.1)), int)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_abs(ad_type):
assert abs(ad_type(2.345)) == pytest.approx(2.345)
assert abs(ad_type(-2.345)) == pytest.approx(2.345)
assert abs(ad_type(0.0)) == 0.0
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_bool(ad_type):
assert bool(ad_type(1.0)) is bool(1.0)
assert bool(ad_type(0.0)) is bool(0.0)
assert bool(ad_type(1.0)) is bool(-1.0)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_mod(ad_type):
assert ad_type(2.7) % 2 == 2.7 % 2
assert ad_type(2.7) % ad_type(2.0) == 2.7 % 2.0
assert 2.7 % ad_type(2.0) == 2.7 % 2.0
assert 2 % ad_type(2.0) == 2 % 2.0
assert ad_type(-2.7) % 2 == -2.7 % 2
assert ad_type(-2.7) % ad_type(2.0) == -2.7 % 2.0
assert -2.7 % ad_type(2.0) == -2.7 % 2.0
assert -2 % ad_type(2.0) == -2 % 2.0
assert ad_type(2.7) % -2 == 2.7 % -2
assert ad_type(2.7) % ad_type(-2.0) == 2.7 % -2.0
assert 2.7 % ad_type(-2.0) == 2.7 % -2.0
assert 2 % ad_type(-2.0) == 2 % -2.0
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_divmod(ad_type):
assert divmod(ad_type(2.7), 2) == divmod(2.7, 2)
assert divmod(ad_type(2.7), ad_type(2.0)) == divmod(2.7, 2.0)
assert divmod(2.7, ad_type(2.0)) == divmod(2.7, 2.0)
assert divmod(2, ad_type(2.0)) == divmod(2, 2.0)
assert divmod(ad_type(-2.7), 2) == divmod(-2.7, 2)
assert divmod(ad_type(-2.7), ad_type(2.0)) == divmod(-2.7, 2.0)
assert divmod(-2.7, ad_type(2.0)) == divmod(-2.7, 2.0)
assert divmod(-2, ad_type(2.0)) == divmod(-2, 2.0)
assert divmod(ad_type(2.7), -2) == divmod(2.7, -2)
assert divmod(ad_type(2.7), ad_type(-2.0)) == divmod(2.7, -2.0)
assert divmod(2.7, ad_type(-2.0)) == divmod(2.7, -2.0)
assert divmod(2, ad_type(-2.0)) == divmod(2, -2.0)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_floordiv(ad_type):
assert ad_type(2.7) // 2 == 2.7 // 2
assert ad_type(2.7) // ad_type(2.0) == 2.7 // 2.0
assert 2.7 // ad_type(2.0) == 2.7 // 2.0
assert 2 // ad_type(2.0) == 2 // 2.0
assert ad_type(-2.7) // 2 == -2.7 // 2
assert ad_type(-2.7) // ad_type(2.0) == -2.7 // 2.0
assert -2.7 // ad_type(2.0) == -2.7 // 2.0
assert -2 // ad_type(2.0) == -2 // 2.0
assert ad_type(2.7) // -2 == 2.7 // -2
assert ad_type(2.7) // ad_type(-2.0) == 2.7 // -2.0
assert 2.7 // ad_type(-2.0) == 2.7 // -2.0
assert 2 // ad_type(-2.0) == 2 // -2.0
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_pow_operator(ad_type):
assert ad_type(2.7) ** 2 == pytest.approx(2.7**2)
assert ad_type(2.7) ** 2.4 == pytest.approx(2.7**2.4)
assert ad_type(2.7) ** ad_type(2.4) == pytest.approx(2.7**2.4)
assert 2.7 ** ad_type(2.4) == pytest.approx(2.7**2.4)
assert 2 ** ad_type(2.4) == pytest.approx(2**2.4)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_hash_method(ad_type):
assert hash(ad_type(2.7)) == hash(2.7)
assert hash(ad_type(-2.7)) == hash(-2.7)
assert hash(ad_type(0)) == hash(0)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_getnewargs_method(ad_type):
assert ad_type(1.2).__getnewargs__() == (1.2,)
assert ad_type(1).__getnewargs__() == (1.0,)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_as_integer_ratio(ad_type):
assert ad_type(1.2).as_integer_ratio() == (1.2).as_integer_ratio()
assert ad_type(-21.2).as_integer_ratio() == (-21.2).as_integer_ratio()
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_conjugate(ad_type):
assert ad_type(1.2).conjugate() == (1.2).conjugate()
assert ad_type(-21.2).conjugate() == (-21.2).conjugate()
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_fromhex(ad_type):
assert ad_type.fromhex("0x3.a7p10") == float.fromhex("0x3.a7p10")
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_hex(ad_type):
assert ad_type(1.23).hex() == (1.23).hex()
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_imag(ad_type):
assert ad_type(1.23).imag() == pytest.approx(0.0)
assert ad_type(-1.23).imag() == pytest.approx(0.0)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_real(ad_type):
assert ad_type(1.23).real() == pytest.approx(1.23)
assert ad_type(-1.23).real() == pytest.approx(-1.23)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_isinteger(ad_type):
assert ad_type(1.23).is_integer() is False
assert ad_type(-1.23).is_integer() is False
assert ad_type(21.0).is_integer() is True
assert ad_type(-1234.0).is_integer() is True
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_format(ad_type):
assert f"{ad_type(1.23):10.5f}" == f"{1.23:10.5f}"
assert "{:10.5f}".format(ad_type(1.23)) == "{:10.5f}".format(1.23)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_value_function(ad_type):
assert value(3) == 3
assert value(3.2) == approx(3.2)
assert value("3") == "3"
assert value(ad_type(3.1)) == approx(3.1)
@pytest.mark.parametrize("ad_type", [AReal, FReal], ids=["adj", "fwd"])
def test_value_property_get(ad_type):
assert ad_type(3.1).value == approx(3.1)
def test_derivative_property_get_fwd():
x = FReal(1.2)
x.setDerivative(1.0)
assert x.derivative == 1.0
def test_derivative_property_set_fwd():
x = FReal(1.2)
x.derivative = 1.0
assert x.getDerivative() == 1.0
def test_derivative_property_get_adj():
x = AReal(1.2)
with Tape() as tape:
tape.registerInput(x)
tape.newRecording()
y = x
tape.registerOutput(y)
y.setDerivative(1.0)
assert y.derivative == 1.0
def test_derivative_property_set_adj():
x = AReal(1.2)
with Tape() as tape:
tape.registerInput(x)
tape.newRecording()
y = x
tape.registerOutput(y)
y.derivative = 1.0
assert y.getDerivative() == 1.0
def test_derivative_function():
x = AReal(3.2)
with Tape() as tape:
tape.registerInput(x)
tape.newRecording()
y_ad = x
tape.registerOutput(y_ad)
y_ad.setDerivative(1.0)
tape.computeAdjoints()
assert derivative(x) == x.getDerivative()
with raises(TypeError):
derivative(1)
def test_should_record():
x = AReal(42.0)
assert x.shouldRecord() is False
with Tape() as tape:
tape.registerInput(x)
assert x.shouldRecord() is True
def test_set_adjoint():
x = AReal(42.0)
with Tape() as tape:
tape.registerInput(x)
tape.newRecording()
y = 4 * x
tape.registerOutput(x)
y.setAdjoint(1.0)
tape.computeAdjoints()
assert derivative(x) == 4.0
@pytest.mark.parametrize("func,x,y,xd", PARAMETERS_FOR_UNARY_ARITHMETICS)
def test_unary_arithmetics_adj(func, x, y, xd):
x_ad = AReal(x)
with Tape() as tape:
tape.registerInput(x_ad)
tape.newRecording()
y_ad = func(x_ad)
tape.registerOutput(y_ad)
y_ad.setDerivative(1.0)
tape.computeAdjoints()
assert y_ad.getValue() == pytest.approx(y)
assert x_ad.getDerivative() == pytest.approx(xd)
@pytest.mark.parametrize("func,x,y,xd", PARAMETERS_FOR_UNARY_ARITHMETICS)
def test_unary_arithmetics_fwd(func, x, y, xd):
x_ad = FReal(x)
x_ad.setDerivative(1.0)
y_ad = func(x_ad)
assert y_ad == y
assert y_ad.getDerivative() == xd
@pytest.mark.parametrize("func,x,y,xd", PARAMETERS_FOR_BINARY_ARITHMETICS_1_ACTIVE_OPERAND)
def test_binary_arithmetics_fwd(func, x, y, xd):
x1_ad = FReal(x)
x1_ad.setDerivative(1.0)
y_ad = func(x1_ad)
assert y_ad.getValue() == pytest.approx(y)
assert y_ad.getDerivative() == pytest.approx(xd)
@pytest.mark.parametrize("func,x,y,xd", PARAMETERS_FOR_BINARY_ARITHMETICS_1_ACTIVE_OPERAND)
def test_binary_arithmetics_adj(func, x, y, xd):
x_ad = AReal(x)
with Tape() as tape:
tape.registerInput(x_ad)
tape.newRecording()
y_ad = func(x_ad)
tape.registerOutput(y_ad)
y_ad.setDerivative(1.0)
tape.computeAdjoints()
assert y_ad.getValue() == pytest.approx(y)
assert x_ad.getDerivative() == pytest.approx(xd)
@pytest.mark.parametrize(
"func,x1, x2,y,xd1, xd2", PARAMETERS_FOR_BINARY_ARITHMETICS_2_ACTIVE_OPERANDS
)
def test_binary_with_2_active_operands_adj(func, x1, x2, y, xd1, xd2):
x1_ad = AReal(x1)
x2_ad = AReal(x2)
with Tape() as tape:
tape.registerInput(x1_ad)
tape.registerInput(x2_ad)
tape.newRecording()
y_ad = func(x1_ad, x2_ad)
tape.registerOutput(y_ad)
y_ad.setDerivative(1.0)
tape.computeAdjoints()
assert y_ad == pytest.approx(y)
assert x1_ad.getDerivative() == pytest.approx(xd1)
assert x2_ad.getDerivative() == pytest.approx(xd2)
@pytest.mark.parametrize(
"func,x1, x2,y,xd1, xd2", PARAMETERS_FOR_BINARY_ARITHMETICS_2_ACTIVE_OPERANDS
)
@pytest.mark.parametrize("deriv", [1, 2])
def test_binary_with_2_active_operands_fwd(func, x1, x2, y, xd1, xd2, deriv):
x1_ad = FReal(x1)
x2_ad = FReal(x2)
if deriv == 1:
x1_ad.setDerivative(1.0)
else:
x2_ad.setDerivative(1.0)
y_ad = func(x1_ad, x2_ad)
assert y_ad.getValue() == pytest.approx(y)
if deriv == 1:
assert y_ad.getDerivative() == pytest.approx(xd1)
else:
assert y_ad.getDerivative() == pytest.approx(xd2)
| 20,374 | Python | .py | 494 | 36.973684 | 91 | 0.624766 | auto-differentiation/xad-py | 8 | 1 | 12 | AGPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,674 | model_cl.py | disungatullina_MinBackProp/model_cl.py | import time
from ransac import RANSAC
from estimators.essential_matrix_estimator_nister import *
from samplers.uniform_sampler import *
from samplers.gumbel_sampler import *
from scorings.msac_score import *
import torch.nn as nn
import torch.nn.functional as F
from cv_utils import *
def batch_episym(x1, x2, F):
batch_size, num_pts = x1.shape[0], x1.shape[1]
x1 = torch.cat([x1, x1.new_ones(batch_size, num_pts, 1)], dim=-1).reshape(
batch_size, num_pts, 3, 1
)
x2 = torch.cat([x2, x2.new_ones(batch_size, num_pts, 1)], dim=-1).reshape(
batch_size, num_pts, 3, 1
)
F = F.reshape(-1, 1, 3, 3).repeat(1, num_pts, 1, 1)
x2Fx1 = torch.matmul(x2.transpose(2, 3), torch.matmul(F, x1)).reshape(
batch_size, num_pts
)
Fx1 = torch.matmul(F, x1).reshape(batch_size, num_pts, 3)
Ftx2 = torch.matmul(F.transpose(2, 3), x2).reshape(batch_size, num_pts, 3)
ys = x2Fx1**2 * (
1.0 / (Fx1[:, :, 0] ** 2 + Fx1[:, :, 1] ** 2 + 1e-15)
+ 1.0 / (Ftx2[:, :, 0] ** 2 + Ftx2[:, :, 1] ** 2 + 1e-15)
)
return ys
def knn(x, k):
inner = -2 * torch.matmul(x.transpose(2, 1), x)
xx = torch.sum(x**2, dim=1, keepdim=True)
pairwise_distance = -xx - inner - xx.transpose(2, 1)
idx = pairwise_distance.topk(k=k, dim=-1)[1] # (batch_size, num_points, k)
return idx[:, :, :]
def get_graph_feature(x, k=20, idx=None):
batch_size = x.size(0)
num_points = x.size(2)
x = x.view(batch_size, -1, num_points)
if idx is None:
idx_out = knn(x, k=k)
else:
idx_out = idx
device = x.device
idx_base = torch.arange(0, batch_size, device=device).view(-1, 1, 1) * num_points
idx = idx_out + idx_base
idx = idx.view(-1)
_, num_dims, _ = x.size()
x = x.transpose(2, 1).contiguous()
feature = x.view(batch_size * num_points, -1)[idx, :]
feature = feature.view(batch_size, num_points, k, num_dims)
x = x.view(batch_size, num_points, 1, num_dims).repeat(1, 1, k, 1)
feature = torch.cat((x, x - feature), dim=3).permute(0, 3, 1, 2).contiguous()
return feature
class ResNet_Block(nn.Module):
def __init__(self, inchannel, outchannel, pre=False):
super(ResNet_Block, self).__init__()
self.pre = pre
self.right = nn.Sequential(
nn.Conv2d(inchannel, outchannel, (1, 1)),
)
self.left = nn.Sequential(
nn.Conv2d(inchannel, outchannel, (1, 1)),
nn.InstanceNorm2d(outchannel),
nn.BatchNorm2d(outchannel),
nn.ReLU(),
nn.Conv2d(outchannel, outchannel, (1, 1)),
nn.InstanceNorm2d(outchannel),
nn.BatchNorm2d(outchannel),
)
def forward(self, x):
x1 = self.right(x) if self.pre is True else x
out = self.left(x)
out = out + x1
return torch.relu(out)
class DGCNN_Block(nn.Module):
def __init__(self, knn_num=9, in_channel=128):
super(DGCNN_Block, self).__init__()
self.knn_num = knn_num
self.in_channel = in_channel
assert self.knn_num == 9 or self.knn_num == 6
if self.knn_num == 9:
self.conv = nn.Sequential(
nn.Conv2d(self.in_channel * 2, self.in_channel, (1, 3), stride=(1, 3)),
nn.BatchNorm2d(self.in_channel),
nn.ReLU(inplace=True),
nn.Conv2d(self.in_channel, self.in_channel, (1, 3)),
nn.BatchNorm2d(self.in_channel),
nn.ReLU(inplace=True),
)
if self.knn_num == 6:
self.conv = nn.Sequential(
nn.Conv2d(self.in_channel * 2, self.in_channel, (1, 3), stride=(1, 3)),
nn.BatchNorm2d(self.in_channel),
nn.ReLU(inplace=True),
nn.Conv2d(self.in_channel, self.in_channel, (1, 2)),
nn.BatchNorm2d(self.in_channel),
nn.ReLU(inplace=True),
)
def forward(self, features):
B, _, N, _ = features.shape
out = get_graph_feature(features, k=self.knn_num)
out = self.conv(out)
return out
class GCN_Block(nn.Module):
def __init__(self, in_channel):
super(GCN_Block, self).__init__()
self.in_channel = in_channel
self.conv = nn.Sequential(
nn.Conv2d(self.in_channel, self.in_channel, (1, 1)),
nn.BatchNorm2d(self.in_channel),
nn.ReLU(inplace=True),
)
def attention(self, w):
w = torch.relu(torch.tanh(w)).unsqueeze(-1)
A = torch.bmm(w.transpose(1, 2), w)
return A
def graph_aggregation(self, x, w):
B, _, N, _ = x.size()
with torch.no_grad():
A = self.attention(w)
I = torch.eye(N).unsqueeze(0).to(x.device, x.dtype).detach()
A = A + I
D_out = torch.sum(A, dim=-1)
D = (1 / D_out) ** 0.5
D = torch.diag_embed(D)
L = torch.bmm(D, A)
L = torch.bmm(L, D)
out = x.squeeze(-1).transpose(1, 2).contiguous()
out = torch.bmm(L, out).unsqueeze(-1)
out = out.transpose(1, 2).contiguous()
return out
def forward(self, x, w):
out = self.graph_aggregation(x, w)
out = self.conv(out)
return out
class RANSACLayer(nn.Module):
def __init__(self, opt, **kwargs):
super(RANSACLayer, self).__init__(**kwargs)
self.opt = opt
if opt.precision == 2:
data_type = torch.float64
elif opt.precision == 0:
data_type = torch.float16
else:
data_type = torch.float32
# Initialize the essential matrix estimator
solver = EssentialMatrixEstimatorNister(opt.device, opt.ift)
sampler = GumbelSoftmaxSampler(
opt.ransac_batch_size,
solver.sample_size,
device=opt.device,
data_type=data_type,
)
scoring = MSACScore(self.opt.device)
# maximal iteration number, fixed when training, adaptive updating while testing
# 5PC
max_iters = 100 if opt.tr else 5000
self.estimator = RANSAC(
solver,
sampler,
scoring,
max_iterations=max_iters,
train=opt.tr,
ransac_batch_size=opt.ransac_batch_size,
threshold=opt.threshold,
ift=opt.ift,
)
def forward(self, points, weights, K1, K2, im_size1, im_size2, ground_truth=None):
# estimator = self.initialize_ransac(points.shape[0], K1, K2)
points_ = points.clone()
start_time = time.time()
models, _, model_score, iterations = self.estimator(
points_, weights, K1, K2, ground_truth
)
ransac_time = time.time() - start_time
# collect all the models from different iterations
if self.opt.tr:
Es = torch.cat(
list(models.values())
) # .cpu().detach().numpy() # no gradient again
else:
Es = models
# masks for removing models containing nan values
nan_filter = [not (torch.isnan(E).any()) for E in Es]
return Es[nan_filter], ransac_time
class DS_Block(nn.Module):
def __init__(
self, initial=False, predict=False, out_channel=128, k_num=8, sampling_rate=0.5
):
super(DS_Block, self).__init__()
self.initial = initial
self.in_channel = 7
self.out_channel = out_channel
self.k_num = k_num
# flag if we predict the parametric models or only weights
self.predict = predict
self.sr = sampling_rate
self.conv = nn.Sequential(
nn.Conv2d(self.in_channel, self.out_channel, (1, 1)),
nn.BatchNorm2d(self.out_channel),
nn.ReLU(inplace=True),
)
self.gcn = GCN_Block(self.out_channel)
self.embed_0 = nn.Sequential(
ResNet_Block(self.out_channel, self.out_channel, pre=False),
ResNet_Block(self.out_channel, self.out_channel, pre=False),
ResNet_Block(self.out_channel, self.out_channel, pre=False),
ResNet_Block(self.out_channel, self.out_channel, pre=False),
DGCNN_Block(self.k_num, self.out_channel),
ResNet_Block(self.out_channel, self.out_channel, pre=False),
ResNet_Block(self.out_channel, self.out_channel, pre=False),
ResNet_Block(self.out_channel, self.out_channel, pre=False),
ResNet_Block(self.out_channel, self.out_channel, pre=False),
)
self.embed_1 = nn.Sequential(
ResNet_Block(self.out_channel, self.out_channel, pre=False),
)
self.linear_0 = nn.Conv2d(self.out_channel, 1, (1, 1))
self.linear_1 = nn.Conv2d(self.out_channel, 1, (1, 1))
if self.predict:
self.embed_2 = ResNet_Block(self.out_channel, self.out_channel, pre=False)
self.linear_2 = nn.Conv2d(self.out_channel, 2, (1, 1))
def down_sampling(self, x, y, weights, indices, features=None, predict=False):
B, _, N, _ = x.size()
indices = indices[:, : int(N * self.sr)]
with torch.no_grad():
y_out = torch.gather(y, dim=-1, index=indices)
w_out = torch.gather(weights, dim=-1, index=indices)
indices = indices.view(B, 1, -1, 1)
if predict:
with torch.no_grad():
x_out = torch.gather(
x[:, :, :, :4], dim=2, index=indices.repeat(1, 1, 1, 4)
)
return x_out, y_out, w_out
else:
with torch.no_grad():
x_out = torch.gather(
x[:, :, :, :4], dim=2, index=indices.repeat(1, 1, 1, 4)
)
feature_out = torch.gather(
features, dim=2, index=indices.repeat(1, 128, 1, 1)
)
return x_out, y_out, w_out, feature_out
def forward(self, x):
B, _, N, _ = x.size()
out = self.conv(x)
out = self.embed_0(out)
w0 = self.linear_0(out).view(B, -1)
out_g = self.gcn(out, w0.detach())
out = out_g + out
out = self.embed_1(out)
w1 = self.linear_1(out).view(B, -1)
return w1
class DeepRansac_CLNet(nn.Module):
def __init__(self, opt):
super(DeepRansac_CLNet, self).__init__()
self.opt = opt
# consensus learning layer, to learn inlier probabilities
self.ds_0 = DS_Block(
initial=True, predict=False, out_channel=128, k_num=9, sampling_rate=1.0
)
# custom-layer, Generalized Differentiable RANSAC, to estimate model
self.ransac_layer = RANSACLayer(opt)
def forward(
self, points, K1, K2, im_size1, im_size2, prob_type=0, gt=None, predict=True
):
B, _, N, _ = points.shape
w1 = self.ds_0(points)
if torch.isnan(w1.std()):
print("output is nan here")
if torch.isnan(w1).any():
raise Exception("the predicted weights are nan")
log_probs = F.logsigmoid(w1).view(B, -1)
# normalization in log space such that probabilities sum to 1
if torch.isnan(log_probs).any():
print("predicted log probs have nan values")
# normalizer = torch.logsumexp(log_probs, dim=1)
# normalizer = normalizer.unsqueeze(1).expand(-1, N)
# logits = log_probs - normalizer
# weights = torch.exp(logits)
weights = torch.exp(log_probs).view(log_probs.shape[0], -1)
normalized_weights = weights / torch.sum(weights, dim=-1).unsqueeze(-1)
if prob_type == 0:
# normalized weights
output_weights = normalized_weights.clone()
elif prob_type == 1:
# unnormalized weights
output_weights = weights.clone()
else:
# logits
output_weights = log_probs.clone()
if torch.isnan(output_weights).any():
# This should never happen! Debug here
print("nan values in weights", weights)
ret = []
avg_time = 0
if predict:
for b in range(B):
if gt is not None:
Es, ransac_time = self.ransac_layer(
points.squeeze(-1)[b, 0:4].T,
output_weights[b],
K1[b],
K2[b],
im_size1[b],
im_size2[b],
gt[b],
)
else:
Es, ransac_time = self.ransac_layer(
points.squeeze(-1)[b, 0:4].T,
output_weights[b],
K1[b],
K2[b],
im_size1[b],
im_size2[b],
)
ret.append(Es)
avg_time += ransac_time
return ret, output_weights, avg_time / B
else:
return output_weights, avg_time / B
class CLNet(nn.Module):
def __init__(self):
super(CLNet, self).__init__()
# consensus learning layer, to learn inlier probabilities
self.ds_0 = DS_Block(
initial=True, predict=False, out_channel=128, k_num=9, sampling_rate=1.0
)
def forward(self, points, prob_type=0):
B, _, N, _ = points.shape
# import pdb; pdb.set_trace()
w1 = self.ds_0(points)
if torch.isnan(w1.std()):
print("output is nan here")
if torch.isnan(w1).any():
raise Exception("the predicted weights are nan")
log_probs = F.logsigmoid(w1).view(B, -1)
# normalization in log space such that probabilities sum to 1
if torch.isnan(log_probs).any():
print("predicted log probs have nan values")
weights = torch.exp(log_probs).view(log_probs.shape[0], -1)
normalized_weights = weights / torch.sum(weights, dim=-1).unsqueeze(-1)
if prob_type == 0:
# normalized weights
output_weights = normalized_weights.clone()
elif prob_type == 1:
# unnormalized weights
output_weights = weights.clone()
else:
# logits
output_weights = log_probs.clone()
if torch.isnan(output_weights).any():
# This should never happen! Debug here
print("nan values in weights", weights)
return output_weights
| 14,555 | Python | .py | 357 | 30.291317 | 88 | 0.551168 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,675 | datasets.py | disungatullina_MinBackProp/datasets.py | import math
import os
import cv2
import h5py
import numpy as np
import torch
import torch.utils.data as data
class Dataset(data.Dataset):
"""From NG-RANSAC collect the correspondences."""
def __init__(self, folders, ratiothreshold=0.8, nfeatures=2000):
# access the input points
self.nfeatures = nfeatures
self.ratiothreshold = ratiothreshold
self.minset = 5
self.files = []
for folder in folders:
self.files += [folder + f for f in os.listdir(folder)]
def __len__(self):
return len(self.files)
def __getitem__(self, index):
data = np.load(self.files[index], allow_pickle=True, encoding="latin1")
# correspondence coordinates and matching ratios (side information)
pts1, pts2, ratios = data[0], data[1], data[2]
# image sizes
im_size1, im_size2 = torch.from_numpy(np.asarray(data[3])), torch.from_numpy(
np.asarray(data[4])
)
# image calibration parameters
K1, K2 = torch.from_numpy(data[5]), torch.from_numpy(data[6])
# ground truth pose
gt_R, gt_t = torch.from_numpy(data[7]), torch.from_numpy(data[8])
# feature scale and orientation
f_size1, f_size2 = torch.from_numpy(np.asarray(data[9])), torch.from_numpy(
np.asarray(data[11])
)
ang1, ang2 = torch.from_numpy(np.asarray(data[10])), torch.from_numpy(
np.asarray(data[12])
)
# des1, des2 = torch.from_numpy(data[13]), torch.from_numpy(data[14])
# applying Lowes ratio criterion
ratio_filter = ratios[0, :, 0] < self.ratiothreshold
if (
ratio_filter.sum() < self.minset
): # ensure a minimum count of correspondences
print(
"WARNING! Ratio filter too strict. Only %d correspondences would be left, so I skip it."
% int(ratio_filter.sum())
)
else:
pts1 = pts1[:, ratio_filter, :]
pts2 = pts2[:, ratio_filter, :]
ratios = ratios[:, ratio_filter, :]
f_size1 = f_size1[:, ratio_filter, :]
f_size2 = f_size2[:, ratio_filter, :]
ang1 = ang1[:, ratio_filter, :]
ang2 = ang2[:, ratio_filter, :]
scale_ratio = f_size2 / f_size1
ang = ((ang2 - ang1) % 180) * (3.141592653 / 180)
# for essential matrices, normalize image coordinate using the calibration parameters
pts1 = cv2.undistortPoints(pts1, K1.numpy(), None)
pts2 = cv2.undistortPoints(pts2, K2.numpy(), None)
# due to the opencv version issue, here transform it
pts1_tran = list([j.tolist() for i in pts1 for j in i])
pts2_tran = list([j.tolist() for i in pts2 for j in i])
# stack image coordinates and side information into one tensor
correspondences = np.concatenate(
(np.array([pts1_tran]), np.array([pts2_tran]), ratios, scale_ratio, ang),
axis=2,
)
# correspondences = np.concatenate((pts1, pts2, ratios, scale_ratio, ang), axis=2)
correspondences = np.transpose(correspondences)
correspondences = torch.from_numpy(correspondences)
if self.nfeatures > 0:
# ensure that there are exactly nfeatures entries in the data tensor
if correspondences.size(1) > self.nfeatures:
rnd = torch.randperm(correspondences.size(1))
correspondences = correspondences[:, rnd, :]
correspondences = correspondences[:, 0 : self.nfeatures]
if correspondences.size(1) < self.nfeatures:
result = correspondences
for i in range(
0, math.ceil(self.nfeatures / correspondences.size(1) - 1)
):
rnd = torch.randperm(correspondences.size(1))
result = torch.cat((result, correspondences[:, rnd, :]), dim=1)
correspondences = result[:, 0 : self.nfeatures]
# construct the ground truth essential matrix from the ground truth relative pose
gt_E = torch.zeros((3, 3), dtype=torch.float32)
gt_E[0, 1] = -float(gt_t[2, 0])
gt_E[0, 2] = float(gt_t[1, 0])
gt_E[1, 0] = float(gt_t[2, 0])
gt_E[1, 2] = -float(gt_t[0, 0])
gt_E[2, 0] = -float(gt_t[1, 0])
gt_E[2, 1] = float(gt_t[0, 0])
gt_E = gt_E.mm(gt_R)
return {
"correspondences": correspondences.float(),
"gt_E": gt_E,
"gt_R": gt_R,
"gt_t": gt_t,
"K1": K1,
"K2": K2,
"im_size1": im_size1,
"im_size2": im_size2,
"files": self.files[index],
}
# class DatasetZero(data.Dataset):
# """From NG-RANSAC collect the correspondences."""
# def __init__(self, folder, ratiothreshold=0.8, nfeatures=2000, fmat=False):
# # access the input points
# self.nfeatures = nfeatures
# self.ratiothreshold = ratiothreshold
# self.fmat = fmat # estimate fundamental matrix instead of essential matrix
# self.minset = 7 if self.fmat else 5
# self.files = []
# self.files += [folder + f for f in os.listdir(folder)]
# def __len__(self):
# return len(self.files)
# def __getitem__(self, index):
# data = np.load(self.files[index], allow_pickle=True, encoding='latin1')
# # correspondence coordinates and matching ratios (side information)
# pts1, pts2, ratios = data[0], data[1], data[2]
# # image sizes
# im_size1, im_size2 = torch.from_numpy(np.asarray(data[3])), torch.from_numpy(np.asarray(data[4]))
# # image calibration parameters
# K1, K2 = torch.from_numpy(data[5]), torch.from_numpy(data[6])
# # ground truth pose
# gt_R, gt_t = torch.from_numpy(data[7]), torch.from_numpy(data[8])
# # feature scale and orientation
# f_size1, f_size2 = torch.from_numpy(np.asarray(data[9])), torch.from_numpy(np.asarray(data[11]))
# ang1, ang2 = torch.from_numpy(np.asarray(data[10])), torch.from_numpy(np.asarray(data[12]))
# # des1, des2 = torch.from_numpy(data[13]), torch.from_numpy(data[14])
# # applying Lowes ratio criterion
# ratio_filter = ratios[0, :, 0] < self.ratiothreshold
# if ratio_filter.sum() < self.minset: # ensure a minimum count of correspondences
# print("WARNING! Ratio filter too strict. Only %d correspondences would be left, so I skip it." % int(
# ratio_filter.sum()))
# else:
# pts1 = pts1[:, ratio_filter, :]
# pts2 = pts2[:, ratio_filter, :]
# ratios = ratios[:, ratio_filter, :]
# f_size1 = f_size1[:, ratio_filter, :]
# f_size2 = f_size2[:, ratio_filter, :]
# ang1 = ang1[:, ratio_filter, :]
# ang2 = ang2[:, ratio_filter, :]
# scale_ratio = f_size2 / f_size1
# ang = ((ang2 - ang1) % 180) * (3.141592653 / 180)
# if self.fmat:
# # for fundamental matrices, normalize image coordinates using the image size
# # (network should be independent to resolution)
# pts1[0, :, 0] -= float(im_size1[1]) / 2
# pts1[0, :, 1] -= float(im_size1[0]) / 2
# pts1 /= float(max(im_size1))
# pts2[0, :, 0] -= float(im_size2[1]) / 2
# pts2[0, :, 1] -= float(im_size2[0]) / 2
# pts2 /= float(max(im_size2))
# #utils.normalize_pts(pts1, im_size1)
# #utils.normalize_pts(pts2, im_size2)
# correspondences = np.concatenate((pts1, pts2, ratios, scale_ratio, ang), axis=2)
# else:
# # for essential matrices, normalize image coordinate using the calibration parameters
# pts1 = cv2.undistortPoints(pts1, K1.numpy(), None)
# pts2 = cv2.undistortPoints(pts2, K2.numpy(), None)
# # due to the opencv version issue, here transform it
# pts1_tran = list([j.tolist() for i in pts1 for j in i])
# pts2_tran = list([j.tolist() for i in pts2 for j in i])
# # stack image coordinates and side information into one tensor
# correspondences = np.concatenate((np.array([pts1_tran]), np.array([pts2_tran]), ratios, scale_ratio, ang),
# axis=2)
# # correspondences = np.concatenate((pts1, pts2, ratios, scale_ratio, ang), axis=2)
# correspondences = np.transpose(correspondences)
# correspondences = torch.from_numpy(correspondences)
# if self.nfeatures > 0:
# # ensure that there are exactly nfeatures entries in the data tensor
# if correspondences.size(1) > self.nfeatures:
# rnd = torch.randperm(correspondences.size(1))
# correspondences = correspondences[:, rnd, :]
# correspondences = correspondences[:, 0:self.nfeatures]
# if correspondences.size(1) < self.nfeatures:
# result = correspondences
# correspondences = torch.zeros(correspondences.size(0), self.nfeatures, correspondences.size(2))
# correspondences[:, 0:result.size(1)] = result
# # construct the ground truth essential matrix from the ground truth relative pose
# gt_E = torch.zeros((3, 3), dtype=torch.float32)
# gt_E[0, 1] = -float(gt_t[2, 0])
# gt_E[0, 2] = float(gt_t[1, 0])
# gt_E[1, 0] = float(gt_t[2, 0])
# gt_E[1, 2] = -float(gt_t[0, 0])
# gt_E[2, 0] = -float(gt_t[1, 0])
# gt_E[2, 1] = float(gt_t[0, 0])
# gt_E = gt_E.mm(gt_R)
# # fundamental matrix from essential matrix
# gt_F = K2.inverse().transpose(0, 1).mm(gt_E).mm(K1.inverse())
# return {'correspondences': correspondences.float(), 'gt_F': gt_F, 'gt_E': gt_E, 'gt_R': gt_R, 'gt_t': gt_t,
# 'K1': K1, 'K2': K2, 'im_size1': im_size1, 'im_size2': im_size2, 'files': self.files[index]}
# class DatasetPictureTest(data.Dataset):
# """Rewrite data collector based on NG-RANSAC collect the correspondences."""
# def __init__(self, folder, ratiothreshold=0.8, nfeatures=2000, fmat=False):
# # access the input points
# self.nfeatures = nfeatures
# self.ratiothreshold = ratiothreshold
# self.fmat = fmat # estimate fundamental matrix instead of essential matrix
# self.minset = 7 if self.fmat else 5
# scene = folder.split('/')[-2]
# keys = np.load(folder.replace(scene + '/', 'evaluation_list/') + scene + '_list.npy')
# self.files = []
# self.files += [folder + f for f in os.listdir(folder)]
# self.files = sorted(self.files)
# self.files_dict = {}
# for given_file in self.files:
# if 'Egt.h5' in given_file:
# self.files_dict['gt_E'] = given_file
# elif 'Fgt.h5' in given_file:
# self.files_dict['gt_F'] = given_file
# elif 'K1_K2.h5' in given_file:
# self.files_dict['K1_K2'] = given_file
# elif 'R.h5' in given_file:
# self.files_dict['R'] = given_file
# elif 'T.h5' in given_file:
# self.files_dict['T'] = given_file
# elif '/images' in given_file:
# self.files_dict['img_dir'] = given_file
# self.pts1_list = []
# self.pts2_list = []
# for k in keys:
# img_id1 = k.split('_')[1] + '_' + k.split('_')[2]
# img_id2 = k.split('_')[3] + '_' + k.split('_')[4].split('.')[0]
# self.pts1_list.append(img_id1)
# self.pts2_list.append(img_id2)
# self.gt_F = loadh5(self.files_dict['gt_F'])
# self.gt_E =loadh5(self.files_dict['gt_E'])
# self.K1_K2 = loadh5(self.files_dict['K1_K2'])
# self.R = loadh5(self.files_dict['R'])
# self.T = loadh5(self.files_dict['T'])
# def __len__(self):
# return len(self.pts1_list)
# def __getitem__(self, index):
# img1 = load_torch_image(self.files_dict['img_dir'] + '/' + self.pts1_list[index] + '.jpg')
# img2 = load_torch_image(self.files_dict['img_dir'] + '/' + self.pts2_list[index] + '.jpg')
# match_id = self.pts1_list[index] + '-' + self.pts2_list[index]
# R1 = self.R[self.pts1_list[index]]
# R2 = self.R[self.pts2_list[index]]
# T1 = self.T[self.pts1_list[index]]
# T2 = self.T[self.pts2_list[index]]
# gt_R = np.dot(R2, R1.T)
# gt_t = T2 - np.dot(gt_R, T1)
# return {"image0": K.color.rgb_to_grayscale(img1).squeeze(0), # LofTR works on grayscale images only
# "image1": K.color.rgb_to_grayscale(img2).squeeze(0),
# 'gt_F': torch.from_numpy(self.gt_F[match_id]),
# 'gt_E': torch.from_numpy(self.gt_E[match_id]),
# 'gt_R': gt_R, 'gt_t': gt_t,
# 'K1': torch.from_numpy(self.K1_K2[match_id][0][0]),
# 'K2': torch.from_numpy(self.K1_K2[match_id][0][1]),
# }
# class Dataset3D(data.Dataset):
# def __init__(self, folders, num=4000):
# # access the input points
# self.files = []
# for folder in folders:
# self.files += [folder + f for f in os.listdir(folder)]
# self.num = num
# def __len__(self):
# return len(self.files)
# def __getitem__(self, index):
# data = np.load(self.files[index])
# gt_pose = data['transform']
# scores = data['corr_scores']
# pts1 = torch.from_numpy(data['src_corr_points'])
# pts2 = torch.from_numpy(data['ref_corr_points'])
# # import pdb; pdb.set_trace()
# try:
# correspondences = np.concatenate((pts1, pts2, np.expand_dims(scores, -1)), axis=-1)
# except:
# import pdb; pdb.set_trace()
# correspondences = torch.from_numpy(correspondences)
# if self.num > 0:
# # ensure that there are exactly nfeatures entries in the data tensor
# if correspondences.shape[0] > self.num:
# rnd = torch.randperm(correspondences.shape[0])
# correspondences = correspondences[rnd, :]
# correspondences = correspondences[0:self.num]
# gt_pose = gt_pose[:self.num]
# if correspondences.shape[0] < self.num:
# # import pdb; pdb.set_trace()
# result = correspondences
# for i in range(0, math.ceil(self.num / correspondences.shape[0] - 1)):
# rnd = torch.randperm(correspondences.shape[0])
# result = torch.cat((result, correspondences[rnd, :]), dim=0)
# correspondences = result[0:self.num]
# return {
# 'correspondences': correspondences,
# 'gt_pose': gt_pose
# }
# class DatasetPicture(data.Dataset):
# """Rewrite data collector based on NG-RANSAC collect the correspondences."""
# def __init__(self, folder, ratiothreshold=0.8, nfeatures=2000, fmat=False, valid=False):
# # access the input points
# self.nfeatures = nfeatures
# self.ratiothreshold = ratiothreshold
# self.fmat = fmat # estimate fundamental matrix instead of essential matrix
# self.minset = 7 if self.fmat else 5
# with h5py.File(folder + 'Fgt.h5', 'r') as h5file:
# keys = list(h5file.keys())
# self.files = []
# scene = folder.split('/')[-2]
# if valid:
# keys = np.load(folder.replace(scene + '/', 'evaluation_list/') + scene + '_list.npy')
# else:
# keys = np.load(folder.replace(scene + '/', 'evaluation_list/') + scene + '_train.npy')
# self.files += [folder + f for f in os.listdir(folder)]
# self.files = sorted(self.files)
# self.files_dict = {}
# for given_file in self.files:
# if 'Egt.h5' in given_file:
# self.files_dict['gt_E'] = given_file
# elif 'Fgt.h5' in given_file:
# self.files_dict['gt_F'] = given_file
# elif 'K1_K2.h5' in given_file:
# self.files_dict['K1_K2'] = given_file
# elif 'R.h5' in given_file:
# self.files_dict['R'] = given_file
# elif 'T.h5' in given_file:
# self.files_dict['T'] = given_file
# elif '/images' in given_file:
# self.files_dict['img_dir'] = given_file
# self.pts1_list = []
# self.pts2_list = []
# for k in keys:
# img_id1 = k.split('_')[1] + '_' + k.split('_')[2]
# img_id2 = k.split('_')[3] + '_' + k.split('_')[4].split('.')[0]
# self.pts1_list.append(img_id1)
# self.pts2_list.append(img_id2)
# self.gt_F = loadh5(self.files_dict['gt_F'])
# self.gt_E =loadh5(self.files_dict['gt_E'])
# self.K1_K2 = loadh5(self.files_dict['K1_K2'])
# self.R = loadh5(self.files_dict['R'])
# self.T = loadh5(self.files_dict['T'])
# def __len__(self):
# return len(self.pts1_list)
# def __getitem__(self, index):
# img1 = load_torch_image(self.files_dict['img_dir'] + '/' + self.pts1_list[index] + '.jpg')
# img2 = load_torch_image(self.files_dict['img_dir'] + '/' + self.pts2_list[index] + '.jpg')
# match_id = self.pts1_list[index] + '-' + self.pts2_list[index]
# R1 = self.R[self.pts1_list[index]]
# R2 = self.R[self.pts2_list[index]]
# T1 = self.T[self.pts1_list[index]]
# T2 = self.T[self.pts2_list[index]]
# gt_R = np.dot(R2, R1.T)
# gt_t = T2 - np.dot(gt_R, T1)
# return {"image0": K.color.rgb_to_grayscale(img1).squeeze(0), # LofTR works on grayscale images only
# "image1": K.color.rgb_to_grayscale(img2).squeeze(0),
# 'gt_F': torch.from_numpy(self.gt_F[match_id]),
# 'gt_E': torch.from_numpy(self.gt_E[match_id]),
# 'gt_R': gt_R, 'gt_t': gt_t,
# 'K1': torch.from_numpy(self.K1_K2[match_id][0][0]),
# 'K2': torch.from_numpy(self.K1_K2[match_id][0][1]),
# }
| 18,453 | Python | .py | 357 | 47.733894 | 120 | 0.553109 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,676 | nodes.py | disungatullina_MinBackProp/nodes.py | import math
import torch
import random
import time
import numpy as np
import torch.nn as nn
from torch.autograd import Function
from ddn.ddn.pytorch.node import *
import estimators.essential_matrix_estimator_nister as ns
############ IFT function ############
class IFTFunction(torch.autograd.Function):
# Note that forward, setup_context, and backward are @staticmethods
@staticmethod
def forward(ctx, minimal_samples, E_true, estimator):
"""
E_true: 3 x 3
minimal_samples : b x 5 x 4
"""
est = estimator.estimate_model(minimal_samples)
solution_num = 10
distances = torch.norm(
est - E_true.unsqueeze(0).repeat(est.shape[0], 1, 1), dim=(1, 2)
).view(est.shape[0], -1)
try:
chosen_indices = torch.argmin(distances.view(-1, solution_num), dim=-1)
chosen_models = torch.stack(
[
(est.view(-1, solution_num, 3, 3))[i, chosen_indices[i], :]
for i in range(int(est.shape[0] / solution_num))
]
)
except ValueError as e:
print(
"not enough models for selection, we choose the first solution in this batch",
e,
est.shape,
)
chosen_models = est[0].unsqueeze(0)
ctx.save_for_backward(minimal_samples, chosen_models)
return chosen_models
@staticmethod
# inputs is a Tuple of all of the inputs passed to forward.
# output is the output of the forward().
def setup_context(ctx, inputs, output):
minimal_samples, _, _ = inputs
ctx.save_for_backward(minimal_samples, output)
# This function has only a single output, so it gets only one gradient
@staticmethod
def backward(ctx, grad_output):
# This is a pattern that is very convenient - at the top of backward
# unpack saved_tensors and initialize all gradients w.r.t. inputs to
# None. Thanks to the fact that additional trailing Nones are
# ignored, the return statement is simple even when the function has
# optional inputs.
minimal_samples, output = ctx.saved_tensors # output -- [b, 3, 3]
grad_E_true = grad_minimal_samples = None
# These needs_input_grad checks are optional and there only to
# improve efficiency. If you want to make your code simpler, you can
# skip them. Returning gradients for inputs that don't require it is
# not an error.
b = grad_output.shape[0]
# E - bx3x3 ; minimal_sample - bx5x4 ; J_Ex - bx9x20 ; grad_output - bx3x3
J_Ex = compute_jacobians(output, minimal_samples) # b x 9 x 20
J_Ex = torch.einsum("bi,bij->bj", grad_output.view(b, 9), J_Ex)
grad_minimal_samples = J_Ex.view(b, 5, 4)
return grad_minimal_samples, None, None
class IFTLayer(nn.Module):
def __init__(self, device, ift):
super().__init__()
self.estimator = ns.EssentialMatrixEstimatorNister(device=device, ift=ift)
def forward(self, minimal_samples, E_true):
return IFTFunction.apply(minimal_samples, E_true, self.estimator)
def compute_jacobians(E, minimal_sample):
"""
E -- b x 3 x 3
minimal_sample -- b x 5 x 4
"""
b = E.shape[0]
E11 = E[:, 0, 0]
E12 = E[:, 0, 1]
E13 = E[:, 0, 2]
E21 = E[:, 1, 0]
E22 = E[:, 1, 1]
E23 = E[:, 1, 2]
E31 = E[:, 2, 0]
E32 = E[:, 2, 1]
E33 = E[:, 2, 2]
x11 = minimal_sample[:, 0, 0]
y11 = minimal_sample[:, 0, 1]
x12 = minimal_sample[:, 0, 2]
y12 = minimal_sample[:, 0, 3]
x21 = minimal_sample[:, 1, 0]
y21 = minimal_sample[:, 1, 1]
x22 = minimal_sample[:, 1, 2]
y22 = minimal_sample[:, 1, 3]
x31 = minimal_sample[:, 2, 0]
y31 = minimal_sample[:, 2, 1]
x32 = minimal_sample[:, 2, 2]
y32 = minimal_sample[:, 2, 3]
x41 = minimal_sample[:, 3, 0]
y41 = minimal_sample[:, 3, 1]
x42 = minimal_sample[:, 3, 2]
y42 = minimal_sample[:, 3, 3]
x51 = minimal_sample[:, 4, 0]
y51 = minimal_sample[:, 4, 1]
x52 = minimal_sample[:, 4, 2]
y52 = minimal_sample[:, 4, 3]
J_E = torch.zeros((b, 16, 9), device=minimal_sample.device)
J_E[:, 0, 0] = x12 * x11
J_E[:, 1, 0] = x22 * x21
J_E[:, 2, 0] = x32 * x31
J_E[:, 3, 0] = x42 * x41
J_E[:, 4, 0] = x52 * x51
J_E[:, 5, 0] = 2 * E11
J_E[:, 6, 0] = (
3 * E11**2
+ E12**2
+ E13**2
+ E21**2
- E22**2
- E23**2
+ E31**2
- E32**2
- E33**2
)
J_E[:, 7, 0] = 2 * E11 * E12 + 2 * E21 * E22 + 2 * E31 * E32
J_E[:, 8, 0] = 2 * E11 * E13 + 2 * E21 * E23 + 2 * E31 * E33
J_E[:, 9, 0] = 2 * E11 * E21 + 2 * E12 * E22 + 2 * E13 * E23
J_E[:, 10, 0] = -2 * E11 * E22 + 2 * E12 * E21
J_E[:, 11, 0] = -2 * E11 * E23 + 2 * E13 * E21
J_E[:, 12, 0] = 2 * E11 * E31 + 2 * E12 * E32 + 2 * E13 * E33
J_E[:, 13, 0] = -2 * E11 * E32 + 2 * E12 * E31
J_E[:, 14, 0] = -2 * E11 * E33 + 2 * E13 * E31
J_E[:, 15, 0] = E22 * E33 - E23 * E32
J_E[:, 0, 1] = x12 * y11
J_E[:, 1, 1] = x22 * y21
J_E[:, 2, 1] = x32 * y31
J_E[:, 3, 1] = x42 * y41
J_E[:, 4, 1] = x52 * y51
J_E[:, 5, 1] = 2 * E12
J_E[:, 6, 1] = 2 * E11 * E12 + 2 * E21 * E22 + 2 * E31 * E32
J_E[:, 7, 1] = (
E11**2
+ 3 * E12**2
+ E13**2
- E21**2
+ E22**2
- E23**2
- E31**2
+ E32**2
- E33**2
)
J_E[:, 8, 1] = 2 * E12 * E13 + 2 * E22 * E23 + 2 * E32 * E33
J_E[:, 9, 1] = 2 * E11 * E22 - 2 * E12 * E21
J_E[:, 10, 1] = 2 * E11 * E21 + 2 * E12 * E22 + 2 * E13 * E23
J_E[:, 11, 1] = -2 * E12 * E23 + 2 * E13 * E22
J_E[:, 12, 1] = 2 * E11 * E32 - 2 * E12 * E31
J_E[:, 13, 1] = 2 * E11 * E31 + 2 * E12 * E32 + 2 * E13 * E33
J_E[:, 14, 1] = -2 * E12 * E33 + 2 * E13 * E32
J_E[:, 15, 1] = -E21 * E33 + E23 * E31
J_E[:, 0, 2] = x12
J_E[:, 1, 2] = x22
J_E[:, 2, 2] = x32
J_E[:, 3, 2] = x42
J_E[:, 4, 2] = x52
J_E[:, 5, 2] = 2 * E13
J_E[:, 6, 2] = 2 * E11 * E13 + 2 * E21 * E23 + 2 * E31 * E33
J_E[:, 7, 2] = 2 * E12 * E13 + 2 * E22 * E23 + 2 * E32 * E33
J_E[:, 8, 2] = (
E11**2
+ E12**2
+ 3 * E13**2
- E21**2
- E22**2
+ E23**2
- E31**2
- E32**2
+ E33**2
)
J_E[:, 9, 2] = 2 * E11 * E23 - 2 * E13 * E21
J_E[:, 10, 2] = 2 * E12 * E23 - 2 * E13 * E22
J_E[:, 11, 2] = 2 * E11 * E21 + 2 * E12 * E22 + 2 * E13 * E23
J_E[:, 12, 2] = 2 * E11 * E33 - 2 * E13 * E31
J_E[:, 13, 2] = 2 * E12 * E33 - 2 * E13 * E32
J_E[:, 14, 2] = 2 * E11 * E31 + 2 * E12 * E32 + 2 * E13 * E33
J_E[:, 15, 2] = E21 * E32 - E22 * E31
J_E[:, 0, 3] = y12 * y11
J_E[:, 1, 3] = y22 * y21
J_E[:, 2, 3] = y32 * y31
J_E[:, 3, 3] = y42 * y41
J_E[:, 4, 3] = y52 * y51
J_E[:, 5, 3] = 2 * E21
J_E[:, 6, 3] = 2 * E11 * E21 + 2 * E12 * E22 + 2 * E13 * E23
J_E[:, 7, 3] = 2 * E11 * E22 - 2 * E12 * E21
J_E[:, 8, 3] = 2 * E11 * E23 - 2 * E13 * E21
J_E[:, 9, 3] = (
E11**2
- E12**2
- E13**2
+ 3 * E21**2
+ E22**2
+ E23**2
+ E31**2
- E32**2
- E33**2
)
J_E[:, 10, 3] = 2 * E11 * E12 + 2 * E21 * E22 + 2 * E31 * E32
J_E[:, 11, 3] = 2 * E11 * E13 + 2 * E21 * E23 + 2 * E31 * E33
J_E[:, 12, 3] = 2 * E21 * E31 + 2 * E22 * E32 + 2 * E23 * E33
J_E[:, 13, 3] = -2 * E21 * E32 + 2 * E22 * E31
J_E[:, 14, 3] = -2 * E21 * E33 + 2 * E23 * E31
J_E[:, 15, 3] = -E12 * E33 + E13 * E32
J_E[:, 0, 4] = y12 * y11
J_E[:, 1, 4] = y22 * y21
J_E[:, 2, 4] = y32 * y31
J_E[:, 3, 4] = y42 * y41
J_E[:, 4, 4] = y52 * y51
J_E[:, 5, 4] = 2 * E22
J_E[:, 6, 4] = -2 * E11 * E22 + 2 * E12 * E21
J_E[:, 7, 4] = 2 * E11 * E21 + 2 * E12 * E22 + 2 * E13 * E23
J_E[:, 8, 4] = 2 * E12 * E23 - 2 * E13 * E22
J_E[:, 9, 4] = 2 * E11 * E12 + 2 * E21 * E22 + 2 * E31 * E32
J_E[:, 10, 4] = (
-(E11**2)
+ E12**2
- E13**2
+ E21**2
+ 3 * E22**2
+ E23**2
- E31**2
+ E32**2
- E33**2
)
J_E[:, 11, 4] = 2 * E12 * E13 + 2 * E22 * E23 + 2 * E32 * E33
J_E[:, 12, 4] = 2 * E21 * E32 - 2 * E22 * E31
J_E[:, 13, 4] = 2 * E21 * E31 + 2 * E22 * E32 + 2 * E23 * E33
J_E[:, 14, 4] = -2 * E22 * E33 + 2 * E23 * E32
J_E[:, 15, 4] = E11 * E33 - E13 * E31
J_E[:, 0, 5] = y12
J_E[:, 1, 5] = y22
J_E[:, 2, 5] = y32
J_E[:, 3, 5] = y42
J_E[:, 4, 5] = y52
J_E[:, 5, 5] = 2 * E23
J_E[:, 6, 5] = -2 * E11 * E23 + 2 * E13 * E21
J_E[:, 7, 5] = -2 * E12 * E23 + 2 * E13 * E22
J_E[:, 8, 5] = 2 * E11 * E21 + 2 * E12 * E22 + 2 * E13 * E23
J_E[:, 9, 5] = 2 * E11 * E13 + 2 * E21 * E23 + 2 * E31 * E33
J_E[:, 10, 5] = 2 * E12 * E13 + 2 * E22 * E23 + 2 * E32 * E33
J_E[:, 11, 5] = (
-(E11**2)
- E12**2
+ E13**2
+ E21**2
+ E22**2
+ 3 * E23**2
- E31**2
- E32**2
+ E33**2
)
J_E[:, 12, 5] = 2 * E21 * E33 - 2 * E23 * E31
J_E[:, 13, 5] = 2 * E22 * E33 - 2 * E23 * E32
J_E[:, 14, 5] = 2 * E21 * E31 + 2 * E22 * E32 + 2 * E23 * E33
J_E[:, 15, 5] = -E11 * E32 + E12 * E31
J_E[:, 0, 6] = x11
J_E[:, 1, 6] = x21
J_E[:, 2, 6] = x31
J_E[:, 3, 6] = x41
J_E[:, 4, 6] = x51
J_E[:, 5, 6] = 2 * E31
J_E[:, 6, 6] = 2 * E11 * E31 + 2 * E12 * E32 + 2 * E13 * E33
J_E[:, 7, 6] = 2 * E11 * E32 - 2 * E12 * E31
J_E[:, 8, 6] = 2 * E11 * E33 - 2 * E13 * E31
J_E[:, 9, 6] = 2 * E21 * E31 + 2 * E22 * E32 + 2 * E23 * E33
J_E[:, 10, 6] = 2 * E21 * E32 - 2 * E22 * E31
J_E[:, 11, 6] = 2 * E21 * E33 - 2 * E23 * E31
J_E[:, 12, 6] = (
E11**2
- E12**2
- E13**2
+ E21**2
- E22**2
- E23**2
+ 3 * E31**2
+ E32**2
+ E33**2
)
J_E[:, 13, 6] = 2 * E11 * E12 + 2 * E21 * E22 + 2 * E31 * E32
J_E[:, 14, 6] = 2 * E11 * E13 + 2 * E21 * E23 + 2 * E31 * E33
J_E[:, 15, 6] = E12 * E23 - E13 * E22
J_E[:, 0, 7] = y11
J_E[:, 1, 7] = y21
J_E[:, 2, 7] = y31
J_E[:, 3, 7] = y41
J_E[:, 4, 7] = y51
J_E[:, 5, 7] = 2 * E32
J_E[:, 6, 7] = -2 * E11 * E32 + 2 * E12 * E31
J_E[:, 7, 7] = 2 * E11 * E31 + 2 * E12 * E32 + 2 * E13 * E33
J_E[:, 8, 7] = 2 * E12 * E33 - 2 * E13 * E32
J_E[:, 9, 7] = -2 * E21 * E32 + 2 * E22 * E31
J_E[:, 10, 7] = 2 * E21 * E31 + 2 * E22 * E32 + 2 * E23 * E33
J_E[:, 11, 7] = 2 * E22 * E33 - 2 * E23 * E32
J_E[:, 12, 7] = 2 * E11 * E12 + 2 * E21 * E22 + 2 * E31 * E32
J_E[:, 13, 7] = (
-(E11**2)
+ E12**2
- E13**2
- E21**2
+ E22**2
- E23**2
+ E31**2
+ 3 * E32**2
+ E33**2
)
J_E[:, 14, 7] = 2 * E12 * E13 + 2 * E22 * E23 + 2 * E32 * E33
J_E[:, 15, 7] = -E11 * E23 + E13 * E21
J_E[:, 0, 8] = 1
J_E[:, 1, 8] = 1
J_E[:, 2, 8] = 1
J_E[:, 3, 8] = 1
J_E[:, 4, 8] = 1
J_E[:, 5, 8] = 2 * E33
J_E[:, 6, 8] = -2 * E11 * E33 + 2 * E13 * E31
J_E[:, 7, 8] = -2 * E12 * E33 + 2 * E13 * E32
J_E[:, 8, 8] = 2 * E11 * E31 + 2 * E12 * E32 + 2 * E13 * E33
J_E[:, 9, 8] = -2 * E21 * E33 + 2 * E23 * E31
J_E[:, 10, 8] = -2 * E22 * E33 + 2 * E23 * E32
J_E[:, 11, 8] = 2 * E21 * E31 + 2 * E22 * E32 + 2 * E23 * E33
J_E[:, 12, 8] = 2 * E11 * E13 + 2 * E21 * E23 + 2 * E31 * E33
J_E[:, 13, 8] = 2 * E12 * E13 + 2 * E22 * E23 + 2 * E32 * E33
J_E[:, 14, 8] = (
-(E11**2)
- E12**2
+ E13**2
- E21**2
- E22**2
+ E23**2
+ E31**2
+ E32**2
+ 3 * E33**2
)
J_E[:, 15, 8] = E11 * E22 - E12 * E21
J_x = torch.zeros((b, 16, 20), device=minimal_sample.device)
J_x[:, 0, 0] = E11 * x12 + E21 * y12 + E31
J_x[:, 1, 0] = 0
J_x[:, 2, 0] = 0
J_x[:, 3, 0] = 0
J_x[:, 4, 0] = 0
J_x[:, 5, 0] = 0
J_x[:, 6, 0] = 0
J_x[:, 7, 0] = 0
J_x[:, 8, 0] = 0
J_x[:, 9, 0] = 0
J_x[:, 10, 0] = 0
J_x[:, 11, 0] = 0
J_x[:, 12, 0] = 0
J_x[:, 13, 0] = 0
J_x[:, 14, 0] = 0
J_x[:, 15, 0] = 0
J_x[:, 0, 1] = E12 * x12 + E22 * y12 + E32
J_x[:, 1, 1] = 0
J_x[:, 2, 1] = 0
J_x[:, 3, 1] = 0
J_x[:, 4, 1] = 0
J_x[:, 5, 1] = 0
J_x[:, 6, 1] = 0
J_x[:, 7, 1] = 0
J_x[:, 8, 1] = 0
J_x[:, 9, 1] = 0
J_x[:, 10, 1] = 0
J_x[:, 11, 1] = 0
J_x[:, 12, 1] = 0
J_x[:, 13, 1] = 0
J_x[:, 14, 1] = 0
J_x[:, 15, 1] = 0
J_x[:, 0, 2] = E11 * x11 + E12 * y11 + E13
J_x[:, 1, 2] = 0
J_x[:, 2, 2] = 0
J_x[:, 3, 2] = 0
J_x[:, 4, 2] = 0
J_x[:, 5, 2] = 0
J_x[:, 6, 2] = 0
J_x[:, 7, 2] = 0
J_x[:, 8, 2] = 0
J_x[:, 9, 2] = 0
J_x[:, 10, 2] = 0
J_x[:, 11, 2] = 0
J_x[:, 12, 2] = 0
J_x[:, 13, 2] = 0
J_x[:, 14, 2] = 0
J_x[:, 15, 2] = 0
J_x[:, 0, 3] = E21 * x11 + E22 * y11 + E23
J_x[:, 1, 3] = 0
J_x[:, 2, 3] = 0
J_x[:, 3, 3] = 0
J_x[:, 4, 3] = 0
J_x[:, 5, 3] = 0
J_x[:, 6, 3] = 0
J_x[:, 7, 3] = 0
J_x[:, 8, 3] = 0
J_x[:, 9, 3] = 0
J_x[:, 10, 3] = 0
J_x[:, 11, 3] = 0
J_x[:, 12, 3] = 0
J_x[:, 13, 3] = 0
J_x[:, 14, 3] = 0
J_x[:, 15, 3] = 0
J_x[:, 0, 4] = 0
J_x[:, 1, 4] = E11 * x22 + E21 * y22 + E31
J_x[:, 2, 4] = 0
J_x[:, 3, 4] = 0
J_x[:, 4, 4] = 0
J_x[:, 5, 4] = 0
J_x[:, 6, 4] = 0
J_x[:, 7, 4] = 0
J_x[:, 8, 4] = 0
J_x[:, 9, 4] = 0
J_x[:, 10, 4] = 0
J_x[:, 11, 4] = 0
J_x[:, 12, 4] = 0
J_x[:, 13, 4] = 0
J_x[:, 14, 4] = 0
J_x[:, 15, 4] = 0
J_x[:, 0, 5] = 0
J_x[:, 1, 5] = E12 * x22 + E22 * y22 + E32
J_x[:, 2, 5] = 0
J_x[:, 3, 5] = 0
J_x[:, 4, 5] = 0
J_x[:, 5, 5] = 0
J_x[:, 6, 5] = 0
J_x[:, 7, 5] = 0
J_x[:, 8, 5] = 0
J_x[:, 9, 5] = 0
J_x[:, 10, 5] = 0
J_x[:, 11, 5] = 0
J_x[:, 12, 5] = 0
J_x[:, 13, 5] = 0
J_x[:, 14, 5] = 0
J_x[:, 15, 5] = 0
J_x[:, 0, 6] = 0
J_x[:, 1, 6] = E11 * x21 + E12 * y21 + E13
J_x[:, 2, 6] = 0
J_x[:, 3, 6] = 0
J_x[:, 4, 6] = 0
J_x[:, 5, 6] = 0
J_x[:, 6, 6] = 0
J_x[:, 7, 6] = 0
J_x[:, 8, 6] = 0
J_x[:, 9, 6] = 0
J_x[:, 10, 6] = 0
J_x[:, 11, 6] = 0
J_x[:, 12, 6] = 0
J_x[:, 13, 6] = 0
J_x[:, 14, 6] = 0
J_x[:, 15, 6] = 0
J_x[:, 0, 7] = 0
J_x[:, 1, 7] = E21 * x21 + E22 * y21 + E23
J_x[:, 2, 7] = 0
J_x[:, 3, 7] = 0
J_x[:, 4, 7] = 0
J_x[:, 5, 7] = 0
J_x[:, 6, 7] = 0
J_x[:, 7, 7] = 0
J_x[:, 8, 7] = 0
J_x[:, 9, 7] = 0
J_x[:, 10, 7] = 0
J_x[:, 11, 7] = 0
J_x[:, 12, 7] = 0
J_x[:, 13, 7] = 0
J_x[:, 14, 7] = 0
J_x[:, 15, 7] = 0
J_x[:, 0, 8] = 0
J_x[:, 1, 8] = 0
J_x[:, 2, 8] = E11 * x32 + E21 * y32 + E31
J_x[:, 3, 8] = 0
J_x[:, 4, 8] = 0
J_x[:, 5, 8] = 0
J_x[:, 6, 8] = 0
J_x[:, 7, 8] = 0
J_x[:, 8, 8] = 0
J_x[:, 9, 8] = 0
J_x[:, 10, 8] = 0
J_x[:, 11, 8] = 0
J_x[:, 12, 8] = 0
J_x[:, 13, 8] = 0
J_x[:, 14, 8] = 0
J_x[:, 15, 8] = 0
J_x[:, 0, 9] = 0
J_x[:, 1, 9] = 0
J_x[:, 2, 9] = E12 * x32 + E22 * y32 + E32
J_x[:, 3, 9] = 0
J_x[:, 4, 9] = 0
J_x[:, 5, 9] = 0
J_x[:, 6, 9] = 0
J_x[:, 7, 9] = 0
J_x[:, 8, 9] = 0
J_x[:, 9, 9] = 0
J_x[:, 10, 9] = 0
J_x[:, 11, 9] = 0
J_x[:, 12, 9] = 0
J_x[:, 13, 9] = 0
J_x[:, 14, 9] = 0
J_x[:, 15, 9] = 0
J_x[:, 0, 10] = 0
J_x[:, 1, 10] = 0
J_x[:, 2, 10] = E11 * x31 + E12 * y31 + E13
J_x[:, 3, 10] = 0
J_x[:, 4, 10] = 0
J_x[:, 5, 10] = 0
J_x[:, 6, 10] = 0
J_x[:, 7, 10] = 0
J_x[:, 8, 10] = 0
J_x[:, 9, 10] = 0
J_x[:, 10, 10] = 0
J_x[:, 11, 10] = 0
J_x[:, 12, 10] = 0
J_x[:, 13, 10] = 0
J_x[:, 14, 10] = 0
J_x[:, 15, 10] = 0
J_x[:, 0, 11] = 0
J_x[:, 1, 11] = 0
J_x[:, 2, 11] = E21 * x31 + E22 * y31 + E23
J_x[:, 3, 11] = 0
J_x[:, 4, 11] = 0
J_x[:, 5, 11] = 0
J_x[:, 6, 11] = 0
J_x[:, 7, 11] = 0
J_x[:, 8, 11] = 0
J_x[:, 9, 11] = 0
J_x[:, 10, 11] = 0
J_x[:, 11, 11] = 0
J_x[:, 12, 11] = 0
J_x[:, 13, 11] = 0
J_x[:, 14, 11] = 0
J_x[:, 15, 11] = 0
J_x[:, 0, 12] = 0
J_x[:, 1, 12] = 0
J_x[:, 2, 12] = 0
J_x[:, 3, 12] = E11 * x42 + E21 * y42 + E31
J_x[:, 4, 12] = 0
J_x[:, 5, 12] = 0
J_x[:, 6, 12] = 0
J_x[:, 7, 12] = 0
J_x[:, 8, 12] = 0
J_x[:, 9, 12] = 0
J_x[:, 10, 12] = 0
J_x[:, 11, 12] = 0
J_x[:, 12, 12] = 0
J_x[:, 13, 12] = 0
J_x[:, 14, 12] = 0
J_x[:, 15, 12] = 0
J_x[:, 0, 13] = 0
J_x[:, 1, 13] = 0
J_x[:, 2, 13] = 0
J_x[:, 3, 13] = E12 * x42 + E22 * y42 + E32
J_x[:, 4, 13] = 0
J_x[:, 5, 13] = 0
J_x[:, 6, 13] = 0
J_x[:, 7, 13] = 0
J_x[:, 8, 13] = 0
J_x[:, 9, 13] = 0
J_x[:, 10, 13] = 0
J_x[:, 11, 13] = 0
J_x[:, 12, 13] = 0
J_x[:, 13, 13] = 0
J_x[:, 14, 13] = 0
J_x[:, 15, 13] = 0
J_x[:, 0, 14] = 0
J_x[:, 1, 14] = 0
J_x[:, 2, 14] = 0
J_x[:, 3, 14] = E11 * x41 + E12 * y41 + E13
J_x[:, 4, 14] = 0
J_x[:, 5, 14] = 0
J_x[:, 6, 14] = 0
J_x[:, 7, 14] = 0
J_x[:, 8, 14] = 0
J_x[:, 9, 14] = 0
J_x[:, 10, 14] = 0
J_x[:, 11, 14] = 0
J_x[:, 12, 14] = 0
J_x[:, 13, 14] = 0
J_x[:, 14, 14] = 0
J_x[:, 15, 14] = 0
J_x[:, 0, 15] = 0
J_x[:, 1, 15] = 0
J_x[:, 2, 15] = 0
J_x[:, 3, 15] = E21 * x41 + E22 * y41 + E23
J_x[:, 4, 15] = 0
J_x[:, 5, 15] = 0
J_x[:, 6, 15] = 0
J_x[:, 7, 15] = 0
J_x[:, 8, 15] = 0
J_x[:, 9, 15] = 0
J_x[:, 10, 15] = 0
J_x[:, 11, 15] = 0
J_x[:, 12, 15] = 0
J_x[:, 13, 15] = 0
J_x[:, 14, 15] = 0
J_x[:, 15, 15] = 0
J_x[:, 0, 16] = 0
J_x[:, 1, 16] = 0
J_x[:, 2, 16] = 0
J_x[:, 3, 16] = 0
J_x[:, 4, 16] = E11 * x52 + E21 * y52 + E31
J_x[:, 5, 16] = 0
J_x[:, 6, 16] = 0
J_x[:, 7, 16] = 0
J_x[:, 8, 16] = 0
J_x[:, 9, 16] = 0
J_x[:, 10, 16] = 0
J_x[:, 11, 16] = 0
J_x[:, 12, 16] = 0
J_x[:, 13, 16] = 0
J_x[:, 14, 16] = 0
J_x[:, 15, 16] = 0
J_x[:, 0, 17] = 0
J_x[:, 1, 17] = 0
J_x[:, 2, 17] = 0
J_x[:, 3, 17] = 0
J_x[:, 4, 17] = E12 * x52 + E22 * y52 + E32
J_x[:, 5, 17] = 0
J_x[:, 6, 17] = 0
J_x[:, 7, 17] = 0
J_x[:, 8, 17] = 0
J_x[:, 9, 17] = 0
J_x[:, 10, 17] = 0
J_x[:, 11, 17] = 0
J_x[:, 12, 17] = 0
J_x[:, 13, 17] = 0
J_x[:, 14, 17] = 0
J_x[:, 15, 17] = 0
J_x[:, 0, 18] = 0
J_x[:, 1, 18] = 0
J_x[:, 2, 18] = 0
J_x[:, 3, 18] = 0
J_x[:, 4, 18] = E11 * x51 + E12 * y51 + E13
J_x[:, 5, 18] = 0
J_x[:, 6, 18] = 0
J_x[:, 7, 18] = 0
J_x[:, 8, 18] = 0
J_x[:, 9, 18] = 0
J_x[:, 10, 18] = 0
J_x[:, 11, 18] = 0
J_x[:, 12, 18] = 0
J_x[:, 13, 18] = 0
J_x[:, 14, 18] = 0
J_x[:, 15, 18] = 0
J_x[:, 0, 19] = 0
J_x[:, 1, 19] = 0
J_x[:, 2, 19] = 0
J_x[:, 3, 19] = 0
J_x[:, 4, 19] = E21 * x51 + E22 * y51 + E23
J_x[:, 5, 19] = 0
J_x[:, 6, 19] = 0
J_x[:, 7, 19] = 0
J_x[:, 8, 19] = 0
J_x[:, 9, 19] = 0
J_x[:, 10, 19] = 0
J_x[:, 11, 19] = 0
J_x[:, 12, 19] = 0
J_x[:, 13, 19] = 0
J_x[:, 14, 19] = 0
J_x[:, 15, 19] = 0
J_E9 = torch.zeros((b, 9, 9), device=minimal_sample.device)
J_x9 = torch.zeros((b, 9, 20), device=minimal_sample.device)
J_Ex = torch.zeros((b, 9, 20), device=minimal_sample.device)
J_E9[:, :6, :] = J_E[:, :6, :]
J_x9[:, :6, :] = J_x[:, :6, :]
rows = []
for i in range(3):
rows.append(random.sample(range(7, 15), 3))
J_E9[:, 6, :] = (
J_E[:, rows[0][0], :] + J_E[:, rows[0][1], :] + J_E[:, rows[0][2], :]
)
J_E9[:, 7, :] = (
J_E[:, rows[1][0], :] + J_E[:, rows[1][1], :] + J_E[:, rows[1][2], :]
)
J_E9[:, 8, :] = (
J_E[:, rows[2][0], :] + J_E[:, rows[2][1], :] + J_E[:, rows[2][2], :]
)
J_x9[:, 6, :] = (
J_x[:, rows[0][0], :] + J_x[:, rows[0][1], :] + J_x[:, rows[0][2], :]
)
J_x9[:, 7, :] = (
J_x[:, rows[1][0], :] + J_x[:, rows[1][1], :] + J_x[:, rows[1][2], :]
)
J_x9[:, 8, :] = (
J_x[:, rows[2][0], :] + J_x[:, rows[2][1], :] + J_x[:, rows[2][2], :]
)
tmp = torch.eye(9, 9, dtype=torch.float, device=minimal_sample.device)
for i in range(b):
try:
J_Ex[i, :, :] = -torch.inverse(J_E9[i, :, :]).mm(J_x9[i, :, :])
tmp = J_E9[i, :, :]
except Exception as e:
J_Ex[i, :, :] = -torch.inverse(tmp).mm(
J_x9[i, :, :]
) # or -torch.linalg.pinv(J_E9[i, :, :]).mm(J_x9[i, :, :])
return J_Ex
############ DDN with constraint ############
class EssentialMatrixNode(EqConstDeclarativeNode):
"""Declarative Essential matrix estimation node constraint"""
def __init__(self, device, ift):
super().__init__()
self.estimator = ns.EssentialMatrixEstimatorNister(device=device, ift=ift)
def objective(self, minimal_samples, E_true, y):
"""
minimal_samples : b x 5 x 4
E_true: 3 x 3
y : b x 3 x 3
"""
batch_size = minimal_samples[:, :, :2].shape[0]
w = torch.ones(
(batch_size, 5), dtype=torch.float, device=minimal_samples.device
) / float(5.0)
A_ = (
torch.cat(
(
minimal_samples[:, :, :2],
torch.ones((batch_size, 5, 1), device=minimal_samples.device),
),
-1,
)
).unsqueeze(-2)
B_ = (
torch.cat(
(
minimal_samples[:, :, 2:],
torch.ones((batch_size, 5, 1), device=minimal_samples.device),
),
-1,
)
).unsqueeze(-1)
M = A_ * B_ # [8 x 5 x 3 x 3]
res = ((M.view(batch_size, -1, 9)).matmul(y.view(batch_size, 9, 1))) ** 2
out = torch.einsum("bn,bn->b", (w, res.squeeze(-1)))
return out
def equality_constraints(self, minimal_samples, E_true, y):
E_Et = y.matmul(y.permute(0, 2, 1))
E_Et_trace = torch.einsum("bii->b", E_Et)
eq_constr1 = 2 * E_Et.matmul(y) - torch.einsum("b,bnm->bnm", E_Et_trace, y)
eq_constr1 = (eq_constr1**2).sum(dim=(-1, -2))
eq_constr2 = (y.view(-1, 9) ** 2).sum(dim=-1) - 1.0
return torch.cat((eq_constr1.unsqueeze(1), eq_constr2.unsqueeze(1)), 1)
def solve(self, minimal_samples, E_true):
minimal_samples = minimal_samples.detach()
y = self._solve_(minimal_samples, E_true).requires_grad_()
return y.detach(), None
def _solve_(self, minimal_samples, E_true):
"""
minimal_samples : b x 5 x 4
E_true: 3 x 3
"""
est = self.estimator.estimate_minimal_model(minimal_samples)
solution_num = 10
distances = torch.norm(
est - E_true.unsqueeze(0).repeat(est.shape[0], 1, 1), dim=(1, 2)
).view(est.shape[0], -1)
try:
chosen_indices = torch.argmin(distances.view(-1, solution_num), dim=-1)
chosen_models = torch.stack(
[
(est.view(-1, solution_num, 3, 3))[i, chosen_indices[i], :]
for i in range(int(est.shape[0] / solution_num))
]
)
except ValueError as e:
print(
"not enough models for selection, we choose the first solution in this batch",
e,
est.shape,
)
chosen_models = est[0].unsqueeze(0)
return chosen_models
| 23,922 | Python | .py | 774 | 24.359173 | 94 | 0.400972 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,677 | test.py | disungatullina_MinBackProp/test.py | import torch
from tqdm import tqdm
from model_cl import *
from utils import *
from datasets import Dataset
def test(model, test_loader, opt):
OUT_DIR = "results/"
with torch.no_grad():
if opt.precision == 2:
data_type = torch.float64
elif opt.precision == 0:
data_type = torch.float16
else:
data_type = torch.float32
errRs, errTs = [], []
max_errors = []
avg_F1 = 0
avg_inliers = 0
epi_errors = []
avg_ransac_time = 0
invalid_pairs = 0
model.to(data_type)
for idx, test_data in enumerate(tqdm(test_loader)):
correspondences, K1, K2 = (
test_data["correspondences"].to(opt.device, data_type),
test_data["K1"].to(opt.device, data_type),
test_data["K2"].to(opt.device, data_type),
)
im_size1, im_size2 = test_data["im_size1"].to(
opt.device, data_type
), test_data["im_size2"].to(opt.device, data_type)
gt_E, gt_R, gt_t = (
test_data["gt_E"].to(data_type),
test_data["gt_R"].to(opt.device, data_type),
test_data["gt_t"].to(data_type),
)
files = test_data["files"]
# estimate model, return the model, predicted inlier probabilities and normalization.
models, weights, ransac_time = model(
correspondences, K1, K2, im_size1, im_size2
)
K1_, K2_ = K1.cpu().detach().numpy(), K2.cpu().detach().numpy()
im_size1, im_size2 = (
im_size1.cpu().detach().numpy(),
im_size2.cpu().detach().numpy(),
)
for b, est_model in enumerate(models):
pts1 = correspondences[b, 0:2].squeeze(-1).cpu().detach().numpy().T
pts2 = correspondences[b, 2:4].squeeze(-1).cpu().detach().numpy().T
E = est_model
errR, errT = eval_essential_matrix(pts1, pts2, E, gt_R[b], gt_t[b])
errRs.append(float(errR))
errTs.append(float(errT))
max_errors.append(max(float(errR), float(errT)))
avg_ransac_time += ransac_time
avg_ransac_time /= len(test_loader)
out = OUT_DIR + opt.model
print(
f"Rotation error = {np.mean(np.array(errRs))} | Translation error = {np.mean(np.array(errTs))}"
)
print(
f"Rotation error median= {np.median(np.array(errRs))} | Translation error median= {np.median(np.array(errTs))}"
)
print(f"AUC scores = {AUC(max_errors)} ")
print("Run time: %.2f ms" % (avg_ransac_time * 1000))
if not os.path.isdir(out):
os.makedirs(out)
with open(out + "/test.txt", "a", 1) as f:
f.write(
"%f %f %f %f ms"
% (
AUC(max_errors)[0],
AUC(max_errors)[1],
AUC(max_errors)[2],
avg_ransac_time * 1000,
)
)
f.write("\n")
if __name__ == "__main__":
# Parse the parameters
parser = create_parser(description="Generalized Differentiable RANSAC.")
opt = parser.parse_args()
# check if gpu device is available
opt.device = torch.device(
"cuda:0" if torch.cuda.is_available() and opt.device != "cpu" else "cpu"
)
print(f"Running on {opt.device}")
# collect datasets to be used for testing
if opt.batch_mode:
scenes = test_datasets
print(
"\n=== BATCH MODE: Doing evaluation on",
len(scenes),
"datasets. =================",
)
else:
scenes = [opt.datasets]
model = DeepRansac_CLNet(opt).to(opt.device)
for seq in scenes:
print(f"Working on {seq} with scoring {opt.scoring}")
scene_data_path = os.path.join(opt.data_path)
dataset = Dataset(
[scene_data_path + "/" + seq + "/test_data_rs/"],
opt.snn,
nfeatures=opt.nfeatures,
)
test_loader = torch.utils.data.DataLoader(
dataset,
batch_size=opt.batch_size,
num_workers=0,
pin_memory=False,
shuffle=False,
)
print(f"Loading test data: {len(dataset)} image pairs.")
# if opt.model is not None:
model.load_state_dict(torch.load(opt.model, map_location=opt.device))
model.eval()
test(model, test_loader, opt)
| 4,507 | Python | .py | 118 | 27.830508 | 119 | 0.535453 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,678 | test_magsac.py | disungatullina_MinBackProp/test_magsac.py | import numpy as np
import torch
import time
import pymagsac
from tqdm import tqdm
from model_cl import *
from utils import *
from datasets import Dataset
def test(model, test_loader, opt):
with torch.no_grad():
avg_model_time = 0 # runtime of the network forward pass
avg_ransac_time = 0 # runtime of RANSAC
# essential matrix evaluation
pose_losses = []
avg_F1 = 0
avg_inliers = 0
epi_errors = []
invalid_pairs = 0
for idx, test_data in enumerate(tqdm(test_loader)):
correspondences, K1, K2 = (
test_data["correspondences"].to(opt.device),
test_data["K1"].to(opt.device),
test_data["K2"].to(opt.device),
)
im_size1, im_size2 = test_data["im_size1"].to(opt.device), test_data[
"im_size2"
].to(opt.device)
gt_E, gt_R, gt_t = (
test_data["gt_E"].numpy(),
test_data["gt_R"].numpy(),
test_data["gt_t"].numpy(),
)
batch_size = correspondences.size(0)
# predicted inlier probabilities and normalization.
inlier_weights, _ = model(
correspondences.float(),
K1,
K2,
im_size1,
im_size2,
opt.prob,
predict=False,
)
K1, K2 = K1.cpu().detach().numpy(), K2.cpu().detach().numpy()
im_size1, im_size2 = (
im_size1.cpu().detach().numpy(),
im_size2.cpu().detach().numpy(),
)
# sorted_indices_batch = torch.argsort(logits, descending=True, dim=1).cpu().detach()
ransac_time = 0
correspondences = correspondences.cpu().detach()
for b in range(batch_size):
inliers = torch.zeros(1, 2000, 1) # inlier mask of the estimated model
# sorted_indices = sorted_indices_batch[b]
weights = inlier_weights[b].cpu().detach().numpy()
sorted_indices = np.argsort(weights)[::-1]
# === CASE ESSENTIAL MATRIX =========================================
pts1 = correspondences[b, 0:2].squeeze().numpy().T
pts2 = correspondences[b, 2:4].squeeze().numpy().T
# rank the points according to their probabilities
sorted_pts1 = pts1[sorted_indices]
sorted_pts2 = pts2[sorted_indices]
weights = weights[sorted_indices]
start_time = time.time()
E, mask, save_samples = pymagsac.findEssentialMatrix(
np.ascontiguousarray(sorted_pts1).astype(
np.float64
), # pts[sorted_indices]
np.ascontiguousarray(sorted_pts2).astype(np.float64),
K1[b],
K2[b],
float(im_size1[b][0]),
float(im_size1[b][1]),
float(im_size2[b][0]),
float(im_size2[b][1]),
# probabilities=get_probabilities(sorted_pts1.shape[0])
probabilities=weights,
use_magsac_plus_plus=True,
sigma_th=opt.threshold,
sampler_id=3,
save_samples=True,
)
ransac_time += time.time() - start_time
# count inlier number
incount = np.sum(mask)
incount /= correspondences.size(2)
if incount == 0:
E = np.identity(3)
else:
# update inliers
# inliers[0, :, 0] = torch.tensor(mask)
sorted_index = sorted_indices[mask]
inliers[0, sorted_index, 0] = 1
# pts for recovering the pose
pts1 = correspondences[b, 0:2].numpy()
pts2 = correspondences[b, 2:4].numpy()
pts1_1 = pts1.transpose(2, 1, 0)
pts2_2 = pts2.transpose(2, 1, 0)
inliers = inliers.byte().numpy().ravel()
K = np.eye(3)
R = np.eye(3)
t = np.zeros((3, 1))
# evaluation of relative pose (essential matrix)
cv2.recoverPose(
E,
np.ascontiguousarray(pts1_1).astype(np.float64),
np.ascontiguousarray(pts2_2).astype(np.float64),
K,
R,
t,
inliers,
)
dR, dT = pose_error(R, gt_R[b], t, gt_t[b])
pose_losses.append(max(float(dR), float(dT)))
avg_ransac_time += ransac_time / batch_size
print(
"\nAvg. Model Time: %dms"
% (avg_model_time / len(test_loader) * 1000 + 0.00000001)
)
print(
"Avg. RANSAC Time: %dms"
% (avg_ransac_time / len(test_loader) * 1000 + 0.00000001)
)
# calculate AUC of pose losses
thresholds = [5, 10, 20]
AUC_scores = AUC(
losses=pose_losses, thresholds=thresholds, binsize=5
) # opt.evalbinsize)
print("\n=== Relative Pose Accuracy ===========================")
print(
"AUC for %ddeg/%ddeg/%ddeg: %.2f/%.2f/%.2f\n"
% (
thresholds[0],
thresholds[1],
thresholds[2],
AUC_scores[0],
AUC_scores[1],
AUC_scores[2],
)
)
# write evaluation results to fil
if not os.path.isdir("results/" + opt.model):
os.makedirs("results/" + opt.model)
with open("results/" + opt.model + "/test.txt", "a", 1) as f:
f.write(
"%f %f %f %f ms "
% (
AUC_scores[0],
AUC_scores[1],
AUC_scores[2],
avg_ransac_time / len(test_loader) * 1000,
)
)
f.write("\n")
if __name__ == "__main__":
# Parse the parameters
parser = create_parser(description="Generalized Differentiable RANSAC.")
opt = parser.parse_args()
opt.device = torch.device(
"cuda:0" if torch.cuda.is_available() and opt.device != "cpu" else "cpu"
)
print(f"Running on {opt.device}")
# collect dataset list to be used for testing
if opt.batch_mode:
scenes = test_datasets
print(
"\n=== BATCH MODE: Doing evaluation on",
len(scenes),
"datasets. =================",
)
else:
scenes = [opt.datasets]
model = DeepRansac_CLNet(opt).to(opt.device)
for seq in scenes:
print(f"Working on {seq} with scoring {opt.scoring}")
scene_data_path = os.path.join(opt.data_path)
dataset = Dataset(
[scene_data_path + "/" + seq + "/test_data_rs/"],
opt.snn,
nfeatures=opt.nfeatures,
)
test_loader = torch.utils.data.DataLoader(
dataset,
batch_size=opt.batch_size,
num_workers=0,
pin_memory=False,
shuffle=False,
)
print(f"Loading test data: {len(dataset)} image pairs.")
# if opt.model is not None:
model.load_state_dict(torch.load(opt.model, map_location=opt.device))
model.eval()
test(model, test_loader, opt)
| 7,654 | Python | .py | 193 | 25.891192 | 97 | 0.480301 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,679 | utils.py | disungatullina_MinBackProp/utils.py | import cv2
import torch
import argparse
import torch.nn as nn
def create_parser(description):
"""Create a default command line parser with the most common options.
Keyword arguments:
description -- description of the main functionality of a script/program
"""
parser = argparse.ArgumentParser(
description=description, formatter_class=argparse.ArgumentDefaultsHelpFormatter
)
parser.add_argument(
"--model",
"-m",
default=None, # EF_hist_size_10_snn_0_85_thr_3.pth
help="The name of the model to be used",
)
parser.add_argument(
"--data_path",
"-pth",
default="dataset", # EF_hist_size_10_snn_0_85_thr_3.pth
help="The path you sed the dataset.",
)
parser.add_argument("--device", "-d", default="cuda", help="The device")
parser.add_argument(
"--detector",
"-dt",
default="rootsift",
help="The detector used for obtaining local features. Values = loftr, sift",
)
parser.add_argument(
"--snn", "-snn", default=0.80, help="The SNN ratio threshold for SIFT."
)
parser.add_argument(
"--nfeatures",
"-nf",
type=int,
default=2000,
help="The expected number of features in SIFT.",
)
parser.add_argument("--batch_size", "-bs", type=int, default=32, help="batch size")
parser.add_argument(
"--ransac_batch_size", "-rbs", type=int, default=64, help="ransac batch size"
)
parser.add_argument(
"--scoring",
"-s",
type=int,
default=1,
help="The used scoring function. 0 - RANSAC, 1 - MSAC",
)
parser.add_argument(
"--precision",
"-pr",
type=int,
default=1,
help="The used data precision. 0 - float16, 1 - float32, 2-float64",
)
parser.add_argument("--tr", "-tr", type=int, default=0, help="1 - train, 0v- test")
parser.add_argument(
"--threshold",
"-t",
type=float,
default=0.75,
help="Inlier-outlier threshold. "
"It will be normalized for E matrix estimation inside the code using focal length.",
)
parser.add_argument(
"--epochs",
"-e",
type=int,
default=10,
help="Epochs for training. "
"It will be the epoch number used inside training.",
)
parser.add_argument(
"--learning_rate",
"-lr",
type=float,
default=1e-4,
help="learning rate for network optimizer.",
)
parser.add_argument(
"--num_workers",
"-nw",
type=int,
default=0,
help="how many workers for data loader",
)
parser.add_argument(
"--datasets",
"-ds",
default="st_peters_square",
help="the datasets we would like to use",
)
parser.add_argument(
"--batch_mode", "-bm", type=int, default=0, help="use the provided data list"
)
parser.add_argument(
"--prob",
"-p",
type=int,
default=2,
help="the way we use the weights, 0-normalized weights, 1-unnormarlized weights, 2-logits",
)
parser.add_argument(
"--session",
"-sid",
default="",
help="custom session name appended to output files, "
"useful to separate different runs of a script",
)
parser.add_argument(
"--topk",
"-topk",
default=False,
help="use the errors of the best k models as the loss, otherwise, taaake the average.",
)
parser.add_argument(
"--k",
"-k",
type=int,
default=300,
help="the number of the best models included in the loss.",
)
parser.add_argument(
"--ift",
"-ift",
type=int,
default=1,
help="the method to backpropagate; 0-autograd, 1-ift, 2-ddn; 1 is default",
)
return parser
def init_weights(m):
"""Customize the weight initialization process as ResNet does.
https://github.com/pytorch/vision/blob/main/torchvision/models/resnet.py#L208
"""
if isinstance(m, nn.Conv2d):
nn.init.kaiming_normal_(m.weight, mode="fan_out", nonlinearity="relu")
elif isinstance(m, (nn.BatchNorm2d, nn.GroupNorm)):
nn.init.constant_(m.weight, 1)
nn.init.constant_(m.bias, 0)
def create_session_string(prefix, epochs, nfeatures, ratio, session, threshold):
"""Create an identifier string from the most common parameter options.
Keyword arguments:
prefix -- custom string appended at the beginning of the session string
epochs -- how many epochs you trained
orb -- bool indicating whether ORB features or SIFT features are used
rootsift -- bool indicating whether RootSIFT normalization is used
ratio -- threshold for Lowe's ratio filter
session -- custom string appended at the end of the session string
"""
session_string = prefix + "_"
session_string += "E_"
session_string += "e_" + str(epochs) + "_"
# if rootsift: session_string += 'rs_'
session_string += "rs_" + str(nfeatures)
session_string += "_r%.2f_" % ratio
session_string += "t%.2f_" % threshold
# specific id if we train the same config for times
session_string += session
return session_string
outdoor_test_datasets = [
"buckingham_palace",
"brandenburg_gate",
"colosseum_exterior",
"grand_place_brussels",
"notre_dame_front_facade",
"palace_of_westminster",
"pantheon_exterior",
"prague_old_town_square",
"sacre_coeur",
"taj_mahal",
"trevi_fountain",
"westminster_abbey",
]
test_datasets = outdoor_test_datasets
| 5,708 | Python | .py | 178 | 25.320225 | 99 | 0.611061 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,680 | train.py | disungatullina_MinBackProp/train.py | import numpy as np
import torch
import torch.nn.functional as F
from tqdm import tqdm
from loss import *
from model_cl import *
from datasets import Dataset
from tensorboardX import SummaryWriter
from sklearn.model_selection import train_test_split
import time
import warnings
warnings.filterwarnings("ignore")
RANDOM_SEED = 535
random.seed(RANDOM_SEED)
torch.manual_seed(RANDOM_SEED)
np.random.seed(RANDOM_SEED)
def train_step(train_data, model, opt, loss_fn):
if opt.precision == 2:
data_type = torch.float64
elif opt.precision == 0:
data_type = torch.float16
else:
data_type = torch.float32
model.to(data_type)
# fetch the points, ground truth extrinsic and intrinsic matrices
correspondences, K1, K2 = (
train_data["correspondences"].to(opt.device, data_type),
train_data["K1"].to(opt.device, data_type),
train_data["K2"].to(opt.device, data_type),
)
gt_R, gt_t = train_data["gt_R"].to(opt.device, data_type), train_data["gt_t"].to(
opt.device, data_type
)
gt_E = train_data["gt_E"].to(opt.device, data_type)
im_size1, im_size2 = train_data["im_size1"].to(opt.device, data_type), train_data[
"im_size2"
].to(opt.device, data_type)
ground_truth = gt_E
if opt.tr:
# 5PC
prob_type = 0
else:
prob_type = opt.prob
# collect all the models
Es, weights, _ = model(
correspondences.to(data_type),
K1,
K2,
im_size1,
im_size2,
prob_type,
ground_truth,
)
pts1 = correspondences.squeeze(-1)[:, 0:2].transpose(-1, -2)
pts2 = correspondences.squeeze(-1)[:, 2:4].transpose(-1, -2)
train_loss = loss_fn.forward(
Es, gt_E.cpu().detach().numpy(), pts1, pts2, K1, K2, im_size1, im_size2
)
return train_loss, Es
def train(model, train_loader, valid_loader, opt):
# the name of the folder we save models, logs
saved_file = create_session_string(
"train", opt.epochs, opt.nfeatures, opt.snn, opt.session, opt.threshold
)
writer = SummaryWriter("results/" + saved_file + "/vision", comment="model_vis")
optimizer = torch.optim.Adam(model.parameters(), lr=opt.learning_rate)
loss_function = MatchLoss()
valid_loader_iter = iter(valid_loader)
# save the losses to npy file
train_losses = []
valid_losses = []
time_history = []
# start epoch
for epoch in range(opt.epochs):
# each step
for idx, train_data in enumerate(tqdm(train_loader)):
model.train()
# one step
optimizer.zero_grad()
train_loss, Es = train_step(train_data, model, opt, loss_function)
train_loss.retain_grad()
for i in Es:
i.retain_grad()
# gradient calculation, ready for back propagation
if torch.isnan(train_loss):
print("pls check, there is nan value in loss!", train_loss)
continue
try:
start = time.time()
train_loss.backward()
end = time.time()
time_history.append(end - start)
print("successfully back-propagation", train_loss)
except Exception as e:
print("we have trouble with back-propagation, pls check!", e)
continue
if torch.isnan(train_loss.grad):
print(
"pls check, there is nan value in the gradient of loss!",
train_loss.grad,
)
continue
for E in Es:
if torch.isnan(E.grad).any():
print(
"pls check, there is nan value in the gradient of estimated models!",
E.grad,
)
continue
train_losses.append(train_loss.cpu().detach().numpy())
# for vision
writer.add_scalar(
"train_loss", train_loss, global_step=epoch * len(train_loader) + idx
)
# add gradient clipping after backward to avoid gradient exploding
torch.nn.utils.clip_grad_norm_(model.parameters(), max_norm=5)
# check if the gradients of the training parameters contain nan values
nans = sum(
[
torch.isnan(param.grad).any()
for param in list(model.parameters())
if param.grad is not None
]
)
if nans != 0:
print("parameter gradients includes {} nan values".format(nans))
continue
optimizer.step()
# check check if the training parameters contain nan values
nan_num = sum(
[
torch.isnan(param).any()
for param in optimizer.param_groups[0]["params"]
]
)
if nan_num != 0:
print("parameters includes {} nan values".format(nan_num))
continue
print("_______________________________________________________")
# store the network every so often
torch.save(
model.state_dict(), "results/" + saved_file + "/model" + str(epoch) + ".net"
)
print("Mean backward time: ", np.array(time_history).mean())
np.save(
os.path.join("results", saved_file, "backward_time.npy"),
np.array(time_history).mean(),
)
# validation
with torch.no_grad():
model.eval()
try:
valid_data = next(valid_loader_iter)
except StopIteration:
pass
valid_loss, _ = train_step(valid_data, model, opt, loss_function)
valid_losses.append(valid_loss.item())
writer.add_scalar(
"valid_loss", valid_loss, global_step=epoch * len(train_loader) + idx
)
writer.flush()
print(
"Step: {:02d}| Train loss: {:.4f}| Validation loss: {:.4f}".format(
epoch * len(train_loader) + idx, train_loss, valid_loss
),
"\n",
)
np.save(
"results/" + saved_file + "/" + "loss_record.npy", (train_losses, valid_losses)
)
if __name__ == "__main__":
OUT_DIR = "results/"
# Parse the parameters
parser = create_parser(description="Generalized Differentiable RANSAC.")
config = parser.parse_args()
# check if gpu device is available
config.device = torch.device(
"cuda:0" if torch.cuda.is_available() and config.device != "cpu" else "cpu"
)
print(f"Running on {config.device}")
train_model = DeepRansac_CLNet(config).to(config.device)
# use the pretrained model to initialize the weights if provided.
if len(config.model) > 0:
train_model.load_state_dict(
torch.load(config.model, map_location=config.device)
)
else:
train_model.apply(init_weights)
train_model.train()
# collect dataset list
if config.batch_mode:
scenes = test_datasets
print(
"\n=== BATCH MODE: Training on", len(scenes), "datasets. ================="
)
else:
scenes = [config.datasets]
print(f"Working on {scenes} with scoring {config.scoring}")
folders = [config.data_path + "/" + seq + "/train_data_rs/" for seq in scenes]
dataset = Dataset(folders, nfeatures=config.nfeatures)
# split the data to train and validation
train_dataset, valid_dataset = train_test_split(
dataset, test_size=0.25, shuffle=True
)
train_data_loader = torch.utils.data.DataLoader(
train_dataset,
batch_size=config.batch_size,
num_workers=config.num_workers,
pin_memory=True,
shuffle=True,
)
print(f"Loading training data: {len(train_dataset)} image pairs.")
valid_data_loader = torch.utils.data.DataLoader(
valid_dataset,
batch_size=config.batch_size,
num_workers=0,
pin_memory=True,
shuffle=True,
)
print(f"Loading validation data: {len(valid_dataset)} image pairs.")
# with torch.autograd.set_detect_anomaly(True):
train(train_model, train_data_loader, valid_data_loader, config)
| 8,402 | Python | .py | 222 | 28.171171 | 93 | 0.572919 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,681 | feature_utils.py | disungatullina_MinBackProp/feature_utils.py | import torch
import torch.nn.functional as F
# import kornia as K
# import kornia.feature as KF
import cv2
import os
import h5py
import numpy as np
from utils import *
# from kornia_moons.feature import *
def load_h5(filename):
"""Loads dictionary from hdf5 file."""
dict_to_load = {}
if not os.path.exists(filename):
print("Cannot find file {}".format(filename))
return dict_to_load
with h5py.File(filename, "r") as f:
keys = [key for key in f.keys()]
for key in keys:
dict_to_load[key] = f[key][()]
return dict_to_load
def normalize_keypoints(keypoints, K):
"""Normalize keypoints using the calibration data."""
C_x = K[0, 2]
C_y = K[1, 2]
f_x = K[0, 0]
f_y = K[1, 1]
keypoints = (keypoints - np.array([[C_x, C_y]])) / np.array([[f_x, f_y]])
return keypoints
def normalize_keypoints_tensor(keypoints, K):
"""Normalize keypoints using the calibration data."""
C_x = K[0, 2]
C_y = K[1, 2]
f_x = K[0, 0]
f_y = K[1, 1]
keypoints = (
keypoints - torch.as_tensor([[C_x, C_y]], device=keypoints.device)
) / torch.as_tensor([[f_x, f_y]], device=keypoints.device)
return keypoints
# A function to convert the point ordering to probabilities used in NG-RANSAC's sampler or AR-Sampler.
def get_probabilities(len_tentatives):
probabilities = []
# Since the correspondences are assumed to be ordered by their SNN ratio a priori,
# we just assign a probability according to their order.
for i in range(len_tentatives):
probabilities.append(1.0 - i / len_tentatives)
return probabilities
| 1,651 | Python | .py | 47 | 30.382979 | 102 | 0.65932 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,682 | ransac.py | disungatullina_MinBackProp/ransac.py | import math
from feature_utils import *
from samplers.uniform_sampler import *
from nodes import IFTLayer, EssentialMatrixNode
from ddn.ddn.pytorch.node import *
class RANSAC(object):
def __init__(
self,
estimator,
sampler,
scoring,
train=False,
ransac_batch_size=64,
threshold=1e-3,
confidence=0.999,
max_iterations=5000,
lo=0, # 2,
lo_iters=64,
eps=1e-5,
ift=1,
):
if ift == 1:
self.optimization_layer = IFTLayer(estimator.device, ift)
elif ift == 2:
self.node = EssentialMatrixNode(estimator.device, ift)
self.optimization_layer = DeclarativeLayer(self.node)
self.estimator = estimator
self.sampler = sampler
self.scoring = scoring
self.lo = lo
self.lo_iters = lo_iters
self.train = train
self.ransac_batch_size = ransac_batch_size
self.threshold = threshold
self.confidence = confidence
self.max_iterations = max_iterations
self.eps = eps
self.ift = ift
def __call__(self, matches, logits, K1, K2, gt_model):
iterations = 0
best_score = 0
point_number = matches.shape[0]
best_mask = []
best_model = []
models = {}
normalized_multipler = (K1[0, 0] + K1[1, 1] + K1[0, 0] + K2[1, 1]) / 4
threshold = self.threshold / normalized_multipler
max_iters = self.max_iterations
while iterations < max_iters:
samples, soft_weights = self.sampler.sample(logits)
points = matches.repeat([self.ransac_batch_size, 1, 1]) * samples.unsqueeze(
-1
)
minimal_samples = points[samples != 0].view(
self.ransac_batch_size, -1, matches.shape[-1]
)
# when there is no minimal sample comes, skip
if minimal_samples.shape[1] == 0:
continue
if self.train:
# Estimate models' parameters, can propagate gradient
if self.ift == 1 or self.ift == 2:
estimated_models = self.optimization_layer(
minimal_samples, gt_model
)
chosen_models = estimated_models
else:
estimated_models = self.estimator.estimate_model(minimal_samples)
# for learning, return all models and sum the pose errors of all models instead of selecting the best
# choose the best model from each sample, in the case of generating more than one models from the sample
if estimated_models.shape[0] == 0 or estimated_models is None:
continue
solution_num = 10
distances = torch.norm(
estimated_models - gt_model, dim=(1, 2)
).view(estimated_models.shape[0], -1)
try:
chosen_indices = torch.argmin(
distances.view(-1, solution_num), dim=-1
)
chosen_models = torch.stack(
[
(estimated_models.view(-1, solution_num, 3, 3))[
i, chosen_indices[i], :
]
for i in range(
int(estimated_models.shape[0] / solution_num)
)
]
)
except ValueError as e:
print(
"not enough models for selection, we choose the first solution in this batch",
e,
estimated_models.shape,
)
chosen_models = estimated_models[0].unsqueeze(0)
if torch.isnan(chosen_models).any():
# deal with the error of linalg.slove,
# "The diagonal element 1 is zero, the solver could not completed because the input singular matrix)
print("Delete those models having problems with singular matrix.")
nan_filter = [not (torch.isnan(model).any()) for model in chosen_models]
models[iterations] = chosen_models[torch.as_tensor(nan_filter)]
else:
estimated_models = self.estimator.estimate_model(minimal_samples)
# Calculate the scores of the models
scores, inlier_masks = self.scoring.score(
matches, estimated_models, threshold
)
# Select the best model
best_idx = torch.argmax(scores)
# Update the best model if this iteration is better
if scores[best_idx] > best_score or iterations == 0:
best_score = scores[best_idx]
best_mask = inlier_masks[best_idx]
best_model = estimated_models[best_idx]
best_inlier_number = torch.sum(best_mask)
# Apply local optimization if needed
if self.lo:
(
best_score,
best_mask,
best_model,
best_inlier_number,
) = self.localOptimization(
best_score,
best_mask,
best_model,
best_inlier_number,
matches,
K1,
K2,
threshold,
)
# use adaptive iteration number when testing, update the max iteration number by inlier counts
max_iters = min(
self.max_iterations,
self.adaptive_iteration_number(
best_inlier_number, point_number, self.confidence
),
)
iterations += self.ransac_batch_size
# not needed for learning, so no differentiability is needed
# Final refitting on the inliers
if not self.train:
inlier_indices = best_mask.nonzero(as_tuple=True)
inlier_points = matches[inlier_indices].unsqueeze(0)
estimated_models = self.estimator.estimate_model(
matches.unsqueeze(0).double(),
K1=K1.cpu().detach().numpy(),
K2=K2.cpu().detach().numpy(),
inlier_indices=inlier_indices[0]
.cpu()
.detach()
.numpy()
.astype(np.uint64),
best_model=best_model.cpu().detach().numpy().T,
unnormalzied_threshold=0.75,
best_score=best_score,
)
# Select the best if more than one models are returned
if estimated_models is None:
best_model = torch.eye(
3, 3, device=best_model.device, dtype=best_model.dtype
)
elif estimated_models.shape[0] == 0:
best_model = torch.eye(
3, 3, device=estimated_models.device, dtype=estimated_models.dtype
)
elif estimated_models.shape[0] >= 1:
if estimated_models.dtype != matches.dtype:
estimated_models = estimated_models.to(matches.dtype)
# if estimated_models.type() == 'torch.cuda.DoubleTensor' or 'torch.DoubleTensor':
# estimated_models = estimated_models.to(torch.float)
# Calculate the scores of the models
scores, inlier_masks = self.scoring.score(
matches, estimated_models, threshold
)
if max(scores) > best_score:
best_idx = torch.argmax(scores)
best_model = estimated_models[best_idx]
best_score = scores[best_idx]
else:
best_model = estimated_models[0]
if not self.scoring.provides_inliers:
best_model, best_mask = self.scoring.get_inliers(
matches,
best_model.unsqueeze(0),
self.estimator,
threshold=threshold,
)
else:
best_model = models
# if best_model.shape[0] == 0:
# best_model = torch.eye(3, 3, device=best_model.device, dtype=best_model.dtype)
return best_model, best_mask, best_score, iterations
def adaptive_iteration_number(self, inlier_number, point_number, confidence):
inlier_ratio = inlier_number / point_number
probability = 1.0 - inlier_ratio**self.estimator.sample_size
if probability >= 1.0 - self.eps:
return self.max_iterations
try:
max(
0.0,
(
math.log10(1.0 - confidence)
/ (
math.log10(1 - inlier_ratio**self.estimator.sample_size)
+ self.eps
)
),
)
except ValueError:
print(
"add eps to avoid math domain error of log",
1 - inlier_ratio**self.estimator.sample_size,
"\n",
)
return max(
0.0,
(
math.log10(1.0 - confidence)
/ (
math.log10(
1 - inlier_ratio**self.estimator.sample_size + self.eps
)
)
),
)
def localOptimization(
self,
best_score,
best_mask,
best_model,
best_inlier_number,
matches,
K1,
K2,
threshold,
):
# Do a single or iterated LSQ fitting
if self.lo < 3:
iters = 1
if self.lo == 2:
iters = self.lo_iters
for iter_i in range(iters):
# Select the inliers
indices = best_mask.nonzero(as_tuple=True)
points = torch.unsqueeze(matches[indices], 0)
# Estimate the model from all points
models = self.estimator.estimate_model(
points,
K1=K1.cpu().detach().numpy(),
K2=K2.cpu().detach().numpy(),
inlier_indices=indices[0].cpu().detach().numpy().astype(np.uint64),
best_model=best_model.cpu().detach().numpy().T,
unnormalzied_threshold=0.75,
best_score=best_score,
)
if models is None:
models = torch.eye(3).unsqueeze(0).to(points.device)
# Calculate the score
scores, inlier_masks = self.scoring.score(matches, models, threshold)
# Select the best model
best_idx = torch.argmax(scores)
if scores[best_idx] >= best_score:
best_score = scores[best_idx]
best_mask = inlier_masks[best_idx]
best_model = models[best_idx]
best_inlier_number = torch.sum(best_mask)
else:
break
elif self.lo == 3: # Do inner RANSAC
# Calculate the sample size
sample_size = self.estimator.sample_size
if best_inlier_number < sample_size:
sample_size = self.estimator.sample_size
# Initialize the LO sampler
lo_sampler = UniformSampler(self.lo_iters, sample_size, matches.shape[0])
for iter_i in range(self.lo_iters):
# Select minimal samples for the current batch
minimal_sample_indices = lo_sampler.sample()
minimal_samples = matches[minimal_sample_indices]
# Estimate the models' parameters
estimated_models = self.estimator.estimate_model(minimal_samples)
# Calculate the scores of the models
scores, inlier_masks = self.scoring.score(
matches, estimated_models, threshold
)
# Select the best model
best_idx = torch.argmax(scores)
# The loss should be: sum_{1}^k pose_error(model_k, model_gt) (where k is iteration number/batch size)
# Update the previous best model if needed
if scores[best_idx] > best_score:
best_score = scores[best_idx]
best_mask = inlier_masks[best_idx]
best_model = estimated_models[best_idx]
best_inlier_number = torch.sum(best_mask)
# Re-calculate the sample size
sample_size = self.estimator.sample_size
if best_inlier_number < sample_size:
sample_size = self.estimator.sample_size
# Re-initialize the LO sampler
lo_sampler = UniformSampler(
self.ransac_batch_size, sample_size, matches.shape[0]
)
else:
break
return best_score, best_mask, best_model, best_inlier_number
| 13,751 | Python | .py | 309 | 27.63754 | 124 | 0.493659 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,683 | cv_utils.py | disungatullina_MinBackProp/cv_utils.py | import cv2
import math
import torch
import numpy as np
def normalize_pts(pts, im_size):
"""Normalize image coordinate using the image size.
Pre-processing of correspondences before passing them to the network to be
independent of image resolution.
Re-scales points such that max image dimension goes from -0.5 to 0.5.
In-place operation.
Keyword arguments:
pts -- 3-dim array conainting x and y coordinates in the last dimension, first dimension should have size 1.
im_size -- image height and width
"""
ret = pts.clone() / max(im_size) - torch.stack((im_size[1] / 2, im_size[0] / 2))
return ret
def denormalize_pts_inplace(pts, im_size):
"""Undo image coordinate normalization using the image size.
Keyword arguments:
pts -- N-dim array conainting x and y coordinates in the first dimension
im_size -- image height and width
"""
pts *= max(im_size)
pts[0] += im_size[1] / 2
pts[1] += im_size[0] / 2
def denormalize_pts(pts, im_size):
"""Undo image coordinate normalization using the image size.
Keyword arguments:
pts -- N-dim array containing x and y coordinates in the first dimension
im_size -- image height and width
"""
ret = pts.clone() * max(im_size) + torch.stack((im_size[1] / 2, im_size[0] / 2))
return ret
def recoverPose(model, p1, p2, svd, distanceThreshold=50):
"""Recover the relative poses (R, t) from essential matrix, and choose the correct solution from 4."""
# decompose E matrix to get R1, R2, t, -t
if svd:
R1, R2, t = decompose_E(model)
else:
R1, R2, t = new_decompose_E(model)
# four solutions
P = []
P.append(torch.eye(3, 4, device=model.device, dtype=model.dtype))
P.append(torch.cat((R1, t), 1))
P.append(torch.cat((R2, t), 1))
P.append(torch.cat((R1, -t), 1))
P.append(torch.cat((R2, -t), 1))
# cheirality check
mask = torch.zeros(4, p1.shape[0])
for i in range(len(P) - 1):
mask[i] = cheirality_check(P[0], P[i + 1], p1, p2, distanceThreshold)
good = torch.sum(mask, dim=1)
best_index = torch.argmax(good)
if best_index == 0:
return R1, t
elif best_index == 1:
return R2, t
elif best_index == 2:
return R1, -t
else:
return R2, -t
def decompose_E(model):
try:
u, s, vT = torch.linalg.svd(model)
except Exception as e:
print(e)
model = torch.eye(3, device=model.device)
u, s, vT = torch.linalg.svd(model)
try:
if torch.sum(torch.isnan(u)) > 0:
print("wrong")
except Exception as e:
print(e)
w = torch.tensor([[0, -1, 0], [1, 0, 0], [0, 0, 1]], dtype=u.dtype, device=u.device)
z = torch.tensor([[0, -1, 0], [1, 0, 0], [0, 0, 0]], dtype=u.dtype, device=u.device)
u_ = u * (-1.0) if torch.det(u) < 0 else u
vT_ = vT * (-1.0) if torch.det(vT) < 0 else vT
R1 = u_ @ w @ vT_
R2 = u_ @ w.transpose(0, 1) @ vT_
t = u[:, -1] # real
return R1, R2, t.unsqueeze(1)
def new_decompose_E(model):
"""
recover rotation and translation from essential matrices without SVD
reference: Horn, Berthold KP. Recovering baseline and orientation from essential matrix[J]. J. Opt. Soc. Am, 1990, 110.
input: essential matrix (3, 3)
output: two possible solutions of rotation matrices, R1, R2; translation t
"""
# assert model.shape == (3, 3)
# Eq.18, choose the largest of the three possible pairwise cross-products
e1, e2, e3 = model[:, 0], model[:, 1], model[:, 2]
bs = [
torch.norm(torch.cross(e1, e2)),
torch.norm(torch.cross(e2, e3)),
torch.norm(torch.cross(e3, e1)),
]
largest = torch.argmax(torch.stack(bs))
bb = bs[largest]
# sqrt(1/2 trace(EE^T))
scale_factor = torch.sqrt(0.5 * torch.trace(model @ model.transpose(0, -1)))
if largest == 0:
b1 = scale_factor * torch.cross(e1, e2) / torch.norm(torch.cross(e1, e2))
elif largest == 1:
b1 = scale_factor * torch.cross(e2, e3) / torch.norm(torch.cross(e2, e3))
else:
b1 = scale_factor * torch.cross(e3, e1) / torch.norm(torch.cross(e3, e1))
# nomalization
b1_ = b1 / torch.norm(b1)
# skew-symmetric matrix
t0, t1, t2 = b1
B1 = torch.tensor([[0, -t2, t1], [t2, 0, -t0], [-t1, t0, 0]], device=b1.device)
# the second translation and rotation
b2 = -b1
B2 = -B1
# Eq.24, recover R
# (bb)R = Cofactors(E)^T - BE
R1 = (matrix_cofactor_tensor(model) - B1 @ model) / (b1.dot(b1))
R2 = (matrix_cofactor_tensor(model) - B2 @ model) / (b1.dot(b1))
return R1, R2, b1_.unsqueeze(-1)
def matrix_cofactor_tensor(matrix):
"""Cofactor matrix, refer to the numpy doc."""
try:
det = torch.det(matrix)
if det != 0:
cofactor = None
cofactor = torch.linalg.inv(matrix).T * det
# return cofactor matrix of the given matrix
return cofactor
else:
raise Exception("singular matrix")
except Exception as e:
print("could not find cofactor matrix due to", e)
def cheirality_check(P0, P, p1, p2, distanceThreshold):
# Q = kornia.geometry.epipolar.triangulate_points(P0.repeat(1024, 1, 1), P, p1, p2)
# make sure the P type, complex tensor with cause error here
Q = torch.tensor(
cv2.triangulatePoints(
P0.cpu().detach().numpy(), P.cpu().detach().numpy(), p1.T, p2.T
),
dtype=P0.dtype,
device=P0.device,
)
Q_homogeneous = torch.stack([Q[i] / Q[-1] for i in range(Q.shape[0])])
Q_ = P @ Q_homogeneous
mask = (
(Q[2].mul(Q[3]) > 0)
& (Q_homogeneous[2] < distanceThreshold)
& (Q_[2] > 0)
& (Q_[2] < distanceThreshold)
)
return mask
def quaternion_from_matrix(matrix, isprecise=False):
"""Return quaternion from rotation matrix.
If isprecise is True, the input matrix is assumed to be a precise rotation
matrix and a faster algorithm is used.
>>> q = quaternion_from_matrix(numpy.identity(4), True)
>>> numpy.allclose(q, [1, 0, 0, 0])
True
>>> q = quaternion_from_matrix(numpy.diag([1, -1, -1, 1]))
>>> numpy.allclose(q, [0, 1, 0, 0]) or numpy.allclose(q, [0, -1, 0, 0])
True
>>> R = rotation_matrix(0.123, (1, 2, 3))
>>> q = quaternion_from_matrix(R, True)
>>> numpy.allclose(q, [0.9981095, 0.0164262, 0.0328524, 0.0492786])
True
>>> R = [[-0.545, 0.797, 0.260, 0], [0.733, 0.603, -0.313, 0],
... [-0.407, 0.021, -0.913, 0], [0, 0, 0, 1]]
>>> q = quaternion_from_matrix(R)
>>> numpy.allclose(q, [0.19069, 0.43736, 0.87485, -0.083611])
True
>>> R = [[0.395, 0.362, 0.843, 0], [-0.626, 0.796, -0.056, 0],
... [-0.677, -0.498, 0.529, 0], [0, 0, 0, 1]]
>>> q = quaternion_from_matrix(R)
>>> numpy.allclose(q, [0.82336615, -0.13610694, 0.46344705, -0.29792603])
True
>>> R = random_rotation_matrix()
>>> q = quaternion_from_matrix(R)
>>> is_same_transform(R, quaternion_matrix(q))
True
>>> R = euler_matrix(0.0, 0.0, numpy.pi/2.0)
>>> numpy.allclose(quaternion_from_matrix(R, isprecise=False),
... quaternion_from_matrix(R, isprecise=True))
True
"""
M = np.array(matrix, dtype=np.float64, copy=False)[:4, :4]
if isprecise:
q = np.empty((4,))
t = np.trace(M)
if t > M[3, 3]:
q[0] = t
q[3] = M[1, 0] - M[0, 1]
q[2] = M[0, 2] - M[2, 0]
q[1] = M[2, 1] - M[1, 2]
else:
i, j, k = 1, 2, 3
if M[1, 1] > M[0, 0]:
i, j, k = 2, 3, 1
if M[2, 2] > M[i, i]:
i, j, k = 3, 1, 2
t = M[i, i] - (M[j, j] + M[k, k]) + M[3, 3]
q[i] = t
q[j] = M[i, j] + M[j, i]
q[k] = M[k, i] + M[i, k]
q[3] = M[k, j] - M[j, k]
q *= 0.5 / math.sqrt(t * M[3, 3])
else:
m00 = M[0, 0]
m01 = M[0, 1]
m02 = M[0, 2]
m10 = M[1, 0]
m11 = M[1, 1]
m12 = M[1, 2]
m20 = M[2, 0]
m21 = M[2, 1]
m22 = M[2, 2]
# symmetric matrix K
K = np.array(
[
[m00 - m11 - m22, 0.0, 0.0, 0.0],
[m01 + m10, m11 - m00 - m22, 0.0, 0.0],
[m02 + m20, m12 + m21, m22 - m00 - m11, 0.0],
[m21 - m12, m02 - m20, m10 - m01, m00 + m11 + m22],
]
)
K /= 3.0
# quaternion is eigenvector of K that corresponds to largest eigenvalue
w, V = np.linalg.eigh(K)
q = V[[3, 0, 1, 2], np.argmax(w)]
if q[0] < 0.0:
np.negative(q, q)
return q
def quaternion_from_matrix_tensor(matrix, isprecise=False):
"""Return quaternion from rotation matrix.
If isprecise is True, the input matrix is assumed to be a precise rotation
matrix and a faster algorithm is used.
>>> q = quaternion_from_matrix(numpy.identity(4), True)
>>> numpy.allclose(q, [1, 0, 0, 0])
True
>>> q = quaternion_from_matrix(numpy.diag([1, -1, -1, 1]))
>>> numpy.allclose(q, [0, 1, 0, 0]) or numpy.allclose(q, [0, -1, 0, 0])
True
>>> R = rotation_matrix(0.123, (1, 2, 3))
>>> q = quaternion_from_matrix(R, True)
>>> numpy.allclose(q, [0.9981095, 0.0164262, 0.0328524, 0.0492786])
True
>>> R = [[-0.545, 0.797, 0.260, 0], [0.733, 0.603, -0.313, 0],
... [-0.407, 0.021, -0.913, 0], [0, 0, 0, 1]]
>>> q = quaternion_from_matrix(R)
>>> numpy.allclose(q, [0.19069, 0.43736, 0.87485, -0.083611])
True
>>> R = [[0.395, 0.362, 0.843, 0], [-0.626, 0.796, -0.056, 0],
... [-0.677, -0.498, 0.529, 0], [0, 0, 0, 1]]
>>> q = quaternion_from_matrix(R)
>>> numpy.allclose(q, [0.82336615, -0.13610694, 0.46344705, -0.29792603])
True
>>> R = random_rotation_matrix()
>>> q = quaternion_from_matrix(R)
>>> is_same_transform(R, quaternion_matrix(q))
True
>>> R = euler_matrix(0.0, 0.0, numpy.pi/2.0)
>>> numpy.allclose(quaternion_from_matrix(R, isprecise=False),
... quaternion_from_matrix(R, isprecise=True))
True
"""
# M = torch.tensor(matrix, dtype=torch.float64, device=matrix.device)[:4, :4]
M = matrix
if isprecise:
q = np.empty((4,))
t = np.trace(M)
if t > M[3, 3]:
q[0] = t
q[3] = M[1, 0] - M[0, 1]
q[2] = M[0, 2] - M[2, 0]
q[1] = M[2, 1] - M[1, 2]
else:
i, j, k = 1, 2, 3
if M[1, 1] > M[0, 0]:
i, j, k = 2, 3, 1
if M[2, 2] > M[i, i]:
i, j, k = 3, 1, 2
t = M[i, i] - (M[j, j] + M[k, k]) + M[3, 3]
q[i] = t
q[j] = M[i, j] + M[j, i]
q[k] = M[k, i] + M[i, k]
q[3] = M[k, j] - M[j, k]
q *= 0.5 / math.sqrt(t * M[3, 3])
else:
m00 = M[0, 0]
m01 = M[0, 1]
m02 = M[0, 2]
m10 = M[1, 0]
m11 = M[1, 1]
m12 = M[1, 2]
m20 = M[2, 0]
m21 = M[2, 1]
m22 = M[2, 2]
# symmetric matrix K
K = torch.tensor(
[
[m00 - m11 - m22, 0.0, 0.0, 0.0],
[m01 + m10, m11 - m00 - m22, 0.0, 0.0],
[m02 + m20, m12 + m21, m22 - m00 - m11, 0.0],
[m21 - m12, m02 - m20, m10 - m01, m00 + m11 + m22],
],
device=matrix.device,
)
K /= 3.0
# quaternion is an eigenvector of K that corresponds to the largest eigenvalue
w, V = torch.linalg.eigh(K)
q = V[[3, 0, 1, 2], torch.argmax(w)]
if q[0] < 0.0:
torch.negative(q)
return q
def evaluate_R_t_tensor(R_gt, t_gt, R, t, q_gt=None):
t = t.flatten()
t_gt = t_gt.flatten().to(t.device)
eps = torch.tensor(1e-8).to(t.device)
err_q = torch.arccos(
torch.max(
torch.min(
(torch.trace(R @ R_gt.transpose(0, 1)) - 1) * 0.5,
torch.tensor(1.0, device=R.device),
),
torch.tensor(-1.0, device=R.device),
)
)
t_gt_ = t_gt / (torch.linalg.norm(t_gt) + eps)
loss_t = torch.max(eps, 1.0 - torch.sum(t * t_gt_) ** 2) # torch.clamp((), min=eps)
err_t = torch.arccos(torch.sqrt(1 - loss_t + eps))
if torch.sum(torch.isnan(err_q)) or torch.sum(torch.isnan(err_t)):
print("This should never happen! Debug here", R_gt, t_gt, R, t, q_gt)
import IPython
IPython.embed()
return err_q, err_t
def evaluate_R_t_tensor_batch(R_gt, t_gt, R, t, q_gt=None):
t = t.flatten(-2, -1)
t_gt = t_gt.flatten().to(t.device)
eps = torch.tensor(1e-15).to(t.device)
# rotation error
err_q = torch.arccos(
torch.clamp(
(
torch.diagonal(
R @ R_gt.repeat(R.shape[0], 1, 1).transpose(-2, -1),
dim1=-2,
dim2=-1,
).sum(-1)
- 1
)
* 0.5,
min=-1.0,
max=1.0,
)
)
# translation error
t = t / (torch.norm(t, dim=-1) + eps).unsqueeze(-1)
t_gt_ = t_gt / (torch.linalg.norm(t_gt) + eps)
loss_t = torch.clamp((1.0 - torch.sum(t * t_gt_, dim=-1) ** 2), min=eps)
err_t = torch.arccos(torch.sqrt(1 - loss_t + 1e-8))
if torch.sum(torch.isnan(err_q)) or torch.sum(torch.isnan(err_t)):
# This should never happen! Debug here
print(R_gt, t_gt, R, t, q_gt)
import IPython
IPython.embed()
return err_q, err_t
def evaluate_R_t(R_gt, t_gt, R, t, q_gt=None):
t = t.flatten()
t_gt = t_gt.flatten()
eps = 1e-15
if q_gt is None:
q_gt = quaternion_from_matrix(R_gt)
q = quaternion_from_matrix(R)
q = q / (np.linalg.norm(q) + eps)
q_gt = q_gt / (np.linalg.norm(q_gt) + eps)
loss_q = np.maximum(eps, (1.0 - np.sum(q * q_gt) ** 2))
err_q = np.arccos(1 - 2 * loss_q)
t = t / (np.linalg.norm(t) + eps)
t_gt = t_gt / (np.linalg.norm(t_gt) + eps)
loss_t = np.maximum(eps, (1.0 - np.sum(t * t_gt) ** 2))
err_t = np.arccos(np.sqrt(1 - loss_t))
if np.sum(np.isnan(err_q)) or np.sum(np.isnan(err_t)):
print("This should never happen! Debug here", R_gt, t_gt, R, t, q_gt)
import IPython
IPython.embed()
return err_q, err_t
def orientation_error(pts1, pts2, M, ang):
"""Orientation error calculation for E or F matrix."""
# 2D coordinates to 3D homogeneous coordinates
num_pts = pts1.shape[0]
# get homogeneous coordinates
hom_pts1 = torch.cat((pts1, torch.ones((num_pts, 1), device=M.device)), dim=-1)
hom_pts2 = torch.cat((pts2, torch.ones((num_pts, 1), device=M.device)), dim=-1)
# calculate the ang between n1 and n2
l1 = M.transpose(-2, -1) @ hom_pts2.transpose(-2, -1)[0:2]
l2 = M @ hom_pts1.transpose(-2, -1)[0:2]
n1 = l1[:, 0:2, :]
n2 = l2[:, 0:2, :]
n1_norm = 1 / torch.norm(n1, axis=0)
n1 = torch.dot(n1, n1_norm)
n2_norm = 1 / torch.norm(n2, axis=0)
n2 = torch.dot(n2, n2_norm)
alpha = torch.arccos(n1.T.dot(n2))
ori_error = abs(alpha - ang)
return ori_error
def scale_error(pts1, pts2, M, scale_ratio):
"""Scale error of the essential matrix."""
num_pts = pts1.shape[0]
# get homogeneous coordinates
hom_pts1 = torch.cat((pts1, torch.ones((num_pts, 1), device=M.device)), dim=-1)
hom_pts2 = torch.cat((pts2, torch.ones((num_pts, 1), device=M.device)), dim=-1)
# calculate the angle between n1 and n2
l1 = (M.transpose(-2, -1) @ (hom_pts2.transpose(-2, -1)))[:, 0:2]
l2 = (M @ (hom_pts1.transpose(-2, -1)))[:, 0:2]
l1_norm = torch.norm(scale_ratio * l1, dim=(-1, -2))
l2_norm = torch.norm(l2, dim=(-1, -2))
return abs(l1_norm - l2_norm)
def eval_essential_matrix_numpy(p1n, p2n, E, dR, dt):
"""Recover the rotation and translation matrices through OpneCV and return their errors."""
if len(p1n) != len(p2n):
raise RuntimeError("Size mismatch in the keypoint lists")
if p1n.shape[0] < 5:
return np.pi, np.pi / 2
if E is not None: # .size > 0:
_, R, t, _ = cv2.recoverPose(
E.cpu().detach().numpy().astype(np.float64), p1n, p2n
)
# R, t = recoverPose(E, p1n, p2n)
try:
err_q, err_t = evaluate_R_t(dR, dt, R, t)
except:
err_q = np.pi
err_t = np.pi / 2
else:
err_q = np.pi
err_t = np.pi / 2
return err_q / np.pi * 180.0, err_t / np.pi * 180.0
def eval_essential_matrix(p1n, p2n, E, dR, dt, svd=True):
"""Evaluate the essential matrix, decompose E to R and t, return the rotation and translation error."""
if len(p1n) != len(p2n):
raise RuntimeError("Size mismatch in the keypoint lists")
if p1n.shape[0] < 5:
return np.pi, np.pi / 2
if E is not None:
# recover the relative pose from E
R, t = recoverPose(E, p1n, p2n, svd)
try:
err_q, err_t = evaluate_R_t_tensor(dR, dt, R, t)
except:
err_q = np.pi
err_t = np.pi / 2
else:
err_q = np.pi
err_t = np.pi / 2
return err_q / np.pi * 180.0, err_t / np.pi * 180.0
def AUC(losses, thresholds=[5, 10, 20], binsize=5):
"""From NG-RANSAC Compute the AUC up to a set of error thresholds.
Return multiple AUC corresponding to multiple threshold provided.
Keyword arguments:
losses -- list of losses which the AUC should be calculated for
thresholds -- list of threshold values up to which the AUC should be calculated
binsize -- bin size to be used to the cumulative histogram when calculating the AUC, the finer the more accurate
"""
bin_num = int(max(thresholds) / binsize)
bins = np.arange(bin_num + 1) * binsize
hist, _ = np.histogram(losses, bins) # histogram up to the max threshold
hist = hist.astype(np.float32) / len(losses) # normalized histogram
hist = np.cumsum(hist) # cumulative normalized histogram
# calculate AUC for each threshold
return [np.mean(hist[: int(t / binsize)]) for t in thresholds]
def AUC_tensor(losses, thresholds=[5, 10, 20], binsize=5):
"""Re-implementation in PyTorch from NG-RANSAC Compute the AUC up to a set of error thresholds.
Return multiple AUC corresponding to multiple threshold provided.
Keyword arguments:
losses -- list of losses which the AUC should be calculated for
thresholds -- list of threshold values up to which the AUC should be calculated
binsize -- bin size to be used to the cumulative histogram when calculating the AUC, the finer the more accurate
"""
bin_num = int(max(thresholds) / binsize)
bins = torch.arange(bin_num + 1) * binsize
hist, _ = torch.histogram(losses, bins) # histogram up to the max threshold
hist = hist.astype(torch.float32) / len(losses) # normalized histogram
hist = torch.cumsum(hist) # cumulative normalized histogram
# calculate AUC for each threshold
return [torch.mean(hist[: int(t / binsize)]) for t in thresholds]
# for checking, kornia
def cross_product_matrix(x):
r"""Return the cross_product_matrix symmetric matrix of a vector.
Args:
x: The input vector to construct the matrix in the shape :math:`(*, 3)`.
Returns:
The constructed cross_product_matrix symmetric matrix with shape :math:`(*, 3, 3)`.
"""
if not x.shape[-1] == 3:
raise AssertionError(x.shape)
# get vector components
x0 = x[..., 0]
x1 = x[..., 1]
x2 = x[..., 2]
# construct the matrix, reshape to 3x3 and return
zeros = torch.zeros_like(x0)
cross_product_matrix_flat = torch.stack(
[zeros, -x2, x1, x2, zeros, -x0, -x1, x0, zeros], dim=-1
)
shape_ = x.shape[:-1] + (3, 3)
return cross_product_matrix_flat.view(*shape_)
def pose_error(R, gt_R, t, gt_t):
"""NG-RANSAC, Compute the angular error between two rotation matrices and two translation vectors.
Keyword arguments:
R -- 2D numpy array containing an estimated rotation
gt_R -- 2D numpy array containing the corresponding ground truth rotation
t -- 2D numpy array containing an estimated translation as column
gt_t -- 2D numpy array containing the corresponding ground truth translation
"""
# calculate angle between provided rotations
dR = np.matmul(R, np.transpose(gt_R))
dR = cv2.Rodrigues(dR)[0]
dR = np.linalg.norm(dR) * 180 / math.pi
# calculate angle between provided translations
dT = float(np.dot(gt_t.T, t))
dT /= float(np.linalg.norm(gt_t))
if dT > 1 or dT < -1:
print("Domain warning! dT:", dT)
dT = max(-1, min(1, dT))
dT = math.acos(dT) * 180 / math.pi
return dR, dT
def batch_episym(x1, x2, F):
"""Epipolar symmetric error from CLNet."""
batch_size, num_pts = x1.shape[0], x1.shape[1]
x1 = torch.cat([x1, x1.new_ones(batch_size, num_pts, 1)], dim=-1).reshape(
batch_size, num_pts, 3, 1
)
x2 = torch.cat([x2, x2.new_ones(batch_size, num_pts, 1)], dim=-1).reshape(
batch_size, num_pts, 3, 1
)
F = F.reshape(-1, 1, 3, 3).repeat(1, num_pts, 1, 1)
x2Fx1 = torch.matmul(x2.transpose(2, 3), torch.matmul(F, x1)).reshape(
batch_size, num_pts
)
Fx1 = torch.matmul(F, x1).reshape(batch_size, num_pts, 3)
Ftx2 = torch.matmul(F.transpose(2, 3), x2).reshape(batch_size, num_pts, 3)
ys = x2Fx1**2 * (
1.0 / (Fx1[:, :, 0] ** 2 + Fx1[:, :, 1] ** 2 + 1e-15)
+ 1.0 / (Ftx2[:, :, 0] ** 2 + Ftx2[:, :, 1] ** 2 + 1e-15)
)
if torch.isnan(ys).any():
print("ys is nan in batch_episym")
return ys
| 21,871 | Python | .py | 547 | 32.817185 | 123 | 0.56399 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,684 | loss.py | disungatullina_MinBackProp/loss.py | import cv2
import torch
import torch.nn as nn
from cv_utils import *
from math_utils import *
import numpy as np
from scorings.msac_score import *
from feature_utils import *
class MatchLoss(object):
"""Rewrite Match loss from CLNet, symmetric epipolar distance"""
def __init__(self):
self.scoring_fun = MSACScore()
def forward(
self, models, gt_E, pts1, pts2, K1, K2, im_size1, im_size2, topk_flag=False, k=1
):
essential_loss = []
for b in range(gt_E.shape[0]):
pts1_1 = pts1[b].clone()
pts2_2 = pts2[b].clone()
Es = models[b]
_, gt_R_1, gt_t_1, gt_inliers = cv2.recoverPose(
gt_E[b].astype(np.float64),
pts1_1.unsqueeze(1).cpu().detach().numpy(),
pts2_2.unsqueeze(1).cpu().detach().numpy(),
np.eye(3, dtype=gt_E.dtype),
)
# find the ground truth inliers
gt_mask = np.where(gt_inliers.ravel() > 0, 1.0, 0.0).astype(bool)
gt_mask = torch.from_numpy(gt_mask).to(pts1_1.device)
# symmetric epipolar errors based on gt inliers
geod = batch_episym(
pts1_1[gt_mask].repeat(Es.shape[0], 1, 1),
pts2_2[gt_mask].repeat(Es.shape[0], 1, 1),
Es,
)
e_l = torch.min(geod, geod.new_ones(geod.shape))
if torch.isnan(e_l.mean()).any():
print("nan values in pose loss") # .1*
if topk_flag:
topk_indices = torch.topk(e_l.mean(1), k=k, largest=False).indices
essential_loss.append(e_l[topk_indices].mean())
else:
essential_loss.append(e_l.mean())
# average
return sum(essential_loss) / gt_E.shape[0]
| 1,811 | Python | .py | 45 | 29.733333 | 88 | 0.546644 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,685 | math_utils.py | disungatullina_MinBackProp/math_utils.py | import math
import torch
def multi_cubic(a0, b0, c0, d0, all_roots=True):
"""Analytical closed-form solver for multiple cubic equations (3rd order polynomial), based on `numpy`
functions.
Parameters
----------
a0, b0, c0, d0: array_like
Input data are coefficients of the Cubic polynomial::
a0*x^3 + b0*x^2 + c0*x + d0 = 0
all_roots: bool, optional
If set to `True` (default) all three roots are computed and returned.
If set to `False` only one (real) root is computed and returned.
Returns
-------
roots: ndarray
Output data is an array of three roots of given polynomials of size
(3, M) if `all_roots=True`, and an array of one root of size (M,)
if `all_roots=False`.
"""
""" Reduce the cubic equation to to form:
x^3 + a*x^2 + bx + c = 0"""
a, b, c = b0 / a0, c0 / a0, d0 / a0
device = a0.device
# Some repeating constants and variables
third = 1.0 / 3.0
a13 = a * third
a2 = a13 * a13
sqr3 = math.sqrt(3)
# Additional intermediate variables
f = third * b - a2
g = a13 * (2 * a2 - b) + c
h = 0.25 * g * g + f * f * f
# Masks for different combinations of roots
m1 = (f == 0) & (g == 0) & (h == 0) # roots are real and equal
m2 = (~m1) & (h <= 0) # roots are real and distinct
m3 = (~m1) & (~m2) # one real root and two complex
def cubic_root(x):
"""Compute cubic root of a number while maintaining its sign."""
root = torch.zeros_like(x)
positive = x >= 0
negative = ~positive
root[positive] = x[positive] ** third
root[negative] = -((-x[negative]) ** third)
return root
def roots_all_real_equal(c):
"""Compute cubic roots if all roots are real and equal."""
r1 = -cubic_root(c).type(torch.cfloat)
if all_roots:
return torch.stack((r1, r1, r1), dim=0)
else:
return r1
def roots_all_real_distinct(a13, f, g, h):
"""Compute cubic roots if all roots are real and distinct."""
j = torch.sqrt(-f)
k = torch.arccos(-0.5 * g / (j * j * j))
m = torch.cos(third * k)
r1 = 2 * j * m - a13
if all_roots:
n = sqr3 * torch.sin(third * k)
r2 = -j * (m + n) - a13
r3 = -j * (m - n) - a13
return torch.stack((r1, r2, r3), dim=0).type(torch.cfloat)
else:
return r1
def roots_one_real(a13, g, h):
"""Compute cubic roots if one root is real and other two are complex."""
sqrt_h = torch.sqrt(h)
S = cubic_root(-0.5 * g + sqrt_h)
U = cubic_root(-0.5 * g - sqrt_h)
S_plus_U = S + U
r1 = S_plus_U - a13
if all_roots:
S_minus_U = S - U
r2 = -0.5 * S_plus_U - a13 + S_minus_U * sqr3 * 0.5j
r3 = -0.5 * S_plus_U - a13 - S_minus_U * sqr3 * 0.5j
return torch.stack((r1, r2, r3), dim=0).type(torch.cfloat)
else:
return r1
# Compute roots
if all_roots:
roots = torch.zeros((3, len(a)), device=device, dtype=torch.cfloat)
roots[:, m1] = roots_all_real_equal(c[m1])
roots[:, m2] = roots_all_real_distinct(a13[m2], f[m2], g[m2], h[m2])
roots[:, m3] = roots_one_real(a13[m3], g[m3], h[m3])
else:
roots = torch.zeros(len(a), device=device, dtype=torch.cfloat)
roots[m1] = roots_all_real_equal(c[m1])
roots[m2] = roots_all_real_distinct(a13[m2], f[m2], g[m2], h[m2])
roots[m3] = roots_one_real(a13[m3], g[m3], h[m3])
return roots
class StrumPolynomialSolver(object):
"""
Python reimplementation of https://github.com/danini/graph-cut-ransac/blob/master/src/pygcransac/include/maths/sturm_polynomial_solver.h
polynomial solver, use for various degrees.
"""
def __init__(self, n):
self.n = n
def build_sturm_seq(self, fvec):
f = torch.zeros(3 * self.n, dtype=torch.float64, device=fvec.device)
f[: 2 * self.n + 1] = fvec
f[2 * self.n + 1 :] = torch.tensor(
[-9.2559631349317831e61] * (self.n - 1), dtype=torch.float64
)
f1 = 0
f2 = self.n + 1
f3 = 2 * self.n + 1
svec = torch.zeros(3 * self.n, dtype=torch.float64, device=fvec.device)
for i in range(self.n - 1):
q1 = f[f1 + self.n - i] * f[f2 + self.n - 1 - i]
q0 = (
f[f1 + self.n - 1 - i] * f[f2 + self.n - 1 - i]
- f[f1 + self.n - i] * f[f2 + self.n - 2 - i]
)
f[f3] = f[f1] - q0 * f[f2]
for j in range(1, self.n - 1 - i):
f[f3 + j] = f[f1 + j] - q1 * f[f2 + j - 1] - q0 * f[f2 + j]
c = -abs(f[f3 + self.n - 2 - i])
for j in range(0, self.n - 1 - i):
f[f3 + j] = f[f3 + j] * (1 / c)
# juggle pointers(f1, f2, f3) -> (f2, f3, f1)
tmp = f1
f1, f2, f3 = f2, f3, tmp
# svec = torch.stack(q0, q1, c) # columns
svec[3 * i] = q0
svec[3 * i + 1] = q1
svec[3 * i + 2] = c
svec[3 * self.n - 3] = f[f1]
svec[3 * self.n - 2] = f[f1 + 1]
svec[3 * self.n - 1] = f[f2]
return svec
def get_bounds(self, fvec):
max_ = 0
for i in range(self.n):
max_ = max([max_, abs(fvec[i])])
return 1 + max_
def flag_negative(self, f, n):
if n <= 0:
return f[0] < 0
else:
return (int(f[n] < 0) << n) | self.flag_negative(
f, n - 1
) # '<<' will cause lshift_cuda' not implemented for bool
def change_sign(self, svec, x):
f = torch.tensor(
[-9.2559631349317831e61] * (self.n + 1),
dtype=torch.float64,
device=svec.device,
)
f[self.n] = svec[3 * self.n - 1]
f[self.n - 1] = svec[3 * self.n - 3] + x * svec[3 * self.n - 2]
for i in range(self.n - 2, -1, -1):
f[i] = (svec[3 * i] + x * svec[3 * i + 1]) * f[i + 1] + svec[3 * i + 2] * f[
i + 2
]
# negative flag
S = self.flag_negative(f, self.n)
return self.NumberOf1((S ^ (S >> 1)) & ~(0xFFFFFFFF << self.n))
def NumberOf1(self, n):
return bin(n & 0xFFFFFFFF).count("1")
def polyval(self, f, x, n):
fx = x + f[n - 1]
for i in range(n - 2, -1, -1):
fx = x * fx + f[i]
return fx
def ridders_method_newton(self, fvec, a, b, tol, tol_newton=1e-3 / 2, n_roots=None):
"""Applies Ridder's bracketing method until we get close to root, followed by newton iterations."""
fa = self.polyval(fvec, a, self.n)
fb = self.polyval(fvec, b, self.n)
if not ((fa * fb) < 0):
return 0, 0
for i in range(30):
if abs(a - b) < tol_newton:
break
c = (a + b) * 1 / 2
fc = self.polyval(fvec, c, self.n)
s = torch.sqrt(fc**2 - fa * fb)
if not s:
break
d = c + (a - c) * fc / s if (fa < fb) else c + (c - a) * fc / s
fd = self.polyval(fvec, d, self.n)
if (fc < 0) if (fd >= 0) else (fc > 0):
a = c
fa = fc
b = d
fb = fd
elif (fa < 0) if (fd >= 0) else (fa > 0):
b = d
fb = fd
else:
a = d
fa = fd
# We switch to Newton's method once we are close to the root
x = (a + b) * 0.5
fpvec = fvec[self.n + 1 :]
for i in range(0, 10):
fx = self.polyval(fvec, x, self.n)
if abs(fx) < tol:
break
fpx = self.n * self.polyval(fpvec, x, self.n - 1)
dx = fx / fpx
x = x - dx
if abs(dx) < tol:
break
n_roots += 1
return n_roots, x
def isolate_roots(
self, fvec, svec, a, b, sa, sb, tol, depth, n_roots=None, roots=None
):
if depth > 30:
return 0, roots
if (sa - sb) > 1:
c = 1 / 2 * (a + b)
sc = self.change_sign(svec, c)
n_roots, roots = self.isolate_roots(
fvec, svec, a, c, sa, sc, tol, depth + 1, n_roots=n_roots, roots=roots
)
n_roots, roots = self.isolate_roots(
fvec, svec, c, b, sc, sb, tol, depth + 1, n_roots=n_roots, roots=roots
)
elif (sa - sb) == 1:
n_roots, x = self.ridders_method_newton(fvec, a, b, tol, n_roots=n_roots)
roots[n_roots - 1] = x
return n_roots, roots
def bisect_sturm(self, coeffs, tol=1e-10):
if coeffs[self.n - 1] == 0.0:
return 0, None
# fvec is the polynomial and its first derivative.
fvec = torch.zeros(2 * self.n + 1, dtype=torch.float64, device=coeffs.device)
fvec[: self.n + 1], fvec[self.n + 1 :] = coeffs, torch.tensor(
[-9.2559631349317831e61] * (self.n), dtype=torch.float64
)
fvec[: self.n + 1] *= 1 / fvec[self.n]
fvec[self.n] = 1
# Compute the derivative with normalized coefficients
for i in range(self.n - 1):
fvec[self.n + 1 + i] = fvec[i + 1] * ((i + 1) / self.n)
fvec[2 * self.n] = 1
# Compute sturm sequences
svec = self.build_sturm_seq(fvec)
# All real roots are in the interval [-r0, r0]
r0 = self.get_bounds(fvec)
sa = self.change_sign(svec, -r0)
sb = self.change_sign(svec, r0)
n_roots = sa - sb
if n_roots <= 0:
return 0, None
roots = torch.zeros(n_roots, device=fvec.device)
n_roots = 0
n_roots, roots = self.isolate_roots(
fvec, svec, -r0, r0, sa, sb, tol, 0, n_roots=n_roots, roots=roots
)
return n_roots, roots
class StrumPolynomialSolverBatch(object):
"""
Python reimplementation of https://github.com/danini/graph-cut-ransac/blob/master/src/pygcransac/include/maths/sturm_polynomial_solver.h
polynomial solver, use for batches of polynomials in various degrees.
"""
def __init__(self, n, batch_size):
self.n = n
self.batch_size = batch_size
def build_sturm_seq(self, fvec):
f = torch.zeros(
self.batch_size, 3 * self.n, dtype=torch.float64, device=fvec.device
)
f[:, : 2 * self.n + 1] = fvec
f[:, 2 * self.n + 1 :] = torch.tensor(
[-9.2559631349317831e61] * (self.batch_size * (self.n - 1)),
dtype=torch.float64,
).view(self.batch_size, -1)
f1 = 0
f2 = self.n + 1
f3 = 2 * self.n + 1
svec = torch.zeros(
self.batch_size, 3 * self.n, dtype=torch.float64, device=fvec.device
)
for i in range(self.n - 1):
q1 = f[:, f1 + self.n - i] * f[:, f2 + self.n - 1 - i]
q0 = (
f[:, f1 + self.n - 1 - i] * f[:, f2 + self.n - 1 - i]
- f[:, f1 + self.n - i] * f[:, f2 + self.n - 2 - i]
)
f[:, f3] = f[:, f1] - q0 * f[:, f2]
for j in range(1, self.n - 1 - i):
f[:, f3 + j] = f[:, f1 + j] - q1 * f[:, f2 + j - 1] - q0 * f[:, f2 + j]
c = -abs(f[:, f3 + self.n - 2 - i])
for j in range(0, self.n - 1 - i):
f[:, f3 + j] = f[:, f3 + j] * (1 / c)
# juggle pointers(f1, f2, f3) -> (f2, f3, f1)
tmp = f1
f1, f2, f3 = f2, f3, tmp
# svec = torch.stack(q0, q1, c) # columns
svec[:, 3 * i] = q0
svec[:, 3 * i + 1] = q1
svec[:, 3 * i + 2] = c
svec[:, 3 * self.n - 3] = f[:, f1]
svec[:, 3 * self.n - 2] = f[:, f1 + 1]
svec[:, 3 * self.n - 1] = f[:, f2]
return svec
def get_bounds(self, fvec):
max_, _ = torch.max(abs(fvec[:, :10]), dim=-1)
return 1 + max_
def flag_negative(self, f, n):
if n <= 0:
return f[0] < 0
else:
return (int(f[n] < 0) << n) | self.flag_negative(f, n - 1)
def change_sign(self, svec, x):
f = torch.tensor(
[-9.2559631349317831e61] * (self.n + 1),
dtype=torch.float64,
device=svec.device,
)
f[self.n] = svec[3 * self.n - 1]
f[self.n - 1] = svec[3 * self.n - 3] + x * svec[3 * self.n - 2]
for i in range(self.n - 2, -1, -1):
f[i] = (svec[3 * i] + x * svec[3 * i + 1]) * f[i + 1] + svec[3 * i + 2] * f[
i + 2
]
S = self.flag_negative(f, self.n)
return self.NumberOf1((S ^ (S >> 1)) & ~(0xFFFFFFFF << self.n))
def change_sign_batch(self, svec, x):
f = torch.tensor(
[-9.2559631349317831e61] * (self.batch_size * (self.n + 1)),
dtype=torch.float64,
device=svec.device,
).view(self.batch_size, -1)
f[:, self.n] = svec[:, 3 * self.n - 1]
f[:, self.n - 1] = svec[:, 3 * self.n - 3] + x * svec[:, 3 * self.n - 2]
for i in range(self.n - 2, -1, -1):
f[:, i] = (svec[:, 3 * i] + x * svec[:, 3 * i + 1]) * f[:, i + 1] + svec[
:, 3 * i + 2
] * f[:, i + 2]
ret = []
# negative flag
for i in range(f.shape[0]):
S = self.flag_negative(f[i], self.n)
ret.append(
torch.tensor(
self.NumberOf1((S ^ (S >> 1)) & ~(0xFFFFFFFF << self.n)),
device=f.device,
)
)
return torch.stack(ret)
def NumberOf1(self, n):
return bin(n & 0xFFFFFFFF).count("1")
def polyval(self, f, x, n):
fx = x + f[n - 1]
for i in range(n - 2, -1, -1):
fx = x * fx + f[i]
return fx
def ridders_method_newton(self, fvec, a, b, tol, tol_newton=1e-3 / 2, n_roots=None):
"""Applies Ridder's bracketing method until we get close to root, followed by newton iterations."""
fa = self.polyval(fvec, a, self.n)
fb = self.polyval(fvec, b, self.n)
if not ((fa * fb) < 0):
return 0, torch.zeros(1, device=fvec.device)
for i in range(30):
if abs(a - b) < tol_newton:
break
c = (a + b) * 1 / 2
fc = self.polyval(fvec, c, self.n)
s = torch.sqrt(fc**2 - fa * fb)
if not s:
break
d = c + (a - c) * fc / s if (fa < fb) else c + (c - a) * fc / s
fd = self.polyval(fvec, d, self.n)
if (fc < 0) if (fd >= 0) else (fc > 0):
a = c
fa = fc
b = d
fb = fd
elif (fa < 0) if (fd >= 0) else (fa > 0):
b = d
fb = fd
else:
a = d
fa = fd
# We switch to Newton's method once we are close to the root
x = (a + b) * 0.5
fpvec = fvec[self.n + 1 :]
for i in range(0, 10):
fx = self.polyval(fvec, x, self.n)
if abs(fx) < tol:
break
fpx = self.n * self.polyval(fpvec, x, self.n - 1)
dx = fx / fpx
x = x - dx
if abs(dx) < tol:
break
n_roots += 1
return n_roots, x
def isolate_roots(
self, fvec, svec, a, b, sa, sb, tol, depth, n_roots=None, roots=None
):
if depth > 30:
return 0, roots
if (sa - sb) > 1:
c = 1 / 2 * (a + b)
sc = self.change_sign(svec, c)
n_roots, roots = self.isolate_roots(
fvec, svec, a, c, sa, sc, tol, depth + 1, n_roots=n_roots, roots=roots
)
n_roots, roots = self.isolate_roots(
fvec, svec, c, b, sc, sb, tol, depth + 1, n_roots=n_roots, roots=roots
)
elif (sa - sb) == 1:
try:
n_roots, x = self.ridders_method_newton(
fvec, a, b, tol, n_roots=n_roots
)
except ValueError:
print("")
roots[n_roots - 1] = x
return n_roots, roots
def bisect_sturm(self, coeffs, custom_sols=0, tol=1e-10):
# fvec is the polynomial and its first derivative.
fvec = torch.zeros(
self.batch_size, 2 * self.n + 1, dtype=torch.float64, device=coeffs.device
)
fvec[:, : self.n + 1], fvec[:, self.n + 1 :] = coeffs, torch.tensor(
[-9.2559631349317831e61] * (self.batch_size * self.n), dtype=torch.float64
).view(self.batch_size, -1)
fvec[:, : self.n + 1] = (
torch.bmm(
(fvec[:, : self.n + 1].clone()).unsqueeze(-1),
(1 / fvec[:, self.n].clone()).unsqueeze(-1).unsqueeze(-1),
)
).squeeze(-1)
fvec[:, self.n] = torch.ones(self.batch_size)
# Compute the derivative with normalized coefficients
for i in range(self.n - 1):
fvec[:, self.n + 1 + i] = fvec[:, i + 1] * ((i + 1) / self.n)
fvec[:, 2 * self.n] = torch.ones(self.batch_size)
# Compute sturm sequences
svec = self.build_sturm_seq(fvec)
# All real roots are in the interval [-r0, r0]
r0 = self.get_bounds(fvec)
sa = self.change_sign_batch(svec, -r0)
sb = self.change_sign_batch(svec, r0)
roots = []
if custom_sols == 0:
n_roots = sa - sb
else:
n_roots = torch.ones(self.batch_size, device=fvec.device) * custom_sols
for i in range(self.batch_size):
if n_roots[i] <= 0:
root = torch.zeros(1, device=fvec.device)
else:
root = torch.zeros(int(n_roots[i]), device=fvec.device)
n_root = 0
n_root, root = self.isolate_roots(
fvec[i],
svec[i],
-r0[i],
r0[i],
sa[i],
sb[i],
tol,
0,
n_roots=n_root,
roots=root,
)
roots.append(root)
return n_roots, roots
| 18,515 | Python | .py | 465 | 28.793548 | 140 | 0.470654 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,686 | essential_matrix_estimator_nister.py | disungatullina_MinBackProp/estimators/essential_matrix_estimator_nister.py | import torch
import numpy as np
from math_utils import *
from utils import *
from cv_utils import *
try:
from pymagsac import optimizeEssentialMatrix
pymagsac_available = 1
def numerical_optimization(
matches,
weights,
K1,
K2,
inlier_indices,
best_model,
unnormalzied_threshold,
best_score,
):
# bundle adjustment
estimated_models, _ = optimizeEssentialMatrix(
matches.squeeze().cpu().detach().numpy(),
K1,
K2,
inlier_indices,
best_model,
unnormalzied_threshold,
float(best_score),
)
# normalize the models
estimated_models = torch.from_numpy(estimated_models).to(
matches.device, matches.dtype
).unsqueeze(0) / torch.norm(
torch.from_numpy(estimated_models)
.to(matches.device, matches.dtype)
.unsqueeze(0),
dim=(1, 2),
)
return estimated_models
except ImportError:
pymagsac_available = 0
class EssentialMatrixEstimatorNister(object):
def __init__(self, device="cuda", ift=1):
self.sample_size = 5
self.device = device
self.drop = (
not ift
) # True for the original autograd, False for the IFT and the DDN; False means to keep the batch size unchanged
def estimate_model(
self,
matches,
weights=None,
K1=None,
K2=None,
inlier_indices=None,
best_model=None,
unnormalzied_threshold=None,
best_score=0,
):
# minimal solver
if matches.shape[1] == self.sample_size:
return self.estimate_minimal_model(matches, weights)
# non-minial solver with numerical optimization in pymagsac c++
elif matches.shape[1] > self.sample_size:
if pymagsac_available:
return numerical_optimization(
matches,
weights,
K1,
K2,
inlier_indices,
best_model,
unnormalzied_threshold,
best_score,
)
else:
return self.estimate_minimal_model(matches, weights)
return None
def estimate_minimal_model(self, pts, weights=None): # x1 y1 x2 y2
"""Using Nister's 5 PC to estimate Essential matrix."""
try:
pts.shape[1] == self.sample_size
except ValueError:
print("This is not a minimal sample.")
batch_size, num, _ = pts.shape
pts1 = pts[:, :, 0:2]
pts2 = pts[:, :, 2:4]
# get the points
x1, y1 = pts1[:, :, 0], pts1[:, :, 1]
x2, y2 = pts2[:, :, 0], pts2[:, :, 1]
# Step1: construct the A matrix, A F = 0.
# 5 equations for 9 variables, A is 5x9 matrix containing epipolar constraints
# Essential matrix is a linear combination of the 4 vectors spanning the null space of A
a_59 = torch.ones_like(x1) # .shape)
if weights is not None:
A_s = weights.unsqueeze(-1) * torch.stack(
(
torch.mul(x1, x2),
torch.mul(x1, y2),
x1,
torch.mul(y1, x2),
torch.mul(y1, y2),
y1,
x2,
y2,
a_59,
),
dim=-1,
)
else:
A_s = torch.stack(
(
torch.mul(x1, x2),
torch.mul(x1, y2),
x1,
torch.mul(y1, x2),
torch.mul(y1, y2),
y1,
x2,
y2,
a_59,
),
dim=-1,
)
_, _, v = torch.linalg.svd(
A_s.transpose(-1, -2) @ A_s
) # .transpose(-1, -2)@A_s)# eigenvalues in increasing order
null_ = v[:, -4:, :].transpose(-1, -2) # the last four rows
nullSpace = v[:, -4:, :]
coeffs = torch.zeros(batch_size, 10, 20, device=null_.device, dtype=null_.dtype)
d = torch.zeros(batch_size, 60, device=null_.device, dtype=null_.dtype)
fun = lambda i, j: null_[:, 3 * j + i]
# Determinant constraint
coeffs[:, 9] = (
self.o2(
self.o1(fun(0, 1), fun(1, 2)) - self.o1(fun(0, 2), fun(1, 1)), fun(2, 0)
)
+ self.o2(
self.o1(fun(0, 2), fun(1, 0)) - self.o1(fun(0, 0), fun(1, 2)), fun(2, 1)
)
+ self.o2(
self.o1(fun(0, 0), fun(1, 1)) - self.o1(fun(0, 1), fun(1, 0)), fun(2, 2)
)
)
indices = torch.tensor([[0, 10, 20], [10, 40, 30], [20, 30, 50]])
# Compute EE^T (equation 20 in paper)
for i in range(3):
for j in range(3):
d[:, indices[i, j] : indices[i, j] + 10] = (
self.o1(fun(i, 0), fun(j, 0))
+ self.o1(fun(i, 1), fun(j, 1))
+ self.o1(fun(i, 2), fun(j, 2))
)
for i in range(10):
t = 0.5 * (
d[:, indices[0, 0] + i]
+ d[:, indices[1, 1] + i]
+ d[:, indices[2, 2] + i]
)
d[:, indices[0, 0] + i] -= t
d[:, indices[1, 1] + i] -= t
d[:, indices[2, 2] + i] -= t
cnt = 0
for i in range(3):
for j in range(3):
row = (
self.o2(d[:, indices[i, 0] : indices[i, 0] + 10], fun(0, j))
+ self.o2(d[:, indices[i, 1] : indices[i, 1] + 10], fun(1, j))
+ self.o2(d[:, indices[i, 2] : indices[i, 2] + 10], fun(2, j))
)
coeffs[:, cnt] = row
cnt += 1
b = coeffs[:, :, 10:]
if self.drop:
singular_filter = torch.linalg.matrix_rank(coeffs[:, :, :10]) >= torch.max(
torch.linalg.matrix_rank(coeffs),
torch.ones_like(torch.linalg.matrix_rank(coeffs[:, :, :10])) * 10,
)
try:
if self.drop:
eliminated_mat = torch.linalg.solve(
coeffs[singular_filter, :, :10], b[singular_filter]
)
else:
eliminated_mat = torch.linalg.solve(coeffs[:, :, :10], b[:])
except Exception as e:
print(e)
return (
torch.eye(3, device=pts.device, dtype=pts.dtype)
.unsqueeze(0)
.repeat(640, 1, 1)
)
if self.drop:
coeffs_ = torch.concat(
(coeffs[singular_filter, :, :10], eliminated_mat), dim=-1
)
else:
coeffs_ = torch.concat((coeffs[:, :, :10], eliminated_mat), dim=-1)
A = torch.zeros(
coeffs_.shape[0], 3, 13, device=coeffs_.device, dtype=coeffs_.dtype
)
for i in range(3):
A[:, i, 0] = 0.0
A[:, i : i + 1, 1:4] = coeffs_[:, 4 + 2 * i : 5 + 2 * i, 10:13]
A[:, i : i + 1, 0:3] -= coeffs_[:, 5 + 2 * i : 6 + 2 * i, 10:13]
A[:, i, 4] = 0.0
A[:, i : i + 1, 5:8] = coeffs_[:, 4 + 2 * i : 5 + 2 * i, 13:16]
A[:, i : i + 1, 4:7] -= coeffs_[:, 5 + 2 * i : 6 + 2 * i, 13:16]
A[:, i, 8] = 0.0
A[:, i : i + 1, 9:13] = coeffs_[:, 4 + 2 * i : 5 + 2 * i, 16:20]
A[:, i : i + 1, 8:12] -= coeffs_[:, 5 + 2 * i : 6 + 2 * i, 16:20]
cs = torch.zeros(A.shape[0], 11, device=A.device, dtype=A.dtype)
cs[:, 0] = (
A[:, 0, 12] * A[:, 1, 3] * A[:, 2, 7]
- A[:, 0, 12] * A[:, 1, 7] * A[:, 2, 3]
- A[:, 0, 3] * A[:, 2, 7] * A[:, 1, 12]
+ A[:, 0, 7] * A[:, 2, 3] * A[:, 1, 12]
+ A[:, 0, 3] * A[:, 1, 7] * A[:, 2, 12]
- A[:, 0, 7] * A[:, 1, 3] * A[:, 2, 12]
)
cs[:, 1] = (
A[:, 0, 11] * A[:, 1, 3] * A[:, 2, 7]
- A[:, 0, 11] * A[:, 1, 7] * A[:, 2, 3]
+ A[:, 0, 12] * A[:, 1, 2] * A[:, 2, 7]
+ A[:, 0, 12] * A[:, 1, 3] * A[:, 2, 6]
- A[:, 0, 12] * A[:, 1, 6] * A[:, 2, 3]
- A[:, 0, 12] * A[:, 1, 7] * A[:, 2, 2]
- A[:, 0, 2] * A[:, 2, 7] * A[:, 1, 12]
- A[:, 0, 3] * A[:, 2, 6] * A[:, 1, 12]
- A[:, 0, 3] * A[:, 2, 7] * A[:, 1, 11]
+ A[:, 0, 6] * A[:, 2, 3] * A[:, 1, 12]
+ A[:, 0, 7] * A[:, 2, 2] * A[:, 1, 12]
+ A[:, 0, 7] * A[:, 2, 3] * A[:, 1, 11]
+ A[:, 0, 2] * A[:, 1, 7] * A[:, 2, 12]
+ A[:, 0, 3] * A[:, 1, 6] * A[:, 2, 12]
+ A[:, 0, 3] * A[:, 1, 7] * A[:, 2, 11]
- A[:, 0, 6] * A[:, 1, 3] * A[:, 2, 12]
- A[:, 0, 7] * A[:, 1, 2] * A[:, 2, 12]
- A[:, 0, 7] * A[:, 1, 3] * A[:, 2, 11]
)
cs[:, 2] = (
A[:, 0, 10] * A[:, 1, 3] * A[:, 2, 7]
- A[:, 0, 10] * A[:, 1, 7] * A[:, 2, 3]
+ A[:, 0, 11] * A[:, 1, 2] * A[:, 2, 7]
+ A[:, 0, 11] * A[:, 1, 3] * A[:, 2, 6]
- A[:, 0, 11] * A[:, 1, 6] * A[:, 2, 3]
- A[:, 0, 11] * A[:, 1, 7] * A[:, 2, 2]
+ A[:, 1, 1] * A[:, 0, 12] * A[:, 2, 7]
+ A[:, 0, 12] * A[:, 1, 2] * A[:, 2, 6]
+ A[:, 0, 12] * A[:, 1, 3] * A[:, 2, 5]
- A[:, 0, 12] * A[:, 1, 5] * A[:, 2, 3]
- A[:, 0, 12] * A[:, 1, 6] * A[:, 2, 2]
- A[:, 0, 12] * A[:, 1, 7] * A[:, 2, 1]
- A[:, 0, 1] * A[:, 2, 7] * A[:, 1, 12]
- A[:, 0, 2] * A[:, 2, 6] * A[:, 1, 12]
- A[:, 0, 2] * A[:, 2, 7] * A[:, 1, 11]
- A[:, 0, 3] * A[:, 2, 5] * A[:, 1, 12]
- A[:, 0, 3] * A[:, 2, 6] * A[:, 1, 11]
- A[:, 0, 3] * A[:, 2, 7] * A[:, 1, 10]
+ A[:, 0, 5] * A[:, 2, 3] * A[:, 1, 12]
+ A[:, 0, 6] * A[:, 2, 2] * A[:, 1, 12]
+ A[:, 0, 6] * A[:, 2, 3] * A[:, 1, 11]
+ A[:, 0, 7] * A[:, 2, 1] * A[:, 1, 12]
+ A[:, 0, 7] * A[:, 2, 2] * A[:, 1, 11]
+ A[:, 0, 7] * A[:, 2, 3] * A[:, 1, 10]
+ A[:, 0, 1] * A[:, 1, 7] * A[:, 2, 12]
+ A[:, 0, 2] * A[:, 1, 6] * A[:, 2, 12]
+ A[:, 0, 2] * A[:, 1, 7] * A[:, 2, 11]
+ A[:, 0, 3] * A[:, 1, 5] * A[:, 2, 12]
+ A[:, 0, 3] * A[:, 1, 6] * A[:, 2, 11]
+ A[:, 0, 3] * A[:, 1, 7] * A[:, 2, 10]
- A[:, 0, 5] * A[:, 1, 3] * A[:, 2, 12]
- A[:, 0, 6] * A[:, 1, 2] * A[:, 2, 12]
- A[:, 0, 6] * A[:, 1, 3] * A[:, 2, 11]
- A[:, 0, 7] * A[:, 1, 1] * A[:, 2, 12]
- A[:, 0, 7] * A[:, 1, 2] * A[:, 2, 11]
- A[:, 0, 7] * A[:, 1, 3] * A[:, 2, 10]
)
cs[:, 3] = (
A[:, 0, 3] * A[:, 1, 7] * A[:, 2, 9]
- A[:, 0, 3] * A[:, 1, 9] * A[:, 2, 7]
- A[:, 0, 7] * A[:, 1, 3] * A[:, 2, 9]
+ A[:, 0, 7] * A[:, 1, 9] * A[:, 2, 3]
+ A[:, 0, 9] * A[:, 1, 3] * A[:, 2, 7]
- A[:, 0, 9] * A[:, 1, 7] * A[:, 2, 3]
+ A[:, 0, 10] * A[:, 1, 2] * A[:, 2, 7]
+ A[:, 0, 10] * A[:, 1, 3] * A[:, 2, 6]
- A[:, 0, 10] * A[:, 1, 6] * A[:, 2, 3]
- A[:, 0, 10] * A[:, 1, 7] * A[:, 2, 2]
+ A[:, 1, 0] * A[:, 0, 12] * A[:, 2, 7]
+ A[:, 0, 11] * A[:, 1, 1] * A[:, 2, 7]
+ A[:, 0, 11] * A[:, 1, 2] * A[:, 2, 6]
+ A[:, 0, 11] * A[:, 1, 3] * A[:, 2, 5]
- A[:, 0, 11] * A[:, 1, 5] * A[:, 2, 3]
- A[:, 0, 11] * A[:, 1, 6] * A[:, 2, 2]
- A[:, 0, 11] * A[:, 1, 7] * A[:, 2, 1]
+ A[:, 1, 1] * A[:, 0, 12] * A[:, 2, 6]
+ A[:, 0, 12] * A[:, 1, 2] * A[:, 2, 5]
+ A[:, 0, 12] * A[:, 1, 3] * A[:, 2, 4]
- A[:, 0, 12] * A[:, 1, 4] * A[:, 2, 3]
- A[:, 0, 12] * A[:, 1, 5] * A[:, 2, 2]
- A[:, 0, 12] * A[:, 1, 6] * A[:, 2, 1]
- A[:, 0, 12] * A[:, 1, 7] * A[:, 2, 0]
- A[:, 0, 0] * A[:, 2, 7] * A[:, 1, 12]
- A[:, 0, 1] * A[:, 2, 6] * A[:, 1, 12]
- A[:, 0, 1] * A[:, 2, 7] * A[:, 1, 11]
- A[:, 0, 2] * A[:, 2, 5] * A[:, 1, 12]
- A[:, 0, 2] * A[:, 2, 6] * A[:, 1, 11]
- A[:, 0, 2] * A[:, 2, 7] * A[:, 1, 10]
- A[:, 0, 3] * A[:, 2, 4] * A[:, 1, 12]
- A[:, 0, 3] * A[:, 2, 5] * A[:, 1, 11]
- A[:, 0, 3] * A[:, 2, 6] * A[:, 1, 10]
+ A[:, 0, 4] * A[:, 2, 3] * A[:, 1, 12]
+ A[:, 0, 5] * A[:, 2, 2] * A[:, 1, 12]
+ A[:, 0, 5] * A[:, 2, 3] * A[:, 1, 11]
+ A[:, 0, 6] * A[:, 2, 1] * A[:, 1, 12]
+ A[:, 0, 6] * A[:, 2, 2] * A[:, 1, 11]
+ A[:, 0, 6] * A[:, 2, 3] * A[:, 1, 10]
+ A[:, 0, 7] * A[:, 2, 0] * A[:, 1, 12]
+ A[:, 0, 7] * A[:, 2, 1] * A[:, 1, 11]
+ A[:, 0, 7] * A[:, 2, 2] * A[:, 1, 10]
+ A[:, 0, 0] * A[:, 1, 7] * A[:, 2, 12]
+ A[:, 0, 1] * A[:, 1, 6] * A[:, 2, 12]
+ A[:, 0, 1] * A[:, 1, 7] * A[:, 2, 11]
+ A[:, 0, 2] * A[:, 1, 5] * A[:, 2, 12]
+ A[:, 0, 2] * A[:, 1, 6] * A[:, 2, 11]
+ A[:, 0, 2] * A[:, 1, 7] * A[:, 2, 10]
+ A[:, 0, 3] * A[:, 1, 4] * A[:, 2, 12]
+ A[:, 0, 3] * A[:, 1, 5] * A[:, 2, 11]
+ A[:, 0, 3] * A[:, 1, 6] * A[:, 2, 10]
- A[:, 0, 4] * A[:, 1, 3] * A[:, 2, 12]
- A[:, 0, 5] * A[:, 1, 2] * A[:, 2, 12]
- A[:, 0, 5] * A[:, 1, 3] * A[:, 2, 11]
- A[:, 0, 6] * A[:, 1, 1] * A[:, 2, 12]
- A[:, 0, 6] * A[:, 1, 2] * A[:, 2, 11]
- A[:, 0, 6] * A[:, 1, 3] * A[:, 2, 10]
- A[:, 0, 7] * A[:, 1, 0] * A[:, 2, 12]
- A[:, 0, 7] * A[:, 1, 1] * A[:, 2, 11]
- A[:, 0, 7] * A[:, 1, 2] * A[:, 2, 10]
)
cs[:, 4] = (
A[:, 0, 2] * A[:, 1, 7] * A[:, 2, 9]
- A[:, 0, 2] * A[:, 1, 9] * A[:, 2, 7]
+ A[:, 0, 3] * A[:, 1, 6] * A[:, 2, 9]
+ A[:, 0, 3] * A[:, 1, 7] * A[:, 2, 8]
- A[:, 0, 3] * A[:, 1, 8] * A[:, 2, 7]
- A[:, 0, 3] * A[:, 1, 9] * A[:, 2, 6]
- A[:, 0, 6] * A[:, 1, 3] * A[:, 2, 9]
+ A[:, 0, 6] * A[:, 1, 9] * A[:, 2, 3]
- A[:, 0, 7] * A[:, 1, 2] * A[:, 2, 9]
- A[:, 0, 7] * A[:, 1, 3] * A[:, 2, 8]
+ A[:, 0, 7] * A[:, 1, 8] * A[:, 2, 3]
+ A[:, 0, 7] * A[:, 1, 9] * A[:, 2, 2]
+ A[:, 0, 8] * A[:, 1, 3] * A[:, 2, 7]
- A[:, 0, 8] * A[:, 1, 7] * A[:, 2, 3]
+ A[:, 0, 9] * A[:, 1, 2] * A[:, 2, 7]
+ A[:, 0, 9] * A[:, 1, 3] * A[:, 2, 6]
- A[:, 0, 9] * A[:, 1, 6] * A[:, 2, 3]
- A[:, 0, 9] * A[:, 1, 7] * A[:, 2, 2]
+ A[:, 0, 10] * A[:, 1, 1] * A[:, 2, 7]
+ A[:, 0, 10] * A[:, 1, 2] * A[:, 2, 6]
+ A[:, 0, 10] * A[:, 1, 3] * A[:, 2, 5]
- A[:, 0, 10] * A[:, 1, 5] * A[:, 2, 3]
- A[:, 0, 10] * A[:, 1, 6] * A[:, 2, 2]
- A[:, 0, 10] * A[:, 1, 7] * A[:, 2, 1]
+ A[:, 1, 0] * A[:, 0, 11] * A[:, 2, 7]
+ A[:, 1, 0] * A[:, 0, 12] * A[:, 2, 6]
+ A[:, 0, 11] * A[:, 1, 1] * A[:, 2, 6]
+ A[:, 0, 11] * A[:, 1, 2] * A[:, 2, 5]
+ A[:, 0, 11] * A[:, 1, 3] * A[:, 2, 4]
- A[:, 0, 11] * A[:, 1, 4] * A[:, 2, 3]
- A[:, 0, 11] * A[:, 1, 5] * A[:, 2, 2]
- A[:, 0, 11] * A[:, 1, 6] * A[:, 2, 1]
- A[:, 0, 11] * A[:, 1, 7] * A[:, 2, 0]
+ A[:, 1, 1] * A[:, 0, 12] * A[:, 2, 5]
+ A[:, 0, 12] * A[:, 1, 2] * A[:, 2, 4]
- A[:, 0, 12] * A[:, 1, 4] * A[:, 2, 2]
- A[:, 0, 12] * A[:, 1, 5] * A[:, 2, 1]
- A[:, 0, 12] * A[:, 1, 6] * A[:, 2, 0]
- A[:, 0, 0] * A[:, 2, 6] * A[:, 1, 12]
- A[:, 0, 0] * A[:, 2, 7] * A[:, 1, 11]
- A[:, 0, 1] * A[:, 2, 5] * A[:, 1, 12]
- A[:, 0, 1] * A[:, 2, 6] * A[:, 1, 11]
- A[:, 0, 1] * A[:, 2, 7] * A[:, 1, 10]
- A[:, 0, 2] * A[:, 2, 4] * A[:, 1, 12]
- A[:, 0, 2] * A[:, 2, 5] * A[:, 1, 11]
- A[:, 0, 2] * A[:, 2, 6] * A[:, 1, 10]
- A[:, 0, 3] * A[:, 2, 4] * A[:, 1, 11]
- A[:, 0, 3] * A[:, 2, 5] * A[:, 1, 10]
+ A[:, 0, 4] * A[:, 2, 2] * A[:, 1, 12]
+ A[:, 0, 4] * A[:, 2, 3] * A[:, 1, 11]
+ A[:, 0, 5] * A[:, 2, 1] * A[:, 1, 12]
+ A[:, 0, 5] * A[:, 2, 2] * A[:, 1, 11]
+ A[:, 0, 5] * A[:, 2, 3] * A[:, 1, 10]
+ A[:, 0, 6] * A[:, 2, 0] * A[:, 1, 12]
+ A[:, 0, 6] * A[:, 2, 1] * A[:, 1, 11]
+ A[:, 0, 6] * A[:, 2, 2] * A[:, 1, 10]
+ A[:, 0, 7] * A[:, 2, 0] * A[:, 1, 11]
+ A[:, 0, 7] * A[:, 2, 1] * A[:, 1, 10]
+ A[:, 0, 0] * A[:, 1, 6] * A[:, 2, 12]
+ A[:, 0, 0] * A[:, 1, 7] * A[:, 2, 11]
+ A[:, 0, 1] * A[:, 1, 5] * A[:, 2, 12]
+ A[:, 0, 1] * A[:, 1, 6] * A[:, 2, 11]
+ A[:, 0, 1] * A[:, 1, 7] * A[:, 2, 10]
+ A[:, 0, 2] * A[:, 1, 4] * A[:, 2, 12]
+ A[:, 0, 2] * A[:, 1, 5] * A[:, 2, 11]
+ A[:, 0, 2] * A[:, 1, 6] * A[:, 2, 10]
+ A[:, 0, 3] * A[:, 1, 4] * A[:, 2, 11]
+ A[:, 0, 3] * A[:, 1, 5] * A[:, 2, 10]
- A[:, 0, 4] * A[:, 1, 2] * A[:, 2, 12]
- A[:, 0, 4] * A[:, 1, 3] * A[:, 2, 11]
- A[:, 0, 5] * A[:, 1, 1] * A[:, 2, 12]
- A[:, 0, 5] * A[:, 1, 2] * A[:, 2, 11]
- A[:, 0, 5] * A[:, 1, 3] * A[:, 2, 10]
- A[:, 0, 6] * A[:, 1, 0] * A[:, 2, 12]
- A[:, 0, 6] * A[:, 1, 1] * A[:, 2, 11]
- A[:, 0, 6] * A[:, 1, 2] * A[:, 2, 10]
- A[:, 0, 7] * A[:, 1, 0] * A[:, 2, 11]
- A[:, 0, 7] * A[:, 1, 1] * A[:, 2, 10]
)
cs[:, 5] = (
A[:, 0, 1] * A[:, 1, 7] * A[:, 2, 9]
- A[:, 0, 1] * A[:, 1, 9] * A[:, 2, 7]
+ A[:, 0, 2] * A[:, 1, 6] * A[:, 2, 9]
+ A[:, 0, 2] * A[:, 1, 7] * A[:, 2, 8]
- A[:, 0, 2] * A[:, 1, 8] * A[:, 2, 7]
- A[:, 0, 2] * A[:, 1, 9] * A[:, 2, 6]
+ A[:, 0, 3] * A[:, 1, 5] * A[:, 2, 9]
+ A[:, 0, 3] * A[:, 1, 6] * A[:, 2, 8]
- A[:, 0, 3] * A[:, 1, 8] * A[:, 2, 6]
- A[:, 0, 3] * A[:, 1, 9] * A[:, 2, 5]
- A[:, 0, 5] * A[:, 1, 3] * A[:, 2, 9]
+ A[:, 0, 5] * A[:, 1, 9] * A[:, 2, 3]
- A[:, 0, 6] * A[:, 1, 2] * A[:, 2, 9]
- A[:, 0, 6] * A[:, 1, 3] * A[:, 2, 8]
+ A[:, 0, 6] * A[:, 1, 8] * A[:, 2, 3]
+ A[:, 0, 6] * A[:, 1, 9] * A[:, 2, 2]
- A[:, 0, 7] * A[:, 1, 1] * A[:, 2, 9]
- A[:, 0, 7] * A[:, 1, 2] * A[:, 2, 8]
+ A[:, 0, 7] * A[:, 1, 8] * A[:, 2, 2]
+ A[:, 0, 7] * A[:, 1, 9] * A[:, 2, 1]
+ A[:, 0, 8] * A[:, 1, 2] * A[:, 2, 7]
+ A[:, 0, 8] * A[:, 1, 3] * A[:, 2, 6]
- A[:, 0, 8] * A[:, 1, 6] * A[:, 2, 3]
- A[:, 0, 8] * A[:, 1, 7] * A[:, 2, 2]
+ A[:, 0, 9] * A[:, 1, 1] * A[:, 2, 7]
+ A[:, 0, 9] * A[:, 1, 2] * A[:, 2, 6]
+ A[:, 0, 9] * A[:, 1, 3] * A[:, 2, 5]
- A[:, 0, 9] * A[:, 1, 5] * A[:, 2, 3]
- A[:, 0, 9] * A[:, 1, 6] * A[:, 2, 2]
- A[:, 0, 9] * A[:, 1, 7] * A[:, 2, 1]
+ A[:, 0, 10] * A[:, 1, 0] * A[:, 2, 7]
+ A[:, 0, 10] * A[:, 1, 1] * A[:, 2, 6]
+ A[:, 0, 10] * A[:, 1, 2] * A[:, 2, 5]
+ A[:, 0, 10] * A[:, 1, 3] * A[:, 2, 4]
- A[:, 0, 10] * A[:, 1, 4] * A[:, 2, 3]
- A[:, 0, 10] * A[:, 1, 5] * A[:, 2, 2]
- A[:, 0, 10] * A[:, 1, 6] * A[:, 2, 1]
- A[:, 0, 10] * A[:, 1, 7] * A[:, 2, 0]
+ A[:, 1, 0] * A[:, 0, 11] * A[:, 2, 6]
+ A[:, 1, 0] * A[:, 0, 12] * A[:, 2, 5]
+ A[:, 0, 11] * A[:, 1, 1] * A[:, 2, 5]
+ A[:, 0, 11] * A[:, 1, 2] * A[:, 2, 4]
- A[:, 0, 11] * A[:, 1, 4] * A[:, 2, 2]
- A[:, 0, 11] * A[:, 1, 5] * A[:, 2, 1]
- A[:, 0, 11] * A[:, 1, 6] * A[:, 2, 0]
+ A[:, 1, 1] * A[:, 0, 12] * A[:, 2, 4]
- A[:, 0, 12] * A[:, 1, 4] * A[:, 2, 1]
- A[:, 0, 12] * A[:, 1, 5] * A[:, 2, 0]
- A[:, 0, 0] * A[:, 2, 5] * A[:, 1, 12]
- A[:, 0, 0] * A[:, 2, 6] * A[:, 1, 11]
- A[:, 0, 0] * A[:, 2, 7] * A[:, 1, 10]
- A[:, 0, 1] * A[:, 2, 4] * A[:, 1, 12]
- A[:, 0, 1] * A[:, 2, 5] * A[:, 1, 11]
- A[:, 0, 1] * A[:, 2, 6] * A[:, 1, 10]
- A[:, 0, 2] * A[:, 2, 4] * A[:, 1, 11]
- A[:, 0, 2] * A[:, 2, 5] * A[:, 1, 10]
- A[:, 0, 3] * A[:, 2, 4] * A[:, 1, 10]
+ A[:, 0, 4] * A[:, 2, 1] * A[:, 1, 12]
+ A[:, 0, 4] * A[:, 2, 2] * A[:, 1, 11]
+ A[:, 0, 4] * A[:, 2, 3] * A[:, 1, 10]
+ A[:, 0, 5] * A[:, 2, 0] * A[:, 1, 12]
+ A[:, 0, 5] * A[:, 2, 1] * A[:, 1, 11]
+ A[:, 0, 5] * A[:, 2, 2] * A[:, 1, 10]
+ A[:, 0, 6] * A[:, 2, 0] * A[:, 1, 11]
+ A[:, 0, 6] * A[:, 2, 1] * A[:, 1, 10]
+ A[:, 0, 7] * A[:, 2, 0] * A[:, 1, 10]
+ A[:, 0, 0] * A[:, 1, 5] * A[:, 2, 12]
+ A[:, 0, 0] * A[:, 1, 6] * A[:, 2, 11]
+ A[:, 0, 0] * A[:, 1, 7] * A[:, 2, 10]
+ A[:, 0, 1] * A[:, 1, 4] * A[:, 2, 12]
+ A[:, 0, 1] * A[:, 1, 5] * A[:, 2, 11]
+ A[:, 0, 1] * A[:, 1, 6] * A[:, 2, 10]
+ A[:, 0, 2] * A[:, 1, 4] * A[:, 2, 11]
+ A[:, 0, 2] * A[:, 1, 5] * A[:, 2, 10]
+ A[:, 0, 3] * A[:, 1, 4] * A[:, 2, 10]
- A[:, 0, 4] * A[:, 1, 1] * A[:, 2, 12]
- A[:, 0, 4] * A[:, 1, 2] * A[:, 2, 11]
- A[:, 0, 4] * A[:, 1, 3] * A[:, 2, 10]
- A[:, 0, 5] * A[:, 1, 0] * A[:, 2, 12]
- A[:, 0, 5] * A[:, 1, 1] * A[:, 2, 11]
- A[:, 0, 5] * A[:, 1, 2] * A[:, 2, 10]
- A[:, 0, 6] * A[:, 1, 0] * A[:, 2, 11]
- A[:, 0, 6] * A[:, 1, 1] * A[:, 2, 10]
- A[:, 0, 7] * A[:, 1, 0] * A[:, 2, 10]
)
cs[:, 6] = (
A[:, 0, 0] * A[:, 1, 7] * A[:, 2, 9]
- A[:, 0, 0] * A[:, 1, 9] * A[:, 2, 7]
+ A[:, 0, 1] * A[:, 1, 6] * A[:, 2, 9]
+ A[:, 0, 1] * A[:, 1, 7] * A[:, 2, 8]
- A[:, 0, 1] * A[:, 1, 8] * A[:, 2, 7]
- A[:, 0, 1] * A[:, 1, 9] * A[:, 2, 6]
+ A[:, 0, 2] * A[:, 1, 5] * A[:, 2, 9]
+ A[:, 0, 2] * A[:, 1, 6] * A[:, 2, 8]
- A[:, 0, 2] * A[:, 1, 8] * A[:, 2, 6]
- A[:, 0, 2] * A[:, 1, 9] * A[:, 2, 5]
+ A[:, 0, 3] * A[:, 1, 4] * A[:, 2, 9]
+ A[:, 0, 3] * A[:, 1, 5] * A[:, 2, 8]
- A[:, 0, 3] * A[:, 1, 8] * A[:, 2, 5]
- A[:, 0, 3] * A[:, 1, 9] * A[:, 2, 4]
- A[:, 0, 4] * A[:, 1, 3] * A[:, 2, 9]
+ A[:, 0, 4] * A[:, 1, 9] * A[:, 2, 3]
- A[:, 0, 5] * A[:, 1, 2] * A[:, 2, 9]
- A[:, 0, 5] * A[:, 1, 3] * A[:, 2, 8]
+ A[:, 0, 5] * A[:, 1, 8] * A[:, 2, 3]
+ A[:, 0, 5] * A[:, 1, 9] * A[:, 2, 2]
- A[:, 0, 6] * A[:, 1, 1] * A[:, 2, 9]
- A[:, 0, 6] * A[:, 1, 2] * A[:, 2, 8]
+ A[:, 0, 6] * A[:, 1, 8] * A[:, 2, 2]
+ A[:, 0, 6] * A[:, 1, 9] * A[:, 2, 1]
- A[:, 0, 7] * A[:, 1, 0] * A[:, 2, 9]
- A[:, 0, 7] * A[:, 1, 1] * A[:, 2, 8]
+ A[:, 0, 7] * A[:, 1, 8] * A[:, 2, 1]
+ A[:, 0, 7] * A[:, 1, 9] * A[:, 2, 0]
+ A[:, 0, 8] * A[:, 1, 1] * A[:, 2, 7]
+ A[:, 0, 8] * A[:, 1, 2] * A[:, 2, 6]
+ A[:, 0, 8] * A[:, 1, 3] * A[:, 2, 5]
- A[:, 0, 8] * A[:, 1, 5] * A[:, 2, 3]
- A[:, 0, 8] * A[:, 1, 6] * A[:, 2, 2]
- A[:, 0, 8] * A[:, 1, 7] * A[:, 2, 1]
+ A[:, 0, 9] * A[:, 1, 0] * A[:, 2, 7]
+ A[:, 0, 9] * A[:, 1, 1] * A[:, 2, 6]
+ A[:, 0, 9] * A[:, 1, 2] * A[:, 2, 5]
+ A[:, 0, 9] * A[:, 1, 3] * A[:, 2, 4]
- A[:, 0, 9] * A[:, 1, 4] * A[:, 2, 3]
- A[:, 0, 9] * A[:, 1, 5] * A[:, 2, 2]
- A[:, 0, 9] * A[:, 1, 6] * A[:, 2, 1]
- A[:, 0, 9] * A[:, 1, 7] * A[:, 2, 0]
+ A[:, 0, 10] * A[:, 1, 0] * A[:, 2, 6]
+ A[:, 0, 10] * A[:, 1, 1] * A[:, 2, 5]
+ A[:, 0, 10] * A[:, 1, 2] * A[:, 2, 4]
- A[:, 0, 10] * A[:, 1, 4] * A[:, 2, 2]
- A[:, 0, 10] * A[:, 1, 5] * A[:, 2, 1]
- A[:, 0, 10] * A[:, 1, 6] * A[:, 2, 0]
+ A[:, 1, 0] * A[:, 0, 11] * A[:, 2, 5]
+ A[:, 1, 0] * A[:, 0, 12] * A[:, 2, 4]
+ A[:, 0, 11] * A[:, 1, 1] * A[:, 2, 4]
- A[:, 0, 11] * A[:, 1, 4] * A[:, 2, 1]
- A[:, 0, 11] * A[:, 1, 5] * A[:, 2, 0]
- A[:, 0, 12] * A[:, 1, 4] * A[:, 2, 0]
- A[:, 0, 0] * A[:, 2, 4] * A[:, 1, 12]
- A[:, 0, 0] * A[:, 2, 5] * A[:, 1, 11]
- A[:, 0, 0] * A[:, 2, 6] * A[:, 1, 10]
- A[:, 0, 1] * A[:, 2, 4] * A[:, 1, 11]
- A[:, 0, 1] * A[:, 2, 5] * A[:, 1, 10]
- A[:, 0, 2] * A[:, 2, 4] * A[:, 1, 10]
+ A[:, 0, 4] * A[:, 2, 0] * A[:, 1, 12]
+ A[:, 0, 4] * A[:, 2, 1] * A[:, 1, 11]
+ A[:, 0, 4] * A[:, 2, 2] * A[:, 1, 10]
+ A[:, 0, 5] * A[:, 2, 0] * A[:, 1, 11]
+ A[:, 0, 5] * A[:, 2, 1] * A[:, 1, 10]
+ A[:, 0, 6] * A[:, 2, 0] * A[:, 1, 10]
+ A[:, 0, 0] * A[:, 1, 4] * A[:, 2, 12]
+ A[:, 0, 0] * A[:, 1, 5] * A[:, 2, 11]
+ A[:, 0, 0] * A[:, 1, 6] * A[:, 2, 10]
+ A[:, 0, 1] * A[:, 1, 4] * A[:, 2, 11]
+ A[:, 0, 1] * A[:, 1, 5] * A[:, 2, 10]
+ A[:, 0, 2] * A[:, 1, 4] * A[:, 2, 10]
- A[:, 0, 4] * A[:, 1, 0] * A[:, 2, 12]
- A[:, 0, 4] * A[:, 1, 1] * A[:, 2, 11]
- A[:, 0, 4] * A[:, 1, 2] * A[:, 2, 10]
- A[:, 0, 5] * A[:, 1, 0] * A[:, 2, 11]
- A[:, 0, 5] * A[:, 1, 1] * A[:, 2, 10]
- A[:, 0, 6] * A[:, 1, 0] * A[:, 2, 10]
)
cs[:, 7] = (
A[:, 0, 0] * A[:, 1, 6] * A[:, 2, 9]
+ A[:, 0, 0] * A[:, 1, 7] * A[:, 2, 8]
- A[:, 0, 0] * A[:, 1, 8] * A[:, 2, 7]
- A[:, 0, 0] * A[:, 1, 9] * A[:, 2, 6]
+ A[:, 0, 1] * A[:, 1, 5] * A[:, 2, 9]
+ A[:, 0, 1] * A[:, 1, 6] * A[:, 2, 8]
- A[:, 0, 1] * A[:, 1, 8] * A[:, 2, 6]
- A[:, 0, 1] * A[:, 1, 9] * A[:, 2, 5]
+ A[:, 0, 2] * A[:, 1, 4] * A[:, 2, 9]
+ A[:, 0, 2] * A[:, 1, 5] * A[:, 2, 8]
- A[:, 0, 2] * A[:, 1, 8] * A[:, 2, 5]
- A[:, 0, 2] * A[:, 1, 9] * A[:, 2, 4]
+ A[:, 0, 3] * A[:, 1, 4] * A[:, 2, 8]
- A[:, 0, 3] * A[:, 1, 8] * A[:, 2, 4]
- A[:, 0, 4] * A[:, 1, 2] * A[:, 2, 9]
- A[:, 0, 4] * A[:, 1, 3] * A[:, 2, 8]
+ A[:, 0, 4] * A[:, 1, 8] * A[:, 2, 3]
+ A[:, 0, 4] * A[:, 1, 9] * A[:, 2, 2]
- A[:, 0, 5] * A[:, 1, 1] * A[:, 2, 9]
- A[:, 0, 5] * A[:, 1, 2] * A[:, 2, 8]
+ A[:, 0, 5] * A[:, 1, 8] * A[:, 2, 2]
+ A[:, 0, 5] * A[:, 1, 9] * A[:, 2, 1]
- A[:, 0, 6] * A[:, 1, 0] * A[:, 2, 9]
- A[:, 0, 6] * A[:, 1, 1] * A[:, 2, 8]
+ A[:, 0, 6] * A[:, 1, 8] * A[:, 2, 1]
+ A[:, 0, 6] * A[:, 1, 9] * A[:, 2, 0]
- A[:, 0, 7] * A[:, 1, 0] * A[:, 2, 8]
+ A[:, 0, 7] * A[:, 1, 8] * A[:, 2, 0]
+ A[:, 0, 8] * A[:, 1, 0] * A[:, 2, 7]
+ A[:, 0, 8] * A[:, 1, 1] * A[:, 2, 6]
+ A[:, 0, 8] * A[:, 1, 2] * A[:, 2, 5]
+ A[:, 0, 8] * A[:, 1, 3] * A[:, 2, 4]
- A[:, 0, 8] * A[:, 1, 4] * A[:, 2, 3]
- A[:, 0, 8] * A[:, 1, 5] * A[:, 2, 2]
- A[:, 0, 8] * A[:, 1, 6] * A[:, 2, 1]
- A[:, 0, 8] * A[:, 1, 7] * A[:, 2, 0]
+ A[:, 0, 9] * A[:, 1, 0] * A[:, 2, 6]
+ A[:, 0, 9] * A[:, 1, 1] * A[:, 2, 5]
+ A[:, 0, 9] * A[:, 1, 2] * A[:, 2, 4]
- A[:, 0, 9] * A[:, 1, 4] * A[:, 2, 2]
- A[:, 0, 9] * A[:, 1, 5] * A[:, 2, 1]
- A[:, 0, 9] * A[:, 1, 6] * A[:, 2, 0]
+ A[:, 0, 10] * A[:, 1, 0] * A[:, 2, 5]
+ A[:, 0, 10] * A[:, 1, 1] * A[:, 2, 4]
- A[:, 0, 10] * A[:, 1, 4] * A[:, 2, 1]
- A[:, 0, 10] * A[:, 1, 5] * A[:, 2, 0]
+ A[:, 1, 0] * A[:, 0, 11] * A[:, 2, 4]
- A[:, 0, 11] * A[:, 1, 4] * A[:, 2, 0]
- A[:, 0, 0] * A[:, 2, 4] * A[:, 1, 11]
- A[:, 0, 0] * A[:, 2, 5] * A[:, 1, 10]
- A[:, 0, 1] * A[:, 2, 4] * A[:, 1, 10]
+ A[:, 0, 4] * A[:, 2, 0] * A[:, 1, 11]
+ A[:, 0, 4] * A[:, 2, 1] * A[:, 1, 10]
+ A[:, 0, 5] * A[:, 2, 0] * A[:, 1, 10]
+ A[:, 0, 0] * A[:, 1, 4] * A[:, 2, 11]
+ A[:, 0, 0] * A[:, 1, 5] * A[:, 2, 10]
+ A[:, 0, 1] * A[:, 1, 4] * A[:, 2, 10]
- A[:, 0, 4] * A[:, 1, 0] * A[:, 2, 11]
- A[:, 0, 4] * A[:, 1, 1] * A[:, 2, 10]
- A[:, 0, 5] * A[:, 1, 0] * A[:, 2, 10]
)
cs[:, 8] = (
A[:, 0, 0] * A[:, 1, 5] * A[:, 2, 9]
+ A[:, 0, 0] * A[:, 1, 6] * A[:, 2, 8]
- A[:, 0, 0] * A[:, 1, 8] * A[:, 2, 6]
- A[:, 0, 0] * A[:, 1, 9] * A[:, 2, 5]
+ A[:, 0, 1] * A[:, 1, 4] * A[:, 2, 9]
+ A[:, 0, 1] * A[:, 1, 5] * A[:, 2, 8]
- A[:, 0, 1] * A[:, 1, 8] * A[:, 2, 5]
- A[:, 0, 1] * A[:, 1, 9] * A[:, 2, 4]
+ A[:, 0, 2] * A[:, 1, 4] * A[:, 2, 8]
- A[:, 0, 2] * A[:, 1, 8] * A[:, 2, 4]
- A[:, 0, 4] * A[:, 1, 1] * A[:, 2, 9]
- A[:, 0, 4] * A[:, 1, 2] * A[:, 2, 8]
+ A[:, 0, 4] * A[:, 1, 8] * A[:, 2, 2]
+ A[:, 0, 4] * A[:, 1, 9] * A[:, 2, 1]
- A[:, 0, 5] * A[:, 1, 0] * A[:, 2, 9]
- A[:, 0, 5] * A[:, 1, 1] * A[:, 2, 8]
+ A[:, 0, 5] * A[:, 1, 8] * A[:, 2, 1]
+ A[:, 0, 5] * A[:, 1, 9] * A[:, 2, 0]
- A[:, 0, 6] * A[:, 1, 0] * A[:, 2, 8]
+ A[:, 0, 6] * A[:, 1, 8] * A[:, 2, 0]
+ A[:, 0, 8] * A[:, 1, 0] * A[:, 2, 6]
+ A[:, 0, 8] * A[:, 1, 1] * A[:, 2, 5]
+ A[:, 0, 8] * A[:, 1, 2] * A[:, 2, 4]
- A[:, 0, 8] * A[:, 1, 4] * A[:, 2, 2]
- A[:, 0, 8] * A[:, 1, 5] * A[:, 2, 1]
- A[:, 0, 8] * A[:, 1, 6] * A[:, 2, 0]
+ A[:, 0, 9] * A[:, 1, 0] * A[:, 2, 5]
+ A[:, 0, 9] * A[:, 1, 1] * A[:, 2, 4]
- A[:, 0, 9] * A[:, 1, 4] * A[:, 2, 1]
- A[:, 0, 9] * A[:, 1, 5] * A[:, 2, 0]
+ A[:, 0, 10] * A[:, 1, 0] * A[:, 2, 4]
- A[:, 0, 10] * A[:, 1, 4] * A[:, 2, 0]
- A[:, 0, 0] * A[:, 2, 4] * A[:, 1, 10]
+ A[:, 0, 4] * A[:, 2, 0] * A[:, 1, 10]
+ A[:, 0, 0] * A[:, 1, 4] * A[:, 2, 10]
- A[:, 0, 4] * A[:, 1, 0] * A[:, 2, 10]
)
cs[:, 9] = (
A[:, 0, 0] * A[:, 1, 4] * A[:, 2, 9]
+ A[:, 0, 0] * A[:, 1, 5] * A[:, 2, 8]
- A[:, 0, 0] * A[:, 1, 8] * A[:, 2, 5]
- A[:, 0, 0] * A[:, 1, 9] * A[:, 2, 4]
+ A[:, 0, 1] * A[:, 1, 4] * A[:, 2, 8]
- A[:, 0, 1] * A[:, 1, 8] * A[:, 2, 4]
- A[:, 0, 4] * A[:, 1, 0] * A[:, 2, 9]
- A[:, 0, 4] * A[:, 1, 1] * A[:, 2, 8]
+ A[:, 0, 4] * A[:, 1, 8] * A[:, 2, 1]
+ A[:, 0, 4] * A[:, 1, 9] * A[:, 2, 0]
- A[:, 0, 5] * A[:, 1, 0] * A[:, 2, 8]
+ A[:, 0, 5] * A[:, 1, 8] * A[:, 2, 0]
+ A[:, 0, 8] * A[:, 1, 0] * A[:, 2, 5]
+ A[:, 0, 8] * A[:, 1, 1] * A[:, 2, 4]
- A[:, 0, 8] * A[:, 1, 4] * A[:, 2, 1]
- A[:, 0, 8] * A[:, 1, 5] * A[:, 2, 0]
+ A[:, 0, 9] * A[:, 1, 0] * A[:, 2, 4]
- A[:, 0, 9] * A[:, 1, 4] * A[:, 2, 0]
)
cs[:, 10] = (
A[:, 0, 0] * A[:, 1, 4] * A[:, 2, 8]
- A[:, 0, 0] * A[:, 1, 8] * A[:, 2, 4]
- A[:, 0, 4] * A[:, 1, 0] * A[:, 2, 8]
+ A[:, 0, 4] * A[:, 1, 8] * A[:, 2, 0]
+ A[:, 0, 8] * A[:, 1, 0] * A[:, 2, 4]
- A[:, 0, 8] * A[:, 1, 4] * A[:, 2, 0]
)
E_models = []
# s = StrumPolynomialSolver(10)
# n_solss, rootss = s.bisect_sturm(cs)
# for loop because of different numbers of solutions
if not self.drop:
tmp = torch.rand((10, 9), dtype=torch.float32, device=pts.device)
for bi in range(A.shape[0]):
A_i = A[bi]
null_i = nullSpace[bi]
# companion matrix solver
# try:
C = torch.zeros((10, 10), device=cs.device, dtype=cs.dtype)
C[0:-1, 1:] = torch.eye(
C[0:-1, 0:-1].shape[0], device=cs.device, dtype=cs.dtype
)
C[-1, :] = -cs[bi][:-1] / cs[bi][-1]
# check if the companion matrix contains nans or infs
if torch.isnan(C).any() or torch.isinf(C).any():
if not self.drop:
E_models.append(tmp)
continue
# n_sols, roots = s.bisect_sturm(cs[bi])
# print("nan in C")
else:
roots = torch.real(torch.linalg.eigvals(C))
# except ValueError:
# n_sols, roots = s.bisect_sturm(cs[bi])
if roots is None:
if not self.drop:
E_models.append(tmp)
continue
n_sols = roots.size()
if n_sols == 0:
if not self.drop:
E_models.append(tmp)
continue
Bs = torch.stack(
(
A_i[:3, :1] * (roots**3)
+ A_i[:3, 1:2] * roots.square()
+ A_i[0:3, 2:3] * (roots)
+ A_i[0:3, 3:4],
A_i[0:3, 4:5] * (roots**3)
+ A_i[0:3, 5:6] * roots.square()
+ A_i[0:3, 6:7] * (roots)
+ A_i[0:3, 7:8],
),
dim=0,
).transpose(0, -1)
bs = (
A_i[0:3, 8:9] * (roots**4)
+ A_i[0:3, 9:10] * (roots**3)
+ A_i[0:3, 10:11] * roots.square()
+ A_i[0:3, 11:12] * roots
+ A_i[0:3, 12:13]
).T.unsqueeze(-1)
# We try to solve using top two rows, if fails, will use matrix decomposition to solve Ax=b.
try:
xzs = Bs[:, 0:2, 0:2].inverse() @ (bs[:, 0:2])
except:
if not self.drop:
E_models.append(tmp)
continue
mask = (
abs(Bs[:, 2].unsqueeze(1) @ xzs - bs[:, 2].unsqueeze(1)) > 1e-3
).flatten()
if torch.sum(mask) != 0:
q, r = torch.linalg.qr(Bs[mask].clone()) #
xzs[mask] = torch.linalg.solve(
r, q.transpose(-1, -2) @ bs[mask]
) # [mask]
# models
Es = (
null_i[0] * (-xzs[:, 0])
+ null_i[1] * (-xzs[:, 1])
+ null_i[2] * roots.unsqueeze(-1)
+ null_i[3]
)
# Since the rows of N are orthogonal unit vectors, we can normalize the coefficients instead
inv = 1.0 / torch.sqrt(
(-xzs[:, 0]) ** 2 + (-xzs[:, 1]) ** 2 + roots.unsqueeze(-1) ** 2 + 1.0
)
Es *= inv
if Es.shape[0] < 10:
Es = torch.concat(
(
Es.clone(),
torch.eye(3, device=Es.device, dtype=Es.dtype)
.repeat(10 - Es.shape[0], 1)
.reshape(-1, 9),
)
)
if not self.drop:
tmp = Es.clone()
E_models.append(Es)
if not E_models:
return torch.eye(3, device=cs.device, dtype=cs.dtype).unsqueeze(0)
else:
return torch.concat(E_models).view(-1, 3, 3).transpose(-1, -2)
# be careful of the differences between c++ and python, transpose
def o1(self, a, b):
"""A, b are first order polys [x,y,z,1] c is degree 2 poly with order [ x^2, x*y, x*z, x, y^2, y*z, y, z^2,
z, 1]"""
# print(a[0] * b[2] + a[2] * b[0])
return torch.stack(
[
a[:, 0] * b[:, 0],
a[:, 0] * b[:, 1] + a[:, 1] * b[:, 0],
a[:, 0] * b[:, 2] + a[:, 2] * b[:, 0],
a[:, 0] * b[:, 3] + a[:, 3] * b[:, 0],
a[:, 1] * b[:, 1],
a[:, 1] * b[:, 2] + a[:, 2] * b[:, 1],
a[:, 1] * b[:, 3] + a[:, 3] * b[:, 1],
a[:, 2] * b[:, 2],
a[:, 2] * b[:, 3] + a[:, 3] * b[:, 2],
a[:, 3] * b[:, 3],
],
dim=-1,
)
def o2(self, a, b): # 10 4 20
"""A is second degree poly with order [ x^2, x*y, x*z, x, y^2, y*z, y, z^2, z, 1] b is first degree with
order [x y z 1] c is third degree with order (same as nister's paper) [ x^3, y^3, x^2*y, x*y^2, x^2*z, x^2,
y^2*z, y^2, x*y*z, x*y, x*z^2, x*z, x, y*z^2, y*z, y, z^3, z^2, z, 1]"""
return torch.stack(
[
a[:, 0] * b[:, 0],
a[:, 4] * b[:, 1],
a[:, 0] * b[:, 1] + a[:, 1] * b[:, 0],
a[:, 1] * b[:, 1] + a[:, 4] * b[:, 0],
a[:, 0] * b[:, 2] + a[:, 2] * b[:, 0],
a[:, 0] * b[:, 3] + a[:, 3] * b[:, 0],
a[:, 4] * b[:, 2] + a[:, 5] * b[:, 1],
a[:, 4] * b[:, 3] + a[:, 6] * b[:, 1],
a[:, 1] * b[:, 2] + a[:, 2] * b[:, 1] + a[:, 5] * b[:, 0],
a[:, 1] * b[:, 3] + a[:, 3] * b[:, 1] + a[:, 6] * b[:, 0],
a[:, 2] * b[:, 2] + a[:, 7] * b[:, 0],
a[:, 2] * b[:, 3] + a[:, 3] * b[:, 2] + a[:, 8] * b[:, 0],
a[:, 3] * b[:, 3] + a[:, 9] * b[:, 0],
a[:, 5] * b[:, 2] + a[:, 7] * b[:, 1],
a[:, 5] * b[:, 3] + a[:, 6] * b[:, 2] + a[:, 8] * b[:, 1],
a[:, 6] * b[:, 3] + a[:, 9] * b[:, 1],
a[:, 7] * b[:, 2],
a[:, 7] * b[:, 3] + a[:, 8] * b[:, 2],
a[:, 8] * b[:, 3] + a[:, 9] * b[:, 2],
a[:, 9] * b[:, 3],
],
dim=-1,
)
| 39,248 | Python | .py | 861 | 32.341463 | 120 | 0.26462 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,687 | uniform_sampler.py | disungatullina_MinBackProp/samplers/uniform_sampler.py | import torch
import random
class UniformSampler(object):
"""Random sampling the points, return the indices for each unique subset, or in batch."""
def __init__(self, batch_size, num_samples, num_points):
self.batch_size = batch_size
self.num_samples = num_samples
self.num_points = num_points
def unique_generate(self, num_points=None):
num_points = self.num_points if num_points is None else num_points
sample_indices = torch.tensor(
[random.randint(0, len(num_points) - 1) for _ in range(self.num_samples)]
)
return sample_indices
def batch_generate(self, num_points=None):
num_points = self.num_points if num_points is None else num_points
sample_indices = torch.randint(
0, num_points - 1, (self.batch_size, self.num_samples)
)
return sample_indices
def sample(self):
sample_indices = self.batch_generate()
return sample_indices
| 987 | Python | .py | 23 | 35.217391 | 93 | 0.658664 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,688 | gumbel_sampler.py | disungatullina_MinBackProp/samplers/gumbel_sampler.py | import torch
# from estimators.fundamental_matrix_estimator import *
# from estimators.essential_matrix_estimator_stewenius import *
from loss import *
import numpy as np
import random
class GumbelSoftmaxSampler:
"""Sample based on a Gumbel-Max distribution.
Use re-param trick for back-prop
"""
def __init__(
self, batch_size, num_samples, tau=1.0, device="cuda", data_type="torch.float32"
):
self.batch_size = batch_size
self.num_samples = num_samples
# self.num_points = num_points
self.device = device
self.dtype = data_type
self.gumbel_dist = torch.distributions.gumbel.Gumbel(
torch.tensor(0.0, device=self.device, dtype=self.dtype),
torch.tensor(1.0, device=self.device, dtype=self.dtype),
)
self.tau = tau
def sample(self, logits=None, num_points=2000, selected=None):
if logits == None:
logits = torch.ones(
[self.batch_size, num_points],
device=self.device,
dtype=self.dtype,
requires_grad=True,
)
else:
logits = logits.to(self.dtype).to(self.device).repeat([self.batch_size, 1])
if selected is None:
gumbels = self.gumbel_dist.sample(logits.shape)
gumbels = (logits + gumbels) / self.tau
y_soft = gumbels.softmax(-1)
topk = torch.topk(gumbels, self.num_samples, dim=-1)
y_hard = torch.zeros_like(
logits, memory_format=torch.legacy_contiguous_format
).scatter_(-1, topk.indices, 1.0)
ret = y_hard - y_soft.detach() + y_soft
else:
pass
return ret, y_soft # , topk.indices
| 1,763 | Python | .py | 45 | 29.733333 | 88 | 0.6 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,689 | estimate_rotation.py | disungatullina_MinBackProp/toy_examples/estimate_rotation.py | import os
import sys
import torch
import argparse
from math import degrees
sys.path.append(os.path.join(os.path.dirname(os.path.abspath(__file__)), ".."))
import rotation.losses as L
from ddn.ddn.pytorch.node import *
from rotation.nodes import RigitNodeConstraint, SVDLayer, IFTLayer
from rotation.datasets import get_dataset
from utils import get_initial_weights, plot_graphs_w, plot_graphs_loss
import warnings
warnings.filterwarnings("ignore")
# set main options
torch.set_printoptions(linewidth=200)
torch.set_printoptions(precision=4)
def run_optimization(optimization_type, P, Q, R_true, opt):
print()
print(optimization_type)
# get the batch size and the number of points
b, _, n = P.shape
# set upper-level objective J
if opt.upper_level == "geometric":
J = L.angle_error
elif opt.upper_level == "algebraic":
J = L.frobenius_norm
else:
raise Exception("Upper-level loss is undefined.")
# init weights
w_init = get_initial_weights(b, n, opt.init_weights)
w = w_init.clone().detach().requires_grad_()
if optimization_type == "IFT":
optimization_layer = IFTLayer()
elif optimization_type == "DDN":
node = RigitNodeConstraint()
optimization_layer = DeclarativeLayer(node)
elif optimization_type == "SVD":
optimization_layer = SVDLayer
else:
raise Exception("Wrong optimization type.")
# set optimizer
optimizer = torch.optim.SGD([w], lr=opt.lr)
loss_history = []
w_history = [[w[0, 0].item()], [w[0, 1].item()], [w[0, 2].item()], [w[0, 3].item()]]
def reevaluate():
optimizer.zero_grad()
R = optimization_layer(P, Q, w)
loss = J(R_true, R)
loss_history.append(loss[0].item())
loss.backward()
torch.nn.utils.clip_grad_norm_([w], 1.0)
return loss
# optimize
for i in range(opt.num_iter):
optimizer.step(reevaluate)
w_history[0].append(torch.nn.functional.relu(w[0, 0]).item())
w_history[1].append(torch.nn.functional.relu(w[0, 1]).item())
w_history[2].append(torch.nn.functional.relu(w[0, 2]).item())
w_history[3].append(torch.nn.functional.relu(w[0, 3]).item())
# get final results
w = torch.nn.functional.relu(w) # enforce non-negativity
R = optimization_layer(P, Q, w)
# compute errors
angle_error = L.angle_error(R_true, R)
frob_norm = L.frobenius_norm(R_true, R)
# print errors
print(
"Rotation Error: {:0.4f} degrees".format(
degrees(angle_error[0, ...].squeeze().detach().numpy())
)
)
print("Algebraic Error: {}".format(frob_norm[0, ...].detach().numpy()))
return w_history, loss_history
def main(opt):
print("Rotation matrix estimation")
# load dataset
P, Q, R_true = get_dataset()
w_history_svd = None
w_history_ddn = None
loss_history_svd = None
loss_history_ddn = None
# run optimization
w_history_ift, loss_history_ift = run_optimization(
"IFT", P, Q, R_true, opt
) # True by default
if opt.autograd:
w_history_svd, loss_history_svd = run_optimization("SVD", P, Q, R_true, opt)
if opt.ddn:
w_history_ddn, loss_history_ddn = run_optimization("DDN", P, Q, R_true, opt)
# plot values of w and global loss
if opt.plot:
plot_graphs_w(
w_history_ift,
w_history_svd=w_history_svd,
w_history_ddn=w_history_ddn,
out_dir=os.path.join(opt.out, "rotation"),
)
plot_graphs_loss(
loss_history_ift,
loss_history_svd=loss_history_svd,
loss_history_ddn=loss_history_ddn,
out_dir=os.path.join(opt.out, "rotation"),
)
print()
print("done")
return 0
if __name__ == "__main__":
PARSER = argparse.ArgumentParser(description="Rotation matrix estimation")
PARSER.add_argument(
"--plot",
action="store_true",
help="plot inlier and outlier values, default False",
)
PARSER.add_argument(
"--ift",
action="store_true",
help="compute R and w with backpropagation via IFT, default True",
)
PARSER.add_argument(
"--ddn",
action="store_true",
help="compute R and w with backpropagation via DDN, default False",
)
PARSER.add_argument(
"--autograd",
action="store_true",
help="compute R and w with backpropagation via autograd, default False",
)
PARSER.add_argument(
"--init_weights",
type=str,
default="uniform",
help="initialization for weights: uniform|random , default 'uniform'",
)
PARSER.add_argument(
"--upper_level",
type=str,
default="geometric",
help="upper-level objective: geometric|algebraic , default 'geometric'",
)
PARSER.add_argument(
"--out",
type=str,
default="results",
help="directory to save graphs",
)
PARSER.add_argument(
"--num_iter",
type=int,
default=30,
help="the number of iterations, default 30",
)
# PARSER.add_argument("-bs", "--batch_size", type=int, default=1, help="batch size")
PARSER.add_argument(
"--lr",
type=float,
default=1e-1,
help="learning rate, default 0.1",
)
ARGS = PARSER.parse_args()
main(ARGS)
| 5,443 | Python | .py | 161 | 27.118012 | 88 | 0.621143 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,690 | estimate_fundamental.py | disungatullina_MinBackProp/toy_examples/estimate_fundamental.py | import os
import sys
import torch
import argparse
import warnings
sys.path.append(os.path.join(os.path.dirname(os.path.abspath(__file__)), ".."))
from ddn.ddn.pytorch.node import *
import fundamental.losses as L
from fundamental.datasets import get_dataset
from fundamental.nodes import SVDLayer, FundamentalNodeConstraint, IFTLayer
from utils import get_initial_weights, plot_graphs_w, plot_graphs_loss
torch.set_printoptions(precision=4)
warnings.filterwarnings("ignore")
def run_optimization(optimization_type, A, B, F_true, opt):
print(optimization_type)
# get the batch size and the number of points
b, n, _ = A.shape
# set upper-level objective J
J = L.frobenius_norm
# init weights
w_init = get_initial_weights(b, n, opt.init_weights)
w = w_init.clone().detach().requires_grad_()
if optimization_type == "IFT":
optimization_layer = IFTLayer()
elif optimization_type == "DDN":
node = FundamentalNodeConstraint()
optimization_layer = DeclarativeLayer(node)
elif optimization_type == "SVD":
optimization_layer = SVDLayer
else:
raise Exception("Wrong optimization type.")
# set optimizer
optimizer = torch.optim.SGD(
[w],
lr=opt.lr,
)
loss_history = []
w_history = [[w[0, i].item()] for i in range(n)]
def reevaluate():
optimizer.zero_grad()
F = optimization_layer(A, B, w)
if (F * F_true).sum(dim=(-2, -1)) < 0:
F_ = -F
else:
F_ = F
loss = J(F_true, F_)
loss_history.append(loss[0].item())
loss.backward()
torch.nn.utils.clip_grad_norm_([w], 1.0)
return loss
for i in range(opt.num_iter):
optimizer.step(reevaluate)
w_ = torch.nn.functional.relu(w)
w_ /= w_.sum(dim=1, keepdim=True)
for i in range(n):
w_history[i].append(torch.nn.functional.relu(w_[0, i]).item())
# get final results
w = torch.nn.functional.relu(w)
w /= w.sum(dim=1, keepdim=True)
F = optimization_layer(A, B, w)
F = F / torch.norm(F)
if (F * F_true).sum(dim=(-2, -1)) < 0:
F = -F
# compute error
frob_norm = L.frobenius_norm(F_true, F)
print("Algebraic Error: {}".format(frob_norm[0, ...].detach().numpy()))
return w_history, loss_history
def main(opt):
print("Fundamental matrix estimation")
print()
# load dataset
A, B, F_true, w_true = get_dataset()
w_history_svd = None
w_history_ddn = None
loss_history_svd = None
loss_history_ddn = None
# run optimization
w_history_ift, loss_history_ift = run_optimization(
"IFT", A, B, F_true, opt
) # True by default
if opt.autograd:
print()
w_history_svd, loss_history_svd = run_optimization("SVD", A, B, F_true, opt)
if opt.ddn:
print()
w_history_ddn, loss_history_ddn = run_optimization("DDN", A, B, F_true, opt)
# plot values of w and global loss
if opt.plot:
plot_graphs_w(
w_history_ift,
w_history_svd=w_history_svd,
w_history_ddn=w_history_ddn,
out_dir=os.path.join(opt.out, "fundamental"),
)
plot_graphs_loss(
loss_history_ift,
loss_history_svd=loss_history_svd,
loss_history_ddn=loss_history_ddn,
out_dir=os.path.join(opt.out, "fundamental"),
)
print()
print("done")
return 0
if __name__ == "__main__":
PARSER = argparse.ArgumentParser(description="Fundamental matrix estimation")
PARSER.add_argument(
"--plot",
action="store_true",
help="plot inlier and outlier values, default False",
)
PARSER.add_argument(
"--ift",
action="store_true",
help="compute F and w with backpropagation via IFT, default True",
)
PARSER.add_argument(
"--ddn",
action="store_true",
help="compute F and w with backpropagation via DDN, default False",
)
PARSER.add_argument(
"--autograd",
action="store_true",
help="compute F and w with backpropagation via autograd, default False",
)
PARSER.add_argument(
"--init_weights",
type=str,
default="uniform",
help="initialization for weights: uniform|random , default 'uniform'",
)
PARSER.add_argument(
"--out",
type=str,
default="results",
help="directory to save graphs",
)
PARSER.add_argument(
"--num_iter",
type=int,
default=30,
help="the number of iterations, default 30",
)
# PARSER.add_argument("-bs", "--batch_size", type=int, default=1, help="batch size")
PARSER.add_argument(
"--lr",
type=float,
default=1000.0,
help="learning rate, default 1000.",
)
ARGS = PARSER.parse_args()
main(ARGS)
| 4,941 | Python | .py | 152 | 25.605263 | 88 | 0.607653 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,691 | utils.py | disungatullina_MinBackProp/toy_examples/utils.py | import os
import torch
import matplotlib.pyplot as plt
def get_initial_weights(b, n, init_type):
# Generate weights (uniform):
if init_type == "uniform":
w = torch.ones(b, n, dtype=torch.float) # b x n
w = w.div(w.sum(-1).unsqueeze(-1))
# Generate weights (random):
elif init_type == "random":
w = torch.rand(b, n, dtype=torch.float)
else:
w = None
return w
def plot_graphs_w(
w_history_ift, w_history_svd=None, w_history_ddn=None, out_dir="results"
):
plt.rcParams["font.size"] = 14
for i in range(len(w_history_ift)):
if i == 0:
Y_LABEL = "weight of the outlier"
else:
Y_LABEL = "weight of an inlier"
plt.figure(figsize=(9, 6))
plt.axes()
if w_history_svd is not None:
plt.plot(w_history_svd[i], label="SVD", color="red", linewidth=4)
if w_history_ddn is not None:
plt.plot(w_history_ddn[i], "--", label="DDN", linewidth=4)
plt.plot(w_history_ift[i], "--", label="IFT", color="green", linewidth=4)
plt.ylabel(
Y_LABEL,
fontsize=18,
)
plt.xlabel(
"# iterations",
fontsize=18,
)
plt.xticks(
fontsize=18,
)
plt.yticks(fontsize=18)
plt.legend(loc="lower right")
if not os.path.exists(out_dir):
os.makedirs(out_dir)
plt.savefig(os.path.join(out_dir, "w_{}.png".format(i)))
plt.show()
def plot_graphs_loss(
loss_history_ift, loss_history_svd=None, loss_history_ddn=None, out_dir="results"
):
plt.figure(figsize=(9, 6))
if loss_history_svd is not None:
plt.plot(loss_history_svd, label="SVD", color="red", linewidth=4)
if loss_history_ddn is not None:
plt.plot(loss_history_ddn, "--", label="DDN", linewidth=4)
plt.plot(loss_history_ift, "--", label="IFT", color="green", linewidth=4)
plt.ylabel(
"global loss",
fontsize=18,
)
plt.xlabel(
"# iterations",
fontsize=18,
)
plt.legend(loc="upper right")
if not os.path.exists(out_dir):
os.makedirs(out_dir)
plt.savefig(os.path.join(out_dir, "global_loss.png"))
| 2,245 | Python | .py | 68 | 25.514706 | 85 | 0.576232 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,692 | datasets.py | disungatullina_MinBackProp/toy_examples/fundamental/datasets.py | import torch
def create_toy_dataset():
"""
N = 15 correspondences, without noise added; b = 1
A : b x N x 3
B : b x N x 3
F_true : b x 3 x 3
gt_mask : b x N
"""
A = torch.tensor(
[
[
[-915.685, 834.329, 1.0],
[646.367, 254.628, 1.0],
[-22.876, 595.962, 1.0],
[578.168, 443.949, 1.0],
[192.419, 282.905, 1.0],
[52.794, 306.947, 1.0],
[736.152, 258.855, 1.0],
[779.226, 153.273, 1.0],
[-203.857, 206.508, 1.0],
[-177.886, -223.585, 1.0],
[514.813, 356.933, 1.0],
[-673.211, -458.384, 1.0],
[303.542, -685.049, 1.0],
[-5.934, 357.504, 1.0],
[1086.569, -558.349, 1.0],
]
]
)
B = torch.tensor(
[
[
[-248.194, -100.591, 1.0],
[1976.495, 1481.327, 1.0],
[1127.706, 927.001, 1.0],
[1470.325, 1127.142, 1.0],
[1330.03, 1018.398, 1.0],
[1386.336, 583.886, 1.0],
[1949.827, 1584.303, 1.0],
[2428.351, 1934.385, 1.0],
[1330.216, 663.379, 1.0],
[2618.936, 603.683, 1.0],
[1640.894, 1124.457, 1.0],
[1970.587, 582.818, 1.0],
[2299.292, 1607.329, 1.0],
[1272.829, 479.930, 1.0],
[2306.285, 2028.933, 1.0],
]
]
)
F_true = torch.tensor(
[
[
[-1.11028e-06, 8.61480e-07, 3.03012e-04],
[4.66710e-07, -1.33660e-06, 5.36742e-04],
[7.91556e-04, 5.36159e-04, -9.99999e-01],
]
],
dtype=torch.float64,
)
gt_mask = torch.tensor(
[[0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]]
)
return A, B, F_true, gt_mask
def get_dataset():
return create_toy_dataset()
| 2,096 | Python | .py | 67 | 19.268657 | 85 | 0.383094 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,693 | nodes.py | disungatullina_MinBackProp/toy_examples/fundamental/nodes.py | import torch
import torch.nn as nn
from ddn.ddn.pytorch.node import *
mask = torch.ones(3)
mask[2] = 0.0
############ DDN with constraint ############
class FundamentalNodeConstraint(EqConstDeclarativeNode):
"""Declarative Fundamental matrix estimation node constraint"""
def __init__(self):
super().__init__()
def objective(self, A, B, w, y):
"""
A : b x N x 3
B : b x N x 3
y : b x 3 x 3
w : b x N
"""
w = nn.functional.relu(w)
outs = []
for batch in range(w.size(0)):
a_ = A[batch].view((-1, 1, 3)) # N x 1 x 3
b_ = B[batch].view((-1, 3, 1)) # N x 3 x 1
M = a_ * b_
M = M.view(-1, 9) # 10 x 9
res = M.mm(y[batch].view(9, 1))
res = res**2
res = res.squeeze(1)
out = torch.einsum("n,n-> ", (w[batch] ** 2, res))
outs.append(out.unsqueeze(0))
outs = torch.cat(outs, 0)
return outs
def equality_constraints(self, A, B, w, y):
ones = torch.ones(y.shape[0])
constr1 = (
torch.einsum("bk,bk->b", [y.view(y.shape[0], 9), y.view(y.shape[0], 9)])
- ones
)
constr2 = torch.linalg.det(y)
return torch.cat(((constr1).unsqueeze(1), (constr2 * 100).unsqueeze(1)), 1)
def solve(self, A, B, w):
w = nn.functional.relu(w)
A = A.detach()
B = B.detach()
w = w.detach()
y = self.__solve(A, B, w).requires_grad_()
return y.detach(), None
def __solve(self, A, B, w):
"""
A : b x N x 3
B : b x N x 3
y : b x 3 x 3
w : b x N
"""
out_batch = []
for batch in range(w.size(0)):
w_ = (w[batch]).view(w[batch].size(0), 1, 1) # N x 1 x 1
a_ = A[batch].view((-1, 1, 3)) # N x 1 x 3
b_ = B[batch].view((-1, 3, 1)) # N x 3 x 1
M = w_**2 * a_ * b_
M = M.view(-1, 9)
_, _, Vh = torch.linalg.svd(M)
F8 = Vh[-1, :].view(3, 3)
[u, s, vh] = torch.linalg.svd(F8)
S_ = torch.diag(s * mask)
F_ = u.mm(S_.mm(vh))
F_ = F_ / torch.norm(F_)
out_batch.append(F_.unsqueeze(0))
F = torch.cat(out_batch, 0)
return F
############ SVD Layer ############
def SVDLayer(A, B, w):
"""
A : b x N x 3
B : b x N x 3
w : b x N
A and B are normalized points
"""
w = nn.functional.relu(w)
out_batch = []
for batch in range(w.size(0)):
w_ = (w[batch]).view(w[batch].size(0), 1, 1) # N x 1 x 1
a_ = A[batch].view((-1, 1, 3)) # N x 1 x 3
b_ = B[batch].view((-1, 3, 1)) # N x 3 x 1
M = w_**2 * a_ * b_
M = M.view(-1, 9)
_, _, Vh = torch.linalg.svd(M)
F8 = Vh[-1, :].view(3, 3)
[u, s, vh] = torch.linalg.svd(F8)
S_ = torch.diag(s * mask)
F_ = u.mm(S_.mm(vh))
F_ = F_ / torch.norm(F_)
out_batch.append(F_.unsqueeze(0))
F = torch.cat(out_batch, 0)
return F
############ IFT function ############
class IFTFunction(torch.autograd.Function):
@staticmethod
def forward(A, B, w):
"""
A : b x N x 3
B : b x N x 3
w : b x N
"""
w = nn.functional.relu(w)
out_batch = []
for batch in range(w.size(0)):
w_ = (w[batch]).view(w[batch].size(0), 1, 1) # N x 1 x 1
a_ = A[batch].view((-1, 1, 3)) # N x 1 x 3
b_ = B[batch].view((-1, 3, 1)) # N x 3 x 1
M = w_**2 * a_ * b_
M = M.view(-1, 9)
_, _, Vh = torch.linalg.svd(M)
F8 = Vh[-1, :].view(3, 3)
[u, s, vh] = torch.linalg.svd(F8)
S_ = torch.diag(s * mask)
F_ = u.mm(S_.mm(vh))
F_ = F_ / torch.norm(F_)
out_batch.append(F_.unsqueeze(0))
F = torch.cat(out_batch, 0)
return F
@staticmethod
def setup_context(ctx, inputs, output):
A, B, w = inputs
ctx.save_for_backward(A, B, w, output)
@staticmethod
def backward(ctx, grad_output):
A, B, w, output = ctx.saved_tensors # output : b x 3 x 3
grad_A = grad_B = None
b = grad_output.shape[0]
w = nn.functional.relu(w)
# F : b x 3 x 3 ; w : b x 15 ; J_Fw : b x 9 x 15 ; grad_output : b x 3 x 3
J_Fw = compute_jacobians(
output, w, A.permute(0, 2, 1), B.permute(0, 2, 1)
) # b x 9 x 15
J_Fw = torch.einsum("bi,bij->bj", grad_output.view(b, 9), J_Fw)
grad_w = J_Fw.view(b, 15)
return None, None, grad_w
class IFTLayer(nn.Module):
def __init__(self):
super().__init__()
def forward(self, A, B, w):
return IFTFunction.apply(A, B, w)
def compute_jacobians(F, w, A, B):
"""
F : b x 3 x 3
w : b x N
A : b x 3 x N
B : b x 3 x N
"""
b = F.shape[0]
F11 = F[:, 0, 0]
F12 = F[:, 0, 1]
F13 = F[:, 0, 2]
F21 = F[:, 1, 0]
F22 = F[:, 1, 1]
F23 = F[:, 1, 2]
F31 = F[:, 2, 0]
F32 = F[:, 2, 1]
F33 = F[:, 2, 2]
x11 = A[:, 0, 0]
y11 = A[:, 1, 0]
x12 = B[:, 0, 0]
y12 = B[:, 1, 0]
x21 = A[:, 0, 1]
y21 = A[:, 1, 1]
x22 = B[:, 0, 1]
y22 = B[:, 1, 1]
x31 = A[:, 0, 2]
y31 = A[:, 1, 2]
x32 = B[:, 0, 2]
y32 = B[:, 1, 2]
x41 = A[:, 0, 3]
y41 = A[:, 1, 3]
x42 = B[:, 0, 3]
y42 = B[:, 1, 3]
x51 = A[:, 0, 4]
y51 = A[:, 1, 4]
x52 = B[:, 0, 4]
y52 = B[:, 1, 4]
x61 = A[:, 0, 5]
y61 = A[:, 1, 5]
x62 = B[:, 0, 5]
y62 = B[:, 1, 5]
x71 = A[:, 0, 6]
y71 = A[:, 1, 6]
x72 = B[:, 0, 6]
y72 = B[:, 1, 6]
x81 = A[:, 0, 7]
y81 = A[:, 1, 7]
x82 = B[:, 0, 7]
y82 = B[:, 1, 7]
x91 = A[:, 0, 8]
y91 = A[:, 1, 8]
x92 = B[:, 0, 8]
y92 = B[:, 1, 8]
x10_1 = A[:, 0, 9]
y10_1 = A[:, 1, 9]
x10_2 = B[:, 0, 9]
y10_2 = B[:, 1, 9]
x11_1 = A[:, 0, 10]
y11_1 = A[:, 1, 10]
x11_2 = B[:, 0, 10]
y11_2 = B[:, 1, 10]
x12_1 = A[:, 0, 11]
y12_1 = A[:, 1, 11]
x12_2 = B[:, 0, 11]
y12_2 = B[:, 1, 11]
x13_1 = A[:, 0, 12]
y13_1 = A[:, 1, 12]
x13_2 = B[:, 0, 12]
y13_2 = B[:, 1, 12]
x14_1 = A[:, 0, 13]
y14_1 = A[:, 1, 13]
x14_2 = B[:, 0, 13]
y14_2 = B[:, 1, 13]
x15_1 = A[:, 0, 14]
y15_1 = A[:, 1, 14]
x15_2 = B[:, 0, 14]
y15_2 = B[:, 1, 14]
w1 = w[:, 0]
w2 = w[:, 1]
w3 = w[:, 2]
w4 = w[:, 3]
w5 = w[:, 4]
w6 = w[:, 5]
w7 = w[:, 6]
w8 = w[:, 7]
w9 = w[:, 8]
w10 = w[:, 9]
w11 = w[:, 10]
w12 = w[:, 11]
w13 = w[:, 12]
w14 = w[:, 13]
w15 = w[:, 14]
J_F = torch.zeros((b, 17, 9), device=F.device)
# F11
J_F[:, 0, 0] = (
-2
* (F22 * F33 - F23 * F32)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
+ w5**2 * x51 * x52
+ w6**2 * x61 * x62
+ w7**2 * x71 * x72
+ w8**2 * x81 * x82
+ w9**2 * x91 * x92
+ w10**2 * x10_1 * x10_2
+ w11**2 * x11_1 * x11_2
+ w12**2 * x12_1 * x12_2
+ w13**2 * x13_1 * x13_2
+ w14**2 * x14_1 * x14_2
+ w15**2 * x15_1 * x15_2
)
/ (F11 * F22 - F12 * F21)
+ 2
* (F22 * F33 - F23 * F32)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F22
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12**2 * x11**2
+ 2 * w2**2 * x22**2 * x21**2
+ 2 * w3**2 * x32**2 * x31**2
+ 2 * w4**2 * x42**2 * x41**2
+ 2 * w5**2 * x52**2 * x51**2
+ 2 * w6**2 * x62**2 * x61**2
+ 2 * w7**2 * x72**2 * x71**2
+ 2 * w8**2 * x82**2 * x81**2
+ 2 * w9**2 * x92**2 * x91**2
+ 2 * w10**2 * x10_2**2 * x10_1**2
+ 2 * w11**2 * x11_2**2 * x11_1**2
+ 2 * w12**2 * x12_2**2 * x12_1**2
+ 2 * w13**2 * x13_2**2 * x13_1**2
+ 2 * w14**2 * x14_2**2 * x14_1**2
+ 2 * w15**2 * x15_2**2 * x15_1**2
)
J_F[:, 1, 0] = (
-2
* (-F21 * F33 + F23 * F31)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
+ w5**2 * x51 * x52
+ w6**2 * x61 * x62
+ w7**2 * x71 * x72
+ w8**2 * x81 * x82
+ w9**2 * x91 * x92
+ w10**2 * x10_1 * x10_2
+ w11**2 * x11_1 * x11_2
+ w12**2 * x12_1 * x12_2
+ w13**2 * x13_1 * x13_2
+ w14**2 * x14_1 * x14_2
+ w15**2 * x15_1 * x15_2
)
/ (F11 * F22 - F12 * F21)
+ 2
* (-F21 * F33 + F23 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F22
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12**2 * x11 * y11
+ 2 * w2**2 * x22**2 * x21 * y21
+ 2 * w3**2 * x32**2 * x31 * y31
+ 2 * w4**2 * x42**2 * x41 * y41
+ 2 * w5**2 * x52**2 * x51 * y51
+ 2 * w6**2 * x62**2 * x61 * y61
+ 2 * w7**2 * x72**2 * x71 * y71
+ 2 * w8**2 * x82**2 * x81 * y81
+ 2 * w9**2 * x92**2 * x91 * y91
+ 2 * w10**2 * x10_2**2 * x10_1 * y10_1
+ 2 * w11**2 * x11_2**2 * x11_1 * y11_1
+ 2 * w12**2 * x12_2**2 * x12_1 * y12_1
+ 2 * w13**2 * x13_2**2 * x13_1 * y13_1
+ 2 * w14**2 * x14_2**2 * x14_1 * y14_1
+ 2 * w15**2 * x15_2**2 * x15_1 * y15_1
)
J_F[:, 2, 0] = (
-2
* (F21 * F32 - F22 * F31)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
+ w5**2 * x51 * x52
+ w6**2 * x61 * x62
+ w7**2 * x71 * x72
+ w8**2 * x81 * x82
+ w9**2 * x91 * x92
+ w10**2 * x10_1 * x10_2
+ w11**2 * x11_1 * x11_2
+ w12**2 * x12_1 * x12_2
+ w13**2 * x13_1 * x13_2
+ w14**2 * x14_1 * x14_2
+ w15**2 * x15_1 * x15_2
)
/ (F11 * F22 - F12 * F21)
+ 2
* (F21 * F32 - F22 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F22
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12**2 * x11
+ 2 * w2**2 * x22**2 * x21
+ 2 * w3**2 * x32**2 * x31
+ 2 * w4**2 * x42**2 * x41
+ 2 * w5**2 * x52**2 * x51
+ 2 * w6**2 * x62**2 * x61
+ 2 * w7**2 * x72**2 * x71
+ 2 * w8**2 * x82**2 * x81
+ 2 * w9**2 * x92**2 * x91
+ 2 * w10**2 * x10_2**2 * x10_1
+ 2 * w11**2 * x11_2**2 * x11_1
+ 2 * w12**2 * x12_2**2 * x12_1
+ 2 * w13**2 * x13_2**2 * x13_1
+ 2 * w14**2 * x14_2**2 * x14_1
+ 2 * w15**2 * x15_2**2 * x15_1
)
J_F[:, 3, 0] = (
-2
* (-F12 * F33 + F13 * F32)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
+ w5**2 * x51 * x52
+ w6**2 * x61 * x62
+ w7**2 * x71 * x72
+ w8**2 * x81 * x82
+ w9**2 * x91 * x92
+ w10**2 * x10_1 * x10_2
+ w11**2 * x11_1 * x11_2
+ w12**2 * x12_1 * x12_2
+ w13**2 * x13_1 * x13_2
+ w14**2 * x14_1 * x14_2
+ w15**2 * x15_1 * x15_2
)
/ (F11 * F22 - F12 * F21)
+ 2
* (-F12 * F33 + F13 * F32)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F22
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * x11**2 * y12
+ 2 * w2**2 * x22 * x21**2 * y22
+ 2 * w3**2 * x32 * x31**2 * y32
+ 2 * w4**2 * x42 * x41**2 * y42
+ 2 * w5**2 * x52 * x51**2 * y52
+ 2 * w6**2 * x62 * x61**2 * y62
+ 2 * w7**2 * x72 * x71**2 * y72
+ 2 * w8**2 * x82 * x81**2 * y82
+ 2 * w9**2 * x92 * x91**2 * y92
+ 2 * w10**2 * x10_2 * x10_1**2 * y10_2
+ 2 * w11**2 * x11_2 * x11_1**2 * y11_2
+ 2 * w12**2 * x12_2 * x12_1**2 * y12_2
+ 2 * w13**2 * x13_2 * x13_1**2 * y13_2
+ 2 * w14**2 * x14_2 * x14_1**2 * y14_2
+ 2 * w15**2 * x15_2 * x15_1**2 * y15_2
)
J_F[:, 4, 0] = (
-2
* F33
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F11 * F33 - F13 * F31)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
+ w5**2 * x51 * x52
+ w6**2 * x61 * x62
+ w7**2 * x71 * x72
+ w8**2 * x81 * x82
+ w9**2 * x91 * x92
+ w10**2 * x10_1 * x10_2
+ w11**2 * x11_1 * x11_2
+ w12**2 * x12_1 * x12_2
+ w13**2 * x13_1 * x13_2
+ w14**2 * x14_1 * x14_2
+ w15**2 * x15_1 * x15_2
)
/ (F11 * F22 - F12 * F21)
+ 2
* (F11 * F33 - F13 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F22
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * x11 * y12 * y11
+ 2 * w2**2 * x22 * x21 * y22 * y21
+ 2 * w3**2 * x32 * x31 * y32 * y31
+ 2 * w4**2 * x42 * x41 * y42 * y41
+ 2 * w5**2 * x52 * x51 * y52 * y51
+ 2 * w6**2 * x62 * x61 * y62 * y61
+ 2 * w7**2 * x72 * x71 * y72 * y71
+ 2 * w8**2 * x82 * x81 * y82 * y81
+ 2 * w9**2 * x92 * x91 * y92 * y91
+ 2 * w10**2 * x10_2 * x10_1 * y10_2 * y10_1
+ 2 * w11**2 * x11_2 * x11_1 * y11_2 * y11_1
+ 2 * w12**2 * x12_2 * x12_1 * y12_2 * y12_1
+ 2 * w13**2 * x13_2 * x13_1 * y13_2 * y13_1
+ 2 * w14**2 * x14_2 * x14_1 * y14_2 * y14_1
+ 2 * w15**2 * x15_2 * x15_1 * y15_2 * y15_1
)
J_F[:, 5, 0] = (
2
* F32
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F11 * F32 + F12 * F31)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
+ w5**2 * x51 * x52
+ w6**2 * x61 * x62
+ w7**2 * x71 * x72
+ w8**2 * x81 * x82
+ w9**2 * x91 * x92
+ w10**2 * x10_1 * x10_2
+ w11**2 * x11_1 * x11_2
+ w12**2 * x12_1 * x12_2
+ w13**2 * x13_1 * x13_2
+ w14**2 * x14_1 * x14_2
+ w15**2 * x15_1 * x15_2
)
/ (F11 * F22 - F12 * F21)
+ 2
* (-F11 * F32 + F12 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F22
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * x11 * y12
+ 2 * w2**2 * x22 * x21 * y22
+ 2 * w3**2 * x32 * x31 * y32
+ 2 * w4**2 * x42 * x41 * y42
+ 2 * w5**2 * x52 * x51 * y52
+ 2 * w6**2 * x62 * x61 * y62
+ 2 * w7**2 * x72 * x71 * y72
+ 2 * w8**2 * x82 * x81 * y82
+ 2 * w9**2 * x92 * x91 * y92
+ 2 * w10**2 * x10_2 * x10_1 * y10_2
+ 2 * w11**2 * x11_2 * x11_1 * y11_2
+ 2 * w12**2 * x12_2 * x12_1 * y12_2
+ 2 * w13**2 * x13_2 * x13_1 * y13_2
+ 2 * w14**2 * x14_2 * x14_1 * y14_2
+ 2 * w15**2 * x15_2 * x15_1 * y15_2
)
J_F[:, 6, 0] = (
-2
* (F12 * F23 - F13 * F22)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
+ w5**2 * x51 * x52
+ w6**2 * x61 * x62
+ w7**2 * x71 * x72
+ w8**2 * x81 * x82
+ w9**2 * x91 * x92
+ w10**2 * x10_1 * x10_2
+ w11**2 * x11_1 * x11_2
+ w12**2 * x12_1 * x12_2
+ w13**2 * x13_1 * x13_2
+ w14**2 * x14_1 * x14_2
+ w15**2 * x15_1 * x15_2
)
/ (F11 * F22 - F12 * F21)
+ 2
* (F12 * F23 - F13 * F22)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F22
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * x11**2
+ 2 * w2**2 * x22 * x21**2
+ 2 * w3**2 * x32 * x31**2
+ 2 * w4**2 * x42 * x41**2
+ 2 * w5**2 * x52 * x51**2
+ 2 * w6**2 * x62 * x61**2
+ 2 * w7**2 * x72 * x71**2
+ 2 * w8**2 * x82 * x81**2
+ 2 * w9**2 * x92 * x91**2
+ 2 * w10**2 * x10_2 * x10_1**2
+ 2 * w11**2 * x11_2 * x11_1**2
+ 2 * w12**2 * x12_2 * x12_1**2
+ 2 * w13**2 * x13_2 * x13_1**2
+ 2 * w14**2 * x14_2 * x14_1**2
+ 2 * w15**2 * x15_2 * x15_1**2
)
J_F[:, 7, 0] = (
2
* F23
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F11 * F23 + F13 * F21)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
+ w5**2 * x51 * x52
+ w6**2 * x61 * x62
+ w7**2 * x71 * x72
+ w8**2 * x81 * x82
+ w9**2 * x91 * x92
+ w10**2 * x10_1 * x10_2
+ w11**2 * x11_1 * x11_2
+ w12**2 * x12_1 * x12_2
+ w13**2 * x13_1 * x13_2
+ w14**2 * x14_1 * x14_2
+ w15**2 * x15_1 * x15_2
)
/ (F11 * F22 - F12 * F21)
+ 2
* (-F11 * F23 + F13 * F21)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F22
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * x11 * y11
+ 2 * w2**2 * x22 * x21 * y21
+ 2 * w3**2 * x32 * x31 * y31
+ 2 * w4**2 * x42 * x41 * y41
+ 2 * w5**2 * x52 * x51 * y51
+ 2 * w6**2 * x62 * x61 * y61
+ 2 * w7**2 * x72 * x71 * y71
+ 2 * w8**2 * x82 * x81 * y81
+ 2 * w9**2 * x92 * x91 * y91
+ 2 * w10**2 * x10_2 * x10_1 * y10_1
+ 2 * w11**2 * x11_2 * x11_1 * y11_1
+ 2 * w12**2 * x12_2 * x12_1 * y12_1
+ 2 * w13**2 * x13_2 * x13_1 * y13_1
+ 2 * w14**2 * x14_2 * x14_1 * y14_1
+ 2 * w15**2 * x15_2 * x15_1 * y15_1
)
J_F[:, 8, 0] = 0
# F12
J_F[:, 0, 1] = (
-2
* (F22 * F33 - F23 * F32)
* (
w1**2 * x12 * y11
+ w2**2 * x22 * y21
+ w3**2 * x32 * y31
+ w4**2 * x42 * y41
+ w5**2 * x52 * y51
+ w6**2 * x62 * y61
+ w7**2 * x72 * y71
+ w8**2 * x82 * y81
+ w9**2 * x92 * y91
+ w10**2 * x10_2 * y10_1
+ w11**2 * x11_2 * y11_1
+ w12**2 * x12_2 * y12_1
+ w13**2 * x13_2 * y13_1
+ w14**2 * x14_2 * y14_1
+ w15**2 * x15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
- 2
* (F22 * F33 - F23 * F32)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F21
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12**2 * x11 * y11
+ 2 * w2**2 * x22**2 * x21 * y21
+ 2 * w3**2 * x32**2 * x31 * y31
+ 2 * w4**2 * x42**2 * x41 * y41
+ 2 * w5**2 * x52**2 * x51 * y51
+ 2 * w6**2 * x62**2 * x61 * y61
+ 2 * w7**2 * x72**2 * x71 * y71
+ 2 * w8**2 * x82**2 * x81 * y81
+ 2 * w9**2 * x92**2 * x91 * y91
+ 2 * w10**2 * x10_2**2 * x10_1 * y10_1
+ 2 * w11**2 * x11_2**2 * x11_1 * y11_1
+ 2 * w12**2 * x12_2**2 * x12_1 * y12_1
+ 2 * w13**2 * x13_2**2 * x13_1 * y13_1
+ 2 * w14**2 * x14_2**2 * x14_1 * y14_1
+ 2 * w15**2 * x15_2**2 * x15_1 * y15_1
)
J_F[:, 1, 1] = (
-2
* (-F21 * F33 + F23 * F31)
* (
w1**2 * x12 * y11
+ w2**2 * x22 * y21
+ w3**2 * x32 * y31
+ w4**2 * x42 * y41
+ w5**2 * x52 * y51
+ w6**2 * x62 * y61
+ w7**2 * x72 * y71
+ w8**2 * x82 * y81
+ w9**2 * x92 * y91
+ w10**2 * x10_2 * y10_1
+ w11**2 * x11_2 * y11_1
+ w12**2 * x12_2 * y12_1
+ w13**2 * x13_2 * y13_1
+ w14**2 * x14_2 * y14_1
+ w15**2 * x15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F21 * F33 + F23 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F21
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12**2 * y11**2
+ 2 * w2**2 * x22**2 * y21**2
+ 2 * w3**2 * x32**2 * y31**2
+ 2 * w4**2 * x42**2 * y41**2
+ 2 * w5**2 * x52**2 * y51**2
+ 2 * w6**2 * x62**2 * y61**2
+ 2 * w7**2 * x72**2 * y71**2
+ 2 * w8**2 * x82**2 * y81**2
+ 2 * w9**2 * x92**2 * y91**2
+ 2 * w10**2 * x10_2**2 * y10_1**2
+ 2 * w11**2 * x11_2**2 * y11_1**2
+ 2 * w12**2 * x12_2**2 * y12_1**2
+ 2 * w13**2 * x13_2**2 * y13_1**2
+ 2 * w14**2 * x14_2**2 * y14_1**2
+ 2 * w15**2 * x15_2**2 * y15_1**2
)
J_F[:, 2, 1] = (
-2
* (F21 * F32 - F22 * F31)
* (
w1**2 * x12 * y11
+ w2**2 * x22 * y21
+ w3**2 * x32 * y31
+ w4**2 * x42 * y41
+ w5**2 * x52 * y51
+ w6**2 * x62 * y61
+ w7**2 * x72 * y71
+ w8**2 * x82 * y81
+ w9**2 * x92 * y91
+ w10**2 * x10_2 * y10_1
+ w11**2 * x11_2 * y11_1
+ w12**2 * x12_2 * y12_1
+ w13**2 * x13_2 * y13_1
+ w14**2 * x14_2 * y14_1
+ w15**2 * x15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
- 2
* (F21 * F32 - F22 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F21
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12**2 * y11
+ 2 * w2**2 * x22**2 * y21
+ 2 * w3**2 * x32**2 * y31
+ 2 * w4**2 * x42**2 * y41
+ 2 * w5**2 * x52**2 * y51
+ 2 * w6**2 * x62**2 * y61
+ 2 * w7**2 * x72**2 * y71
+ 2 * w8**2 * x82**2 * y81
+ 2 * w9**2 * x92**2 * y91
+ 2 * w10**2 * x10_2**2 * y10_1
+ 2 * w11**2 * x11_2**2 * y11_1
+ 2 * w12**2 * x12_2**2 * y12_1
+ 2 * w13**2 * x13_2**2 * y13_1
+ 2 * w14**2 * x14_2**2 * y14_1
+ 2 * w15**2 * x15_2**2 * y15_1
)
J_F[:, 3, 1] = (
2
* F33
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F12 * F33 + F13 * F32)
* (
w1**2 * x12 * y11
+ w2**2 * x22 * y21
+ w3**2 * x32 * y31
+ w4**2 * x42 * y41
+ w5**2 * x52 * y51
+ w6**2 * x62 * y61
+ w7**2 * x72 * y71
+ w8**2 * x82 * y81
+ w9**2 * x92 * y91
+ w10**2 * x10_2 * y10_1
+ w11**2 * x11_2 * y11_1
+ w12**2 * x12_2 * y12_1
+ w13**2 * x13_2 * y13_1
+ w14**2 * x14_2 * y14_1
+ w15**2 * x15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F12 * F33 + F13 * F32)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F21
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * x11 * y12 * y11
+ 2 * w2**2 * x22 * x21 * y22 * y21
+ 2 * w3**2 * x32 * x31 * y32 * y31
+ 2 * w4**2 * x42 * x41 * y42 * y41
+ 2 * w5**2 * x52 * x51 * y52 * y51
+ 2 * w6**2 * x62 * x61 * y62 * y61
+ 2 * w7**2 * x72 * x71 * y72 * y71
+ 2 * w8**2 * x82 * x81 * y82 * y81
+ 2 * w9**2 * x92 * x91 * y92 * y91
+ 2 * w10**2 * x10_2 * x10_1 * y10_2 * y10_1
+ 2 * w11**2 * x11_2 * x11_1 * y11_2 * y11_1
+ 2 * w12**2 * x12_2 * x12_1 * y12_2 * y12_1
+ 2 * w13**2 * x13_2 * x13_1 * y13_2 * y13_1
+ 2 * w14**2 * x14_2 * x14_1 * y14_2 * y14_1
+ 2 * w15**2 * x15_2 * x15_1 * y15_2 * y15_1
)
J_F[:, 4, 1] = (
-2
* (F11 * F33 - F13 * F31)
* (
w1**2 * x12 * y11
+ w2**2 * x22 * y21
+ w3**2 * x32 * y31
+ w4**2 * x42 * y41
+ w5**2 * x52 * y51
+ w6**2 * x62 * y61
+ w7**2 * x72 * y71
+ w8**2 * x82 * y81
+ w9**2 * x92 * y91
+ w10**2 * x10_2 * y10_1
+ w11**2 * x11_2 * y11_1
+ w12**2 * x12_2 * y12_1
+ w13**2 * x13_2 * y13_1
+ w14**2 * x14_2 * y14_1
+ w15**2 * x15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
- 2
* (F11 * F33 - F13 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F21
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * y11**2 * y12
+ 2 * w2**2 * x22 * y21**2 * y22
+ 2 * w3**2 * x32 * y31**2 * y32
+ 2 * w4**2 * x42 * y41**2 * y42
+ 2 * w5**2 * x52 * y51**2 * y52
+ 2 * w6**2 * x62 * y61**2 * y62
+ 2 * w7**2 * x72 * y71**2 * y72
+ 2 * w8**2 * x82 * y81**2 * y82
+ 2 * w9**2 * x92 * y91**2 * y92
+ 2 * w10**2 * x10_2 * y10_1**2 * y10_2
+ 2 * w11**2 * x11_2 * y11_1**2 * y11_2
+ 2 * w12**2 * x12_2 * y12_1**2 * y12_2
+ 2 * w13**2 * x13_2 * y13_1**2 * y13_2
+ 2 * w14**2 * x14_2 * y14_1**2 * y14_2
+ 2 * w15**2 * x15_2 * y15_1**2 * y15_2
)
J_F[:, 5, 1] = (
-2
* (F11 * F33 - F13 * F31)
* (
w1**2 * x12 * y11
+ w2**2 * x22 * y21
+ w3**2 * x32 * y31
+ w4**2 * x42 * y41
+ w5**2 * x52 * y51
+ w6**2 * x62 * y61
+ w7**2 * x72 * y71
+ w8**2 * x82 * y81
+ w9**2 * x92 * y91
+ w10**2 * x10_2 * y10_1
+ w11**2 * x11_2 * y11_1
+ w12**2 * x12_2 * y12_1
+ w13**2 * x13_2 * y13_1
+ w14**2 * x14_2 * y14_1
+ w15**2 * x15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
- 2
* (F11 * F33 - F13 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F21
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * y11**2 * y12
+ 2 * w2**2 * x22 * y21**2 * y22
+ 2 * w3**2 * x32 * y31**2 * y32
+ 2 * w4**2 * x42 * y41**2 * y42
+ 2 * w5**2 * x52 * y51**2 * y52
+ 2 * w6**2 * x62 * y61**2 * y62
+ 2 * w7**2 * x72 * y71**2 * y72
+ 2 * w8**2 * x82 * y81**2 * y82
+ 2 * w9**2 * x92 * y91**2 * y92
+ 2 * w10**2 * x10_2 * y10_1**2 * y10_2
+ 2 * w11**2 * x11_2 * y11_1**2 * y11_2
+ 2 * w12**2 * x12_2 * y12_1**2 * y12_2
+ 2 * w13**2 * x13_2 * y13_1**2 * y13_2
+ 2 * w14**2 * x14_2 * y14_1**2 * y14_2
+ 2 * w15**2 * x15_2 * y15_1**2 * y15_2
)
J_F[:, 6, 1] = (
-2
* F23
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F12 * F23 - F13 * F22)
* (
w1**2 * x12 * y11
+ w2**2 * x22 * y21
+ w3**2 * x32 * y31
+ w4**2 * x42 * y41
+ w5**2 * x52 * y51
+ w6**2 * x62 * y61
+ w7**2 * x72 * y71
+ w8**2 * x82 * y81
+ w9**2 * x92 * y91
+ w10**2 * x10_2 * y10_1
+ w11**2 * x11_2 * y11_1
+ w12**2 * x12_2 * y12_1
+ w13**2 * x13_2 * y13_1
+ w14**2 * x14_2 * y14_1
+ w15**2 * x15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
- 2
* (F12 * F23 - F13 * F22)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F21
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * x11 * y11
+ 2 * w2**2 * x22 * x21 * y21
+ 2 * w3**2 * x32 * x31 * y31
+ 2 * w4**2 * x42 * x41 * y41
+ 2 * w5**2 * x52 * x51 * y51
+ 2 * w6**2 * x62 * x61 * y61
+ 2 * w7**2 * x72 * x71 * y71
+ 2 * w8**2 * x82 * x81 * y81
+ 2 * w9**2 * x92 * x91 * y91
+ 2 * w10**2 * x10_2 * x10_1 * y10_1
+ 2 * w11**2 * x11_2 * x11_1 * y11_1
+ 2 * w12**2 * x12_2 * x12_1 * y12_1
+ 2 * w13**2 * x13_2 * x13_1 * y13_1
+ 2 * w14**2 * x14_2 * x14_1 * y14_1
+ 2 * w15**2 * x15_2 * x15_1 * y15_1
)
J_F[:, 7, 1] = (
-2
* (-F11 * F23 + F13 * F21)
* (
w1**2 * x12 * y11
+ w2**2 * x22 * y21
+ w3**2 * x32 * y31
+ w4**2 * x42 * y41
+ w5**2 * x52 * y51
+ w6**2 * x62 * y61
+ w7**2 * x72 * y71
+ w8**2 * x82 * y81
+ w9**2 * x92 * y91
+ w10**2 * x10_2 * y10_1
+ w11**2 * x11_2 * y11_1
+ w12**2 * x12_2 * y12_1
+ w13**2 * x13_2 * y13_1
+ w14**2 * x14_2 * y14_1
+ w15**2 * x15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F11 * F23 + F13 * F21)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F21
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * y11**2
+ 2 * w2**2 * x22 * y21**2
+ 2 * w3**2 * x32 * y31**2
+ 2 * w4**2 * x42 * y41**2
+ 2 * w5**2 * x52 * y51**2
+ 2 * w6**2 * x62 * y61**2
+ 2 * w7**2 * x72 * y71**2
+ 2 * w8**2 * x82 * y81**2
+ 2 * w9**2 * x92 * y91**2
+ 2 * w10**2 * x10_2 * y10_1**2
+ 2 * w11**2 * x11_2 * y11_1**2
+ 2 * w12**2 * x12_2 * y12_1**2
+ 2 * w13**2 * x13_2 * y13_1**2
+ 2 * w14**2 * x14_2 * y14_1**2
+ 2 * w15**2 * x15_2 * y15_1**2
)
J_F[:, 8, 1] = 0
# F13
J_F[:, 0, 2] = (
-2
* (F22 * F33 - F23 * F32)
* (
w1**2 * x12
+ w10**2 * x10_2
+ w11**2 * x11_2
+ w12**2 * x12_2
+ w13**2 * x13_2
+ w14**2 * x14_2
+ w15**2 * x15_2
+ w2**2 * x22
+ w3**2 * x32
+ w4**2 * x42
+ w5**2 * x52
+ w6**2 * x62
+ w7**2 * x72
+ w8**2 * x82
+ w9**2 * x92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12**2 * x11
+ 2 * w2**2 * x22**2 * x21
+ 2 * w3**2 * x32**2 * x31
+ 2 * w4**2 * x42**2 * x41
+ 2 * w5**2 * x52**2 * x51
+ 2 * w6**2 * x62**2 * x61
+ 2 * w7**2 * x72**2 * x71
+ 2 * w8**2 * x82**2 * x81
+ 2 * w9**2 * x92**2 * x91
+ 2 * w10**2 * x10_2**2 * x10_1
+ 2 * w11**2 * x11_2**2 * x11_1
+ 2 * w12**2 * x12_2**2 * x12_1
+ 2 * w13**2 * x13_2**2 * x13_1
+ 2 * w14**2 * x14_2**2 * x14_1
+ 2 * w15**2 * x15_2**2 * x15_1
)
J_F[:, 1, 2] = (
-2
* (-F21 * F33 + F23 * F31)
* (
w1**2 * x12
+ w10**2 * x10_2
+ w11**2 * x11_2
+ w12**2 * x12_2
+ w13**2 * x13_2
+ w14**2 * x14_2
+ w15**2 * x15_2
+ w2**2 * x22
+ w3**2 * x32
+ w4**2 * x42
+ w5**2 * x52
+ w6**2 * x62
+ w7**2 * x72
+ w8**2 * x82
+ w9**2 * x92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12**2 * y11
+ 2 * w2**2 * x22**2 * y21
+ 2 * w3**2 * x32**2 * y31
+ 2 * w4**2 * x42**2 * y41
+ 2 * w5**2 * x52**2 * y51
+ 2 * w6**2 * x62**2 * y61
+ 2 * w7**2 * x72**2 * y71
+ 2 * w8**2 * x82**2 * y81
+ 2 * w9**2 * x92**2 * y91
+ 2 * w10**2 * x10_2**2 * y10_1
+ 2 * w11**2 * x11_2**2 * y11_1
+ 2 * w12**2 * x12_2**2 * y12_1
+ 2 * w13**2 * x13_2**2 * y13_1
+ 2 * w14**2 * x14_2**2 * y14_1
+ 2 * w15**2 * x15_2**2 * y15_1
)
J_F[:, 2, 2] = (
-2
* (F21 * F32 - F22 * F31)
* (
w1**2 * x12
+ w10**2 * x10_2
+ w11**2 * x11_2
+ w12**2 * x12_2
+ w13**2 * x13_2
+ w14**2 * x14_2
+ w15**2 * x15_2
+ w2**2 * x22
+ w3**2 * x32
+ w4**2 * x42
+ w5**2 * x52
+ w6**2 * x62
+ w7**2 * x72
+ w8**2 * x82
+ w9**2 * x92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12**2
+ 2 * w2**2 * x22**2
+ 2 * w3**2 * x32**2
+ 2 * w4**2 * x42**2
+ 2 * w5**2 * x52**2
+ 2 * w6**2 * x62**2
+ 2 * w7**2 * x72**2
+ 2 * w8**2 * x82**2
+ 2 * w9**2 * x92**2
+ 2 * w10**2 * x10_2**2
+ 2 * w11**2 * x11_2**2
+ 2 * w12**2 * x12_2**2
+ 2 * w13**2 * x13_2**2
+ 2 * w14**2 * x14_2**2
+ 2 * w15**2 * x15_2**2
)
J_F[:, 3, 2] = (
-2
* F32
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F12 * F33 + F13 * F32)
* (
w1**2 * x12
+ w10**2 * x10_2
+ w11**2 * x11_2
+ w12**2 * x12_2
+ w13**2 * x13_2
+ w14**2 * x14_2
+ w15**2 * x15_2
+ w2**2 * x22
+ w3**2 * x32
+ w4**2 * x42
+ w5**2 * x52
+ w6**2 * x62
+ w7**2 * x72
+ w8**2 * x82
+ w9**2 * x92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * x11 * y12
+ 2 * w2**2 * x22 * x21 * y22
+ 2 * w3**2 * x32 * x31 * y32
+ 2 * w4**2 * x42 * x41 * y42
+ 2 * w5**2 * x52 * x51 * y52
+ 2 * w6**2 * x62 * x61 * y62
+ 2 * w7**2 * x72 * x71 * y72
+ 2 * w8**2 * x82 * x81 * y82
+ 2 * w9**2 * x92 * x91 * y92
+ 2 * w10**2 * x10_2 * x10_1 * y10_2
+ 2 * w11**2 * x11_2 * x11_1 * y11_2
+ 2 * w12**2 * x12_2 * x12_1 * y12_2
+ 2 * w13**2 * x13_2 * x13_1 * y13_2
+ 2 * w14**2 * x14_2 * x14_1 * y14_2
+ 2 * w15**2 * x15_2 * x15_1 * y15_2
)
J_F[:, 4, 2] = (
2
* F31
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F11 * F33 - F13 * F31)
* (
w1**2 * x12
+ w10**2 * x10_2
+ w11**2 * x11_2
+ w12**2 * x12_2
+ w13**2 * x13_2
+ w14**2 * x14_2
+ w15**2 * x15_2
+ w2**2 * x22
+ w3**2 * x32
+ w4**2 * x42
+ w5**2 * x52
+ w6**2 * x62
+ w7**2 * x72
+ w8**2 * x82
+ w9**2 * x92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * y11 * y12
+ 2 * w2**2 * x22 * y21 * y22
+ 2 * w3**2 * x32 * y31 * y32
+ 2 * w4**2 * x42 * y41 * y42
+ 2 * w5**2 * x52 * y51 * y52
+ 2 * w6**2 * x62 * y61 * y62
+ 2 * w7**2 * x72 * y71 * y72
+ 2 * w8**2 * x82 * y81 * y82
+ 2 * w9**2 * x92 * y91 * y92
+ 2 * w10**2 * x10_2 * y10_1 * y10_2
+ 2 * w11**2 * x11_2 * y11_1 * y11_2
+ 2 * w12**2 * x12_2 * y12_1 * y12_2
+ 2 * w13**2 * x13_2 * y13_1 * y13_2
+ 2 * w14**2 * x14_2 * y14_1 * y14_2
+ 2 * w15**2 * x15_2 * y15_1 * y15_2
)
J_F[:, 5, 2] = (
-2
* (-F11 * F32 + F12 * F31)
* (
w1**2 * x12
+ w10**2 * x10_2
+ w11**2 * x11_2
+ w12**2 * x12_2
+ w13**2 * x13_2
+ w14**2 * x14_2
+ w15**2 * x15_2
+ w2**2 * x22
+ w3**2 * x32
+ w4**2 * x42
+ w5**2 * x52
+ w6**2 * x62
+ w7**2 * x72
+ w8**2 * x82
+ w9**2 * x92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * y12
+ 2 * w2**2 * x22 * y22
+ 2 * w3**2 * x32 * y32
+ 2 * w4**2 * x42 * y42
+ 2 * w5**2 * x52 * y52
+ 2 * w6**2 * x62 * y62
+ 2 * w7**2 * x72 * y72
+ 2 * w8**2 * x82 * y82
+ 2 * w9**2 * x92 * y92
+ 2 * w10**2 * x10_2 * y10_2
+ 2 * w11**2 * x11_2 * y11_2
+ 2 * w12**2 * x12_2 * y12_2
+ 2 * w13**2 * x13_2 * y13_2
+ 2 * w14**2 * x14_2 * y14_2
+ 2 * w15**2 * x15_2 * y15_2
)
J_F[:, 6, 2] = (
2
* F22
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F12 * F23 - F13 * F22)
* (
w1**2 * x12
+ w10**2 * x10_2
+ w11**2 * x11_2
+ w12**2 * x12_2
+ w13**2 * x13_2
+ w14**2 * x14_2
+ w15**2 * x15_2
+ w2**2 * x22
+ w3**2 * x32
+ w4**2 * x42
+ w5**2 * x52
+ w6**2 * x62
+ w7**2 * x72
+ w8**2 * x82
+ w9**2 * x92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x11 * x12
+ 2 * w2**2 * x21 * x22
+ 2 * w3**2 * x31 * x32
+ 2 * w4**2 * x41 * x42
+ 2 * w5**2 * x51 * x52
+ 2 * w6**2 * x61 * x62
+ 2 * w7**2 * x71 * x72
+ 2 * w8**2 * x81 * x82
+ 2 * w9**2 * x91 * x92
+ 2 * w10**2 * x10_1 * x10_2
+ 2 * w11**2 * x11_1 * x11_2
+ 2 * w12**2 * x12_1 * x12_2
+ 2 * w13**2 * x13_1 * x13_2
+ 2 * w14**2 * x14_1 * x14_2
+ 2 * w15**2 * x15_1 * x15_2
)
J_F[:, 7, 2] = (
-2
* F21
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F11 * F23 + F13 * F21)
* (
w1**2 * x12
+ w10**2 * x10_2
+ w11**2 * x11_2
+ w12**2 * x12_2
+ w13**2 * x13_2
+ w14**2 * x14_2
+ w15**2 * x15_2
+ w2**2 * x22
+ w3**2 * x32
+ w4**2 * x42
+ w5**2 * x52
+ w6**2 * x62
+ w7**2 * x72
+ w8**2 * x82
+ w9**2 * x92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * y11
+ 2 * w2**2 * x22 * y21
+ 2 * w3**2 * x32 * y31
+ 2 * w4**2 * x42 * y41
+ 2 * w5**2 * x52 * y51
+ 2 * w6**2 * x62 * y61
+ 2 * w7**2 * x72 * y71
+ 2 * w8**2 * x82 * y81
+ 2 * w9**2 * x92 * y91
+ 2 * w10**2 * x10_2 * y10_1
+ 2 * w11**2 * x11_2 * y11_1
+ 2 * w12**2 * x12_2 * y12_1
+ 2 * w13**2 * x13_2 * y13_1
+ 2 * w14**2 * x14_2 * y14_1
+ 2 * w15**2 * x15_2 * y15_1
)
J_F[:, 8, 2] = 0
# F21
J_F[:, 0, 3] = (
-2
* (F22 * F33 - F23 * F32)
* (
w1**2 * x11 * y12
+ w2**2 * x21 * y22
+ w3**2 * x31 * y32
+ w4**2 * x41 * y42
+ w5**2 * x51 * y52
+ w6**2 * x61 * y62
+ w7**2 * x71 * y72
+ w8**2 * x81 * y82
+ w9**2 * x91 * y92
+ w10**2 * x10_1 * y10_2
+ w11**2 * x11_1 * y11_2
+ w12**2 * x12_1 * y12_2
+ w13**2 * x13_1 * y13_2
+ w14**2 * x14_1 * y14_2
+ w15**2 * x15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F22 * F33 - F23 * F32)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F12
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * x11**2 * y12
+ 2 * w2**2 * x22 * x21**2 * y22
+ 2 * w3**2 * x32 * x31**2 * y32
+ 2 * w4**2 * x42 * x41**2 * y42
+ 2 * w5**2 * x52 * x51**2 * y52
+ 2 * w6**2 * x62 * x61**2 * y62
+ 2 * w7**2 * x72 * x71**2 * y72
+ 2 * w8**2 * x82 * x81**2 * y82
+ 2 * w9**2 * x92 * x91**2 * y92
+ 2 * w10**2 * x10_2 * x10_1**2 * y10_2
+ 2 * w11**2 * x11_2 * x11_1**2 * y11_2
+ 2 * w12**2 * x12_2 * x12_1**2 * y12_2
+ 2 * w13**2 * x13_2 * x13_1**2 * y13_2
+ 2 * w14**2 * x14_2 * x14_1**2 * y14_2
+ 2 * w15**2 * x15_2 * x15_1**2 * y15_2
)
J_F[:, 1, 3] = (
2
* F33
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F21 * F33 + F23 * F31)
* (
w1**2 * x11 * y12
+ w2**2 * x21 * y22
+ w3**2 * x31 * y32
+ w4**2 * x41 * y42
+ w5**2 * x51 * y52
+ w6**2 * x61 * y62
+ w7**2 * x71 * y72
+ w8**2 * x81 * y82
+ w9**2 * x91 * y92
+ w10**2 * x10_1 * y10_2
+ w11**2 * x11_1 * y11_2
+ w12**2 * x12_1 * y12_2
+ w13**2 * x13_1 * y13_2
+ w14**2 * x14_1 * y14_2
+ w15**2 * x15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F21 * F33 + F23 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F12
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * x11 * y12 * y11
+ 2 * w2**2 * x22 * x21 * y22 * y21
+ 2 * w3**2 * x32 * x31 * y32 * y31
+ 2 * w4**2 * x42 * x41 * y42 * y41
+ 2 * w5**2 * x52 * x51 * y52 * y51
+ 2 * w6**2 * x62 * x61 * y62 * y61
+ 2 * w7**2 * x72 * x71 * y72 * y71
+ 2 * w8**2 * x82 * x81 * y82 * y81
+ 2 * w9**2 * x92 * x91 * y92 * y91
+ 2 * w10**2 * x10_2 * x10_1 * y10_2 * y10_1
+ 2 * w11**2 * x11_2 * x11_1 * y11_2 * y11_1
+ 2 * w12**2 * x12_2 * x12_1 * y12_2 * y12_1
+ 2 * w13**2 * x13_2 * x13_1 * y13_2 * y13_1
+ 2 * w14**2 * x14_2 * x14_1 * y14_2 * y14_1
+ 2 * w15**2 * x15_2 * x15_1 * y15_2 * y15_1
)
J_F[:, 2, 3] = (
-2
* F32
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F21 * F32 - F22 * F31)
* (
w1**2 * x11 * y12
+ w2**2 * x21 * y22
+ w3**2 * x31 * y32
+ w4**2 * x41 * y42
+ w5**2 * x51 * y52
+ w6**2 * x61 * y62
+ w7**2 * x71 * y72
+ w8**2 * x81 * y82
+ w9**2 * x91 * y92
+ w10**2 * x10_1 * y10_2
+ w11**2 * x11_1 * y11_2
+ w12**2 * x12_1 * y12_2
+ w13**2 * x13_1 * y13_2
+ w14**2 * x14_1 * y14_2
+ w15**2 * x15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F21 * F32 - F22 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F12
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * x11 * y12
+ 2 * w2**2 * x22 * x21 * y22
+ 2 * w3**2 * x32 * x31 * y32
+ 2 * w4**2 * x42 * x41 * y42
+ 2 * w5**2 * x52 * x51 * y52
+ 2 * w6**2 * x62 * x61 * y62
+ 2 * w7**2 * x72 * x71 * y72
+ 2 * w8**2 * x82 * x81 * y82
+ 2 * w9**2 * x92 * x91 * y92
+ 2 * w10**2 * x10_2 * x10_1 * y10_2
+ 2 * w11**2 * x11_2 * x11_1 * y11_2
+ 2 * w12**2 * x12_2 * x12_1 * y12_2
+ 2 * w13**2 * x13_2 * x13_1 * y13_2
+ 2 * w14**2 * x14_2 * x14_1 * y14_2
+ 2 * w15**2 * x15_2 * x15_1 * y15_2
)
J_F[:, 3, 3] = (
-2
* (-F12 * F33 + F13 * F32)
* (
w1**2 * x11 * y12
+ w2**2 * x21 * y22
+ w3**2 * x31 * y32
+ w4**2 * x41 * y42
+ w5**2 * x51 * y52
+ w6**2 * x61 * y62
+ w7**2 * x71 * y72
+ w8**2 * x81 * y82
+ w9**2 * x91 * y92
+ w10**2 * x10_1 * y10_2
+ w11**2 * x11_1 * y11_2
+ w12**2 * x12_1 * y12_2
+ w13**2 * x13_1 * y13_2
+ w14**2 * x14_1 * y14_2
+ w15**2 * x15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F12 * F33 + F13 * F32)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F12
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * y12**2 * x11**2
+ 2 * w2**2 * y22**2 * x21**2
+ 2 * w3**2 * y32**2 * x31**2
+ 2 * w4**2 * y42**2 * x41**2
+ 2 * w5**2 * y52**2 * x51**2
+ 2 * w6**2 * y62**2 * x61**2
+ 2 * w7**2 * y72**2 * x71**2
+ 2 * w8**2 * y82**2 * x81**2
+ 2 * w9**2 * y92**2 * x91**2
+ 2 * w10**2 * y10_2**2 * x10_1**2
+ 2 * w11**2 * y11_2**2 * x11_1**2
+ 2 * w12**2 * y12_2**2 * x12_1**2
+ 2 * w13**2 * y13_2**2 * x13_1**2
+ 2 * w14**2 * y14_2**2 * x14_1**2
+ 2 * w15**2 * y15_2**2 * x15_1**2
)
J_F[:, 4, 3] = (
-2
* (F11 * F33 - F13 * F31)
* (
w1**2 * x11 * y12
+ w2**2 * x21 * y22
+ w3**2 * x31 * y32
+ w4**2 * x41 * y42
+ w5**2 * x51 * y52
+ w6**2 * x61 * y62
+ w7**2 * x71 * y72
+ w8**2 * x81 * y82
+ w9**2 * x91 * y92
+ w10**2 * x10_1 * y10_2
+ w11**2 * x11_1 * y11_2
+ w12**2 * x12_1 * y12_2
+ w13**2 * x13_1 * y13_2
+ w14**2 * x14_1 * y14_2
+ w15**2 * x15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F11 * F33 - F13 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F12
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * y12**2 * x11 * y11
+ 2 * w2**2 * y22**2 * x21 * y21
+ 2 * w3**2 * y32**2 * x31 * y31
+ 2 * w4**2 * y42**2 * x41 * y41
+ 2 * w5**2 * y52**2 * x51 * y51
+ 2 * w6**2 * y62**2 * x61 * y61
+ 2 * w7**2 * y72**2 * x71 * y71
+ 2 * w8**2 * y82**2 * x81 * y81
+ 2 * w9**2 * y92**2 * x91 * y91
+ 2 * w10**2 * y10_2**2 * x10_1 * y10_1
+ 2 * w11**2 * y11_2**2 * x11_1 * y11_1
+ 2 * w12**2 * y12_2**2 * x12_1 * y12_1
+ 2 * w13**2 * y13_2**2 * x13_1 * y13_1
+ 2 * w14**2 * y14_2**2 * x14_1 * y14_1
+ 2 * w15**2 * y15_2**2 * x15_1 * y15_1
)
J_F[:, 5, 3] = (
-2
* (-F11 * F32 + F12 * F31)
* (
w1**2 * x11 * y12
+ w2**2 * x21 * y22
+ w3**2 * x31 * y32
+ w4**2 * x41 * y42
+ w5**2 * x51 * y52
+ w6**2 * x61 * y62
+ w7**2 * x71 * y72
+ w8**2 * x81 * y82
+ w9**2 * x91 * y92
+ w10**2 * x10_1 * y10_2
+ w11**2 * x11_1 * y11_2
+ w12**2 * x12_1 * y12_2
+ w13**2 * x13_1 * y13_2
+ w14**2 * x14_1 * y14_2
+ w15**2 * x15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F11 * F32 + F12 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F12
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * y12**2 * x11
+ 2 * w2**2 * y22**2 * x21
+ 2 * w3**2 * y32**2 * x31
+ 2 * w4**2 * y42**2 * x41
+ 2 * w5**2 * y52**2 * x51
+ 2 * w6**2 * y62**2 * x61
+ 2 * w7**2 * y72**2 * x71
+ 2 * w8**2 * y82**2 * x81
+ 2 * w9**2 * y92**2 * x91
+ 2 * w10**2 * y10_2**2 * x10_1
+ 2 * w11**2 * y11_2**2 * x11_1
+ 2 * w12**2 * y12_2**2 * x12_1
+ 2 * w13**2 * y13_2**2 * x13_1
+ 2 * w14**2 * y14_2**2 * x14_1
+ 2 * w15**2 * y15_2**2 * x15_1
)
J_F[:, 6, 3] = (
-2
* (F12 * F23 - F13 * F22)
* (
w1**2 * x11 * y12
+ w2**2 * x21 * y22
+ w3**2 * x31 * y32
+ w4**2 * x41 * y42
+ w5**2 * x51 * y52
+ w6**2 * x61 * y62
+ w7**2 * x71 * y72
+ w8**2 * x81 * y82
+ w9**2 * x91 * y92
+ w10**2 * x10_1 * y10_2
+ w11**2 * x11_1 * y11_2
+ w12**2 * x12_1 * y12_2
+ w13**2 * x13_1 * y13_2
+ w14**2 * x14_1 * y14_2
+ w15**2 * x15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F12 * F23 - F13 * F22)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F12
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * y12 * x11**2
+ 2 * w2**2 * y22 * x21**2
+ 2 * w3**2 * y32 * x31**2
+ 2 * w4**2 * y42 * x41**2
+ 2 * w5**2 * y52 * x51**2
+ 2 * w6**2 * y62 * x61**2
+ 2 * w7**2 * y72 * x71**2
+ 2 * w8**2 * y82 * x81**2
+ 2 * w9**2 * y92 * x91**2
+ 2 * w10**2 * y10_2 * x10_1**2
+ 2 * w11**2 * y11_2 * x11_1**2
+ 2 * w12**2 * y12_2 * x12_1**2
+ 2 * w13**2 * y13_2 * x13_1**2
+ 2 * w14**2 * y14_2 * x14_1**2
+ 2 * w15**2 * y15_2 * x15_1**2
)
J_F[:, 7, 3] = (
-2
* F13
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F11 * F23 + F13 * F21)
* (
w1**2 * x11 * y12
+ w2**2 * x21 * y22
+ w3**2 * x31 * y32
+ w4**2 * x41 * y42
+ w5**2 * x51 * y52
+ w6**2 * x61 * y62
+ w7**2 * x71 * y72
+ w8**2 * x81 * y82
+ w9**2 * x91 * y92
+ w10**2 * x10_1 * y10_2
+ w11**2 * x11_1 * y11_2
+ w12**2 * x12_1 * y12_2
+ w13**2 * x13_1 * y13_2
+ w14**2 * x14_1 * y14_2
+ w15**2 * x15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F11 * F23 + F13 * F21)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F12
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * y12 * x11 * y11
+ 2 * w2**2 * y22 * x21 * y21
+ 2 * w3**2 * y32 * x31 * y31
+ 2 * w4**2 * y42 * x41 * y41
+ 2 * w5**2 * y52 * x51 * y51
+ 2 * w6**2 * y62 * x61 * y61
+ 2 * w7**2 * y72 * x71 * y71
+ 2 * w8**2 * y82 * x81 * y81
+ 2 * w9**2 * y92 * x91 * y91
+ 2 * w10**2 * y10_2 * x10_1 * y10_1
+ 2 * w11**2 * y11_2 * x11_1 * y11_1
+ 2 * w12**2 * y12_2 * x12_1 * y12_1
+ 2 * w13**2 * y13_2 * x13_1 * y13_1
+ 2 * w14**2 * y14_2 * x14_1 * y14_1
+ 2 * w15**2 * y15_2 * x15_1 * y15_1
)
J_F[:, 8, 3] = 0
# F22
J_F[:, 0, 4] = (
-2
* F33
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F22 * F33 - F23 * F32)
* (
w1**2 * y12 * y11
+ w2**2 * y22 * y21
+ w3**2 * y32 * y31
+ w4**2 * y42 * y41
+ w5**2 * y52 * y51
+ w6**2 * y62 * y61
+ w7**2 * y72 * y71
+ w8**2 * y82 * y81
+ w9**2 * y92 * y91
+ w10**2 * y10_2 * y10_1
+ w11**2 * y11_2 * y11_1
+ w12**2 * y12_2 * y12_1
+ w13**2 * y13_2 * y13_1
+ w14**2 * y14_2 * y14_1
+ w15**2 * y15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
+ 2
* (F22 * F33 - F23 * F32)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F11
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * x11 * y12 * y11
+ 2 * w2**2 * x22 * x21 * y22 * y21
+ 2 * w3**2 * x32 * x31 * y32 * y31
+ 2 * w4**2 * x42 * x41 * y42 * y41
+ 2 * w5**2 * x52 * x51 * y52 * y51
+ 2 * w6**2 * x62 * x61 * y62 * y61
+ 2 * w7**2 * x72 * x71 * y72 * y71
+ 2 * w8**2 * x82 * x81 * y82 * y81
+ 2 * w9**2 * x92 * x91 * y92 * y91
+ 2 * w10**2 * x10_2 * x10_1 * y10_2 * y10_1
+ 2 * w11**2 * x11_2 * x11_1 * y11_2 * y11_1
+ 2 * w12**2 * x12_2 * x12_1 * y12_2 * y12_1
+ 2 * w13**2 * x13_2 * x13_1 * y13_2 * y13_1
+ 2 * w14**2 * x14_2 * x14_1 * y14_2 * y14_1
+ 2 * w15**2 * x15_2 * x15_1 * y15_2 * y15_1
)
J_F[:, 1, 4] = (
-2
* (-F21 * F33 + F23 * F31)
* (
w1**2 * y12 * y11
+ w2**2 * y22 * y21
+ w3**2 * y32 * y31
+ w4**2 * y42 * y41
+ w5**2 * y52 * y51
+ w6**2 * y62 * y61
+ w7**2 * y72 * y71
+ w8**2 * y82 * y81
+ w9**2 * y92 * y91
+ w10**2 * y10_2 * y10_1
+ w11**2 * y11_2 * y11_1
+ w12**2 * y12_2 * y12_1
+ w13**2 * y13_2 * y13_1
+ w14**2 * y14_2 * y14_1
+ w15**2 * y15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
+ 2
* (-F21 * F33 + F23 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F11
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * y11**2 * y12
+ 2 * w2**2 * x22 * y21**2 * y22
+ 2 * w3**2 * x32 * y31**2 * y32
+ 2 * w4**2 * x42 * y41**2 * y42
+ 2 * w5**2 * x52 * y51**2 * y52
+ 2 * w6**2 * x62 * y61**2 * y62
+ 2 * w7**2 * x72 * y71**2 * y72
+ 2 * w8**2 * x82 * y81**2 * y82
+ 2 * w9**2 * x92 * y91**2 * y92
+ 2 * w10**2 * x10_2 * y10_1**2 * y10_2
+ 2 * w11**2 * x11_2 * y11_1**2 * y11_2
+ 2 * w12**2 * x12_2 * y12_1**2 * y12_2
+ 2 * w13**2 * x13_2 * y13_1**2 * y13_2
+ 2 * w14**2 * x14_2 * y14_1**2 * y14_2
+ 2 * w15**2 * x15_2 * y15_1**2 * y15_2
)
J_F[:, 2, 4] = (
2
* F31
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F21 * F32 - F22 * F31)
* (
w1**2 * y12 * y11
+ w2**2 * y22 * y21
+ w3**2 * y32 * y31
+ w4**2 * y42 * y41
+ w5**2 * y52 * y51
+ w6**2 * y62 * y61
+ w7**2 * y72 * y71
+ w8**2 * y82 * y81
+ w9**2 * y92 * y91
+ w10**2 * y10_2 * y10_1
+ w11**2 * y11_2 * y11_1
+ w12**2 * y12_2 * y12_1
+ w13**2 * y13_2 * y13_1
+ w14**2 * y14_2 * y14_1
+ w15**2 * y15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
+ 2
* (F21 * F32 - F22 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F11
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * x12 * y11 * y12
+ 2 * w2**2 * x22 * y21 * y22
+ 2 * w3**2 * x32 * y31 * y32
+ 2 * w4**2 * x42 * y41 * y42
+ 2 * w5**2 * x52 * y51 * y52
+ 2 * w6**2 * x62 * y61 * y62
+ 2 * w7**2 * x72 * y71 * y72
+ 2 * w8**2 * x82 * y81 * y82
+ 2 * w9**2 * x92 * y91 * y92
+ 2 * w10**2 * x10_2 * y10_1 * y10_2
+ 2 * w11**2 * x11_2 * y11_1 * y11_2
+ 2 * w12**2 * x12_2 * y12_1 * y12_2
+ 2 * w13**2 * x13_2 * y13_1 * y13_2
+ 2 * w14**2 * x14_2 * y14_1 * y14_2
+ 2 * w15**2 * x15_2 * y15_1 * y15_2
)
J_F[:, 3, 4] = (
-2
* (-F12 * F33 + F13 * F32)
* (
w1**2 * y12 * y11
+ w2**2 * y22 * y21
+ w3**2 * y32 * y31
+ w4**2 * y42 * y41
+ w5**2 * y52 * y51
+ w6**2 * y62 * y61
+ w7**2 * y72 * y71
+ w8**2 * y82 * y81
+ w9**2 * y92 * y91
+ w10**2 * y10_2 * y10_1
+ w11**2 * y11_2 * y11_1
+ w12**2 * y12_2 * y12_1
+ w13**2 * y13_2 * y13_1
+ w14**2 * y14_2 * y14_1
+ w15**2 * y15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
+ 2
* (-F12 * F33 + F13 * F32)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F11
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * y12**2 * x11 * y11
+ 2 * w2**2 * y22**2 * x21 * y21
+ 2 * w3**2 * y32**2 * x31 * y31
+ 2 * w4**2 * y42**2 * x41 * y41
+ 2 * w5**2 * y52**2 * x51 * y51
+ 2 * w6**2 * y62**2 * x61 * y61
+ 2 * w7**2 * y72**2 * x71 * y71
+ 2 * w8**2 * y82**2 * x81 * y81
+ 2 * w9**2 * y92**2 * x91 * y91
+ 2 * w10**2 * y10_2**2 * x10_1 * y10_1
+ 2 * w11**2 * y11_2**2 * x11_1 * y11_1
+ 2 * w12**2 * y12_2**2 * x12_1 * y12_1
+ 2 * w13**2 * y13_2**2 * x13_1 * y13_1
+ 2 * w14**2 * y14_2**2 * x14_1 * y14_1
+ 2 * w15**2 * y15_2**2 * x15_1 * y15_1
)
J_F[:, 4, 4] = (
-2
* (F11 * F33 - F13 * F31)
* (
w1**2 * y12 * y11
+ w2**2 * y22 * y21
+ w3**2 * y32 * y31
+ w4**2 * y42 * y41
+ w5**2 * y52 * y51
+ w6**2 * y62 * y61
+ w7**2 * y72 * y71
+ w8**2 * y82 * y81
+ w9**2 * y92 * y91
+ w10**2 * y10_2 * y10_1
+ w11**2 * y11_2 * y11_1
+ w12**2 * y12_2 * y12_1
+ w13**2 * y13_2 * y13_1
+ w14**2 * y14_2 * y14_1
+ w15**2 * y15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
+ 2
* (F11 * F33 - F13 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F11
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * y12**2 * y11**2
+ 2 * w2**2 * y22**2 * y21**2
+ 2 * w3**2 * y32**2 * y31**2
+ 2 * w4**2 * y42**2 * y41**2
+ 2 * w5**2 * y52**2 * y51**2
+ 2 * w6**2 * y62**2 * y61**2
+ 2 * w7**2 * y72**2 * y71**2
+ 2 * w8**2 * y82**2 * y81**2
+ 2 * w9**2 * y92**2 * y91**2
+ 2 * w10**2 * y10_2**2 * y10_1**2
+ 2 * w11**2 * y11_2**2 * y11_1**2
+ 2 * w12**2 * y12_2**2 * y12_1**2
+ 2 * w13**2 * y13_2**2 * y13_1**2
+ 2 * w14**2 * y14_2**2 * y14_1**2
+ 2 * w15**2 * y15_2**2 * y15_1**2
)
J_F[:, 5, 4] = (
-2
* (-F11 * F32 + F12 * F31)
* (
w1**2 * y12 * y11
+ w2**2 * y22 * y21
+ w3**2 * y32 * y31
+ w4**2 * y42 * y41
+ w5**2 * y52 * y51
+ w6**2 * y62 * y61
+ w7**2 * y72 * y71
+ w8**2 * y82 * y81
+ w9**2 * y92 * y91
+ w10**2 * y10_2 * y10_1
+ w11**2 * y11_2 * y11_1
+ w12**2 * y12_2 * y12_1
+ w13**2 * y13_2 * y13_1
+ w14**2 * y14_2 * y14_1
+ w15**2 * y15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
+ 2
* (-F11 * F32 + F12 * F31)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F11
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * y12**2 * y11
+ 2 * w2**2 * y22**2 * y21
+ 2 * w3**2 * y32**2 * y31
+ 2 * w4**2 * y42**2 * y41
+ 2 * w5**2 * y52**2 * y51
+ 2 * w6**2 * y62**2 * y61
+ 2 * w7**2 * y72**2 * y71
+ 2 * w8**2 * y82**2 * y81
+ 2 * w9**2 * y92**2 * y91
+ 2 * w10**2 * y10_2**2 * y10_1
+ 2 * w11**2 * y11_2**2 * y11_1
+ 2 * w12**2 * y12_2**2 * y12_1
+ 2 * w13**2 * y13_2**2 * y13_1
+ 2 * w14**2 * y14_2**2 * y14_1
+ 2 * w15**2 * y15_2**2 * y15_1
)
J_F[:, 6, 4] = (
2
* F13
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F12 * F23 - F13 * F22)
* (
w1**2 * y12 * y11
+ w2**2 * y22 * y21
+ w3**2 * y32 * y31
+ w4**2 * y42 * y41
+ w5**2 * y52 * y51
+ w6**2 * y62 * y61
+ w7**2 * y72 * y71
+ w8**2 * y82 * y81
+ w9**2 * y92 * y91
+ w10**2 * y10_2 * y10_1
+ w11**2 * y11_2 * y11_1
+ w12**2 * y12_2 * y12_1
+ w13**2 * y13_2 * y13_1
+ w14**2 * y14_2 * y14_1
+ w15**2 * y15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
+ 2
* (F12 * F23 - F13 * F22)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F11
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * y12 * x11 * y11
+ 2 * w2**2 * y22 * x21 * y21
+ 2 * w3**2 * y32 * x31 * y31
+ 2 * w4**2 * y42 * x41 * y41
+ 2 * w5**2 * y52 * x51 * y51
+ 2 * w6**2 * y62 * x61 * y61
+ 2 * w7**2 * y72 * x71 * y71
+ 2 * w8**2 * y82 * x81 * y81
+ 2 * w9**2 * y92 * x91 * y91
+ 2 * w10**2 * y10_2 * x10_1 * y10_1
+ 2 * w11**2 * y11_2 * x11_1 * y11_1
+ 2 * w12**2 * y12_2 * x12_1 * y12_1
+ 2 * w13**2 * y13_2 * x13_1 * y13_1
+ 2 * w14**2 * y14_2 * x14_1 * y14_1
+ 2 * w15**2 * y15_2 * x15_1 * y15_1
)
J_F[:, 7, 4] = (
-2
* (-F11 * F23 + F13 * F21)
* (
w1**2 * y12 * y11
+ w2**2 * y22 * y21
+ w3**2 * y32 * y31
+ w4**2 * y42 * y41
+ w5**2 * y52 * y51
+ w6**2 * y62 * y61
+ w7**2 * y72 * y71
+ w8**2 * y82 * y81
+ w9**2 * y92 * y91
+ w10**2 * y10_2 * y10_1
+ w11**2 * y11_2 * y11_1
+ w12**2 * y12_2 * y12_1
+ w13**2 * y13_2 * y13_1
+ w14**2 * y14_2 * y14_1
+ w15**2 * y15_2 * y15_1
)
/ (F11 * F22 - F12 * F21)
+ 2
* (-F11 * F23 + F13 * F21)
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
* F11
/ (F11 * F22 - F12 * F21) ** 2
+ 2 * w1**2 * y12 * y11**2
+ 2 * w2**2 * y22 * y21**2
+ 2 * w3**2 * y32 * y31**2
+ 2 * w4**2 * y42 * y41**2
+ 2 * w5**2 * y52 * y51**2
+ 2 * w6**2 * y62 * y61**2
+ 2 * w7**2 * y72 * y71**2
+ 2 * w8**2 * y82 * y81**2
+ 2 * w9**2 * y92 * y91**2
+ 2 * w10**2 * y10_2 * y10_1**2
+ 2 * w11**2 * y11_2 * y11_1**2
+ 2 * w12**2 * y12_2 * y12_1**2
+ 2 * w13**2 * y13_2 * y13_1**2
+ 2 * w14**2 * y14_2 * y14_1**2
+ 2 * w15**2 * y15_2 * y15_1**2
)
J_F[:, 8, 4] = 0
# F23
J_F[:, 0, 5] = (
2
* F32
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F22 * F33 - F23 * F32)
* (
w1**2 * y12
+ w10**2 * y10_2
+ w11**2 * y11_2
+ w12**2 * y12_2
+ w13**2 * y13_2
+ w14**2 * y14_2
+ w15**2 * y15_2
+ w2**2 * y22
+ w3**2 * y32
+ w4**2 * y42
+ w5**2 * y52
+ w6**2 * y62
+ w7**2 * y72
+ w8**2 * y82
+ w9**2 * y92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * x11 * y12
+ 2 * w2**2 * x22 * x21 * y22
+ 2 * w3**2 * x32 * x31 * y32
+ 2 * w4**2 * x42 * x41 * y42
+ 2 * w5**2 * x52 * x51 * y52
+ 2 * w6**2 * x62 * x61 * y62
+ 2 * w7**2 * x72 * x71 * y72
+ 2 * w8**2 * x82 * x81 * y82
+ 2 * w9**2 * x92 * x91 * y92
+ 2 * w10**2 * x10_2 * x10_1 * y10_2
+ 2 * w11**2 * x11_2 * x11_1 * y11_2
+ 2 * w12**2 * x12_2 * x12_1 * y12_2
+ 2 * w13**2 * x13_2 * x13_1 * y13_2
+ 2 * w14**2 * x14_2 * x14_1 * y14_2
+ 2 * w15**2 * x15_2 * x15_1 * y15_2
)
J_F[:, 1, 5] = (
-2
* F31
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F21 * F33 + F23 * F31)
* (
w1**2 * y12
+ w10**2 * y10_2
+ w11**2 * y11_2
+ w12**2 * y12_2
+ w13**2 * y13_2
+ w14**2 * y14_2
+ w15**2 * y15_2
+ w2**2 * y22
+ w3**2 * y32
+ w4**2 * y42
+ w5**2 * y52
+ w6**2 * y62
+ w7**2 * y72
+ w8**2 * y82
+ w9**2 * y92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * y11 * y12
+ 2 * w2**2 * x22 * y21 * y22
+ 2 * w3**2 * x32 * y31 * y32
+ 2 * w4**2 * x42 * y41 * y42
+ 2 * w5**2 * x52 * y51 * y52
+ 2 * w6**2 * x62 * y61 * y62
+ 2 * w7**2 * x72 * y71 * y72
+ 2 * w8**2 * x82 * y81 * y82
+ 2 * w9**2 * x92 * y91 * y92
+ 2 * w10**2 * x10_2 * y10_1 * y10_2
+ 2 * w11**2 * x11_2 * y11_1 * y11_2
+ 2 * w12**2 * x12_2 * y12_1 * y12_2
+ 2 * w13**2 * x13_2 * y13_1 * y13_2
+ 2 * w14**2 * x14_2 * y14_1 * y14_2
+ 2 * w15**2 * x15_2 * y15_1 * y15_2
)
J_F[:, 2, 5] = (
-2
* (F21 * F32 - F22 * F31)
* (
w1**2 * y12
+ w10**2 * y10_2
+ w11**2 * y11_2
+ w12**2 * y12_2
+ w13**2 * y13_2
+ w14**2 * y14_2
+ w15**2 * y15_2
+ w2**2 * y22
+ w3**2 * y32
+ w4**2 * y42
+ w5**2 * y52
+ w6**2 * y62
+ w7**2 * y72
+ w8**2 * y82
+ w9**2 * y92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * y12
+ 2 * w2**2 * x22 * y22
+ 2 * w3**2 * x32 * y32
+ 2 * w4**2 * x42 * y42
+ 2 * w5**2 * x52 * y52
+ 2 * w6**2 * x62 * y62
+ 2 * w7**2 * x72 * y72
+ 2 * w8**2 * x82 * y82
+ 2 * w9**2 * x92 * y92
+ 2 * w10**2 * x10_2 * y10_2
+ 2 * w11**2 * x11_2 * y11_2
+ 2 * w12**2 * x12_2 * y12_2
+ 2 * w13**2 * x13_2 * y13_2
+ 2 * w14**2 * x14_2 * y14_2
+ 2 * w15**2 * x15_2 * y15_2
)
J_F[:, 3, 5] = (
-2
* (-F12 * F33 + F13 * F32)
* (
w1**2 * y12
+ w10**2 * y10_2
+ w11**2 * y11_2
+ w12**2 * y12_2
+ w13**2 * y13_2
+ w14**2 * y14_2
+ w15**2 * y15_2
+ w2**2 * y22
+ w3**2 * y32
+ w4**2 * y42
+ w5**2 * y52
+ w6**2 * y62
+ w7**2 * y72
+ w8**2 * y82
+ w9**2 * y92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y12**2 * x11
+ 2 * w2**2 * y22**2 * x21
+ 2 * w3**2 * y32**2 * x31
+ 2 * w4**2 * y42**2 * x41
+ 2 * w5**2 * y52**2 * x51
+ 2 * w6**2 * y62**2 * x61
+ 2 * w7**2 * y72**2 * x71
+ 2 * w8**2 * y82**2 * x81
+ 2 * w9**2 * y92**2 * x91
+ 2 * w10**2 * y10_2**2 * x10_1
+ 2 * w11**2 * y11_2**2 * x11_1
+ 2 * w12**2 * y12_2**2 * x12_1
+ 2 * w13**2 * y13_2**2 * x13_1
+ 2 * w14**2 * y14_2**2 * x14_1
+ 2 * w15**2 * y15_2**2 * x15_1
)
J_F[:, 4, 5] = (
-2
* (F11 * F33 - F13 * F31)
* (
w1**2 * y12
+ w10**2 * y10_2
+ w11**2 * y11_2
+ w12**2 * y12_2
+ w13**2 * y13_2
+ w14**2 * y14_2
+ w15**2 * y15_2
+ w2**2 * y22
+ w3**2 * y32
+ w4**2 * y42
+ w5**2 * y52
+ w6**2 * y62
+ w7**2 * y72
+ w8**2 * y82
+ w9**2 * y92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y12**2 * y11
+ 2 * w2**2 * y22**2 * y21
+ 2 * w3**2 * y32**2 * y31
+ 2 * w4**2 * y42**2 * y41
+ 2 * w5**2 * y52**2 * y51
+ 2 * w6**2 * y62**2 * y61
+ 2 * w7**2 * y72**2 * y71
+ 2 * w8**2 * y82**2 * y81
+ 2 * w9**2 * y92**2 * y91
+ 2 * w10**2 * y10_2**2 * y10_1
+ 2 * w11**2 * y11_2**2 * y11_1
+ 2 * w12**2 * y12_2**2 * y12_1
+ 2 * w13**2 * y13_2**2 * y13_1
+ 2 * w14**2 * y14_2**2 * y14_1
+ 2 * w15**2 * y15_2**2 * y15_1
)
J_F[:, 5, 5] = (
-2
* (-F11 * F32 + F12 * F31)
* (
w1**2 * y12
+ w10**2 * y10_2
+ w11**2 * y11_2
+ w12**2 * y12_2
+ w13**2 * y13_2
+ w14**2 * y14_2
+ w15**2 * y15_2
+ w2**2 * y22
+ w3**2 * y32
+ w4**2 * y42
+ w5**2 * y52
+ w6**2 * y62
+ w7**2 * y72
+ w8**2 * y82
+ w9**2 * y92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y12**2
+ 2 * w2**2 * y22**2
+ 2 * w3**2 * y32**2
+ 2 * w4**2 * y42**2
+ 2 * w5**2 * y52**2
+ 2 * w6**2 * y62**2
+ 2 * w7**2 * y72**2
+ 2 * w8**2 * y82**2
+ 2 * w9**2 * y92**2
+ 2 * w10**2 * y10_2**2
+ 2 * w11**2 * y11_2**2
+ 2 * w12**2 * y12_2**2
+ 2 * w13**2 * y13_2**2
+ 2 * w14**2 * y14_2**2
+ 2 * w15**2 * y15_2**2
)
J_F[:, 6, 5] = (
-2
* F12
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F12 * F23 - F13 * F22)
* (
w1**2 * y12
+ w10**2 * y10_2
+ w11**2 * y11_2
+ w12**2 * y12_2
+ w13**2 * y13_2
+ w14**2 * y14_2
+ w15**2 * y15_2
+ w2**2 * y22
+ w3**2 * y32
+ w4**2 * y42
+ w5**2 * y52
+ w6**2 * y62
+ w7**2 * y72
+ w8**2 * y82
+ w9**2 * y92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x11 * y12
+ 2 * w2**2 * x21 * y22
+ 2 * w3**2 * x31 * y32
+ 2 * w4**2 * x41 * y42
+ 2 * w5**2 * x51 * y52
+ 2 * w6**2 * x61 * y62
+ 2 * w7**2 * x71 * y72
+ 2 * w8**2 * x81 * y82
+ 2 * w9**2 * x91 * y92
+ 2 * w10**2 * x10_1 * y10_2
+ 2 * w11**2 * x11_1 * y11_2
+ 2 * w12**2 * x12_1 * y12_2
+ 2 * w13**2 * x13_1 * y13_2
+ 2 * w14**2 * x14_1 * y14_2
+ 2 * w15**2 * x15_1 * y15_2
)
J_F[:, 7, 5] = (
2
* F11
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F11 * F23 + F13 * F21)
* (
w1**2 * y12
+ w10**2 * y10_2
+ w11**2 * y11_2
+ w12**2 * y12_2
+ w13**2 * y13_2
+ w14**2 * y14_2
+ w15**2 * y15_2
+ w2**2 * y22
+ w3**2 * y32
+ w4**2 * y42
+ w5**2 * y52
+ w6**2 * y62
+ w7**2 * y72
+ w8**2 * y82
+ w9**2 * y92
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y12 * y11
+ 2 * w2**2 * y22 * y21
+ 2 * w3**2 * y32 * y31
+ 2 * w4**2 * y42 * y41
+ 2 * w5**2 * y52 * y51
+ 2 * w6**2 * y62 * y61
+ 2 * w7**2 * y72 * y71
+ 2 * w8**2 * y82 * y81
+ 2 * w9**2 * y92 * y91
+ 2 * w10**2 * y10_2 * y10_1
+ 2 * w11**2 * y11_2 * y11_1
+ 2 * w12**2 * y12_2 * y12_1
+ 2 * w13**2 * y13_2 * y13_1
+ 2 * w14**2 * y14_2 * y14_1
+ 2 * w15**2 * y15_2 * y15_1
)
J_F[:, 8, 5] = 0
# F31
J_F[:, 0, 6] = (
-2
* (F22 * F33 - F23 * F32)
* (
w1**2 * x11
+ w10**2 * x10_1
+ w11**2 * x11_1
+ w12**2 * x12_1
+ w13**2 * x13_1
+ w14**2 * x14_1
+ w15**2 * x15_1
+ w2**2 * x21
+ w3**2 * x31
+ w4**2 * x41
+ w5**2 * x51
+ w6**2 * x61
+ w7**2 * x71
+ w8**2 * x81
+ w9**2 * x91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * x11**2
+ 2 * w2**2 * x22 * x21**2
+ 2 * w3**2 * x32 * x31**2
+ 2 * w4**2 * x42 * x41**2
+ 2 * w5**2 * x52 * x51**2
+ 2 * w6**2 * x62 * x61**2
+ 2 * w7**2 * x72 * x71**2
+ 2 * w8**2 * x82 * x81**2
+ 2 * w9**2 * x92 * x91**2
+ 2 * w10**2 * x10_2 * x10_1**2
+ 2 * w11**2 * x11_2 * x11_1**2
+ 2 * w12**2 * x12_2 * x12_1**2
+ 2 * w13**2 * x13_2 * x13_1**2
+ 2 * w14**2 * x14_2 * x14_1**2
+ 2 * w15**2 * x15_2 * x15_1**2
)
J_F[:, 1, 6] = (
-2
* F23
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F21 * F33 + F23 * F31)
* (
w1**2 * x11
+ w10**2 * x10_1
+ w11**2 * x11_1
+ w12**2 * x12_1
+ w13**2 * x13_1
+ w14**2 * x14_1
+ w15**2 * x15_1
+ w2**2 * x21
+ w3**2 * x31
+ w4**2 * x41
+ w5**2 * x51
+ w6**2 * x61
+ w7**2 * x71
+ w8**2 * x81
+ w9**2 * x91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * x11 * y11
+ 2 * w2**2 * x22 * x21 * y21
+ 2 * w3**2 * x32 * x31 * y31
+ 2 * w4**2 * x42 * x41 * y41
+ 2 * w5**2 * x52 * x51 * y51
+ 2 * w6**2 * x62 * x61 * y61
+ 2 * w7**2 * x72 * x71 * y71
+ 2 * w8**2 * x82 * x81 * y81
+ 2 * w9**2 * x92 * x91 * y91
+ 2 * w10**2 * x10_2 * x10_1 * y10_1
+ 2 * w11**2 * x11_2 * x11_1 * y11_1
+ 2 * w12**2 * x12_2 * x12_1 * y12_1
+ 2 * w13**2 * x13_2 * x13_1 * y13_1
+ 2 * w14**2 * x14_2 * x14_1 * y14_1
+ 2 * w15**2 * x15_2 * x15_1 * y15_1
)
J_F[:, 2, 6] = (
2
* F22
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F21 * F32 - F22 * F31)
* (
w1**2 * x11
+ w10**2 * x10_1
+ w11**2 * x11_1
+ w12**2 * x12_1
+ w13**2 * x13_1
+ w14**2 * x14_1
+ w15**2 * x15_1
+ w2**2 * x21
+ w3**2 * x31
+ w4**2 * x41
+ w5**2 * x51
+ w6**2 * x61
+ w7**2 * x71
+ w8**2 * x81
+ w9**2 * x91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x11 * x12
+ 2 * w2**2 * x21 * x22
+ 2 * w3**2 * x31 * x32
+ 2 * w4**2 * x41 * x42
+ 2 * w5**2 * x51 * x52
+ 2 * w6**2 * x61 * x62
+ 2 * w7**2 * x71 * x72
+ 2 * w8**2 * x81 * x82
+ 2 * w9**2 * x91 * x92
+ 2 * w10**2 * x10_1 * x10_2
+ 2 * w11**2 * x11_1 * x11_2
+ 2 * w12**2 * x12_1 * x12_2
+ 2 * w13**2 * x13_1 * x13_2
+ 2 * w14**2 * x14_1 * x14_2
+ 2 * w15**2 * x15_1 * x15_2
)
J_F[:, 3, 6] = (
-2
* (-F12 * F33 + F13 * F32)
* (
w1**2 * x11
+ w10**2 * x10_1
+ w11**2 * x11_1
+ w12**2 * x12_1
+ w13**2 * x13_1
+ w14**2 * x14_1
+ w15**2 * x15_1
+ w2**2 * x21
+ w3**2 * x31
+ w4**2 * x41
+ w5**2 * x51
+ w6**2 * x61
+ w7**2 * x71
+ w8**2 * x81
+ w9**2 * x91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y12 * x11**2
+ 2 * w2**2 * y22 * x21**2
+ 2 * w3**2 * y32 * x31**2
+ 2 * w4**2 * y42 * x41**2
+ 2 * w5**2 * y52 * x51**2
+ 2 * w6**2 * y62 * x61**2
+ 2 * w7**2 * y72 * x71**2
+ 2 * w8**2 * y82 * x81**2
+ 2 * w9**2 * y92 * x91**2
+ 2 * w10**2 * y10_2 * x10_1**2
+ 2 * w11**2 * y11_2 * x11_1**2
+ 2 * w12**2 * y12_2 * x12_1**2
+ 2 * w13**2 * y13_2 * x13_1**2
+ 2 * w14**2 * y14_2 * x14_1**2
+ 2 * w15**2 * y15_2 * x15_1**2
)
J_F[:, 4, 6] = (
2
* F13
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F11 * F33 - F13 * F31)
* (
w1**2 * x11
+ w10**2 * x10_1
+ w11**2 * x11_1
+ w12**2 * x12_1
+ w13**2 * x13_1
+ w14**2 * x14_1
+ w15**2 * x15_1
+ w2**2 * x21
+ w3**2 * x31
+ w4**2 * x41
+ w5**2 * x51
+ w6**2 * x61
+ w7**2 * x71
+ w8**2 * x81
+ w9**2 * x91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y12 * x11 * y11
+ 2 * w2**2 * y22 * x21 * y21
+ 2 * w3**2 * y32 * x31 * y31
+ 2 * w4**2 * y42 * x41 * y41
+ 2 * w5**2 * y52 * x51 * y51
+ 2 * w6**2 * y62 * x61 * y61
+ 2 * w7**2 * y72 * x71 * y71
+ 2 * w8**2 * y82 * x81 * y81
+ 2 * w9**2 * y92 * x91 * y91
+ 2 * w10**2 * y10_2 * x10_1 * y10_1
+ 2 * w11**2 * y11_2 * x11_1 * y11_1
+ 2 * w12**2 * y12_2 * x12_1 * y12_1
+ 2 * w13**2 * y13_2 * x13_1 * y13_1
+ 2 * w14**2 * y14_2 * x14_1 * y14_1
+ 2 * w15**2 * y15_2 * x15_1 * y15_1
)
J_F[:, 5, 6] = (
-2
* F12
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F11 * F32 + F12 * F31)
* (
w1**2 * x11
+ w10**2 * x10_1
+ w11**2 * x11_1
+ w12**2 * x12_1
+ w13**2 * x13_1
+ w14**2 * x14_1
+ w15**2 * x15_1
+ w2**2 * x21
+ w3**2 * x31
+ w4**2 * x41
+ w5**2 * x51
+ w6**2 * x61
+ w7**2 * x71
+ w8**2 * x81
+ w9**2 * x91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x11 * y12
+ 2 * w2**2 * x21 * y22
+ 2 * w3**2 * x31 * y32
+ 2 * w4**2 * x41 * y42
+ 2 * w5**2 * x51 * y52
+ 2 * w6**2 * x61 * y62
+ 2 * w7**2 * x71 * y72
+ 2 * w8**2 * x81 * y82
+ 2 * w9**2 * x91 * y92
+ 2 * w10**2 * x10_1 * y10_2
+ 2 * w11**2 * x11_1 * y11_2
+ 2 * w12**2 * x12_1 * y12_2
+ 2 * w13**2 * x13_1 * y13_2
+ 2 * w14**2 * x14_1 * y14_2
+ 2 * w15**2 * x15_1 * y15_2
)
J_F[:, 6, 6] = (
-2
* (F12 * F23 - F13 * F22)
* (
w1**2 * x11
+ w10**2 * x10_1
+ w11**2 * x11_1
+ w12**2 * x12_1
+ w13**2 * x13_1
+ w14**2 * x14_1
+ w15**2 * x15_1
+ w2**2 * x21
+ w3**2 * x31
+ w4**2 * x41
+ w5**2 * x51
+ w6**2 * x61
+ w7**2 * x71
+ w8**2 * x81
+ w9**2 * x91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x11**2
+ 2 * w2**2 * x21**2
+ 2 * w3**2 * x31**2
+ 2 * w4**2 * x41**2
+ 2 * w5**2 * x51**2
+ 2 * w6**2 * x61**2
+ 2 * w7**2 * x71**2
+ 2 * w8**2 * x81**2
+ 2 * w9**2 * x91**2
+ 2 * w10**2 * x10_1**2
+ 2 * w11**2 * x11_1**2
+ 2 * w12**2 * x12_1**2
+ 2 * w13**2 * x13_1**2
+ 2 * w14**2 * x14_1**2
+ 2 * w15**2 * x15_1**2
)
J_F[:, 7, 6] = (
-2
* (-F11 * F23 + F13 * F21)
* (
w1**2 * x11
+ w10**2 * x10_1
+ w11**2 * x11_1
+ w12**2 * x12_1
+ w13**2 * x13_1
+ w14**2 * x14_1
+ w15**2 * x15_1
+ w2**2 * x21
+ w3**2 * x31
+ w4**2 * x41
+ w5**2 * x51
+ w6**2 * x61
+ w7**2 * x71
+ w8**2 * x81
+ w9**2 * x91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x11 * y11
+ 2 * w2**2 * x21 * y21
+ 2 * w3**2 * x31 * y31
+ 2 * w4**2 * x41 * y41
+ 2 * w5**2 * x51 * y51
+ 2 * w6**2 * x61 * y61
+ 2 * w7**2 * x71 * y71
+ 2 * w8**2 * x81 * y81
+ 2 * w9**2 * x91 * y91
+ 2 * w10**2 * x10_1 * y10_1
+ 2 * w11**2 * x11_1 * y11_1
+ 2 * w12**2 * x12_1 * y12_1
+ 2 * w13**2 * x13_1 * y13_1
+ 2 * w14**2 * x14_1 * y14_1
+ 2 * w15**2 * x15_1 * y15_1
)
J_F[:, 8, 6] = 0
# F32
J_F[:, 0, 7] = (
2
* F23
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F22 * F33 - F23 * F32)
* (
w1**2 * y11
+ w10**2 * y10_1
+ w11**2 * y11_1
+ w12**2 * y12_1
+ w13**2 * y13_1
+ w14**2 * y14_1
+ w15**2 * y15_1
+ w2**2 * y21
+ w3**2 * y31
+ w4**2 * y41
+ w5**2 * y51
+ w6**2 * y61
+ w7**2 * y71
+ w8**2 * y81
+ w9**2 * y91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * x11 * y11
+ 2 * w2**2 * x22 * x21 * y21
+ 2 * w3**2 * x32 * x31 * y31
+ 2 * w4**2 * x42 * x41 * y41
+ 2 * w5**2 * x52 * x51 * y51
+ 2 * w6**2 * x62 * x61 * y61
+ 2 * w7**2 * x72 * x71 * y71
+ 2 * w8**2 * x82 * x81 * y81
+ 2 * w9**2 * x92 * x91 * y91
+ 2 * w10**2 * x10_2 * x10_1 * y10_1
+ 2 * w11**2 * x11_2 * x11_1 * y11_1
+ 2 * w12**2 * x12_2 * x12_1 * y12_1
+ 2 * w13**2 * x13_2 * x13_1 * y13_1
+ 2 * w14**2 * x14_2 * x14_1 * y14_1
+ 2 * w15**2 * x15_2 * x15_1 * y15_1
)
J_F[:, 1, 7] = (
-2
* (-F21 * F33 + F23 * F31)
* (
w1**2 * y11
+ w10**2 * y10_1
+ w11**2 * y11_1
+ w12**2 * y12_1
+ w13**2 * y13_1
+ w14**2 * y14_1
+ w15**2 * y15_1
+ w2**2 * y21
+ w3**2 * y31
+ w4**2 * y41
+ w5**2 * y51
+ w6**2 * y61
+ w7**2 * y71
+ w8**2 * y81
+ w9**2 * y91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * y11**2
+ 2 * w2**2 * x22 * y21**2
+ 2 * w3**2 * x32 * y31**2
+ 2 * w4**2 * x42 * y41**2
+ 2 * w5**2 * x52 * y51**2
+ 2 * w6**2 * x62 * y61**2
+ 2 * w7**2 * x72 * y71**2
+ 2 * w8**2 * x82 * y81**2
+ 2 * w9**2 * x92 * y91**2
+ 2 * w10**2 * x10_2 * y10_1**2
+ 2 * w11**2 * x11_2 * y11_1**2
+ 2 * w12**2 * x12_2 * y12_1**2
+ 2 * w13**2 * x13_2 * y13_1**2
+ 2 * w14**2 * x14_2 * y14_1**2
+ 2 * w15**2 * x15_2 * y15_1**2
)
J_F[:, 2, 7] = (
-2
* F21
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F21 * F32 - F22 * F31)
* (
w1**2 * y11
+ w10**2 * y10_1
+ w11**2 * y11_1
+ w12**2 * y12_1
+ w13**2 * y13_1
+ w14**2 * y14_1
+ w15**2 * y15_1
+ w2**2 * y21
+ w3**2 * y31
+ w4**2 * y41
+ w5**2 * y51
+ w6**2 * y61
+ w7**2 * y71
+ w8**2 * y81
+ w9**2 * y91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * y11
+ 2 * w2**2 * x22 * y21
+ 2 * w3**2 * x32 * y31
+ 2 * w4**2 * x42 * y41
+ 2 * w5**2 * x52 * y51
+ 2 * w6**2 * x62 * y61
+ 2 * w7**2 * x72 * y71
+ 2 * w8**2 * x82 * y81
+ 2 * w9**2 * x92 * y91
+ 2 * w10**2 * x10_2 * y10_1
+ 2 * w11**2 * x11_2 * y11_1
+ 2 * w12**2 * x12_2 * y12_1
+ 2 * w13**2 * x13_2 * y13_1
+ 2 * w14**2 * x14_2 * y14_1
+ 2 * w15**2 * x15_2 * y15_1
)
J_F[:, 3, 7] = (
-2
* F13
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F12 * F33 + F13 * F32)
* (
w1**2 * y11
+ w10**2 * y10_1
+ w11**2 * y11_1
+ w12**2 * y12_1
+ w13**2 * y13_1
+ w14**2 * y14_1
+ w15**2 * y15_1
+ w2**2 * y21
+ w3**2 * y31
+ w4**2 * y41
+ w5**2 * y51
+ w6**2 * y61
+ w7**2 * y71
+ w8**2 * y81
+ w9**2 * y91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y12 * x11 * y11
+ 2 * w2**2 * y22 * x21 * y21
+ 2 * w3**2 * y32 * x31 * y31
+ 2 * w4**2 * y42 * x41 * y41
+ 2 * w5**2 * y52 * x51 * y51
+ 2 * w6**2 * y62 * x61 * y61
+ 2 * w7**2 * y72 * x71 * y71
+ 2 * w8**2 * y82 * x81 * y81
+ 2 * w9**2 * y92 * x91 * y91
+ 2 * w10**2 * y10_2 * x10_1 * y10_1
+ 2 * w11**2 * y11_2 * x11_1 * y11_1
+ 2 * w12**2 * y12_2 * x12_1 * y12_1
+ 2 * w13**2 * y13_2 * x13_1 * y13_1
+ 2 * w14**2 * y14_2 * x14_1 * y14_1
+ 2 * w15**2 * y15_2 * x15_1 * y15_1
)
J_F[:, 4, 7] = (
-2
* (F11 * F33 - F13 * F31)
* (
w1**2 * y11
+ w10**2 * y10_1
+ w11**2 * y11_1
+ w12**2 * y12_1
+ w13**2 * y13_1
+ w14**2 * y14_1
+ w15**2 * y15_1
+ w2**2 * y21
+ w3**2 * y31
+ w4**2 * y41
+ w5**2 * y51
+ w6**2 * y61
+ w7**2 * y71
+ w8**2 * y81
+ w9**2 * y91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y12 * y11**2
+ 2 * w2**2 * y22 * y21**2
+ 2 * w3**2 * y32 * y31**2
+ 2 * w4**2 * y42 * y41**2
+ 2 * w5**2 * y52 * y51**2
+ 2 * w6**2 * y62 * y61**2
+ 2 * w7**2 * y72 * y71**2
+ 2 * w8**2 * y82 * y81**2
+ 2 * w9**2 * y92 * y91**2
+ 2 * w10**2 * y10_2 * y10_1**2
+ 2 * w11**2 * y11_2 * y11_1**2
+ 2 * w12**2 * y12_2 * y12_1**2
+ 2 * w13**2 * y13_2 * y13_1**2
+ 2 * w14**2 * y14_2 * y14_1**2
+ 2 * w15**2 * y15_2 * y15_1**2
)
J_F[:, 5, 7] = (
2
* F11
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F11 * F32 + F12 * F31)
* (
w1**2 * y11
+ w10**2 * y10_1
+ w11**2 * y11_1
+ w12**2 * y12_1
+ w13**2 * y13_1
+ w14**2 * y14_1
+ w15**2 * y15_1
+ w2**2 * y21
+ w3**2 * y31
+ w4**2 * y41
+ w5**2 * y51
+ w6**2 * y61
+ w7**2 * y71
+ w8**2 * y81
+ w9**2 * y91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y12 * y11
+ 2 * w2**2 * y22 * y21
+ 2 * w3**2 * y32 * y31
+ 2 * w4**2 * y42 * y41
+ 2 * w5**2 * y52 * y51
+ 2 * w6**2 * y62 * y61
+ 2 * w7**2 * y72 * y71
+ 2 * w8**2 * y82 * y81
+ 2 * w9**2 * y92 * y91
+ 2 * w10**2 * y10_2 * y10_1
+ 2 * w11**2 * y11_2 * y11_1
+ 2 * w12**2 * y12_2 * y12_1
+ 2 * w13**2 * y13_2 * y13_1
+ 2 * w14**2 * y14_2 * y14_1
+ 2 * w15**2 * y15_2 * y15_1
)
J_F[:, 6, 7] = (
-2
* (F12 * F23 - F13 * F22)
* (
w1**2 * y11
+ w10**2 * y10_1
+ w11**2 * y11_1
+ w12**2 * y12_1
+ w13**2 * y13_1
+ w14**2 * y14_1
+ w15**2 * y15_1
+ w2**2 * y21
+ w3**2 * y31
+ w4**2 * y41
+ w5**2 * y51
+ w6**2 * y61
+ w7**2 * y71
+ w8**2 * y81
+ w9**2 * y91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x11 * y11
+ 2 * w2**2 * x21 * y21
+ 2 * w3**2 * x31 * y31
+ 2 * w4**2 * x41 * y41
+ 2 * w5**2 * x51 * y51
+ 2 * w6**2 * x61 * y61
+ 2 * w7**2 * x71 * y71
+ 2 * w8**2 * x81 * y81
+ 2 * w9**2 * x91 * y91
+ 2 * w10**2 * x10_1 * y10_1
+ 2 * w11**2 * x11_1 * y11_1
+ 2 * w12**2 * x12_1 * y12_1
+ 2 * w13**2 * x13_1 * y13_1
+ 2 * w14**2 * x14_1 * y14_1
+ 2 * w15**2 * x15_1 * y15_1
)
J_F[:, 7, 7] = (
-2
* (-F11 * F23 + F13 * F21)
* (
w1**2 * y11
+ w10**2 * y10_1
+ w11**2 * y11_1
+ w12**2 * y12_1
+ w13**2 * y13_1
+ w14**2 * y14_1
+ w15**2 * y15_1
+ w2**2 * y21
+ w3**2 * y31
+ w4**2 * y41
+ w5**2 * y51
+ w6**2 * y61
+ w7**2 * y71
+ w8**2 * y81
+ w9**2 * y91
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y11**2
+ 2 * w2**2 * y21**2
+ 2 * w3**2 * y31**2
+ 2 * w4**2 * y41**2
+ 2 * w5**2 * y51**2
+ 2 * w6**2 * y61**2
+ 2 * w7**2 * y71**2
+ 2 * w8**2 * y81**2
+ 2 * w9**2 * y91**2
+ 2 * w10**2 * y10_1**2
+ 2 * w11**2 * y11_1**2
+ 2 * w12**2 * y12_1**2
+ 2 * w13**2 * y13_1**2
+ 2 * w14**2 * y14_1**2
+ 2 * w15**2 * y15_1**2
)
J_F[:, 8, 7] = 0
# F33
J_F[:, 0, 8] = (
-2
* F22
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F22 * F33 - F23 * F32)
* (
w1**2
+ w10**2
+ w11**2
+ w12**2
+ w13**2
+ w14**2
+ w15**2
+ w2**2
+ w3**2
+ w4**2
+ w5**2
+ w6**2
+ w7**2
+ w8**2
+ w9**2
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x11 * x12
+ 2 * w2**2 * x21 * x22
+ 2 * w3**2 * x31 * x32
+ 2 * w4**2 * x41 * x42
+ 2 * w5**2 * x51 * x52
+ 2 * w6**2 * x61 * x62
+ 2 * w7**2 * x71 * x72
+ 2 * w8**2 * x81 * x82
+ 2 * w9**2 * x91 * x92
+ 2 * w10**2 * x10_1 * x10_2
+ 2 * w11**2 * x11_1 * x11_2
+ 2 * w12**2 * x12_1 * x12_2
+ 2 * w13**2 * x13_1 * x13_2
+ 2 * w14**2 * x14_1 * x14_2
+ 2 * w15**2 * x15_1 * x15_2
)
J_F[:, 1, 8] = (
2
* F21
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F21 * F33 + F23 * F31)
* (
w1**2
+ w10**2
+ w11**2
+ w12**2
+ w13**2
+ w14**2
+ w15**2
+ w2**2
+ w3**2
+ w4**2
+ w5**2
+ w6**2
+ w7**2
+ w8**2
+ w9**2
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12 * y11
+ 2 * w2**2 * x22 * y21
+ 2 * w3**2 * x32 * y31
+ 2 * w4**2 * x42 * y41
+ 2 * w5**2 * x52 * y51
+ 2 * w6**2 * x62 * y61
+ 2 * w7**2 * x72 * y71
+ 2 * w8**2 * x82 * y81
+ 2 * w9**2 * x92 * y91
+ 2 * w10**2 * x10_2 * y10_1
+ 2 * w11**2 * x11_2 * y11_1
+ 2 * w12**2 * x12_2 * y12_1
+ 2 * w13**2 * x13_2 * y13_1
+ 2 * w14**2 * x14_2 * y14_1
+ 2 * w15**2 * x15_2 * y15_1
)
J_F[:, 2, 8] = (
-2
* (F21 * F32 - F22 * F31)
* (
w1**2
+ w10**2
+ w11**2
+ w12**2
+ w13**2
+ w14**2
+ w15**2
+ w2**2
+ w3**2
+ w4**2
+ w5**2
+ w6**2
+ w7**2
+ w8**2
+ w9**2
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x12
+ 2 * w2**2 * x22
+ 2 * w3**2 * x32
+ 2 * w4**2 * x42
+ 2 * w5**2 * x52
+ 2 * w6**2 * x62
+ 2 * w7**2 * x72
+ 2 * w8**2 * x82
+ 2 * w9**2 * x92
+ 2 * w10**2 * x10_2
+ 2 * w11**2 * x11_2
+ 2 * w12**2 * x12_2
+ 2 * w13**2 * x13_2
+ 2 * w14**2 * x14_2
+ 2 * w15**2 * x15_2
)
J_F[:, 3, 8] = (
2
* F12
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (-F12 * F33 + F13 * F32)
* (
w1**2
+ w10**2
+ w11**2
+ w12**2
+ w13**2
+ w14**2
+ w15**2
+ w2**2
+ w3**2
+ w4**2
+ w5**2
+ w6**2
+ w7**2
+ w8**2
+ w9**2
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x11 * y12
+ 2 * w2**2 * x21 * y22
+ 2 * w3**2 * x31 * y32
+ 2 * w4**2 * x41 * y42
+ 2 * w5**2 * x51 * y52
+ 2 * w6**2 * x61 * y62
+ 2 * w7**2 * x71 * y72
+ 2 * w8**2 * x81 * y82
+ 2 * w9**2 * x91 * y92
+ 2 * w10**2 * x10_1 * y10_2
+ 2 * w11**2 * x11_1 * y11_2
+ 2 * w12**2 * x12_1 * y12_2
+ 2 * w13**2 * x13_1 * y13_2
+ 2 * w14**2 * x14_1 * y14_2
+ 2 * w15**2 * x15_1 * y15_2
)
J_F[:, 4, 8] = (
-2
* F11
* (
F33 * w1**2
+ F33 * w2**2
+ F33 * w3**2
+ F33 * w4**2
+ F33 * w5**2
+ F33 * w6**2
+ F33 * w7**2
+ F33 * w8**2
+ F33 * w9**2
+ F33 * w10**2
+ F33 * w11**2
+ F33 * w12**2
+ F33 * w13**2
+ F33 * w14**2
+ F33 * w15**2
+ F31 * w9**2 * x91
+ F32 * w9**2 * y91
+ F13 * w10**2 * x10_2
+ F23 * w10**2 * y10_2
+ F31 * w10**2 * x10_1
+ F32 * w10**2 * y10_1
+ F13 * w11**2 * x11_2
+ F23 * w11**2 * y11_2
+ F31 * w11**2 * x11_1
+ F32 * w11**2 * y11_1
+ F13 * w12**2 * x12_2
+ F23 * w12**2 * y12_2
+ F31 * w12**2 * x12_1
+ F32 * w12**2 * y12_1
+ F13 * w13**2 * x13_2
+ F23 * w13**2 * y13_2
+ F31 * w13**2 * x13_1
+ F32 * w13**2 * y13_1
+ F13 * w14**2 * x14_2
+ F23 * w14**2 * y14_2
+ F31 * w14**2 * x14_1
+ F32 * w14**2 * y14_1
+ F13 * w15**2 * x15_2
+ F23 * w15**2 * y15_2
+ F31 * w15**2 * x15_1
+ F32 * w15**2 * y15_1
+ F23 * w1**2 * y12
+ F31 * w1**2 * x11
+ F32 * w1**2 * y11
+ F13 * w2**2 * x22
+ F23 * w2**2 * y22
+ F31 * w2**2 * x21
+ F32 * w2**2 * y21
+ F13 * w3**2 * x32
+ F23 * w3**2 * y32
+ F31 * w3**2 * x31
+ F32 * w3**2 * y31
+ F13 * w4**2 * x42
+ F23 * w4**2 * y42
+ F31 * w4**2 * x41
+ F32 * w4**2 * y41
+ F13 * w5**2 * x52
+ F23 * w5**2 * y52
+ F31 * w5**2 * x51
+ F32 * w5**2 * y51
+ F13 * w6**2 * x62
+ F23 * w6**2 * y62
+ F31 * w6**2 * x61
+ F32 * w6**2 * y61
+ F13 * w7**2 * x72
+ F23 * w7**2 * y72
+ F31 * w7**2 * x71
+ F32 * w7**2 * y71
+ F13 * w8**2 * x82
+ F23 * w8**2 * y82
+ F31 * w8**2 * x81
+ F32 * w8**2 * y81
+ F13 * w9**2 * x92
+ F23 * w9**2 * y92
+ F13 * w1**2 * x12
+ F11 * w1**2 * x11 * x12
+ F12 * w1**2 * x12 * y11
+ F21 * w1**2 * x11 * y12
+ F22 * w1**2 * y11 * y12
+ F11 * w2**2 * x21 * x22
+ F12 * w2**2 * x22 * y21
+ F21 * w2**2 * x21 * y22
+ F22 * w2**2 * y21 * y22
+ F11 * w3**2 * x31 * x32
+ F12 * w3**2 * x32 * y31
+ F21 * w3**2 * x31 * y32
+ F22 * w3**2 * y31 * y32
+ F11 * w4**2 * x41 * x42
+ F12 * w4**2 * x42 * y41
+ F21 * w4**2 * x41 * y42
+ F22 * w4**2 * y41 * y42
+ F11 * w5**2 * x51 * x52
+ F12 * w5**2 * x52 * y51
+ F21 * w5**2 * x51 * y52
+ F22 * w5**2 * y51 * y52
+ F11 * w6**2 * x61 * x62
+ F12 * w6**2 * x62 * y61
+ F21 * w6**2 * x61 * y62
+ F22 * w6**2 * y61 * y62
+ F11 * w7**2 * x71 * x72
+ F12 * w7**2 * x72 * y71
+ F21 * w7**2 * x71 * y72
+ F22 * w7**2 * y71 * y72
+ F11 * w8**2 * x81 * x82
+ F12 * w8**2 * x82 * y81
+ F21 * w8**2 * x81 * y82
+ F22 * w8**2 * y81 * y82
+ F11 * w9**2 * x91 * x92
+ F12 * w9**2 * x92 * y91
+ F21 * w9**2 * x91 * y92
+ F22 * w9**2 * y91 * y92
+ F11 * w10**2 * x10_1 * x10_2
+ F12 * w10**2 * x10_2 * y10_1
+ F21 * w10**2 * x10_1 * y10_2
+ F22 * w10**2 * y10_1 * y10_2
+ F11 * w11**2 * x11_1 * x11_2
+ F12 * w11**2 * x11_2 * y11_1
+ F21 * w11**2 * x11_1 * y11_2
+ F22 * w11**2 * y11_1 * y11_2
+ F11 * w12**2 * x12_1 * x12_2
+ F12 * w12**2 * x12_2 * y12_1
+ F21 * w12**2 * x12_1 * y12_2
+ F22 * w12**2 * y12_1 * y12_2
+ F11 * w13**2 * x13_1 * x13_2
+ F12 * w13**2 * x13_2 * y13_1
+ F21 * w13**2 * x13_1 * y13_2
+ F22 * w13**2 * y13_1 * y13_2
+ F11 * w14**2 * x14_1 * x14_2
+ F12 * w14**2 * x14_2 * y14_1
+ F21 * w14**2 * x14_1 * y14_2
+ F22 * w14**2 * y14_1 * y14_2
+ F11 * w15**2 * x15_1 * x15_2
+ F12 * w15**2 * x15_2 * y15_1
+ F21 * w15**2 * x15_1 * y15_2
+ F22 * w15**2 * y15_1 * y15_2
)
/ (F11 * F22 - F12 * F21)
- 2
* (F11 * F33 - F13 * F31)
* (
w1**2
+ w10**2
+ w11**2
+ w12**2
+ w13**2
+ w14**2
+ w15**2
+ w2**2
+ w3**2
+ w4**2
+ w5**2
+ w6**2
+ w7**2
+ w8**2
+ w9**2
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y12 * y11
+ 2 * w2**2 * y22 * y21
+ 2 * w3**2 * y32 * y31
+ 2 * w4**2 * y42 * y41
+ 2 * w5**2 * y52 * y51
+ 2 * w6**2 * y62 * y61
+ 2 * w7**2 * y72 * y71
+ 2 * w8**2 * y82 * y81
+ 2 * w9**2 * y92 * y91
+ 2 * w10**2 * y10_2 * y10_1
+ 2 * w11**2 * y11_2 * y11_1
+ 2 * w12**2 * y12_2 * y12_1
+ 2 * w13**2 * y13_2 * y13_1
+ 2 * w14**2 * y14_2 * y14_1
+ 2 * w15**2 * y15_2 * y15_1
)
J_F[:, 5, 8] = (
-2
* (-F11 * F32 + F12 * F31)
* (
w1**2
+ w10**2
+ w11**2
+ w12**2
+ w13**2
+ w14**2
+ w15**2
+ w2**2
+ w3**2
+ w4**2
+ w5**2
+ w6**2
+ w7**2
+ w8**2
+ w9**2
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y12
+ 2 * w2**2 * y22
+ 2 * w3**2 * y32
+ 2 * w4**2 * y42
+ 2 * w5**2 * y52
+ 2 * w6**2 * y62
+ 2 * w7**2 * y72
+ 2 * w8**2 * y82
+ 2 * w9**2 * y92
+ 2 * w10**2 * y10_2
+ 2 * w11**2 * y11_2
+ 2 * w12**2 * y12_2
+ 2 * w13**2 * y13_2
+ 2 * w14**2 * y14_2
+ 2 * w15**2 * y15_2
)
J_F[:, 6, 8] = (
-2
* (F12 * F23 - F13 * F22)
* (
w1**2
+ w10**2
+ w11**2
+ w12**2
+ w13**2
+ w14**2
+ w15**2
+ w2**2
+ w3**2
+ w4**2
+ w5**2
+ w6**2
+ w7**2
+ w8**2
+ w9**2
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * x11
+ 2 * w2**2 * x21
+ 2 * w3**2 * x31
+ 2 * w4**2 * x41
+ 2 * w5**2 * x51
+ 2 * w6**2 * x61
+ 2 * w7**2 * x71
+ 2 * w8**2 * x81
+ 2 * w9**2 * x91
+ 2 * w10**2 * x10_1
+ 2 * w11**2 * x11_1
+ 2 * w12**2 * x12_1
+ 2 * w13**2 * x13_1
+ 2 * w14**2 * x14_1
+ 2 * w15**2 * x15_1
)
J_F[:, 7, 8] = (
-2
* (-F11 * F23 + F13 * F21)
* (
w1**2
+ w10**2
+ w11**2
+ w12**2
+ w13**2
+ w14**2
+ w15**2
+ w2**2
+ w3**2
+ w4**2
+ w5**2
+ w6**2
+ w7**2
+ w8**2
+ w9**2
)
/ (F11 * F22 - F12 * F21)
+ 2 * w1**2 * y11
+ 2 * w2**2 * y21
+ 2 * w3**2 * y31
+ 2 * w4**2 * y41
+ 2 * w5**2 * y51
+ 2 * w6**2 * y61
+ 2 * w7**2 * y71
+ 2 * w8**2 * y81
+ 2 * w9**2 * y91
+ 2 * w10**2 * y10_1
+ 2 * w11**2 * y11_1
+ 2 * w12**2 * y12_1
+ 2 * w13**2 * y13_1
+ 2 * w14**2 * y14_1
+ 2 * w15**2 * y15_1
)
J_F[:, 8, 8] = 0
J_w = torch.zeros((b, 9, 15), device=F.device)
J_w[:, 0, 0] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w1 * x11 * x12
+ 2 * F12 * w1 * x12 * y11
+ 2 * F21 * w1 * x11 * y12
+ 2 * F22 * w1 * y11 * y12
+ 2 * F13 * w1 * x12
+ 2 * F23 * w1 * y12
+ 2 * F31 * w1 * x11
+ 2 * F32 * w1 * y11
+ 2 * F33 * w1
)
/ (F11 * F22 - F12 * F21)
+ 4
* w1
* (
(F11 * x12 + F21 * y12 + F31) * x11
+ (F12 * x12 + F22 * y12 + F32) * y11
+ x12 * F13
+ y12 * F23
+ F33
)
* x12
* x11
)
J_w[:, 1, 0] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w1 * x11 * x12
+ 2 * F12 * w1 * x12 * y11
+ 2 * F21 * w1 * x11 * y12
+ 2 * F22 * w1 * y11 * y12
+ 2 * F13 * w1 * x12
+ 2 * F23 * w1 * y12
+ 2 * F31 * w1 * x11
+ 2 * F32 * w1 * y11
+ 2 * F33 * w1
)
/ (F11 * F22 - F12 * F21)
+ 4
* w1
* (
(F11 * x12 + F21 * y12 + F31) * x11
+ (F12 * x12 + F22 * y12 + F32) * y11
+ x12 * F13
+ y12 * F23
+ F33
)
* x12
* y11
)
J_w[:, 2, 0] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w1 * x11 * x12
+ 2 * F12 * w1 * x12 * y11
+ 2 * F21 * w1 * x11 * y12
+ 2 * F22 * w1 * y11 * y12
+ 2 * F13 * w1 * x12
+ 2 * F23 * w1 * y12
+ 2 * F31 * w1 * x11
+ 2 * F32 * w1 * y11
+ 2 * F33 * w1
)
/ (F11 * F22 - F12 * F21)
+ 4
* w1
* (
(F11 * x12 + F21 * y12 + F31) * x11
+ (F12 * x12 + F22 * y12 + F32) * y11
+ x12 * F13
+ y12 * F23
+ F33
)
* x12
)
J_w[:, 3, 0] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w1 * x11 * x12
+ 2 * F12 * w1 * x12 * y11
+ 2 * F21 * w1 * x11 * y12
+ 2 * F22 * w1 * y11 * y12
+ 2 * F13 * w1 * x12
+ 2 * F23 * w1 * y12
+ 2 * F31 * w1 * x11
+ 2 * F32 * w1 * y11
+ 2 * F33 * w1
)
/ (F11 * F22 - F12 * F21)
+ 4
* w1
* (
(F11 * x12 + F21 * y12 + F31) * x11
+ (F12 * x12 + F22 * y12 + F32) * y11
+ x12 * F13
+ y12 * F23
+ F33
)
* y12
* x11
)
J_w[:, 4, 0] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w1 * x11 * x12
+ 2 * F12 * w1 * x12 * y11
+ 2 * F21 * w1 * x11 * y12
+ 2 * F22 * w1 * y11 * y12
+ 2 * F13 * w1 * x12
+ 2 * F23 * w1 * y12
+ 2 * F31 * w1 * x11
+ 2 * F32 * w1 * y11
+ 2 * F33 * w1
)
/ (F11 * F22 - F12 * F21)
+ 4
* w1
* (
(F11 * x12 + F21 * y12 + F31) * x11
+ (F12 * x12 + F22 * y12 + F32) * y11
+ x12 * F13
+ y12 * F23
+ F33
)
* y12
* y11
)
J_w[:, 5, 0] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w1 * x11 * x12
+ 2 * F12 * w1 * x12 * y11
+ 2 * F21 * w1 * x11 * y12
+ 2 * F22 * w1 * y11 * y12
+ 2 * F13 * w1 * x12
+ 2 * F23 * w1 * y12
+ 2 * F31 * w1 * x11
+ 2 * F32 * w1 * y11
+ 2 * F33 * w1
)
/ (F11 * F22 - F12 * F21)
+ 4
* w1
* (
(F11 * x12 + F21 * y12 + F31) * x11
+ (F12 * x12 + F22 * y12 + F32) * y11
+ x12 * F13
+ y12 * F23
+ F33
)
* y12
)
J_w[:, 6, 0] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w1 * x11 * x12
+ 2 * F12 * w1 * x12 * y11
+ 2 * F21 * w1 * x11 * y12
+ 2 * F22 * w1 * y11 * y12
+ 2 * F13 * w1 * x12
+ 2 * F23 * w1 * y12
+ 2 * F31 * w1 * x11
+ 2 * F32 * w1 * y11
+ 2 * F33 * w1
)
/ (F11 * F22 - F12 * F21)
+ 4
* w1
* (
(F11 * x12 + F21 * y12 + F31) * x11
+ (F12 * x12 + F22 * y12 + F32) * y11
+ x12 * F13
+ y12 * F23
+ F33
)
* x11
)
J_w[:, 7, 0] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w1 * x11 * x12
+ 2 * F12 * w1 * x12 * y11
+ 2 * F21 * w1 * x11 * y12
+ 2 * F22 * w1 * y11 * y12
+ 2 * F13 * w1 * x12
+ 2 * F23 * w1 * y12
+ 2 * F31 * w1 * x11
+ 2 * F32 * w1 * y11
+ 2 * F33 * w1
)
/ (F11 * F22 - F12 * F21)
+ 4
* w1
* (
(F11 * x12 + F21 * y12 + F31) * x11
+ (F12 * x12 + F22 * y12 + F32) * y11
+ x12 * F13
+ y12 * F23
+ F33
)
* y11
)
J_w[:, 8, 0] = (
4
* w1
* (
(F11 * x12 + F21 * y12 + F31) * x11
+ (F12 * x12 + F22 * y12 + F32) * y11
+ x12 * F13
+ y12 * F23
+ F33
)
- 4 * F33 * w1
- 4 * F23 * w1 * y12
- 4 * F31 * w1 * x11
- 4 * F32 * w1 * y11
- 4 * F13 * w1 * x12
- 4 * F11 * w1 * x11 * x12
- 4 * F12 * w1 * x12 * y11
- 4 * F21 * w1 * x11 * y12
- 4 * F22 * w1 * y11 * y12
)
J_w[:, 0, 1] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w2 * x21 * x22
+ 2 * F12 * w2 * x22 * y21
+ 2 * F21 * w2 * x21 * y22
+ 2 * F22 * w2 * y21 * y22
+ 2 * F13 * w2 * x22
+ 2 * F23 * w2 * y22
+ 2 * F31 * w2 * x21
+ 2 * F32 * w2 * y21
+ 2 * F33 * w2
)
/ (F11 * F22 - F12 * F21)
+ 4
* w2
* (
(F11 * x22 + F21 * y22 + F31) * x21
+ (F12 * x22 + F22 * y22 + F32) * y21
+ x22 * F13
+ y22 * F23
+ F33
)
* x22
* x21
)
J_w[:, 1, 1] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w2 * x21 * x22
+ 2 * F12 * w2 * x22 * y21
+ 2 * F21 * w2 * x21 * y22
+ 2 * F22 * w2 * y21 * y22
+ 2 * F13 * w2 * x22
+ 2 * F23 * w2 * y22
+ 2 * F31 * w2 * x21
+ 2 * F32 * w2 * y21
+ 2 * F33 * w2
)
/ (F11 * F22 - F12 * F21)
+ 4
* w2
* (
(F11 * x22 + F21 * y22 + F31) * x21
+ (F12 * x22 + F22 * y22 + F32) * y21
+ x22 * F13
+ y22 * F23
+ F33
)
* x22
* y21
)
J_w[:, 2, 1] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w2 * x21 * x22
+ 2 * F12 * w2 * x22 * y21
+ 2 * F21 * w2 * x21 * y22
+ 2 * F22 * w2 * y21 * y22
+ 2 * F13 * w2 * x22
+ 2 * F23 * w2 * y22
+ 2 * F31 * w2 * x21
+ 2 * F32 * w2 * y21
+ 2 * F33 * w2
)
/ (F11 * F22 - F12 * F21)
+ 4
* w2
* (
(F11 * x22 + F21 * y22 + F31) * x21
+ (F12 * x22 + F22 * y22 + F32) * y21
+ x22 * F13
+ y22 * F23
+ F33
)
* x22
)
J_w[:, 3, 1] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w2 * x21 * x22
+ 2 * F12 * w2 * x22 * y21
+ 2 * F21 * w2 * x21 * y22
+ 2 * F22 * w2 * y21 * y22
+ 2 * F13 * w2 * x22
+ 2 * F23 * w2 * y22
+ 2 * F31 * w2 * x21
+ 2 * F32 * w2 * y21
+ 2 * F33 * w2
)
/ (F11 * F22 - F12 * F21)
+ 4
* w2
* (
(F11 * x22 + F21 * y22 + F31) * x21
+ (F12 * x22 + F22 * y22 + F32) * y21
+ x22 * F13
+ y22 * F23
+ F33
)
* y22
* x21
)
J_w[:, 4, 1] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w2 * x21 * x22
+ 2 * F12 * w2 * x22 * y21
+ 2 * F21 * w2 * x21 * y22
+ 2 * F22 * w2 * y21 * y22
+ 2 * F13 * w2 * x22
+ 2 * F23 * w2 * y22
+ 2 * F31 * w2 * x21
+ 2 * F32 * w2 * y21
+ 2 * F33 * w2
)
/ (F11 * F22 - F12 * F21)
+ 4
* w2
* (
(F11 * x22 + F21 * y22 + F31) * x21
+ (F12 * x22 + F22 * y22 + F32) * y21
+ x22 * F13
+ y22 * F23
+ F33
)
* y22
* y21
)
J_w[:, 5, 1] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w2 * x21 * x22
+ 2 * F12 * w2 * x22 * y21
+ 2 * F21 * w2 * x21 * y22
+ 2 * F22 * w2 * y21 * y22
+ 2 * F13 * w2 * x22
+ 2 * F23 * w2 * y22
+ 2 * F31 * w2 * x21
+ 2 * F32 * w2 * y21
+ 2 * F33 * w2
)
/ (F11 * F22 - F12 * F21)
+ 4
* w2
* (
(F11 * x22 + F21 * y22 + F31) * x21
+ (F12 * x22 + F22 * y22 + F32) * y21
+ x22 * F13
+ y22 * F23
+ F33
)
* y22
)
J_w[:, 6, 1] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w2 * x21 * x22
+ 2 * F12 * w2 * x22 * y21
+ 2 * F21 * w2 * x21 * y22
+ 2 * F22 * w2 * y21 * y22
+ 2 * F13 * w2 * x22
+ 2 * F23 * w2 * y22
+ 2 * F31 * w2 * x21
+ 2 * F32 * w2 * y21
+ 2 * F33 * w2
)
/ (F11 * F22 - F12 * F21)
+ 4
* w2
* (
(F11 * x22 + F21 * y22 + F31) * x21
+ (F12 * x22 + F22 * y22 + F32) * y21
+ x22 * F13
+ y22 * F23
+ F33
)
* x21
)
J_w[:, 7, 1] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w2 * x21 * x22
+ 2 * F12 * w2 * x22 * y21
+ 2 * F21 * w2 * x21 * y22
+ 2 * F22 * w2 * y21 * y22
+ 2 * F13 * w2 * x22
+ 2 * F23 * w2 * y22
+ 2 * F31 * w2 * x21
+ 2 * F32 * w2 * y21
+ 2 * F33 * w2
)
/ (F11 * F22 - F12 * F21)
+ 4
* w2
* (
(F11 * x22 + F21 * y22 + F31) * x21
+ (F12 * x22 + F22 * y22 + F32) * y21
+ x22 * F13
+ y22 * F23
+ F33
)
* y21
)
J_w[:, 8, 1] = (
4
* w2
* (
(F11 * x22 + F21 * y22 + F31) * x21
+ (F12 * x22 + F22 * y22 + F32) * y21
+ x22 * F13
+ y22 * F23
+ F33
)
- 4 * F33 * w2
- 4 * F13 * w2 * x22
- 4 * F23 * w2 * y22
- 4 * F31 * w2 * x21
- 4 * F32 * w2 * y21
- 4 * F11 * w2 * x21 * x22
- 4 * F12 * w2 * x22 * y21
- 4 * F21 * w2 * x21 * y22
- 4 * F22 * w2 * y21 * y22
)
J_w[:, 0, 2] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w3 * x31 * x32
+ 2 * F12 * w3 * x32 * y31
+ 2 * F21 * w3 * x31 * y32
+ 2 * F22 * w3 * y31 * y32
+ 2 * F13 * w3 * x32
+ 2 * F23 * w3 * y32
+ 2 * F31 * w3 * x31
+ 2 * F32 * w3 * y31
+ 2 * F33 * w3
)
/ (F11 * F22 - F12 * F21)
+ 4
* w3
* (
(F11 * x32 + F21 * y32 + F31) * x31
+ (F12 * x32 + F22 * y32 + F32) * y31
+ x32 * F13
+ y32 * F23
+ F33
)
* x32
* x31
)
J_w[:, 1, 2] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w3 * x31 * x32
+ 2 * F12 * w3 * x32 * y31
+ 2 * F21 * w3 * x31 * y32
+ 2 * F22 * w3 * y31 * y32
+ 2 * F13 * w3 * x32
+ 2 * F23 * w3 * y32
+ 2 * F31 * w3 * x31
+ 2 * F32 * w3 * y31
+ 2 * F33 * w3
)
/ (F11 * F22 - F12 * F21)
+ 4
* w3
* (
(F11 * x32 + F21 * y32 + F31) * x31
+ (F12 * x32 + F22 * y32 + F32) * y31
+ x32 * F13
+ y32 * F23
+ F33
)
* x32
* y31
)
J_w[:, 2, 2] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w3 * x31 * x32
+ 2 * F12 * w3 * x32 * y31
+ 2 * F21 * w3 * x31 * y32
+ 2 * F22 * w3 * y31 * y32
+ 2 * F13 * w3 * x32
+ 2 * F23 * w3 * y32
+ 2 * F31 * w3 * x31
+ 2 * F32 * w3 * y31
+ 2 * F33 * w3
)
/ (F11 * F22 - F12 * F21)
+ 4
* w3
* (
(F11 * x32 + F21 * y32 + F31) * x31
+ (F12 * x32 + F22 * y32 + F32) * y31
+ x32 * F13
+ y32 * F23
+ F33
)
* x32
)
J_w[:, 3, 2] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w3 * x31 * x32
+ 2 * F12 * w3 * x32 * y31
+ 2 * F21 * w3 * x31 * y32
+ 2 * F22 * w3 * y31 * y32
+ 2 * F13 * w3 * x32
+ 2 * F23 * w3 * y32
+ 2 * F31 * w3 * x31
+ 2 * F32 * w3 * y31
+ 2 * F33 * w3
)
/ (F11 * F22 - F12 * F21)
+ 4
* w3
* (
(F11 * x32 + F21 * y32 + F31) * x31
+ (F12 * x32 + F22 * y32 + F32) * y31
+ x32 * F13
+ y32 * F23
+ F33
)
* y32
* x31
)
J_w[:, 4, 2] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w3 * x31 * x32
+ 2 * F12 * w3 * x32 * y31
+ 2 * F21 * w3 * x31 * y32
+ 2 * F22 * w3 * y31 * y32
+ 2 * F13 * w3 * x32
+ 2 * F23 * w3 * y32
+ 2 * F31 * w3 * x31
+ 2 * F32 * w3 * y31
+ 2 * F33 * w3
)
/ (F11 * F22 - F12 * F21)
+ 4
* w3
* (
(F11 * x32 + F21 * y32 + F31) * x31
+ (F12 * x32 + F22 * y32 + F32) * y31
+ x32 * F13
+ y32 * F23
+ F33
)
* y32
* y31
)
J_w[:, 5, 2] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w3 * x31 * x32
+ 2 * F12 * w3 * x32 * y31
+ 2 * F21 * w3 * x31 * y32
+ 2 * F22 * w3 * y31 * y32
+ 2 * F13 * w3 * x32
+ 2 * F23 * w3 * y32
+ 2 * F31 * w3 * x31
+ 2 * F32 * w3 * y31
+ 2 * F33 * w3
)
/ (F11 * F22 - F12 * F21)
+ 4
* w3
* (
(F11 * x32 + F21 * y32 + F31) * x31
+ (F12 * x32 + F22 * y32 + F32) * y31
+ x32 * F13
+ y32 * F23
+ F33
)
* y32
)
J_w[:, 6, 2] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w3 * x31 * x32
+ 2 * F12 * w3 * x32 * y31
+ 2 * F21 * w3 * x31 * y32
+ 2 * F22 * w3 * y31 * y32
+ 2 * F13 * w3 * x32
+ 2 * F23 * w3 * y32
+ 2 * F31 * w3 * x31
+ 2 * F32 * w3 * y31
+ 2 * F33 * w3
)
/ (F11 * F22 - F12 * F21)
+ 4
* w3
* (
(F11 * x32 + F21 * y32 + F31) * x31
+ (F12 * x32 + F22 * y32 + F32) * y31
+ x32 * F13
+ y32 * F23
+ F33
)
* x31
)
J_w[:, 7, 2] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w3 * x31 * x32
+ 2 * F12 * w3 * x32 * y31
+ 2 * F21 * w3 * x31 * y32
+ 2 * F22 * w3 * y31 * y32
+ 2 * F13 * w3 * x32
+ 2 * F23 * w3 * y32
+ 2 * F31 * w3 * x31
+ 2 * F32 * w3 * y31
+ 2 * F33 * w3
)
/ (F11 * F22 - F12 * F21)
+ 4
* w3
* (
(F11 * x32 + F21 * y32 + F31) * x31
+ (F12 * x32 + F22 * y32 + F32) * y31
+ x32 * F13
+ y32 * F23
+ F33
)
* y31
)
J_w[:, 8, 2] = (
4
* w3
* (
(F11 * x32 + F21 * y32 + F31) * x31
+ (F12 * x32 + F22 * y32 + F32) * y31
+ x32 * F13
+ y32 * F23
+ F33
)
- 4 * F33 * w3
- 4 * F13 * w3 * x32
- 4 * F23 * w3 * y32
- 4 * F31 * w3 * x31
- 4 * F32 * w3 * y31
- 4 * F11 * w3 * x31 * x32
- 4 * F12 * w3 * x32 * y31
- 4 * F21 * w3 * x31 * y32
- 4 * F22 * w3 * y31 * y32
)
J_w[:, 0, 3] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w4 * x41 * x42
+ 2 * F12 * w4 * x42 * y41
+ 2 * F21 * w4 * x41 * y42
+ 2 * F22 * w4 * y41 * y42
+ 2 * F13 * w4 * x42
+ 2 * F23 * w4 * y42
+ 2 * F31 * w4 * x41
+ 2 * F32 * w4 * y41
+ 2 * F33 * w4
)
/ (F11 * F22 - F12 * F21)
+ 4
* w4
* (
(F11 * x42 + F21 * y42 + F31) * x41
+ (F12 * x42 + F22 * y42 + F32) * y41
+ x42 * F13
+ y42 * F23
+ F33
)
* x42
* x41
)
J_w[:, 1, 3] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w4 * x41 * x42
+ 2 * F12 * w4 * x42 * y41
+ 2 * F21 * w4 * x41 * y42
+ 2 * F22 * w4 * y41 * y42
+ 2 * F13 * w4 * x42
+ 2 * F23 * w4 * y42
+ 2 * F31 * w4 * x41
+ 2 * F32 * w4 * y41
+ 2 * F33 * w4
)
/ (F11 * F22 - F12 * F21)
+ 4
* w4
* (
(F11 * x42 + F21 * y42 + F31) * x41
+ (F12 * x42 + F22 * y42 + F32) * y41
+ x42 * F13
+ y42 * F23
+ F33
)
* x42
* y41
)
J_w[:, 2, 3] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w4 * x41 * x42
+ 2 * F12 * w4 * x42 * y41
+ 2 * F21 * w4 * x41 * y42
+ 2 * F22 * w4 * y41 * y42
+ 2 * F13 * w4 * x42
+ 2 * F23 * w4 * y42
+ 2 * F31 * w4 * x41
+ 2 * F32 * w4 * y41
+ 2 * F33 * w4
)
/ (F11 * F22 - F12 * F21)
+ 4
* w4
* (
(F11 * x42 + F21 * y42 + F31) * x41
+ (F12 * x42 + F22 * y42 + F32) * y41
+ x42 * F13
+ y42 * F23
+ F33
)
* x42
)
J_w[:, 3, 3] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w4 * x41 * x42
+ 2 * F12 * w4 * x42 * y41
+ 2 * F21 * w4 * x41 * y42
+ 2 * F22 * w4 * y41 * y42
+ 2 * F13 * w4 * x42
+ 2 * F23 * w4 * y42
+ 2 * F31 * w4 * x41
+ 2 * F32 * w4 * y41
+ 2 * F33 * w4
)
/ (F11 * F22 - F12 * F21)
+ 4
* w4
* (
(F11 * x42 + F21 * y42 + F31) * x41
+ (F12 * x42 + F22 * y42 + F32) * y41
+ x42 * F13
+ y42 * F23
+ F33
)
* y42
* x41
)
J_w[:, 4, 3] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w4 * x41 * x42
+ 2 * F12 * w4 * x42 * y41
+ 2 * F21 * w4 * x41 * y42
+ 2 * F22 * w4 * y41 * y42
+ 2 * F13 * w4 * x42
+ 2 * F23 * w4 * y42
+ 2 * F31 * w4 * x41
+ 2 * F32 * w4 * y41
+ 2 * F33 * w4
)
/ (F11 * F22 - F12 * F21)
+ 4
* w4
* (
(F11 * x42 + F21 * y42 + F31) * x41
+ (F12 * x42 + F22 * y42 + F32) * y41
+ x42 * F13
+ y42 * F23
+ F33
)
* y42
* y41
)
J_w[:, 5, 3] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w4 * x41 * x42
+ 2 * F12 * w4 * x42 * y41
+ 2 * F21 * w4 * x41 * y42
+ 2 * F22 * w4 * y41 * y42
+ 2 * F13 * w4 * x42
+ 2 * F23 * w4 * y42
+ 2 * F31 * w4 * x41
+ 2 * F32 * w4 * y41
+ 2 * F33 * w4
)
/ (F11 * F22 - F12 * F21)
+ 4
* w4
* (
(F11 * x42 + F21 * y42 + F31) * x41
+ (F12 * x42 + F22 * y42 + F32) * y41
+ x42 * F13
+ y42 * F23
+ F33
)
* y42
)
J_w[:, 6, 3] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w4 * x41 * x42
+ 2 * F12 * w4 * x42 * y41
+ 2 * F21 * w4 * x41 * y42
+ 2 * F22 * w4 * y41 * y42
+ 2 * F13 * w4 * x42
+ 2 * F23 * w4 * y42
+ 2 * F31 * w4 * x41
+ 2 * F32 * w4 * y41
+ 2 * F33 * w4
)
/ (F11 * F22 - F12 * F21)
+ 4
* w4
* (
(F11 * x42 + F21 * y42 + F31) * x41
+ (F12 * x42 + F22 * y42 + F32) * y41
+ x42 * F13
+ y42 * F23
+ F33
)
* x41
)
J_w[:, 7, 3] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w4 * x41 * x42
+ 2 * F12 * w4 * x42 * y41
+ 2 * F21 * w4 * x41 * y42
+ 2 * F22 * w4 * y41 * y42
+ 2 * F13 * w4 * x42
+ 2 * F23 * w4 * y42
+ 2 * F31 * w4 * x41
+ 2 * F32 * w4 * y41
+ 2 * F33 * w4
)
/ (F11 * F22 - F12 * F21)
+ 4
* w4
* (
(F11 * x42 + F21 * y42 + F31) * x41
+ (F12 * x42 + F22 * y42 + F32) * y41
+ x42 * F13
+ y42 * F23
+ F33
)
* y41
)
J_w[:, 8, 3] = (
4
* w4
* (
(F11 * x42 + F21 * y42 + F31) * x41
+ (F12 * x42 + F22 * y42 + F32) * y41
+ x42 * F13
+ y42 * F23
+ F33
)
- 4 * F33 * w4
- 4 * F13 * w4 * x42
- 4 * F23 * w4 * y42
- 4 * F31 * w4 * x41
- 4 * F32 * w4 * y41
- 4 * F11 * w4 * x41 * x42
- 4 * F12 * w4 * x42 * y41
- 4 * F21 * w4 * x41 * y42
- 4 * F22 * w4 * y41 * y42
)
J_w[:, 0, 4] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w5 * x51 * x52
+ 2 * F12 * w5 * x52 * y51
+ 2 * F21 * w5 * x51 * y52
+ 2 * F22 * w5 * y51 * y52
+ 2 * F13 * w5 * x52
+ 2 * F23 * w5 * y52
+ 2 * F31 * w5 * x51
+ 2 * F32 * w5 * y51
+ 2 * F33 * w5
)
/ (F11 * F22 - F12 * F21)
+ 4
* w5
* (
(F11 * x52 + F21 * y52 + F31) * x51
+ (F12 * x52 + F22 * y52 + F32) * y51
+ x52 * F13
+ y52 * F23
+ F33
)
* x52
* x51
)
J_w[:, 1, 4] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w5 * x51 * x52
+ 2 * F12 * w5 * x52 * y51
+ 2 * F21 * w5 * x51 * y52
+ 2 * F22 * w5 * y51 * y52
+ 2 * F13 * w5 * x52
+ 2 * F23 * w5 * y52
+ 2 * F31 * w5 * x51
+ 2 * F32 * w5 * y51
+ 2 * F33 * w5
)
/ (F11 * F22 - F12 * F21)
+ 4
* w5
* (
(F11 * x52 + F21 * y52 + F31) * x51
+ (F12 * x52 + F22 * y52 + F32) * y51
+ x52 * F13
+ y52 * F23
+ F33
)
* x52
* y51
)
J_w[:, 2, 4] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w5 * x51 * x52
+ 2 * F12 * w5 * x52 * y51
+ 2 * F21 * w5 * x51 * y52
+ 2 * F22 * w5 * y51 * y52
+ 2 * F13 * w5 * x52
+ 2 * F23 * w5 * y52
+ 2 * F31 * w5 * x51
+ 2 * F32 * w5 * y51
+ 2 * F33 * w5
)
/ (F11 * F22 - F12 * F21)
+ 4
* w5
* (
(F11 * x52 + F21 * y52 + F31) * x51
+ (F12 * x52 + F22 * y52 + F32) * y51
+ x52 * F13
+ y52 * F23
+ F33
)
* x52
)
J_w[:, 3, 4] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w5 * x51 * x52
+ 2 * F12 * w5 * x52 * y51
+ 2 * F21 * w5 * x51 * y52
+ 2 * F22 * w5 * y51 * y52
+ 2 * F13 * w5 * x52
+ 2 * F23 * w5 * y52
+ 2 * F31 * w5 * x51
+ 2 * F32 * w5 * y51
+ 2 * F33 * w5
)
/ (F11 * F22 - F12 * F21)
+ 4
* w5
* (
(F11 * x52 + F21 * y52 + F31) * x51
+ (F12 * x52 + F22 * y52 + F32) * y51
+ x52 * F13
+ y52 * F23
+ F33
)
* y52
* x51
)
J_w[:, 4, 4] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w5 * x51 * x52
+ 2 * F12 * w5 * x52 * y51
+ 2 * F21 * w5 * x51 * y52
+ 2 * F22 * w5 * y51 * y52
+ 2 * F13 * w5 * x52
+ 2 * F23 * w5 * y52
+ 2 * F31 * w5 * x51
+ 2 * F32 * w5 * y51
+ 2 * F33 * w5
)
/ (F11 * F22 - F12 * F21)
+ 4
* w5
* (
(F11 * x52 + F21 * y52 + F31) * x51
+ (F12 * x52 + F22 * y52 + F32) * y51
+ x52 * F13
+ y52 * F23
+ F33
)
* y52
* y51
)
J_w[:, 5, 4] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w5 * x51 * x52
+ 2 * F12 * w5 * x52 * y51
+ 2 * F21 * w5 * x51 * y52
+ 2 * F22 * w5 * y51 * y52
+ 2 * F13 * w5 * x52
+ 2 * F23 * w5 * y52
+ 2 * F31 * w5 * x51
+ 2 * F32 * w5 * y51
+ 2 * F33 * w5
)
/ (F11 * F22 - F12 * F21)
+ 4
* w5
* (
(F11 * x52 + F21 * y52 + F31) * x51
+ (F12 * x52 + F22 * y52 + F32) * y51
+ x52 * F13
+ y52 * F23
+ F33
)
* y52
)
J_w[:, 6, 4] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w5 * x51 * x52
+ 2 * F12 * w5 * x52 * y51
+ 2 * F21 * w5 * x51 * y52
+ 2 * F22 * w5 * y51 * y52
+ 2 * F13 * w5 * x52
+ 2 * F23 * w5 * y52
+ 2 * F31 * w5 * x51
+ 2 * F32 * w5 * y51
+ 2 * F33 * w5
)
/ (F11 * F22 - F12 * F21)
+ 4
* w5
* (
(F11 * x52 + F21 * y52 + F31) * x51
+ (F12 * x52 + F22 * y52 + F32) * y51
+ x52 * F13
+ y52 * F23
+ F33
)
* x51
)
J_w[:, 7, 4] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w5 * x51 * x52
+ 2 * F12 * w5 * x52 * y51
+ 2 * F21 * w5 * x51 * y52
+ 2 * F22 * w5 * y51 * y52
+ 2 * F13 * w5 * x52
+ 2 * F23 * w5 * y52
+ 2 * F31 * w5 * x51
+ 2 * F32 * w5 * y51
+ 2 * F33 * w5
)
/ (F11 * F22 - F12 * F21)
+ 4
* w5
* (
(F11 * x52 + F21 * y52 + F31) * x51
+ (F12 * x52 + F22 * y52 + F32) * y51
+ x52 * F13
+ y52 * F23
+ F33
)
* y51
)
J_w[:, 8, 4] = (
4
* w5
* (
(F11 * x52 + F21 * y52 + F31) * x51
+ (F12 * x52 + F22 * y52 + F32) * y51
+ x52 * F13
+ y52 * F23
+ F33
)
- 4 * F33 * w5
- 4 * F13 * w5 * x52
- 4 * F23 * w5 * y52
- 4 * F31 * w5 * x51
- 4 * F32 * w5 * y51
- 4 * F11 * w5 * x51 * x52
- 4 * F12 * w5 * x52 * y51
- 4 * F21 * w5 * x51 * y52
- 4 * F22 * w5 * y51 * y52
)
J_w[:, 0, 5] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w6 * x61 * x62
+ 2 * F12 * w6 * x62 * y61
+ 2 * F21 * w6 * x61 * y62
+ 2 * F22 * w6 * y61 * y62
+ 2 * F13 * w6 * x62
+ 2 * F23 * w6 * y62
+ 2 * F31 * w6 * x61
+ 2 * F32 * w6 * y61
+ 2 * F33 * w6
)
/ (F11 * F22 - F12 * F21)
+ 4
* w6
* (
(F11 * x62 + F21 * y62 + F31) * x61
+ (F12 * x62 + F22 * y62 + F32) * y61
+ x62 * F13
+ y62 * F23
+ F33
)
* x62
* x61
)
J_w[:, 1, 5] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w6 * x61 * x62
+ 2 * F12 * w6 * x62 * y61
+ 2 * F21 * w6 * x61 * y62
+ 2 * F22 * w6 * y61 * y62
+ 2 * F13 * w6 * x62
+ 2 * F23 * w6 * y62
+ 2 * F31 * w6 * x61
+ 2 * F32 * w6 * y61
+ 2 * F33 * w6
)
/ (F11 * F22 - F12 * F21)
+ 4
* w6
* (
(F11 * x62 + F21 * y62 + F31) * x61
+ (F12 * x62 + F22 * y62 + F32) * y61
+ x62 * F13
+ y62 * F23
+ F33
)
* x62
* y61
)
J_w[:, 2, 5] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w6 * x61 * x62
+ 2 * F12 * w6 * x62 * y61
+ 2 * F21 * w6 * x61 * y62
+ 2 * F22 * w6 * y61 * y62
+ 2 * F13 * w6 * x62
+ 2 * F23 * w6 * y62
+ 2 * F31 * w6 * x61
+ 2 * F32 * w6 * y61
+ 2 * F33 * w6
)
/ (F11 * F22 - F12 * F21)
+ 4
* w6
* (
(F11 * x62 + F21 * y62 + F31) * x61
+ (F12 * x62 + F22 * y62 + F32) * y61
+ x62 * F13
+ y62 * F23
+ F33
)
* x62
)
J_w[:, 3, 5] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w6 * x61 * x62
+ 2 * F12 * w6 * x62 * y61
+ 2 * F21 * w6 * x61 * y62
+ 2 * F22 * w6 * y61 * y62
+ 2 * F13 * w6 * x62
+ 2 * F23 * w6 * y62
+ 2 * F31 * w6 * x61
+ 2 * F32 * w6 * y61
+ 2 * F33 * w6
)
/ (F11 * F22 - F12 * F21)
+ 4
* w6
* (
(F11 * x62 + F21 * y62 + F31) * x61
+ (F12 * x62 + F22 * y62 + F32) * y61
+ x62 * F13
+ y62 * F23
+ F33
)
* y62
* x61
)
J_w[:, 4, 5] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w6 * x61 * x62
+ 2 * F12 * w6 * x62 * y61
+ 2 * F21 * w6 * x61 * y62
+ 2 * F22 * w6 * y61 * y62
+ 2 * F13 * w6 * x62
+ 2 * F23 * w6 * y62
+ 2 * F31 * w6 * x61
+ 2 * F32 * w6 * y61
+ 2 * F33 * w6
)
/ (F11 * F22 - F12 * F21)
+ 4
* w6
* (
(F11 * x62 + F21 * y62 + F31) * x61
+ (F12 * x62 + F22 * y62 + F32) * y61
+ x62 * F13
+ y62 * F23
+ F33
)
* y62
* y61
)
J_w[:, 5, 5] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w6 * x61 * x62
+ 2 * F12 * w6 * x62 * y61
+ 2 * F21 * w6 * x61 * y62
+ 2 * F22 * w6 * y61 * y62
+ 2 * F13 * w6 * x62
+ 2 * F23 * w6 * y62
+ 2 * F31 * w6 * x61
+ 2 * F32 * w6 * y61
+ 2 * F33 * w6
)
/ (F11 * F22 - F12 * F21)
+ 4
* w6
* (
(F11 * x62 + F21 * y62 + F31) * x61
+ (F12 * x62 + F22 * y62 + F32) * y61
+ x62 * F13
+ y62 * F23
+ F33
)
* y62
)
J_w[:, 6, 5] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w6 * x61 * x62
+ 2 * F12 * w6 * x62 * y61
+ 2 * F21 * w6 * x61 * y62
+ 2 * F22 * w6 * y61 * y62
+ 2 * F13 * w6 * x62
+ 2 * F23 * w6 * y62
+ 2 * F31 * w6 * x61
+ 2 * F32 * w6 * y61
+ 2 * F33 * w6
)
/ (F11 * F22 - F12 * F21)
+ 4
* w6
* (
(F11 * x62 + F21 * y62 + F31) * x61
+ (F12 * x62 + F22 * y62 + F32) * y61
+ x62 * F13
+ y62 * F23
+ F33
)
* x61
)
J_w[:, 7, 5] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w6 * x61 * x62
+ 2 * F12 * w6 * x62 * y61
+ 2 * F21 * w6 * x61 * y62
+ 2 * F22 * w6 * y61 * y62
+ 2 * F13 * w6 * x62
+ 2 * F23 * w6 * y62
+ 2 * F31 * w6 * x61
+ 2 * F32 * w6 * y61
+ 2 * F33 * w6
)
/ (F11 * F22 - F12 * F21)
+ 4
* w6
* (
(F11 * x62 + F21 * y62 + F31) * x61
+ (F12 * x62 + F22 * y62 + F32) * y61
+ x62 * F13
+ y62 * F23
+ F33
)
* y61
)
J_w[:, 8, 5] = (
4
* w6
* (
(F11 * x62 + F21 * y62 + F31) * x61
+ (F12 * x62 + F22 * y62 + F32) * y61
+ x62 * F13
+ y62 * F23
+ F33
)
- 4 * F33 * w6
- 4 * F13 * w6 * x62
- 4 * F23 * w6 * y62
- 4 * F31 * w6 * x61
- 4 * F32 * w6 * y61
- 4 * F11 * w6 * x61 * x62
- 4 * F12 * w6 * x62 * y61
- 4 * F21 * w6 * x61 * y62
- 4 * F22 * w6 * y61 * y62
)
J_w[:, 0, 6] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w7 * x71 * x72
+ 2 * F12 * w7 * x72 * y71
+ 2 * F21 * w7 * x71 * y72
+ 2 * F22 * w7 * y71 * y72
+ 2 * F13 * w7 * x72
+ 2 * F23 * w7 * y72
+ 2 * F31 * w7 * x71
+ 2 * F32 * w7 * y71
+ 2 * F33 * w7
)
/ (F11 * F22 - F12 * F21)
+ 4
* w7
* (
(F11 * x72 + F21 * y72 + F31) * x71
+ (F12 * x72 + F22 * y72 + F32) * y71
+ x72 * F13
+ y72 * F23
+ F33
)
* x72
* x71
)
J_w[:, 1, 6] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w7 * x71 * x72
+ 2 * F12 * w7 * x72 * y71
+ 2 * F21 * w7 * x71 * y72
+ 2 * F22 * w7 * y71 * y72
+ 2 * F13 * w7 * x72
+ 2 * F23 * w7 * y72
+ 2 * F31 * w7 * x71
+ 2 * F32 * w7 * y71
+ 2 * F33 * w7
)
/ (F11 * F22 - F12 * F21)
+ 4
* w7
* (
(F11 * x72 + F21 * y72 + F31) * x71
+ (F12 * x72 + F22 * y72 + F32) * y71
+ x72 * F13
+ y72 * F23
+ F33
)
* x72
* y71
)
J_w[:, 2, 6] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w7 * x71 * x72
+ 2 * F12 * w7 * x72 * y71
+ 2 * F21 * w7 * x71 * y72
+ 2 * F22 * w7 * y71 * y72
+ 2 * F13 * w7 * x72
+ 2 * F23 * w7 * y72
+ 2 * F31 * w7 * x71
+ 2 * F32 * w7 * y71
+ 2 * F33 * w7
)
/ (F11 * F22 - F12 * F21)
+ 4
* w7
* (
(F11 * x72 + F21 * y72 + F31) * x71
+ (F12 * x72 + F22 * y72 + F32) * y71
+ x72 * F13
+ y72 * F23
+ F33
)
* x72
)
J_w[:, 3, 6] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w7 * x71 * x72
+ 2 * F12 * w7 * x72 * y71
+ 2 * F21 * w7 * x71 * y72
+ 2 * F22 * w7 * y71 * y72
+ 2 * F13 * w7 * x72
+ 2 * F23 * w7 * y72
+ 2 * F31 * w7 * x71
+ 2 * F32 * w7 * y71
+ 2 * F33 * w7
)
/ (F11 * F22 - F12 * F21)
+ 4
* w7
* (
(F11 * x72 + F21 * y72 + F31) * x71
+ (F12 * x72 + F22 * y72 + F32) * y71
+ x72 * F13
+ y72 * F23
+ F33
)
* y72
* x71
)
J_w[:, 4, 6] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w7 * x71 * x72
+ 2 * F12 * w7 * x72 * y71
+ 2 * F21 * w7 * x71 * y72
+ 2 * F22 * w7 * y71 * y72
+ 2 * F13 * w7 * x72
+ 2 * F23 * w7 * y72
+ 2 * F31 * w7 * x71
+ 2 * F32 * w7 * y71
+ 2 * F33 * w7
)
/ (F11 * F22 - F12 * F21)
+ 4
* w7
* (
(F11 * x72 + F21 * y72 + F31) * x71
+ (F12 * x72 + F22 * y72 + F32) * y71
+ x72 * F13
+ y72 * F23
+ F33
)
* y72
* y71
)
J_w[:, 5, 6] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w7 * x71 * x72
+ 2 * F12 * w7 * x72 * y71
+ 2 * F21 * w7 * x71 * y72
+ 2 * F22 * w7 * y71 * y72
+ 2 * F13 * w7 * x72
+ 2 * F23 * w7 * y72
+ 2 * F31 * w7 * x71
+ 2 * F32 * w7 * y71
+ 2 * F33 * w7
)
/ (F11 * F22 - F12 * F21)
+ 4
* w7
* (
(F11 * x72 + F21 * y72 + F31) * x71
+ (F12 * x72 + F22 * y72 + F32) * y71
+ x72 * F13
+ y72 * F23
+ F33
)
* y72
)
J_w[:, 6, 6] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w7 * x71 * x72
+ 2 * F12 * w7 * x72 * y71
+ 2 * F21 * w7 * x71 * y72
+ 2 * F22 * w7 * y71 * y72
+ 2 * F13 * w7 * x72
+ 2 * F23 * w7 * y72
+ 2 * F31 * w7 * x71
+ 2 * F32 * w7 * y71
+ 2 * F33 * w7
)
/ (F11 * F22 - F12 * F21)
+ 4
* w7
* (
(F11 * x72 + F21 * y72 + F31) * x71
+ (F12 * x72 + F22 * y72 + F32) * y71
+ x72 * F13
+ y72 * F23
+ F33
)
* x71
)
J_w[:, 7, 6] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w7 * x71 * x72
+ 2 * F12 * w7 * x72 * y71
+ 2 * F21 * w7 * x71 * y72
+ 2 * F22 * w7 * y71 * y72
+ 2 * F13 * w7 * x72
+ 2 * F23 * w7 * y72
+ 2 * F31 * w7 * x71
+ 2 * F32 * w7 * y71
+ 2 * F33 * w7
)
/ (F11 * F22 - F12 * F21)
+ 4
* w7
* (
(F11 * x72 + F21 * y72 + F31) * x71
+ (F12 * x72 + F22 * y72 + F32) * y71
+ x72 * F13
+ y72 * F23
+ F33
)
* y71
)
J_w[:, 8, 6] = (
4
* w7
* (
(F11 * x72 + F21 * y72 + F31) * x71
+ (F12 * x72 + F22 * y72 + F32) * y71
+ x72 * F13
+ y72 * F23
+ F33
)
- 4 * F33 * w7
- 4 * F13 * w7 * x72
- 4 * F23 * w7 * y72
- 4 * F31 * w7 * x71
- 4 * F32 * w7 * y71
- 4 * F11 * w7 * x71 * x72
- 4 * F12 * w7 * x72 * y71
- 4 * F21 * w7 * x71 * y72
- 4 * F22 * w7 * y71 * y72
)
J_w[:, 0, 7] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w8 * x81 * x82
+ 2 * F12 * w8 * x82 * y81
+ 2 * F21 * w8 * x81 * y82
+ 2 * F22 * w8 * y81 * y82
+ 2 * F13 * w8 * x82
+ 2 * F23 * w8 * y82
+ 2 * F31 * w8 * x81
+ 2 * F32 * w8 * y81
+ 2 * F33 * w8
)
/ (F11 * F22 - F12 * F21)
+ 4
* w8
* (
(F11 * x82 + F21 * y82 + F31) * x81
+ (F12 * x82 + F22 * y82 + F32) * y81
+ x82 * F13
+ y82 * F23
+ F33
)
* x82
* x81
)
J_w[:, 1, 7] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w8 * x81 * x82
+ 2 * F12 * w8 * x82 * y81
+ 2 * F21 * w8 * x81 * y82
+ 2 * F22 * w8 * y81 * y82
+ 2 * F13 * w8 * x82
+ 2 * F23 * w8 * y82
+ 2 * F31 * w8 * x81
+ 2 * F32 * w8 * y81
+ 2 * F33 * w8
)
/ (F11 * F22 - F12 * F21)
+ 4
* w8
* (
(F11 * x82 + F21 * y82 + F31) * x81
+ (F12 * x82 + F22 * y82 + F32) * y81
+ x82 * F13
+ y82 * F23
+ F33
)
* x82
* y81
)
J_w[:, 2, 7] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w8 * x81 * x82
+ 2 * F12 * w8 * x82 * y81
+ 2 * F21 * w8 * x81 * y82
+ 2 * F22 * w8 * y81 * y82
+ 2 * F13 * w8 * x82
+ 2 * F23 * w8 * y82
+ 2 * F31 * w8 * x81
+ 2 * F32 * w8 * y81
+ 2 * F33 * w8
)
/ (F11 * F22 - F12 * F21)
+ 4
* w8
* (
(F11 * x82 + F21 * y82 + F31) * x81
+ (F12 * x82 + F22 * y82 + F32) * y81
+ x82 * F13
+ y82 * F23
+ F33
)
* x82
)
J_w[:, 3, 7] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w8 * x81 * x82
+ 2 * F12 * w8 * x82 * y81
+ 2 * F21 * w8 * x81 * y82
+ 2 * F22 * w8 * y81 * y82
+ 2 * F13 * w8 * x82
+ 2 * F23 * w8 * y82
+ 2 * F31 * w8 * x81
+ 2 * F32 * w8 * y81
+ 2 * F33 * w8
)
/ (F11 * F22 - F12 * F21)
+ 4
* w8
* (
(F11 * x82 + F21 * y82 + F31) * x81
+ (F12 * x82 + F22 * y82 + F32) * y81
+ x82 * F13
+ y82 * F23
+ F33
)
* y82
* x81
)
J_w[:, 4, 7] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w8 * x81 * x82
+ 2 * F12 * w8 * x82 * y81
+ 2 * F21 * w8 * x81 * y82
+ 2 * F22 * w8 * y81 * y82
+ 2 * F13 * w8 * x82
+ 2 * F23 * w8 * y82
+ 2 * F31 * w8 * x81
+ 2 * F32 * w8 * y81
+ 2 * F33 * w8
)
/ (F11 * F22 - F12 * F21)
+ 4
* w8
* (
(F11 * x82 + F21 * y82 + F31) * x81
+ (F12 * x82 + F22 * y82 + F32) * y81
+ x82 * F13
+ y82 * F23
+ F33
)
* y82
* y81
)
J_w[:, 5, 7] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w8 * x81 * x82
+ 2 * F12 * w8 * x82 * y81
+ 2 * F21 * w8 * x81 * y82
+ 2 * F22 * w8 * y81 * y82
+ 2 * F13 * w8 * x82
+ 2 * F23 * w8 * y82
+ 2 * F31 * w8 * x81
+ 2 * F32 * w8 * y81
+ 2 * F33 * w8
)
/ (F11 * F22 - F12 * F21)
+ 4
* w8
* (
(F11 * x82 + F21 * y82 + F31) * x81
+ (F12 * x82 + F22 * y82 + F32) * y81
+ x82 * F13
+ y82 * F23
+ F33
)
* y82
)
J_w[:, 6, 7] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w8 * x81 * x82
+ 2 * F12 * w8 * x82 * y81
+ 2 * F21 * w8 * x81 * y82
+ 2 * F22 * w8 * y81 * y82
+ 2 * F13 * w8 * x82
+ 2 * F23 * w8 * y82
+ 2 * F31 * w8 * x81
+ 2 * F32 * w8 * y81
+ 2 * F33 * w8
)
/ (F11 * F22 - F12 * F21)
+ 4
* w8
* (
(F11 * x82 + F21 * y82 + F31) * x81
+ (F12 * x82 + F22 * y82 + F32) * y81
+ x82 * F13
+ y82 * F23
+ F33
)
* x81
)
J_w[:, 7, 7] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w8 * x81 * x82
+ 2 * F12 * w8 * x82 * y81
+ 2 * F21 * w8 * x81 * y82
+ 2 * F22 * w8 * y81 * y82
+ 2 * F13 * w8 * x82
+ 2 * F23 * w8 * y82
+ 2 * F31 * w8 * x81
+ 2 * F32 * w8 * y81
+ 2 * F33 * w8
)
/ (F11 * F22 - F12 * F21)
+ 4
* w8
* (
(F11 * x82 + F21 * y82 + F31) * x81
+ (F12 * x82 + F22 * y82 + F32) * y81
+ x82 * F13
+ y82 * F23
+ F33
)
* y81
)
J_w[:, 8, 7] = (
4
* w8
* (
(F11 * x82 + F21 * y82 + F31) * x81
+ (F12 * x82 + F22 * y82 + F32) * y81
+ x82 * F13
+ y82 * F23
+ F33
)
- 4 * F33 * w8
- 4 * F13 * w8 * x82
- 4 * F23 * w8 * y82
- 4 * F31 * w8 * x81
- 4 * F32 * w8 * y81
- 4 * F11 * w8 * x81 * x82
- 4 * F12 * w8 * x82 * y81
- 4 * F21 * w8 * x81 * y82
- 4 * F22 * w8 * y81 * y82
)
J_w[:, 0, 8] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w9 * x91 * x92
+ 2 * F12 * w9 * x92 * y91
+ 2 * F21 * w9 * x91 * y92
+ 2 * F22 * w9 * y91 * y92
+ 2 * F13 * w9 * x92
+ 2 * F23 * w9 * y92
+ 2 * F31 * w9 * x91
+ 2 * F32 * w9 * y91
+ 2 * F33 * w9
)
/ (F11 * F22 - F12 * F21)
+ 4
* w9
* (
(F11 * x92 + F21 * y92 + F31) * x91
+ (F12 * x92 + F22 * y92 + F32) * y91
+ x92 * F13
+ y92 * F23
+ F33
)
* x92
* x91
)
J_w[:, 1, 8] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w9 * x91 * x92
+ 2 * F12 * w9 * x92 * y91
+ 2 * F21 * w9 * x91 * y92
+ 2 * F22 * w9 * y91 * y92
+ 2 * F13 * w9 * x92
+ 2 * F23 * w9 * y92
+ 2 * F31 * w9 * x91
+ 2 * F32 * w9 * y91
+ 2 * F33 * w9
)
/ (F11 * F22 - F12 * F21)
+ 4
* w9
* (
(F11 * x92 + F21 * y92 + F31) * x91
+ (F12 * x92 + F22 * y92 + F32) * y91
+ x92 * F13
+ y92 * F23
+ F33
)
* x92
* y91
)
J_w[:, 2, 8] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w9 * x91 * x92
+ 2 * F12 * w9 * x92 * y91
+ 2 * F21 * w9 * x91 * y92
+ 2 * F22 * w9 * y91 * y92
+ 2 * F13 * w9 * x92
+ 2 * F23 * w9 * y92
+ 2 * F31 * w9 * x91
+ 2 * F32 * w9 * y91
+ 2 * F33 * w9
)
/ (F11 * F22 - F12 * F21)
+ 4
* w9
* (
(F11 * x92 + F21 * y92 + F31) * x91
+ (F12 * x92 + F22 * y92 + F32) * y91
+ x92 * F13
+ y92 * F23
+ F33
)
* x92
)
J_w[:, 3, 8] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w9 * x91 * x92
+ 2 * F12 * w9 * x92 * y91
+ 2 * F21 * w9 * x91 * y92
+ 2 * F22 * w9 * y91 * y92
+ 2 * F13 * w9 * x92
+ 2 * F23 * w9 * y92
+ 2 * F31 * w9 * x91
+ 2 * F32 * w9 * y91
+ 2 * F33 * w9
)
/ (F11 * F22 - F12 * F21)
+ 4
* w9
* (
(F11 * x92 + F21 * y92 + F31) * x91
+ (F12 * x92 + F22 * y92 + F32) * y91
+ x92 * F13
+ y92 * F23
+ F33
)
* y92
* x91
)
J_w[:, 4, 8] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w9 * x91 * x92
+ 2 * F12 * w9 * x92 * y91
+ 2 * F21 * w9 * x91 * y92
+ 2 * F22 * w9 * y91 * y92
+ 2 * F13 * w9 * x92
+ 2 * F23 * w9 * y92
+ 2 * F31 * w9 * x91
+ 2 * F32 * w9 * y91
+ 2 * F33 * w9
)
/ (F11 * F22 - F12 * F21)
+ 4
* w9
* (
(F11 * x92 + F21 * y92 + F31) * x91
+ (F12 * x92 + F22 * y92 + F32) * y91
+ x92 * F13
+ y92 * F23
+ F33
)
* y92
* y91
)
J_w[:, 5, 8] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w9 * x91 * x92
+ 2 * F12 * w9 * x92 * y91
+ 2 * F21 * w9 * x91 * y92
+ 2 * F22 * w9 * y91 * y92
+ 2 * F13 * w9 * x92
+ 2 * F23 * w9 * y92
+ 2 * F31 * w9 * x91
+ 2 * F32 * w9 * y91
+ 2 * F33 * w9
)
/ (F11 * F22 - F12 * F21)
+ 4
* w9
* (
(F11 * x92 + F21 * y92 + F31) * x91
+ (F12 * x92 + F22 * y92 + F32) * y91
+ x92 * F13
+ y92 * F23
+ F33
)
* y92
)
J_w[:, 6, 8] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w9 * x91 * x92
+ 2 * F12 * w9 * x92 * y91
+ 2 * F21 * w9 * x91 * y92
+ 2 * F22 * w9 * y91 * y92
+ 2 * F13 * w9 * x92
+ 2 * F23 * w9 * y92
+ 2 * F31 * w9 * x91
+ 2 * F32 * w9 * y91
+ 2 * F33 * w9
)
/ (F11 * F22 - F12 * F21)
+ 4
* w9
* (
(F11 * x92 + F21 * y92 + F31) * x91
+ (F12 * x92 + F22 * y92 + F32) * y91
+ x92 * F13
+ y92 * F23
+ F33
)
* x91
)
J_w[:, 7, 8] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w9 * x91 * x92
+ 2 * F12 * w9 * x92 * y91
+ 2 * F21 * w9 * x91 * y92
+ 2 * F22 * w9 * y91 * y92
+ 2 * F13 * w9 * x92
+ 2 * F23 * w9 * y92
+ 2 * F31 * w9 * x91
+ 2 * F32 * w9 * y91
+ 2 * F33 * w9
)
/ (F11 * F22 - F12 * F21)
+ 4
* w9
* (
(F11 * x92 + F21 * y92 + F31) * x91
+ (F12 * x92 + F22 * y92 + F32) * y91
+ x92 * F13
+ y92 * F23
+ F33
)
* y91
)
J_w[:, 8, 8] = (
4
* w9
* (
(F11 * x92 + F21 * y92 + F31) * x91
+ (F12 * x92 + F22 * y92 + F32) * y91
+ x92 * F13
+ y92 * F23
+ F33
)
- 4 * F33 * w9
- 4 * F31 * w9 * x91
- 4 * F32 * w9 * y91
- 4 * F13 * w9 * x92
- 4 * F23 * w9 * y92
- 4 * F11 * w9 * x91 * x92
- 4 * F12 * w9 * x92 * y91
- 4 * F21 * w9 * x91 * y92
- 4 * F22 * w9 * y91 * y92
)
J_w[:, 0, 9] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w10 * x10_1 * x10_2
+ 2 * F12 * w10 * x10_2 * y10_1
+ 2 * F21 * w10 * x10_1 * y10_2
+ 2 * F22 * w10 * y10_1 * y10_2
+ 2 * F13 * w10 * x10_2
+ 2 * F23 * w10 * y10_2
+ 2 * F31 * w10 * x10_1
+ 2 * F32 * w10 * y10_1
+ 2 * F33 * w10
)
/ (F11 * F22 - F12 * F21)
+ 4
* w10
* (
(F11 * x10_2 + F21 * y10_2 + F31) * x10_1
+ (F12 * x10_2 + F22 * y10_2 + F32) * y10_1
+ x10_2 * F13
+ y10_2 * F23
+ F33
)
* x10_2
* x10_1
)
J_w[:, 1, 9] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w10 * x10_1 * x10_2
+ 2 * F12 * w10 * x10_2 * y10_1
+ 2 * F21 * w10 * x10_1 * y10_2
+ 2 * F22 * w10 * y10_1 * y10_2
+ 2 * F13 * w10 * x10_2
+ 2 * F23 * w10 * y10_2
+ 2 * F31 * w10 * x10_1
+ 2 * F32 * w10 * y10_1
+ 2 * F33 * w10
)
/ (F11 * F22 - F12 * F21)
+ 4
* w10
* (
(F11 * x10_2 + F21 * y10_2 + F31) * x10_1
+ (F12 * x10_2 + F22 * y10_2 + F32) * y10_1
+ x10_2 * F13
+ y10_2 * F23
+ F33
)
* x10_2
* y10_1
)
J_w[:, 2, 9] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w10 * x10_1 * x10_2
+ 2 * F12 * w10 * x10_2 * y10_1
+ 2 * F21 * w10 * x10_1 * y10_2
+ 2 * F22 * w10 * y10_1 * y10_2
+ 2 * F13 * w10 * x10_2
+ 2 * F23 * w10 * y10_2
+ 2 * F31 * w10 * x10_1
+ 2 * F32 * w10 * y10_1
+ 2 * F33 * w10
)
/ (F11 * F22 - F12 * F21)
+ 4
* w10
* (
(F11 * x10_2 + F21 * y10_2 + F31) * x10_1
+ (F12 * x10_2 + F22 * y10_2 + F32) * y10_1
+ x10_2 * F13
+ y10_2 * F23
+ F33
)
* x10_2
)
J_w[:, 3, 9] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w10 * x10_1 * x10_2
+ 2 * F12 * w10 * x10_2 * y10_1
+ 2 * F21 * w10 * x10_1 * y10_2
+ 2 * F22 * w10 * y10_1 * y10_2
+ 2 * F13 * w10 * x10_2
+ 2 * F23 * w10 * y10_2
+ 2 * F31 * w10 * x10_1
+ 2 * F32 * w10 * y10_1
+ 2 * F33 * w10
)
/ (F11 * F22 - F12 * F21)
+ 4
* w10
* (
(F11 * x10_2 + F21 * y10_2 + F31) * x10_1
+ (F12 * x10_2 + F22 * y10_2 + F32) * y10_1
+ x10_2 * F13
+ y10_2 * F23
+ F33
)
* y10_2
* x10_1
)
J_w[:, 4, 9] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w10 * x10_1 * x10_2
+ 2 * F12 * w10 * x10_2 * y10_1
+ 2 * F21 * w10 * x10_1 * y10_2
+ 2 * F22 * w10 * y10_1 * y10_2
+ 2 * F13 * w10 * x10_2
+ 2 * F23 * w10 * y10_2
+ 2 * F31 * w10 * x10_1
+ 2 * F32 * w10 * y10_1
+ 2 * F33 * w10
)
/ (F11 * F22 - F12 * F21)
+ 4
* w10
* (
(F11 * x10_2 + F21 * y10_2 + F31) * x10_1
+ (F12 * x10_2 + F22 * y10_2 + F32) * y10_1
+ x10_2 * F13
+ y10_2 * F23
+ F33
)
* y10_2
* y10_1
)
J_w[:, 5, 9] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w10 * x10_1 * x10_2
+ 2 * F12 * w10 * x10_2 * y10_1
+ 2 * F21 * w10 * x10_1 * y10_2
+ 2 * F22 * w10 * y10_1 * y10_2
+ 2 * F13 * w10 * x10_2
+ 2 * F23 * w10 * y10_2
+ 2 * F31 * w10 * x10_1
+ 2 * F32 * w10 * y10_1
+ 2 * F33 * w10
)
/ (F11 * F22 - F12 * F21)
+ 4
* w10
* (
(F11 * x10_2 + F21 * y10_2 + F31) * x10_1
+ (F12 * x10_2 + F22 * y10_2 + F32) * y10_1
+ x10_2 * F13
+ y10_2 * F23
+ F33
)
* y10_2
)
J_w[:, 6, 9] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w10 * x10_1 * x10_2
+ 2 * F12 * w10 * x10_2 * y10_1
+ 2 * F21 * w10 * x10_1 * y10_2
+ 2 * F22 * w10 * y10_1 * y10_2
+ 2 * F13 * w10 * x10_2
+ 2 * F23 * w10 * y10_2
+ 2 * F31 * w10 * x10_1
+ 2 * F32 * w10 * y10_1
+ 2 * F33 * w10
)
/ (F11 * F22 - F12 * F21)
+ 4
* w10
* (
(F11 * x10_2 + F21 * y10_2 + F31) * x10_1
+ (F12 * x10_2 + F22 * y10_2 + F32) * y10_1
+ x10_2 * F13
+ y10_2 * F23
+ F33
)
* x10_1
)
J_w[:, 7, 9] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w10 * x10_1 * x10_2
+ 2 * F12 * w10 * x10_2 * y10_1
+ 2 * F21 * w10 * x10_1 * y10_2
+ 2 * F22 * w10 * y10_1 * y10_2
+ 2 * F13 * w10 * x10_2
+ 2 * F23 * w10 * y10_2
+ 2 * F31 * w10 * x10_1
+ 2 * F32 * w10 * y10_1
+ 2 * F33 * w10
)
/ (F11 * F22 - F12 * F21)
+ 4
* w10
* (
(F11 * x10_2 + F21 * y10_2 + F31) * x10_1
+ (F12 * x10_2 + F22 * y10_2 + F32) * y10_1
+ x10_2 * F13
+ y10_2 * F23
+ F33
)
* y10_1
)
J_w[:, 8, 9] = (
4
* w10
* (
(F11 * x10_2 + F21 * y10_2 + F31) * x10_1
+ (F12 * x10_2 + F22 * y10_2 + F32) * y10_1
+ x10_2 * F13
+ y10_2 * F23
+ F33
)
- 4 * F33 * w10
- 4 * F13 * w10 * x10_2
- 4 * F23 * w10 * y10_2
- 4 * F31 * w10 * x10_1
- 4 * F32 * w10 * y10_1
- 4 * F11 * w10 * x10_1 * x10_2
- 4 * F12 * w10 * x10_2 * y10_1
- 4 * F21 * w10 * x10_1 * y10_2
- 4 * F22 * w10 * y10_1 * y10_2
)
J_w[:, 0, 10] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w11 * x11_1 * x11_2
+ 2 * F12 * w11 * x11_2 * y11_1
+ 2 * F21 * w11 * x11_1 * y11_2
+ 2 * F22 * w11 * y11_1 * y11_2
+ 2 * F13 * w11 * x11_2
+ 2 * F23 * w11 * y11_2
+ 2 * F31 * w11 * x11_1
+ 2 * F32 * w11 * y11_1
+ 2 * F33 * w11
)
/ (F11 * F22 - F12 * F21)
+ 4
* w11
* (
(F11 * x11_2 + F21 * y11_2 + F31) * x11_1
+ (F12 * x11_2 + F22 * y11_2 + F32) * y11_1
+ x11_2 * F13
+ y11_2 * F23
+ F33
)
* x11_2
* x11_1
)
J_w[:, 1, 10] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w11 * x11_1 * x11_2
+ 2 * F12 * w11 * x11_2 * y11_1
+ 2 * F21 * w11 * x11_1 * y11_2
+ 2 * F22 * w11 * y11_1 * y11_2
+ 2 * F13 * w11 * x11_2
+ 2 * F23 * w11 * y11_2
+ 2 * F31 * w11 * x11_1
+ 2 * F32 * w11 * y11_1
+ 2 * F33 * w11
)
/ (F11 * F22 - F12 * F21)
+ 4
* w11
* (
(F11 * x11_2 + F21 * y11_2 + F31) * x11_1
+ (F12 * x11_2 + F22 * y11_2 + F32) * y11_1
+ x11_2 * F13
+ y11_2 * F23
+ F33
)
* x11_2
* y11_1
)
J_w[:, 2, 10] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w11 * x11_1 * x11_2
+ 2 * F12 * w11 * x11_2 * y11_1
+ 2 * F21 * w11 * x11_1 * y11_2
+ 2 * F22 * w11 * y11_1 * y11_2
+ 2 * F13 * w11 * x11_2
+ 2 * F23 * w11 * y11_2
+ 2 * F31 * w11 * x11_1
+ 2 * F32 * w11 * y11_1
+ 2 * F33 * w11
)
/ (F11 * F22 - F12 * F21)
+ 4
* w11
* (
(F11 * x11_2 + F21 * y11_2 + F31) * x11_1
+ (F12 * x11_2 + F22 * y11_2 + F32) * y11_1
+ x11_2 * F13
+ y11_2 * F23
+ F33
)
* x11_2
)
J_w[:, 3, 10] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w11 * x11_1 * x11_2
+ 2 * F12 * w11 * x11_2 * y11_1
+ 2 * F21 * w11 * x11_1 * y11_2
+ 2 * F22 * w11 * y11_1 * y11_2
+ 2 * F13 * w11 * x11_2
+ 2 * F23 * w11 * y11_2
+ 2 * F31 * w11 * x11_1
+ 2 * F32 * w11 * y11_1
+ 2 * F33 * w11
)
/ (F11 * F22 - F12 * F21)
+ 4
* w11
* (
(F11 * x11_2 + F21 * y11_2 + F31) * x11_1
+ (F12 * x11_2 + F22 * y11_2 + F32) * y11_1
+ x11_2 * F13
+ y11_2 * F23
+ F33
)
* y11_2
* x11_1
)
J_w[:, 4, 10] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w11 * x11_1 * x11_2
+ 2 * F12 * w11 * x11_2 * y11_1
+ 2 * F21 * w11 * x11_1 * y11_2
+ 2 * F22 * w11 * y11_1 * y11_2
+ 2 * F13 * w11 * x11_2
+ 2 * F23 * w11 * y11_2
+ 2 * F31 * w11 * x11_1
+ 2 * F32 * w11 * y11_1
+ 2 * F33 * w11
)
/ (F11 * F22 - F12 * F21)
+ 4
* w11
* (
(F11 * x11_2 + F21 * y11_2 + F31) * x11_1
+ (F12 * x11_2 + F22 * y11_2 + F32) * y11_1
+ x11_2 * F13
+ y11_2 * F23
+ F33
)
* y11_2
* y11_1
)
J_w[:, 5, 10] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w11 * x11_1 * x11_2
+ 2 * F12 * w11 * x11_2 * y11_1
+ 2 * F21 * w11 * x11_1 * y11_2
+ 2 * F22 * w11 * y11_1 * y11_2
+ 2 * F13 * w11 * x11_2
+ 2 * F23 * w11 * y11_2
+ 2 * F31 * w11 * x11_1
+ 2 * F32 * w11 * y11_1
+ 2 * F33 * w11
)
/ (F11 * F22 - F12 * F21)
+ 4
* w11
* (
(F11 * x11_2 + F21 * y11_2 + F31) * x11_1
+ (F12 * x11_2 + F22 * y11_2 + F32) * y11_1
+ x11_2 * F13
+ y11_2 * F23
+ F33
)
* y11_2
)
J_w[:, 6, 10] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w11 * x11_1 * x11_2
+ 2 * F12 * w11 * x11_2 * y11_1
+ 2 * F21 * w11 * x11_1 * y11_2
+ 2 * F22 * w11 * y11_1 * y11_2
+ 2 * F13 * w11 * x11_2
+ 2 * F23 * w11 * y11_2
+ 2 * F31 * w11 * x11_1
+ 2 * F32 * w11 * y11_1
+ 2 * F33 * w11
)
/ (F11 * F22 - F12 * F21)
+ 4
* w11
* (
(F11 * x11_2 + F21 * y11_2 + F31) * x11_1
+ (F12 * x11_2 + F22 * y11_2 + F32) * y11_1
+ x11_2 * F13
+ y11_2 * F23
+ F33
)
* x11_1
)
J_w[:, 7, 10] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w11 * x11_1 * x11_2
+ 2 * F12 * w11 * x11_2 * y11_1
+ 2 * F21 * w11 * x11_1 * y11_2
+ 2 * F22 * w11 * y11_1 * y11_2
+ 2 * F13 * w11 * x11_2
+ 2 * F23 * w11 * y11_2
+ 2 * F31 * w11 * x11_1
+ 2 * F32 * w11 * y11_1
+ 2 * F33 * w11
)
/ (F11 * F22 - F12 * F21)
+ 4
* w11
* (
(F11 * x11_2 + F21 * y11_2 + F31) * x11_1
+ (F12 * x11_2 + F22 * y11_2 + F32) * y11_1
+ x11_2 * F13
+ y11_2 * F23
+ F33
)
* y11_1
)
J_w[:, 8, 10] = (
4
* w11
* (
(F11 * x11_2 + F21 * y11_2 + F31) * x11_1
+ (F12 * x11_2 + F22 * y11_2 + F32) * y11_1
+ x11_2 * F13
+ y11_2 * F23
+ F33
)
- 4 * F33 * w11
- 4 * F13 * w11 * x11_2
- 4 * F23 * w11 * y11_2
- 4 * F31 * w11 * x11_1
- 4 * F32 * w11 * y11_1
- 4 * F11 * w11 * x11_1 * x11_2
- 4 * F12 * w11 * x11_2 * y11_1
- 4 * F21 * w11 * x11_1 * y11_2
- 4 * F22 * w11 * y11_1 * y11_2
)
J_w[:, 0, 11] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w12 * x12_1 * x12_2
+ 2 * F12 * w12 * x12_2 * y12_1
+ 2 * F21 * w12 * x12_1 * y12_2
+ 2 * F22 * w12 * y12_1 * y12_2
+ 2 * F13 * w12 * x12_2
+ 2 * F23 * w12 * y12_2
+ 2 * F31 * w12 * x12_1
+ 2 * F32 * w12 * y12_1
+ 2 * F33 * w12
)
/ (F11 * F22 - F12 * F21)
+ 4
* w12
* (
(F11 * x12_2 + F21 * y12_2 + F31) * x12_1
+ (F12 * x12_2 + F22 * y12_2 + F32) * y12_1
+ x12_2 * F13
+ y12_2 * F23
+ F33
)
* x12_2
* x12_1
)
J_w[:, 1, 11] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w12 * x12_1 * x12_2
+ 2 * F12 * w12 * x12_2 * y12_1
+ 2 * F21 * w12 * x12_1 * y12_2
+ 2 * F22 * w12 * y12_1 * y12_2
+ 2 * F13 * w12 * x12_2
+ 2 * F23 * w12 * y12_2
+ 2 * F31 * w12 * x12_1
+ 2 * F32 * w12 * y12_1
+ 2 * F33 * w12
)
/ (F11 * F22 - F12 * F21)
+ 4
* w12
* (
(F11 * x12_2 + F21 * y12_2 + F31) * x12_1
+ (F12 * x12_2 + F22 * y12_2 + F32) * y12_1
+ x12_2 * F13
+ y12_2 * F23
+ F33
)
* x12_2
* y12_1
)
J_w[:, 2, 11] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w12 * x12_1 * x12_2
+ 2 * F12 * w12 * x12_2 * y12_1
+ 2 * F21 * w12 * x12_1 * y12_2
+ 2 * F22 * w12 * y12_1 * y12_2
+ 2 * F13 * w12 * x12_2
+ 2 * F23 * w12 * y12_2
+ 2 * F31 * w12 * x12_1
+ 2 * F32 * w12 * y12_1
+ 2 * F33 * w12
)
/ (F11 * F22 - F12 * F21)
+ 4
* w12
* (
(F11 * x12_2 + F21 * y12_2 + F31) * x12_1
+ (F12 * x12_2 + F22 * y12_2 + F32) * y12_1
+ x12_2 * F13
+ y12_2 * F23
+ F33
)
* x12_2
)
J_w[:, 3, 11] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w12 * x12_1 * x12_2
+ 2 * F12 * w12 * x12_2 * y12_1
+ 2 * F21 * w12 * x12_1 * y12_2
+ 2 * F22 * w12 * y12_1 * y12_2
+ 2 * F13 * w12 * x12_2
+ 2 * F23 * w12 * y12_2
+ 2 * F31 * w12 * x12_1
+ 2 * F32 * w12 * y12_1
+ 2 * F33 * w12
)
/ (F11 * F22 - F12 * F21)
+ 4
* w12
* (
(F11 * x12_2 + F21 * y12_2 + F31) * x12_1
+ (F12 * x12_2 + F22 * y12_2 + F32) * y12_1
+ x12_2 * F13
+ y12_2 * F23
+ F33
)
* y12_2
* x12_1
)
J_w[:, 4, 11] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w12 * x12_1 * x12_2
+ 2 * F12 * w12 * x12_2 * y12_1
+ 2 * F21 * w12 * x12_1 * y12_2
+ 2 * F22 * w12 * y12_1 * y12_2
+ 2 * F13 * w12 * x12_2
+ 2 * F23 * w12 * y12_2
+ 2 * F31 * w12 * x12_1
+ 2 * F32 * w12 * y12_1
+ 2 * F33 * w12
)
/ (F11 * F22 - F12 * F21)
+ 4
* w12
* (
(F11 * x12_2 + F21 * y12_2 + F31) * x12_1
+ (F12 * x12_2 + F22 * y12_2 + F32) * y12_1
+ x12_2 * F13
+ y12_2 * F23
+ F33
)
* y12_2
* y12_1
)
J_w[:, 5, 11] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w12 * x12_1 * x12_2
+ 2 * F12 * w12 * x12_2 * y12_1
+ 2 * F21 * w12 * x12_1 * y12_2
+ 2 * F22 * w12 * y12_1 * y12_2
+ 2 * F13 * w12 * x12_2
+ 2 * F23 * w12 * y12_2
+ 2 * F31 * w12 * x12_1
+ 2 * F32 * w12 * y12_1
+ 2 * F33 * w12
)
/ (F11 * F22 - F12 * F21)
+ 4
* w12
* (
(F11 * x12_2 + F21 * y12_2 + F31) * x12_1
+ (F12 * x12_2 + F22 * y12_2 + F32) * y12_1
+ x12_2 * F13
+ y12_2 * F23
+ F33
)
* y12_2
)
J_w[:, 6, 11] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w12 * x12_1 * x12_2
+ 2 * F12 * w12 * x12_2 * y12_1
+ 2 * F21 * w12 * x12_1 * y12_2
+ 2 * F22 * w12 * y12_1 * y12_2
+ 2 * F13 * w12 * x12_2
+ 2 * F23 * w12 * y12_2
+ 2 * F31 * w12 * x12_1
+ 2 * F32 * w12 * y12_1
+ 2 * F33 * w12
)
/ (F11 * F22 - F12 * F21)
+ 4
* w12
* (
(F11 * x12_2 + F21 * y12_2 + F31) * x12_1
+ (F12 * x12_2 + F22 * y12_2 + F32) * y12_1
+ x12_2 * F13
+ y12_2 * F23
+ F33
)
* x12_1
)
J_w[:, 7, 11] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w12 * x12_1 * x12_2
+ 2 * F12 * w12 * x12_2 * y12_1
+ 2 * F21 * w12 * x12_1 * y12_2
+ 2 * F22 * w12 * y12_1 * y12_2
+ 2 * F13 * w12 * x12_2
+ 2 * F23 * w12 * y12_2
+ 2 * F31 * w12 * x12_1
+ 2 * F32 * w12 * y12_1
+ 2 * F33 * w12
)
/ (F11 * F22 - F12 * F21)
+ 4
* w12
* (
(F11 * x12_2 + F21 * y12_2 + F31) * x12_1
+ (F12 * x12_2 + F22 * y12_2 + F32) * y12_1
+ x12_2 * F13
+ y12_2 * F23
+ F33
)
* y12_1
)
J_w[:, 8, 11] = (
4
* w12
* (
(F11 * x12_2 + F21 * y12_2 + F31) * x12_1
+ (F12 * x12_2 + F22 * y12_2 + F32) * y12_1
+ x12_2 * F13
+ y12_2 * F23
+ F33
)
- 4 * F33 * w12
- 4 * F13 * w12 * x12_2
- 4 * F23 * w12 * y12_2
- 4 * F31 * w12 * x12_1
- 4 * F32 * w12 * y12_1
- 4 * F11 * w12 * x12_1 * x12_2
- 4 * F12 * w12 * x12_2 * y12_1
- 4 * F21 * w12 * x12_1 * y12_2
- 4 * F22 * w12 * y12_1 * y12_2
)
J_w[:, 0, 12] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w13 * x13_1 * x13_2
+ 2 * F12 * w13 * x13_2 * y13_1
+ 2 * F21 * w13 * x13_1 * y13_2
+ 2 * F22 * w13 * y13_1 * y13_2
+ 2 * F13 * w13 * x13_2
+ 2 * F23 * w13 * y13_2
+ 2 * F31 * w13 * x13_1
+ 2 * F32 * w13 * y13_1
+ 2 * F33 * w13
)
/ (F11 * F22 - F12 * F21)
+ 4
* w13
* (
(F11 * x13_2 + F21 * y13_2 + F31) * x13_1
+ (F12 * x13_2 + F22 * y13_2 + F32) * y13_1
+ x13_2 * F13
+ y13_2 * F23
+ F33
)
* x13_2
* x13_1
)
J_w[:, 1, 12] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w13 * x13_1 * x13_2
+ 2 * F12 * w13 * x13_2 * y13_1
+ 2 * F21 * w13 * x13_1 * y13_2
+ 2 * F22 * w13 * y13_1 * y13_2
+ 2 * F13 * w13 * x13_2
+ 2 * F23 * w13 * y13_2
+ 2 * F31 * w13 * x13_1
+ 2 * F32 * w13 * y13_1
+ 2 * F33 * w13
)
/ (F11 * F22 - F12 * F21)
+ 4
* w13
* (
(F11 * x13_2 + F21 * y13_2 + F31) * x13_1
+ (F12 * x13_2 + F22 * y13_2 + F32) * y13_1
+ x13_2 * F13
+ y13_2 * F23
+ F33
)
* x13_2
* y13_1
)
J_w[:, 2, 12] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w13 * x13_1 * x13_2
+ 2 * F12 * w13 * x13_2 * y13_1
+ 2 * F21 * w13 * x13_1 * y13_2
+ 2 * F22 * w13 * y13_1 * y13_2
+ 2 * F13 * w13 * x13_2
+ 2 * F23 * w13 * y13_2
+ 2 * F31 * w13 * x13_1
+ 2 * F32 * w13 * y13_1
+ 2 * F33 * w13
)
/ (F11 * F22 - F12 * F21)
+ 4
* w13
* (
(F11 * x13_2 + F21 * y13_2 + F31) * x13_1
+ (F12 * x13_2 + F22 * y13_2 + F32) * y13_1
+ x13_2 * F13
+ y13_2 * F23
+ F33
)
* x13_2
)
J_w[:, 3, 12] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w13 * x13_1 * x13_2
+ 2 * F12 * w13 * x13_2 * y13_1
+ 2 * F21 * w13 * x13_1 * y13_2
+ 2 * F22 * w13 * y13_1 * y13_2
+ 2 * F13 * w13 * x13_2
+ 2 * F23 * w13 * y13_2
+ 2 * F31 * w13 * x13_1
+ 2 * F32 * w13 * y13_1
+ 2 * F33 * w13
)
/ (F11 * F22 - F12 * F21)
+ 4
* w13
* (
(F11 * x13_2 + F21 * y13_2 + F31) * x13_1
+ (F12 * x13_2 + F22 * y13_2 + F32) * y13_1
+ x13_2 * F13
+ y13_2 * F23
+ F33
)
* y13_2
* x13_1
)
J_w[:, 4, 12] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w13 * x13_1 * x13_2
+ 2 * F12 * w13 * x13_2 * y13_1
+ 2 * F21 * w13 * x13_1 * y13_2
+ 2 * F22 * w13 * y13_1 * y13_2
+ 2 * F13 * w13 * x13_2
+ 2 * F23 * w13 * y13_2
+ 2 * F31 * w13 * x13_1
+ 2 * F32 * w13 * y13_1
+ 2 * F33 * w13
)
/ (F11 * F22 - F12 * F21)
+ 4
* w13
* (
(F11 * x13_2 + F21 * y13_2 + F31) * x13_1
+ (F12 * x13_2 + F22 * y13_2 + F32) * y13_1
+ x13_2 * F13
+ y13_2 * F23
+ F33
)
* y13_2
* y13_1
)
J_w[:, 5, 12] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w13 * x13_1 * x13_2
+ 2 * F12 * w13 * x13_2 * y13_1
+ 2 * F21 * w13 * x13_1 * y13_2
+ 2 * F22 * w13 * y13_1 * y13_2
+ 2 * F13 * w13 * x13_2
+ 2 * F23 * w13 * y13_2
+ 2 * F31 * w13 * x13_1
+ 2 * F32 * w13 * y13_1
+ 2 * F33 * w13
)
/ (F11 * F22 - F12 * F21)
+ 4
* w13
* (
(F11 * x13_2 + F21 * y13_2 + F31) * x13_1
+ (F12 * x13_2 + F22 * y13_2 + F32) * y13_1
+ x13_2 * F13
+ y13_2 * F23
+ F33
)
* y13_2
)
J_w[:, 6, 12] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w13 * x13_1 * x13_2
+ 2 * F12 * w13 * x13_2 * y13_1
+ 2 * F21 * w13 * x13_1 * y13_2
+ 2 * F22 * w13 * y13_1 * y13_2
+ 2 * F13 * w13 * x13_2
+ 2 * F23 * w13 * y13_2
+ 2 * F31 * w13 * x13_1
+ 2 * F32 * w13 * y13_1
+ 2 * F33 * w13
)
/ (F11 * F22 - F12 * F21)
+ 4
* w13
* (
(F11 * x13_2 + F21 * y13_2 + F31) * x13_1
+ (F12 * x13_2 + F22 * y13_2 + F32) * y13_1
+ x13_2 * F13
+ y13_2 * F23
+ F33
)
* x13_1
)
J_w[:, 7, 12] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w13 * x13_1 * x13_2
+ 2 * F12 * w13 * x13_2 * y13_1
+ 2 * F21 * w13 * x13_1 * y13_2
+ 2 * F22 * w13 * y13_1 * y13_2
+ 2 * F13 * w13 * x13_2
+ 2 * F23 * w13 * y13_2
+ 2 * F31 * w13 * x13_1
+ 2 * F32 * w13 * y13_1
+ 2 * F33 * w13
)
/ (F11 * F22 - F12 * F21)
+ 4
* w13
* (
(F11 * x13_2 + F21 * y13_2 + F31) * x13_1
+ (F12 * x13_2 + F22 * y13_2 + F32) * y13_1
+ x13_2 * F13
+ y13_2 * F23
+ F33
)
* y13_1
)
J_w[:, 8, 12] = (
4
* w13
* (
(F11 * x13_2 + F21 * y13_2 + F31) * x13_1
+ (F12 * x13_2 + F22 * y13_2 + F32) * y13_1
+ x13_2 * F13
+ y13_2 * F23
+ F33
)
- 4 * F33 * w13
- 4 * F13 * w13 * x13_2
- 4 * F23 * w13 * y13_2
- 4 * F31 * w13 * x13_1
- 4 * F32 * w13 * y13_1
- 4 * F11 * w13 * x13_1 * x13_2
- 4 * F12 * w13 * x13_2 * y13_1
- 4 * F21 * w13 * x13_1 * y13_2
- 4 * F22 * w13 * y13_1 * y13_2
)
J_w[:, 0, 13] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w14 * x14_1 * x14_2
+ 2 * F12 * w14 * x14_2 * y14_1
+ 2 * F21 * w14 * x14_1 * y14_2
+ 2 * F22 * w14 * y14_1 * y14_2
+ 2 * F13 * w14 * x14_2
+ 2 * F23 * w14 * y14_2
+ 2 * F31 * w14 * x14_1
+ 2 * F32 * w14 * y14_1
+ 2 * F33 * w14
)
/ (F11 * F22 - F12 * F21)
+ 4
* w14
* (
(F11 * x14_2 + F21 * y14_2 + F31) * x14_1
+ (F12 * x14_2 + F22 * y14_2 + F32) * y14_1
+ x14_2 * F13
+ y14_2 * F23
+ F33
)
* x14_2
* x14_1
)
J_w[:, 1, 13] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w14 * x14_1 * x14_2
+ 2 * F12 * w14 * x14_2 * y14_1
+ 2 * F21 * w14 * x14_1 * y14_2
+ 2 * F22 * w14 * y14_1 * y14_2
+ 2 * F13 * w14 * x14_2
+ 2 * F23 * w14 * y14_2
+ 2 * F31 * w14 * x14_1
+ 2 * F32 * w14 * y14_1
+ 2 * F33 * w14
)
/ (F11 * F22 - F12 * F21)
+ 4
* w14
* (
(F11 * x14_2 + F21 * y14_2 + F31) * x14_1
+ (F12 * x14_2 + F22 * y14_2 + F32) * y14_1
+ x14_2 * F13
+ y14_2 * F23
+ F33
)
* x14_2
* y14_1
)
J_w[:, 2, 13] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w14 * x14_1 * x14_2
+ 2 * F12 * w14 * x14_2 * y14_1
+ 2 * F21 * w14 * x14_1 * y14_2
+ 2 * F22 * w14 * y14_1 * y14_2
+ 2 * F13 * w14 * x14_2
+ 2 * F23 * w14 * y14_2
+ 2 * F31 * w14 * x14_1
+ 2 * F32 * w14 * y14_1
+ 2 * F33 * w14
)
/ (F11 * F22 - F12 * F21)
+ 4
* w14
* (
(F11 * x14_2 + F21 * y14_2 + F31) * x14_1
+ (F12 * x14_2 + F22 * y14_2 + F32) * y14_1
+ x14_2 * F13
+ y14_2 * F23
+ F33
)
* x14_2
)
J_w[:, 3, 13] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w14 * x14_1 * x14_2
+ 2 * F12 * w14 * x14_2 * y14_1
+ 2 * F21 * w14 * x14_1 * y14_2
+ 2 * F22 * w14 * y14_1 * y14_2
+ 2 * F13 * w14 * x14_2
+ 2 * F23 * w14 * y14_2
+ 2 * F31 * w14 * x14_1
+ 2 * F32 * w14 * y14_1
+ 2 * F33 * w14
)
/ (F11 * F22 - F12 * F21)
+ 4
* w14
* (
(F11 * x14_2 + F21 * y14_2 + F31) * x14_1
+ (F12 * x14_2 + F22 * y14_2 + F32) * y14_1
+ x14_2 * F13
+ y14_2 * F23
+ F33
)
* y14_2
* x14_1
)
J_w[:, 4, 13] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w14 * x14_1 * x14_2
+ 2 * F12 * w14 * x14_2 * y14_1
+ 2 * F21 * w14 * x14_1 * y14_2
+ 2 * F22 * w14 * y14_1 * y14_2
+ 2 * F13 * w14 * x14_2
+ 2 * F23 * w14 * y14_2
+ 2 * F31 * w14 * x14_1
+ 2 * F32 * w14 * y14_1
+ 2 * F33 * w14
)
/ (F11 * F22 - F12 * F21)
+ 4
* w14
* (
(F11 * x14_2 + F21 * y14_2 + F31) * x14_1
+ (F12 * x14_2 + F22 * y14_2 + F32) * y14_1
+ x14_2 * F13
+ y14_2 * F23
+ F33
)
* y14_2
* y14_1
)
J_w[:, 5, 13] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w14 * x14_1 * x14_2
+ 2 * F12 * w14 * x14_2 * y14_1
+ 2 * F21 * w14 * x14_1 * y14_2
+ 2 * F22 * w14 * y14_1 * y14_2
+ 2 * F13 * w14 * x14_2
+ 2 * F23 * w14 * y14_2
+ 2 * F31 * w14 * x14_1
+ 2 * F32 * w14 * y14_1
+ 2 * F33 * w14
)
/ (F11 * F22 - F12 * F21)
+ 4
* w14
* (
(F11 * x14_2 + F21 * y14_2 + F31) * x14_1
+ (F12 * x14_2 + F22 * y14_2 + F32) * y14_1
+ x14_2 * F13
+ y14_2 * F23
+ F33
)
* y14_2
)
J_w[:, 6, 13] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w14 * x14_1 * x14_2
+ 2 * F12 * w14 * x14_2 * y14_1
+ 2 * F21 * w14 * x14_1 * y14_2
+ 2 * F22 * w14 * y14_1 * y14_2
+ 2 * F13 * w14 * x14_2
+ 2 * F23 * w14 * y14_2
+ 2 * F31 * w14 * x14_1
+ 2 * F32 * w14 * y14_1
+ 2 * F33 * w14
)
/ (F11 * F22 - F12 * F21)
+ 4
* w14
* (
(F11 * x14_2 + F21 * y14_2 + F31) * x14_1
+ (F12 * x14_2 + F22 * y14_2 + F32) * y14_1
+ x14_2 * F13
+ y14_2 * F23
+ F33
)
* x14_1
)
J_w[:, 7, 13] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w14 * x14_1 * x14_2
+ 2 * F12 * w14 * x14_2 * y14_1
+ 2 * F21 * w14 * x14_1 * y14_2
+ 2 * F22 * w14 * y14_1 * y14_2
+ 2 * F13 * w14 * x14_2
+ 2 * F23 * w14 * y14_2
+ 2 * F31 * w14 * x14_1
+ 2 * F32 * w14 * y14_1
+ 2 * F33 * w14
)
/ (F11 * F22 - F12 * F21)
+ 4
* w14
* (
(F11 * x14_2 + F21 * y14_2 + F31) * x14_1
+ (F12 * x14_2 + F22 * y14_2 + F32) * y14_1
+ x14_2 * F13
+ y14_2 * F23
+ F33
)
* y14_1
)
J_w[:, 8, 13] = (
4
* w14
* (
(F11 * x14_2 + F21 * y14_2 + F31) * x14_1
+ (F12 * x14_2 + F22 * y14_2 + F32) * y14_1
+ x14_2 * F13
+ y14_2 * F23
+ F33
)
- 4 * F33 * w14
- 4 * F13 * w14 * x14_2
- 4 * F23 * w14 * y14_2
- 4 * F31 * w14 * x14_1
- 4 * F32 * w14 * y14_1
- 4 * F11 * w14 * x14_1 * x14_2
- 4 * F12 * w14 * x14_2 * y14_1
- 4 * F21 * w14 * x14_1 * y14_2
- 4 * F22 * w14 * y14_1 * y14_2
)
J_w[:, 0, 14] = (
-2
* (F22 * F33 - F23 * F32)
* (
2 * F11 * w15 * x15_1 * x15_2
+ 2 * F12 * w15 * x15_2 * y15_1
+ 2 * F21 * w15 * x15_1 * y15_2
+ 2 * F22 * w15 * y15_1 * y15_2
+ 2 * F13 * w15 * x15_2
+ 2 * F23 * w15 * y15_2
+ 2 * F31 * w15 * x15_1
+ 2 * F32 * w15 * y15_1
+ 2 * F33 * w15
)
/ (F11 * F22 - F12 * F21)
+ 4
* w15
* (
(F11 * x15_2 + F21 * y15_2 + F31) * x15_1
+ (F12 * x15_2 + F22 * y15_2 + F32) * y15_1
+ x15_2 * F13
+ y15_2 * F23
+ F33
)
* x15_2
* x15_1
)
J_w[:, 1, 14] = (
-2
* (-F21 * F33 + F23 * F31)
* (
2 * F11 * w15 * x15_1 * x15_2
+ 2 * F12 * w15 * x15_2 * y15_1
+ 2 * F21 * w15 * x15_1 * y15_2
+ 2 * F22 * w15 * y15_1 * y15_2
+ 2 * F13 * w15 * x15_2
+ 2 * F23 * w15 * y15_2
+ 2 * F31 * w15 * x15_1
+ 2 * F32 * w15 * y15_1
+ 2 * F33 * w15
)
/ (F11 * F22 - F12 * F21)
+ 4
* w15
* (
(F11 * x15_2 + F21 * y15_2 + F31) * x15_1
+ (F12 * x15_2 + F22 * y15_2 + F32) * y15_1
+ x15_2 * F13
+ y15_2 * F23
+ F33
)
* x15_2
* y15_1
)
J_w[:, 2, 14] = (
-2
* (F21 * F32 - F22 * F31)
* (
2 * F11 * w15 * x15_1 * x15_2
+ 2 * F12 * w15 * x15_2 * y15_1
+ 2 * F21 * w15 * x15_1 * y15_2
+ 2 * F22 * w15 * y15_1 * y15_2
+ 2 * F13 * w15 * x15_2
+ 2 * F23 * w15 * y15_2
+ 2 * F31 * w15 * x15_1
+ 2 * F32 * w15 * y15_1
+ 2 * F33 * w15
)
/ (F11 * F22 - F12 * F21)
+ 4
* w15
* (
(F11 * x15_2 + F21 * y15_2 + F31) * x15_1
+ (F12 * x15_2 + F22 * y15_2 + F32) * y15_1
+ x15_2 * F13
+ y15_2 * F23
+ F33
)
* x15_2
)
J_w[:, 3, 14] = (
-2
* (-F12 * F33 + F13 * F32)
* (
2 * F11 * w15 * x15_1 * x15_2
+ 2 * F12 * w15 * x15_2 * y15_1
+ 2 * F21 * w15 * x15_1 * y15_2
+ 2 * F22 * w15 * y15_1 * y15_2
+ 2 * F13 * w15 * x15_2
+ 2 * F23 * w15 * y15_2
+ 2 * F31 * w15 * x15_1
+ 2 * F32 * w15 * y15_1
+ 2 * F33 * w15
)
/ (F11 * F22 - F12 * F21)
+ 4
* w15
* (
(F11 * x15_2 + F21 * y15_2 + F31) * x15_1
+ (F12 * x15_2 + F22 * y15_2 + F32) * y15_1
+ x15_2 * F13
+ y15_2 * F23
+ F33
)
* y15_2
* x15_1
)
J_w[:, 4, 14] = (
-2
* (F11 * F33 - F13 * F31)
* (
2 * F11 * w15 * x15_1 * x15_2
+ 2 * F12 * w15 * x15_2 * y15_1
+ 2 * F21 * w15 * x15_1 * y15_2
+ 2 * F22 * w15 * y15_1 * y15_2
+ 2 * F13 * w15 * x15_2
+ 2 * F23 * w15 * y15_2
+ 2 * F31 * w15 * x15_1
+ 2 * F32 * w15 * y15_1
+ 2 * F33 * w15
)
/ (F11 * F22 - F12 * F21)
+ 4
* w15
* (
(F11 * x15_2 + F21 * y15_2 + F31) * x15_1
+ (F12 * x15_2 + F22 * y15_2 + F32) * y15_1
+ x15_2 * F13
+ y15_2 * F23
+ F33
)
* y15_2
* y15_1
)
J_w[:, 5, 14] = (
-2
* (-F11 * F32 + F12 * F31)
* (
2 * F11 * w15 * x15_1 * x15_2
+ 2 * F12 * w15 * x15_2 * y15_1
+ 2 * F21 * w15 * x15_1 * y15_2
+ 2 * F22 * w15 * y15_1 * y15_2
+ 2 * F13 * w15 * x15_2
+ 2 * F23 * w15 * y15_2
+ 2 * F31 * w15 * x15_1
+ 2 * F32 * w15 * y15_1
+ 2 * F33 * w15
)
/ (F11 * F22 - F12 * F21)
+ 4
* w15
* (
(F11 * x15_2 + F21 * y15_2 + F31) * x15_1
+ (F12 * x15_2 + F22 * y15_2 + F32) * y15_1
+ x15_2 * F13
+ y15_2 * F23
+ F33
)
* y15_2
)
J_w[:, 6, 14] = (
-2
* (F12 * F23 - F13 * F22)
* (
2 * F11 * w15 * x15_1 * x15_2
+ 2 * F12 * w15 * x15_2 * y15_1
+ 2 * F21 * w15 * x15_1 * y15_2
+ 2 * F22 * w15 * y15_1 * y15_2
+ 2 * F13 * w15 * x15_2
+ 2 * F23 * w15 * y15_2
+ 2 * F31 * w15 * x15_1
+ 2 * F32 * w15 * y15_1
+ 2 * F33 * w15
)
/ (F11 * F22 - F12 * F21)
+ 4
* w15
* (
(F11 * x15_2 + F21 * y15_2 + F31) * x15_1
+ (F12 * x15_2 + F22 * y15_2 + F32) * y15_1
+ x15_2 * F13
+ y15_2 * F23
+ F33
)
* x15_1
)
J_w[:, 7, 14] = (
-2
* (-F11 * F23 + F13 * F21)
* (
2 * F11 * w15 * x15_1 * x15_2
+ 2 * F12 * w15 * x15_2 * y15_1
+ 2 * F21 * w15 * x15_1 * y15_2
+ 2 * F22 * w15 * y15_1 * y15_2
+ 2 * F13 * w15 * x15_2
+ 2 * F23 * w15 * y15_2
+ 2 * F31 * w15 * x15_1
+ 2 * F32 * w15 * y15_1
+ 2 * F33 * w15
)
/ (F11 * F22 - F12 * F21)
+ 4
* w15
* (
(F11 * x15_2 + F21 * y15_2 + F31) * x15_1
+ (F12 * x15_2 + F22 * y15_2 + F32) * y15_1
+ x15_2 * F13
+ y15_2 * F23
+ F33
)
* y15_1
)
J_w[:, 8, 14] = (
4
* w15
* (
(F11 * x15_2 + F21 * y15_2 + F31) * x15_1
+ (F12 * x15_2 + F22 * y15_2 + F32) * y15_1
+ x15_2 * F13
+ y15_2 * F23
+ F33
)
- 4 * F33 * w15
- 4 * F13 * w15 * x15_2
- 4 * F23 * w15 * y15_2
- 4 * F31 * w15 * x15_1
- 4 * F32 * w15 * y15_1
- 4 * F11 * w15 * x15_1 * x15_2
- 4 * F12 * w15 * x15_2 * y15_1
- 4 * F21 * w15 * x15_1 * y15_2
- 4 * F22 * w15 * y15_1 * y15_2
)
J_Fw = torch.zeros((b, 9, 15), device=F.device)
tmp = torch.eye(9, 9, dtype=torch.float, device=F.device)
for i in range(b):
try:
J_Fw[i, :, :] = -torch.inverse(J_F[i, :, :].double()).mm(
J_w[i, :, :].double()
)
tmp = J_R[i, :, :]
except Exception as e:
J_Fw[i, :, :] = -torch.inverse(tmp).mm(J_w[i, :, :])
return J_Fw
| 488,776 | Python | .py | 15,261 | 20.190486 | 84 | 0.310999 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,694 | losses.py | disungatullina_MinBackProp/toy_examples/fundamental/losses.py | import torch
def frobenius_norm(F_true, F):
"""Squared Frobenius norm of matrices' difference"""
return ((F - F_true) ** 2).sum(dim=(-2, -1))
| 152 | Python | .py | 4 | 34.5 | 56 | 0.643836 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,695 | datasets.py | disungatullina_MinBackProp/toy_examples/rotation/datasets.py | import torch
def create_toy_dataset():
p1 = torch.Tensor([1, 0, 0]).unsqueeze(0)
p2 = torch.Tensor([0.0472, 0.9299, 0.7934]).unsqueeze(0)
p3 = torch.Tensor([0.7017, 0.1494, 0.7984]).unsqueeze(0)
p4 = torch.Tensor([0.6007, 0.8878, 0.9169]).unsqueeze(0)
P = torch.cat([p1, p2, p3, p4], dim=0).permute(1, 0).unsqueeze(0) # 1 x 3 x 4
q1 = torch.Tensor([0.9, 0.1, 0.0]).unsqueeze(0)
q2 = torch.Tensor([0.0472, 0.9299, 0.7934]).unsqueeze(0)
q3 = torch.Tensor([0.7017, 0.1494, 0.7984]).unsqueeze(0)
q4 = torch.Tensor([0.6007, 0.8878, 0.9169]).unsqueeze(0)
Q = torch.cat([q1, q2, q3, q4], dim=0).permute(1, 0).unsqueeze(0) # 1 x 3 x 4
R_true = torch.eye(3, dtype=torch.float).unsqueeze(0) # 1 x 3 x 3
return P, Q, R_true
def get_dataset():
return create_toy_dataset()
| 822 | Python | .py | 16 | 46.6875 | 82 | 0.619524 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,696 | nodes.py | disungatullina_MinBackProp/toy_examples/rotation/nodes.py | import torch
import torch.nn as nn
from ddn.ddn.pytorch.node import *
############ DDN with constraint ############
class RigitNodeConstraint(EqConstDeclarativeNode):
"""Declarative Rigit node with R^T R = I constraint"""
def __init__(self):
super().__init__()
def objective(self, A, B, w, y):
"""
A : b x 3 x N
B : b x 3 x N
y : b x 3 x 3
w : b x N
"""
w = torch.nn.functional.relu(w)
error = torch.sum((y.bmm(A) - B) ** 2, dim=1)
return torch.einsum("bn,bn->b", (w**2, error))
def equality_constraints(self, A, B, w, y):
eye = torch.eye(y.shape[1])
eye = eye.reshape((1, y.shape[1], y.shape[2]))
eyes = eye.repeat(y.shape[0], 1, 1)
constraint = (y.bmm(y.permute(0, 2, 1)) - eyes) ** 2
return constraint.sum(-1).sum(-1)
def solve(self, A, B, w):
w = torch.nn.functional.relu(w)
A = A.detach()
B = B.detach()
w = w.detach()
y = self.__solve(A, B, w).requires_grad_()
return y.detach(), None
def __solve(self, A, B, w):
out_batch = []
for batch in range(w.size(0)):
W = torch.diag(w[batch])
B_W = B[batch].mm(W)
A_W = A[batch].mm(W)
M = B_W.mm(A_W.permute(1, 0))
U, _, Vh = torch.linalg.svd(M)
R = U.mm(Vh)
det = torch.linalg.det(R)
if det < 0:
Vh[:, 2] *= -1
R = U.mm(Vh)
out_batch.append(R.unsqueeze(0))
R = torch.cat(out_batch, 0)
return R
############ SVD Layer ############
def SVDLayer(A, B, w):
w = torch.nn.functional.relu(w)
out_batch = []
for batch in range(w.size(0)):
W = torch.diag(w[batch])
B_W = B[batch].mm(W)
A_W = A[batch].mm(W)
M = B_W.mm(A_W.permute(1, 0))
U, _, Vh = torch.linalg.svd(M)
R = U.mm(Vh)
det = torch.linalg.det(R)
if det < 0:
Vh_ = Vh.clone()
Vh_[:, 2] *= -1
R = U.mm(Vh_)
out_batch.append(R.unsqueeze(0))
R = torch.cat(out_batch, 0)
return R
############ IFT function ############
class IFTFunction(torch.autograd.Function):
@staticmethod
def forward(A, B, w):
"""
A : b x 3 x N
B : b x 3 x N
w : b x N
"""
w = torch.nn.functional.relu(w)
out_batch = []
for batch in range(w.size(0)):
W = torch.diag(w[batch])
B_W = B[batch].mm(W)
A_W = A[batch].mm(W)
M = B_W.mm(A_W.permute(1, 0))
U, _, Vh = torch.linalg.svd(M)
R = U.mm(Vh)
det = torch.linalg.det(R)
if det < 0:
Vh_ = Vh.clone()
Vh_[:, 2] *= -1
R = U.mm(Vh_)
out_batch.append(R.unsqueeze(0))
R = torch.cat(out_batch, 0)
return R
@staticmethod
def setup_context(ctx, inputs, output):
A, B, w = inputs
ctx.save_for_backward(A, B, w, output)
@staticmethod
def backward(ctx, grad_output):
"""
A : b x 3 x N
B : b x 3 x N
w : b x N
"""
A, B, w, output = ctx.saved_tensors # output: b x 3 x 3
grad_A = grad_B = None
b = grad_output.shape[0]
w = torch.nn.functional.relu(w)
# R: b x 3 x 3; w: b x 4; J_Rw: b x 9 x 4; grad_output: b x 3 x 3
J_Rw = compute_jacobians(output, w, A, B) # b x 9 x 4
J_Rw = torch.einsum("bi,bij->bj", grad_output.view(b, 9), J_Rw)
grad_w = J_Rw.view(b, 4)
return None, None, grad_w
class IFTLayer(nn.Module):
def __init__(self):
super().__init__()
def forward(self, A, B, w):
return IFTFunction.apply(A, B, w)
def compute_jacobians(R, w, A, B):
"""
E : b x 3 x 3
w : b x 4
A : b x 3 x 4
B : b x 3 x 4
"""
b = R.shape[0]
R11 = R[:, 0, 0]
R12 = R[:, 0, 1]
R13 = R[:, 0, 2]
R21 = R[:, 1, 0]
R22 = R[:, 1, 1]
R23 = R[:, 1, 2]
R31 = R[:, 2, 0]
R32 = R[:, 2, 1]
R33 = R[:, 2, 2]
x11 = A[:, 0, 0]
x12 = A[:, 1, 0]
x13 = A[:, 2, 0]
x21 = A[:, 0, 1]
x22 = A[:, 1, 1]
x23 = A[:, 2, 1]
x31 = A[:, 0, 2]
x32 = A[:, 1, 2]
x33 = A[:, 2, 2]
x41 = A[:, 0, 3]
x42 = A[:, 1, 3]
x43 = A[:, 2, 3]
y11 = B[:, 0, 0]
y12 = B[:, 1, 0]
y13 = B[:, 2, 0]
y21 = B[:, 0, 1]
y22 = B[:, 1, 1]
y23 = B[:, 2, 1]
y31 = B[:, 0, 2]
y32 = B[:, 1, 2]
y33 = B[:, 2, 2]
y41 = B[:, 0, 3]
y42 = B[:, 1, 3]
y43 = B[:, 2, 3]
w1 = w[:, 0]
w2 = w[:, 1]
w3 = w[:, 2]
w4 = w[:, 3]
J_R = torch.zeros((b, 9, 9), device=R.device)
# R11
denom_r = 2 * (
R11**2 * R31
+ R11 * R12 * R32
+ R11 * R13 * R33
+ R21**2 * R31
+ R21 * R22 * R32
+ R21 * R23 * R33
+ R31**3
+ R31 * R32**2
+ R31 * R33**2
- R31
)
const_r = (
R31 * w1**2 * x11**2
+ R31 * w2**2 * x21**2
+ R31 * w3**2 * x31**2
+ R31 * w4**2 * x41**2
+ R32 * w1**2 * x11 * x12
+ R32 * w2**2 * x21 * x22
+ R32 * w3**2 * x31 * x32
+ R32 * w4**2 * x41 * x42
+ R33 * w1**2 * x11 * x13
+ R33 * w2**2 * x21 * x23
+ R33 * w3**2 * x31 * x33
+ R33 * w4**2 * x41 * x43
- w1**2 * x11 * y13
- w2**2 * x21 * y23
- w3**2 * x31 * y33
- w4**2 * x41 * y43
)
J_R[:, 0, 0] = (
-1
/ denom_r
* (
12 * R11**2
+ 4 * R12**2
+ 4 * R13**2
+ 4 * R21**2
+ 4 * R31**2
- 4
)
* const_r
+ 1
/ denom_r**2
* (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* const_r
* (4 * R11 * R31 + 2 * R12 * R32 + 2 * R13 * R33)
)
+ 2 * w1**2 * x11**2
+ 2 * w2**2 * x21**2
+ 2 * w3**2 * x31**2
+ 2 * w4**2 * x41**2
)
J_R[:, 1, 0] = (
-1 / denom_r * ((8 * R11 * R12 + 4 * R21 * R22 + 4 * R31 * R32) * const_r)
+ 1
/ denom_r**2
* (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* const_r
* (4 * R11 * R31 + 2 * R12 * R32 + 2 * R13 * R33)
)
+ 2 * w1**2 * x11 * x12
+ 2 * w2**2 * x21 * x22
+ 2 * w3**2 * x31 * x32
+ 2 * w4**2 * x41 * x42
)
J_R[:, 2, 0] = (
-1 / denom_r * ((8 * R11 * R13 + 4 * R21 * R23 + 4 * R31 * R33) * const_r)
+ 1
/ denom_r**2
* (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* const_r
* (4 * R11 * R31 + 2 * R12 * R32 + 2 * R13 * R33)
)
+ 2 * w1**2 * x11 * x13
+ 2 * w2**2 * x21 * x23
+ 2 * w3**2 * x31 * x33
+ 2 * w4**2 * x41 * x43
)
J_R[:, 3, 0] = -1 / denom_r * (
(8 * R11 * R21 + 4 * R12 * R22 + 4 * R13 * R23) * const_r
) + 1 / denom_r**2 * (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* const_r
* (4 * R11 * R31 + 2 * R12 * R32 + 2 * R13 * R33)
)
J_R[:, 4, 0] = -1 / denom_r * (4 * R12 * R21 * const_r) + 1 / denom_r**2 * (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* const_r
* (4 * R11 * R31 + 2 * R12 * R32 + 2 * R13 * R33)
)
J_R[:, 5, 0] = -1 / denom_r * (4 * R13 * R21 * const_r) + 1 / denom_r**2 * (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* const_r
* (4 * R11 * R31 + 2 * R12 * R32 + 2 * R13 * R33)
)
J_R[:, 6, 0] = -1 / denom_r * (
(8 * R11 * R31 + 4 * R12 * R32 + 4 * R13 * R33) * const_r
) + 1 / denom_r**2 * (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* const_r
* (4 * R11 * R31 + 2 * R12 * R32 + 2 * R13 * R33)
)
J_R[:, 7, 0] = -1 / denom_r * ((4 * R12 * R31) * const_r) + 1 / denom_r**2 * (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* const_r
* (4 * R11 * R31 + 2 * R12 * R32 + 2 * R13 * R33)
)
J_R[:, 8, 0] = (
-4 * R13 * R31 * const_r / denom_r
+ (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* const_r
* (4 * R11 * R31 + 2 * R12 * R32 + 2 * R13 * R33)
/ denom_r**2
)
# R12
J_R[:, 0, 1] = (
-1 / denom_r * ((8 * R11 * R12 + 4 * R21 * R22 + 4 * R31 * R32) * const_r)
+ 1
/ denom_r**2
* (
2
* (
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* const_r
* (R11 * R32)
)
+ 2 * w1**2 * x11 * x12
+ 2 * w2**2 * x21 * x22
+ 2 * w3**2 * x31 * x32
+ 2 * w4**2 * x41 * x42
)
J_R[:, 1, 1] = (
-1
/ denom_r
* (
(
4 * R11**2
+ 12 * R12**2
+ 4 * R13**2
+ 4 * R22**2
+ 4 * R32**2
- 4
)
* const_r
)
+ 1
/ denom_r**2
* (
2
* (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* const_r
* (R11 * R32)
)
+ 2 * w1**2 * x12**2
+ 2 * w2**2 * x22**2
+ 2 * w3**2 * x32**2
+ 2 * w4**2 * x42**2
)
J_R[:, 2, 1] = (
-1 / denom_r * ((8 * R12 * R13 + 4 * R22 * R23 + 4 * R32 * R33) * const_r)
+ 1
/ denom_r**2
* (
2
* (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* const_r
* (R11 * R32)
)
+ 2 * w1**2 * x12 * x13
+ 2 * w2**2 * x22 * x23
+ 2 * w3**2 * x32 * x33
+ 2 * w4**2 * x42 * x43
)
J_R[:, 3, 1] = -1 / denom_r * ((4 * R11 * R22) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* const_r
* (R11 * R32)
)
J_R[:, 4, 1] = -1 / denom_r * (
(4 * R11 * R21 + 8 * R12 * R22 + 4 * R13 * R23) * const_r
) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* const_r
* (R11 * R32)
)
J_R[:, 5, 1] = -1 / denom_r * ((4 * R13 * R22) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* const_r
* (R11 * R32)
)
J_R[:, 6, 1] = -1 / denom_r * ((4 * R11 * R32) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* const_r
* (R11 * R32)
)
J_R[:, 7, 1] = -1 / denom_r * (
(4 * R11 * R31 + 8 * R12 * R32 + 4 * R13 * R33) * const_r
) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* const_r
* (R11 * R32)
)
J_R[:, 8, 1] = -1 / denom_r * ((4 * R13 * R32) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* const_r
* (R11 * R32)
)
# R13
J_R[:, 0, 2] = (
-1 / denom_r * ((8 * R11 * R13 + 4 * R21 * R23 + 4 * R31 * R33) * const_r)
+ 1
/ denom_r**2
* (
2
* (
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* const_r
* (R11 * R33)
)
+ 2 * w1**2 * x11 * x13
+ 2 * w2**2 * x21 * x23
+ 2 * w3**2 * x31 * x33
+ 2 * w4**2 * x41 * x43
)
J_R[:, 1, 2] = (
-1 / denom_r * ((8 * R12 * R13 + 4 * R22 * R23 + 4 * R32 * R33) * const_r)
+ 1
/ denom_r**2
* (
2
* (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* const_r
* (R11 * R33)
)
+ 2 * w1**2 * x12 * x13
+ 2 * w2**2 * x22 * x23
+ 2 * w3**2 * x32 * x33
+ 2 * w4**2 * x42 * x43
)
J_R[:, 2, 2] = (
-1
/ denom_r
* (
(
4 * R11**2
+ 4 * R12**2
+ 12 * R13**2
+ 4 * R23**2
+ 4 * R33**2
- 4
)
* const_r
)
+ 1
/ denom_r**2
* (
2
* (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* const_r
* (R11 * R33)
)
+ 2 * w1**2 * x13**2
+ 2 * w2**2 * x23**2
+ 2 * w3**2 * x33**2
+ 2 * w4**2 * x43**2
)
J_R[:, 3, 2] = -1 / denom_r * ((4 * R11 * R23) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* const_r
* (R11 * R33)
)
J_R[:, 4, 2] = -1 / denom_r * ((4 * R12 * R23) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* const_r
* (R11 * R33)
)
J_R[:, 5, 2] = -1 / denom_r * (
(4 * R11 * R21 + 4 * R12 * R22 + 8 * R13 * R23) * const_r
) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* const_r
* (R11 * R33)
)
J_R[:, 6, 2] = -1 / denom_r * ((4 * R11 * R33) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* const_r
* (R11 * R33)
)
J_R[:, 7, 2] = -1 / denom_r * ((4 * R12 * R33) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* const_r
* (R11 * R33)
)
J_R[:, 8, 2] = -1 / denom_r * (
(4 * R11 * R31 + 4 * R12 * R32 + 8 * R13 * R33) * const_r
) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* const_r
* (R11 * R33)
)
# # R21
J_R[:, 0, 3] = -1 / denom_r * (
(8 * R11 * R21 + 4 * R12 * R22 + 4 * R13 * R23) * const_r
) + 1 / denom_r**2 * (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* const_r
* (4 * R21 * R31 + 2 * R22 * R32 + 2 * R23 * R33)
)
J_R[:, 1, 3] = -1 / denom_r * ((4 * R11 * R22) * const_r) + 1 / denom_r**2 * (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* const_r
* (4 * R21 * R31 + 2 * R22 * R32 + 2 * R23 * R33)
)
J_R[:, 2, 3] = -1 / denom_r * ((4 * R23 * R11) * const_r) + 1 / denom_r**2 * (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* const_r
* (4 * R21 * R31 + 2 * R22 * R32 + 2 * R23 * R33)
)
J_R[:, 3, 3] = (
-1
/ denom_r
* (
(
4 * R11**2
+ 12 * R21**2
+ 4 * R22**2
+ 4 * R23**2
+ 4 * R31**2
- 4
)
* const_r
)
+ 1
/ denom_r**2
* (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* const_r
* (4 * R21 * R31 + 2 * R22 * R32 + 2 * R23 * R33)
)
+ 2 * w1**2 * x11**2
+ 2 * w2**2 * x21**2
+ 2 * w3**2 * x31**2
+ 2 * w4**2 * x41**2
)
J_R[:, 4, 3] = (
-1 / denom_r * ((4 * R11 * R12 + 8 * R21 * R22 + 4 * R31 * R32) * const_r)
+ 1
/ denom_r**2
* (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* const_r
* (4 * R21 * R31 + 2 * R22 * R32 + 2 * R23 * R33)
)
+ 2 * w1**2 * x11 * x12
+ 2 * w2**2 * x21 * x22
+ 2 * w3**2 * x31 * x32
+ 2 * w4**2 * x41 * x42
)
J_R[:, 5, 3] = (
-1 / denom_r * ((4 * R11 * R13 + 8 * R21 * R23 + 4 * R31 * R33) * const_r)
+ 1
/ denom_r**2
* (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* const_r
* (4 * R21 * R31 + 2 * R22 * R32 + 2 * R23 * R33)
)
+ 2 * w1**2 * x11 * x13
+ 2 * w2**2 * x21 * x23
+ 2 * w3**2 * x31 * x33
+ 2 * w4**2 * x41 * x43
)
J_R[:, 6, 3] = -1 / denom_r * (
(8 * R21 * R31 + 4 * R22 * R32 + 4 * R23 * R33) * const_r
) + 1 / denom_r**2 * (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* const_r
* (4 * R21 * R31 + 2 * R22 * R32 + 2 * R23 * R33)
)
J_R[:, 7, 3] = -1 / denom_r * ((4 * R22 * R31) * const_r) + 1 / denom_r**2 * (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* const_r
* (4 * R21 * R31 + 2 * R22 * R32 + 2 * R23 * R33)
)
J_R[:, 8, 3] = -1 / denom_r * ((4 * R23 * R31) * const_r) + 1 / denom_r**2 * (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* const_r
* (4 * R21 * R31 + 2 * R22 * R32 + 2 * R23 * R33)
)
# R22
J_R[:, 0, 4] = -1 / denom_r * ((4 * R12 * R21) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* const_r
* (R21 * R32)
)
J_R[:, 1, 4] = -1 / denom_r * (
(4 * R11 * R21 + 8 * R12 * R22 + 4 * R13 * R23) * const_r
) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* const_r
* (R21 * R32)
)
J_R[:, 2, 4] = -1 / denom_r * ((4 * R12 * R23) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* const_r
* (R21 * R32)
)
J_R[:, 3, 4] = (
-1 / denom_r * ((4 * R11 * R12 + 8 * R21 * R22 + 4 * R31 * R32) * const_r)
+ 1
/ denom_r**2
* (
2
* (
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* const_r
* (R21 * R32)
)
+ 2 * w1**2 * x11 * x12
+ 2 * w2**2 * x21 * x22
+ 2 * w3**2 * x31 * x32
+ 2 * w4**2 * x41 * x42
)
J_R[:, 4, 4] = (
-1
/ denom_r
* (
(
4 * R12**2
+ 4 * R21**2
+ 12 * R22**2
+ 4 * R23**2
+ 4 * R32**2
- 4
)
* const_r
)
+ 1
/ denom_r**2
* (
2
* (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* const_r
* (R21 * R32)
)
+ 2 * w1**2 * x12**2
+ 2 * w2**2 * x22**2
+ 2 * w3**2 * x32**2
+ 2 * w4**2 * x42**2
)
J_R[:, 5, 4] = (
-1 / denom_r * ((4 * R12 * R13 + 8 * R22 * R23 + 4 * R32 * R33) * const_r)
+ 1
/ denom_r**2
* (
2
* (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* const_r
* (R21 * R32)
)
+ 2 * w1**2 * x12 * x13
+ 2 * w2**2 * x22 * x23
+ 2 * w3**2 * x32 * x33
+ 2 * w4**2 * x42 * x43
)
J_R[:, 6, 4] = -1 / denom_r * ((4 * R21 * R32) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* const_r
* (R21 * R32)
)
J_R[:, 7, 4] = -1 / denom_r * (
(4 * R21 * R31 + 8 * R22 * R32 + 4 * R23 * R33) * const_r
) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* const_r
* (R21 * R32)
)
J_R[:, 8, 4] = -1 / denom_r * ((4 * R23 * R32) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* const_r
* (R21 * R32)
)
# R23
J_R[:, 0, 5] = -1 / denom_r * ((4 * R13 * R21) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* const_r
* (R21 * R33)
)
J_R[:, 1, 5] = -1 / denom_r * ((4 * R13 * R22) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* const_r
* (R21 * R33)
)
J_R[:, 2, 5] = -1 / denom_r * (
(4 * R11 * R21 + 4 * R12 * R22 + 8 * R13 * R23) * const_r
) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* const_r
* (R21 * R33)
)
J_R[:, 3, 5] = (
-1 / denom_r * ((4 * R11 * R13 + 8 * R21 * R23 + 4 * R31 * R33) * const_r)
+ 1
/ denom_r**2
* (
2
* (
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* const_r
* (R21 * R33)
)
+ 2 * w1**2 * x11 * x13
+ 2 * w2**2 * x21 * x23
+ 2 * w3**2 * x31 * x33
+ 2 * w4**2 * x41 * x43
)
J_R[:, 4, 5] = (
-1 / denom_r * ((4 * R12 * R13 + 8 * R22 * R23 + 4 * R32 * R33) * const_r)
+ 1
/ denom_r**2
* (
2
* (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* const_r
* (R21 * R33)
)
+ 2 * w1**2 * x12 * x13
+ 2 * w2**2 * x22 * x23
+ 2 * w3**2 * x32 * x33
+ 2 * w4**2 * x42 * x43
)
J_R[:, 5, 5] = (
-1
/ denom_r
* (
(
4 * R13**2
+ 4 * R21**2
+ 4 * R22**2
+ 12 * R23**2
+ 4 * R33**2
- 4
)
* const_r
)
+ 1
/ denom_r**2
* (
2
* (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* const_r
* (R21 * R33)
)
+ 2 * w1**2 * x13**2
+ 2 * w2**2 * x23**2
+ 2 * w3**2 * x33**2
+ 2 * w4**2 * x43**2
)
J_R[:, 6, 5] = -1 / denom_r * ((4 * R21 * R33) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* const_r
* (R21 * R33)
)
J_R[:, 7, 5] = -1 / denom_r * ((4 * R22 * R33) * const_r) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* const_r
* (R21 * R33)
)
J_R[:, 8, 5] = -1 / denom_r * (
(4 * R21 * R31 + 4 * R22 * R32 + 8 * R23 * R33) * const_r
) + 1 / denom_r**2 * (
2
* (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* const_r
* (R21 * R33)
)
# R31
J_R[:, 0, 6] = -1 / denom_r * (
(8 * R11 * R31 + 4 * R12 * R32 + 4 * R13 * R33) * const_r
- (
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* (
w1**2 * x11**2
+ w2**2 * x21**2
+ w3**2 * x31**2
+ w4**2 * x41**2
)
) + 1 / denom_r**2 * (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* const_r
* (2 * R11**2 + 2 * R21**2 + 6 * R31**2 + 2 * R32**2 + 2 * R33**2 - 2)
)
J_R[:, 1, 6] = -1 / denom_r * (
(4 * R11 * R32) * const_r
- (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* (
w1**2 * x11**2
+ w2**2 * x21**2
+ w3**2 * x31**2
+ w4**2 * x41**2
)
) + 1 / denom_r**2 * (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* const_r
* (2 * R11**2 + 2 * R21**2 + 6 * R31**2 + 2 * R32**2 + 2 * R33**2 - 2)
)
J_R[:, 2, 6] = -1 / denom_r * (
(4 * R11 * R33) * const_r
- (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* (
w1**2 * x11**2
+ w2**2 * x21**2
+ w3**2 * x31**2
+ w4**2 * x41**2
)
) + 1 / denom_r**2 * (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* const_r
* (2 * R11**2 + 2 * R21**2 + 6 * R31**2 + 2 * R32**2 + 2 * R33**2 - 2)
)
J_R[:, 3, 6] = -1 / denom_r * (
(8 * R21 * R31 + 4 * R22 * R32 + 4 * R23 * R33) * const_r
- (
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* (
w1**2 * x11**2
+ w2**2 * x21**2
+ w3**2 * x31**2
+ w4**2 * x41**2
)
) + 1 / denom_r**2 * (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* const_r
* (2 * R11**2 + 2 * R21**2 + 6 * R31**2 + 2 * R32**2 + 2 * R33**2 - 2)
)
J_R[:, 4, 6] = -1 / denom_r * (
(4 * R21 * R32) * const_r
- (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* (
w1**2 * x11**2
+ w2**2 * x21**2
+ w3**2 * x31**2
+ w4**2 * x41**2
)
) + 1 / denom_r**2 * (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* const_r
* (2 * R11**2 + 2 * R21**2 + 6 * R31**2 + 2 * R32**2 + 2 * R33**2 - 2)
)
J_R[:, 5, 6] = -1 / denom_r * (
(4 * R21 * R33) * const_r
- (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* (
w1**2 * x11**2
+ w2**2 * x21**2
+ w3**2 * x31**2
+ w4**2 * x41**2
)
) + 1 / denom_r**2 * (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* const_r
* (2 * R11**2 + 2 * R21**2 + 6 * R31**2 + 2 * R32**2 + 2 * R33**2 - 2)
)
J_R[:, 6, 6] = (
-1
/ denom_r
* (
(
4 * R11**2
+ 4 * R21**2
+ 12 * R31**2
+ 4 * R32**2
+ 4 * R33**2
- 4
)
* const_r
- (
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* (
w1**2 * x11**2
+ w2**2 * x21**2
+ w3**2 * x31**2
+ w4**2 * x41**2
)
)
+ 1
/ denom_r**2
* (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* const_r
* (
2 * R11**2
+ 2 * R21**2
+ 6 * R31**2
+ 2 * R32**2
+ 2 * R33**2
- 2
)
)
+ 2 * w1**2 * x11**2
+ 2 * w2**2 * x21**2
+ 2 * w3**2 * x31**2
+ 2 * w4**2 * x41**2
)
J_R[:, 7, 6] = (
-1
/ denom_r
* (
(4 * R11 * R12 + 4 * R21 * R22 + 8 * R31 * R32) * const_r
- (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* (
w1**2 * x11**2
+ w2**2 * x21**2
+ w3**2 * x31**2
+ w4**2 * x41**2
)
)
+ 1
/ denom_r**2
* (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* const_r
* (
2 * R11**2
+ 2 * R21**2
+ 6 * R31**2
+ 2 * R32**2
+ 2 * R33**2
- 2
)
)
+ 2 * w1**2 * x11 * x12
+ 2 * w2**2 * x21 * x22
+ 2 * w3**2 * x31 * x32
+ 2 * w4**2 * x41 * x42
)
J_R[:, 8, 6] = (
-1
/ denom_r
* (
(4 * R11 * R13 + 4 * R21 * R23 + 8 * R31 * R33) * const_r
- (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* (
w1**2 * x11**2
+ w2**2 * x21**2
+ w3**2 * x31**2
+ w4**2 * x41**2
)
)
+ 1
/ denom_r**2
* (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* const_r
* (
2 * R11**2
+ 2 * R21**2
+ 6 * R31**2
+ 2 * R32**2
+ 2 * R33**2
- 2
)
)
+ 2 * w1**2 * x11 * x13
+ 2 * w2**2 * x21 * x23
+ 2 * w3**2 * x31 * x33
+ 2 * w4**2 * x41 * x43
)
# R32
J_R[:, 0, 7] = -1 / denom_r * (
(4 * R12 * R31) * const_r
- (
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
)
) + 1 / denom_r**2 * (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* const_r
* (2 * R11 * R12 + 2 * R21 * R22 + 4 * R31 * R32)
)
J_R[:, 1, 7] = -1 / denom_r * (
(4 * R11 * R31 + 8 * R12 * R32 + 4 * R13 * R33) * const_r
- (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
)
) + 1 / denom_r**2 * (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* const_r
* (2 * R11 * R12 + 2 * R21 * R22 + 4 * R31 * R32)
)
J_R[:, 2, 7] = -1 / denom_r * (
(4 * R12 * R33) * const_r
- (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
)
) + 1 / denom_r**2 * (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* const_r
* (2 * R11 * R12 + 2 * R21 * R22 + 4 * R31 * R32)
)
J_R[:, 3, 7] = -1 / denom_r * (
(4 * R22 * R31) * const_r
- (
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
)
) + 1 / denom_r**2 * (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* const_r
* (2 * R11 * R12 + 2 * R21 * R22 + 4 * R31 * R32)
)
J_R[:, 4, 7] = -1 / denom_r * (
(4 * R21 * R31 + 8 * R22 * R32 + 4 * R23 * R33) * const_r
- (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
)
) + 1 / denom_r**2 * (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* const_r
* (2 * R11 * R12 + 2 * R21 * R22 + 4 * R31 * R32)
)
J_R[:, 5, 7] = -1 / denom_r * (
(4 * R22 * R33) * const_r
- (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
)
) + 1 / denom_r**2 * (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* const_r
* (2 * R11 * R12 + 2 * R21 * R22 + 4 * R31 * R32)
)
J_R[:, 6, 7] = (
-1
/ denom_r
* (
(4 * R11 * R12 + 4 * R21 * R22 + 8 * R31 * R32) * const_r
- (
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
)
)
+ 1
/ denom_r**2
* (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* const_r
* (2 * R11 * R12 + 2 * R21 * R22 + 4 * R31 * R32)
)
+ 2 * w1**2 * x11 * x12
+ 2 * w2**2 * x21 * x22
+ 2 * w3**2 * x31 * x32
+ 2 * w4**2 * x41 * x42
)
J_R[:, 7, 7] = (
-1
/ denom_r
* (
(
4 * R12**2
+ 4 * R22**2
+ 4 * R31**2
+ 12 * R32**2
+ 4 * R33**2
- 4
)
* const_r
- (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
)
)
+ 1
/ denom_r**2
* (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* const_r
* (2 * R11 * R12 + 2 * R21 * R22 + 4 * R31 * R32)
)
+ 2 * w1**2 * x12**2
+ 2 * w2**2 * x22**2
+ 2 * w3**2 * x32**2
+ 2 * w4**2 * x42**2
)
J_R[:, 8, 7] = (
-1
/ denom_r
* (
(4 * R12 * R13 + 4 * R22 * R23 + 8 * R32 * R33) * const_r
- (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* (
w1**2 * x11 * x12
+ w2**2 * x21 * x22
+ w3**2 * x31 * x32
+ w4**2 * x41 * x42
)
)
+ 1
/ denom_r**2
* (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* const_r
* (2 * R11 * R12 + 2 * R21 * R22 + 4 * R31 * R32)
)
+ 2 * w1**2 * x12 * x13
+ 2 * w2**2 * x22 * x23
+ 2 * w3**2 * x32 * x33
+ 2 * w4**2 * x42 * x43
)
# R33
J_R[:, 0, 8] = (
-4 * R13 * R31 * const_r / denom_r
- 4
* (
(R11**2 + R21**2 + R31**2 - 1) * R11
+ (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* (
w1**2 * x11 * x13
+ w2**2 * x21 * x23
+ w3**2 * x31 * x33
+ w4**2 * x41 * x43
)
/ denom_r
+ (
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* const_r
* (2 * R11 * R13 + 2 * R21 * R23 + 4 * R31 * R33)
/ denom_r**2
)
J_R[:, 1, 8] = -1 / denom_r * (
(4 * R13 * R32) * const_r
- (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* (
w1**2 * x11 * x13
+ w2**2 * x21 * x23
+ w3**2 * x31 * x33
+ w4**2 * x41 * x43
)
) + 1 / denom_r**2 * (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* const_r
* (2 * R11 * R13 + 2 * R21 * R23 + 4 * R31 * R33)
)
J_R[:, 2, 8] = -1 / denom_r * (
(4 * R11 * R31 + 4 * R12 * R32 + 8 * R13 * R33) * const_r
- (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* (
w1**2 * x11 * x13
+ w2**2 * x21 * x23
+ w3**2 * x31 * x33
+ w4**2 * x41 * x43
)
) + 1 / denom_r**2 * (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* const_r
* (2 * R11 * R13 + 2 * R21 * R23 + 4 * R31 * R33)
)
J_R[:, 3, 8] = -1 / denom_r * (
(4 * R23 * R31) * const_r
- (
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* (
w1**2 * x11 * x13
+ w2**2 * x21 * x23
+ w3**2 * x31 * x33
+ w4**2 * x41 * x43
)
) + 1 / denom_r**2 * (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* const_r
* (2 * R11 * R13 + 2 * R21 * R23 + 4 * R31 * R33)
)
J_R[:, 4, 8] = -1 / denom_r * (
(4 * R23 * R32) * const_r
- (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* (
w1**2 * x11 * x13
+ w2**2 * x21 * x23
+ w3**2 * x31 * x33
+ w4**2 * x41 * x43
)
) + 1 / denom_r**2 * (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* const_r
* (2 * R11 * R13 + 2 * R21 * R23 + 4 * R31 * R33)
)
J_R[:, 5, 8] = -1 / denom_r * (
(4 * R21 * R31 + 4 * R22 * R32 + 8 * R23 * R33) * const_r
- (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* (
w1**2 * x11 * x13
+ w2**2 * x21 * x23
+ w3**2 * x31 * x33
+ w4**2 * x41 * x43
)
) + 1 / denom_r**2 * (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* const_r
* (2 * R11 * R13 + 2 * R21 * R23 + 4 * R31 * R33)
)
J_R[:, 6, 8] = (
-1
/ denom_r
* (
(4 * R11 * R13 + 4 * R21 * R23 + 8 * R31 * R33) * const_r
- (
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* (
w1**2 * x11 * x13
+ w2**2 * x21 * x23
+ w3**2 * x31 * x33
+ w4**2 * x41 * x43
)
)
+ 1
/ denom_r**2
* (
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* const_r
* (2 * R11 * R13 + 2 * R21 * R23 + 4 * R31 * R33)
)
+ 2 * w1**2 * x11 * x13
+ 2 * w2**2 * x21 * x23
+ 2 * w3**2 * x31 * x33
+ 2 * w4**2 * x41 * x43
)
J_R[:, 7, 8] = (
-1
/ denom_r
* (
(4 * R12 * R13 + 4 * R22 * R23 + 8 * R32 * R33) * const_r
- (
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* (
w1**2 * x11 * x13
+ w2**2 * x21 * x23
+ w3**2 * x31 * x33
+ w4**2 * x41 * x43
)
)
+ 1
/ denom_r**2
* (
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* const_r
* (2 * R11 * R13 + 2 * R21 * R23 + 4 * R31 * R33)
)
+ 2 * w1**2 * x12 * x13
+ 2 * w2**2 * x22 * x23
+ 2 * w3**2 * x32 * x33
+ 2 * w4**2 * x42 * x43
)
J_R[:, 8, 8] = (
-1
/ denom_r
* (
(
4 * R13**2
+ 4 * R23**2
+ 4 * R31**2
+ 4 * R32**2
+ 12 * R33**2
- 4
)
* const_r
- (
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* (
w1**2 * x11 * x13
+ w2**2 * x21 * x23
+ w3**2 * x31 * x33
+ w4**2 * x41 * x43
)
)
+ 1
/ denom_r**2
* (
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* const_r
* (2 * R11 * R13 + 2 * R21 * R23 + 4 * R31 * R33)
)
+ 2 * w1**2 * x13**2
+ 2 * w2**2 * x23**2
+ 2 * w3**2 * x33**2
+ 2 * w4**2 * x43**2
)
J_w = torch.zeros((b, 9, 4), device=R.device)
# w1
denom_w = (
2 * R11**2 * R31
+ 2 * R11 * R12 * R32
+ 2 * R11 * R13 * R33
+ 2 * R21**2 * R31
+ 2 * R21 * R22 * R32
+ 2 * R21 * R23 * R33
+ 2 * R31**3
+ 2 * R31 * R32**2
+ 2 * R31 * R33**2
- 2 * R31
)
J_w[:, 0, 0] = (
-(
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* (
2 * R31 * w1 * x11**2
+ 2 * R32 * w1 * x11 * x12
+ 2 * R33 * w1 * x11 * x13
- 2 * w1 * x11 * y13
)
)
/ denom_w
+ 4 * w1 * (R11 * x11 + R12 * x12 + R13 * x13 - y11) * x11
)
J_w[:, 1, 0] = (
-(
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* (
2 * R31 * w1 * x11**2
+ 2 * R32 * w1 * x11 * x12
+ 2 * R33 * w1 * x11 * x13
- 2 * w1 * x11 * y13
)
)
/ denom_w
+ 4 * w1 * (R11 * x11 + R12 * x12 + R13 * x13 - y11) * x12
)
J_w[:, 2, 0] = (
-(
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* (
2 * R31 * w1 * x11**2
+ 2 * R32 * w1 * x11 * x12
+ 2 * R33 * w1 * x11 * x13
- 2 * w1 * x11 * y13
)
)
/ denom_w
+ 4 * w1 * (R11 * x11 + R12 * x12 + R13 * x13 - y11) * x13
)
J_w[:, 3, 0] = (
-(
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* (
2 * R31 * w1 * x11**2
+ 2 * R32 * w1 * x11 * x12
+ 2 * R33 * w1 * x11 * x13
- 2 * w1 * x11 * y13
)
)
/ denom_w
+ 4 * w1 * (R21 * x11 + R22 * x12 + R23 * x13 - y12) * x11
)
J_w[:, 4, 0] = (
-(
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* (
2 * R31 * w1 * x11**2
+ 2 * R32 * w1 * x11 * x12
+ 2 * R33 * w1 * x11 * x13
- 2 * w1 * x11 * y13
)
)
/ denom_w
+ 4 * w1 * (R21 * x11 + R22 * x12 + R23 * x13 - y12) * x12
)
J_w[:, 5, 0] = (
-(
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* (
2 * R31 * w1 * x11**2
+ 2 * R32 * w1 * x11 * x12
+ 2 * R33 * w1 * x11 * x13
- 2 * w1 * x11 * y13
)
)
/ denom_w
+ 4 * w1 * (R21 * x11 + R22 * x12 + R23 * x13 - y12) * x13
)
J_w[:, 6, 0] = (
-(
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* (
2 * R31 * w1 * x11**2
+ 2 * R32 * w1 * x11 * x12
+ 2 * R33 * w1 * x11 * x13
- 2 * w1 * x11 * y13
)
)
/ denom_w
+ 4 * w1 * (R31 * x11 + R32 * x12 + R33 * x13 - y13) * x11
)
J_w[:, 7, 0] = (
-(
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* (
2 * R31 * w1 * x11**2
+ 2 * R32 * w1 * x11 * x12
+ 2 * R33 * w1 * x11 * x13
- 2 * w1 * x11 * y13
)
)
/ denom_w
+ 4 * w1 * (R31 * x11 + R32 * x12 + R33 * x13 - y13) * x12
)
J_w[:, 8, 0] = (
-(
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* (
2 * R31 * w1 * x11**2
+ 2 * R32 * w1 * x11 * x12
+ 2 * R33 * w1 * x11 * x13
- 2 * w1 * x11 * y13
)
)
/ denom_w
+ 4 * w1 * (R31 * x11 + R32 * x12 + R33 * x13 - y13) * x13
)
# w2
J_w[:, 0, 1] = (
-(
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* (
2 * R31 * w2 * x21**2
+ 2 * R32 * w2 * x21 * x22
+ 2 * R33 * w2 * x21 * x23
- 2 * w2 * x21 * y23
)
)
/ denom_w
+ 4 * w2 * (R11 * x21 + R12 * x22 + R13 * x23 - y21) * x21
)
J_w[:, 1, 1] = (
-(
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* (
2 * R31 * w2 * x21**2
+ 2 * R32 * w2 * x21 * x22
+ 2 * R33 * w2 * x21 * x23
- 2 * w2 * x21 * y23
)
)
/ denom_w
+ 4 * w2 * (R11 * x21 + R12 * x22 + R13 * x23 - y21) * x22
)
J_w[:, 2, 1] = (
-(
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* (
2 * R31 * w2 * x21**2
+ 2 * R32 * w2 * x21 * x22
+ 2 * R33 * w2 * x21 * x23
- 2 * w2 * x21 * y23
)
)
/ denom_w
+ 4 * w2 * (R11 * x21 + R12 * x22 + R13 * x23 - y21) * x23
)
J_w[:, 3, 1] = (
-(
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* (
2 * R31 * w2 * x21**2
+ 2 * R32 * w2 * x21 * x22
+ 2 * R33 * w2 * x21 * x23
- 2 * w2 * x21 * y23
)
)
/ denom_w
+ 4 * w2 * (R21 * x21 + R22 * x22 + R23 * x23 - y22) * x21
)
J_w[:, 4, 1] = (
-(
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* (
2 * R31 * w2 * x21**2
+ 2 * R32 * w2 * x21 * x22
+ 2 * R33 * w2 * x21 * x23
- 2 * w2 * x21 * y23
)
)
/ denom_w
+ 4 * w2 * (R21 * x21 + R22 * x22 + R23 * x23 - y22) * x22
)
J_w[:, 5, 1] = (
-(
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* (
2 * R31 * w2 * x21**2
+ 2 * R32 * w2 * x21 * x22
+ 2 * R33 * w2 * x21 * x23
- 2 * w2 * x21 * y23
)
)
/ denom_w
+ 4 * w2 * (R21 * x21 + R22 * x22 + R23 * x23 - y22) * x23
)
J_w[:, 6, 1] = (
-(
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* (
2 * R31 * w2 * x21**2
+ 2 * R32 * w2 * x21 * x22
+ 2 * R33 * w2 * x21 * x23
- 2 * w2 * x21 * y23
)
)
/ denom_w
+ 4 * w2 * (R31 * x21 + R32 * x22 + R33 * x23 - y23) * x21
)
J_w[:, 7, 1] = (
-(
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* (
2 * R31 * w2 * x21**2
+ 2 * R32 * w2 * x21 * x22
+ 2 * R33 * w2 * x21 * x23
- 2 * w2 * x21 * y23
)
)
/ denom_w
+ 4 * w2 * (R31 * x21 + R32 * x22 + R33 * x23 - y23) * x22
)
J_w[:, 8, 1] = (
-(
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* (
2 * R31 * w2 * x21**2
+ 2 * R32 * w2 * x21 * x22
+ 2 * R33 * w2 * x21 * x23
- 2 * w2 * x21 * y23
)
)
/ denom_w
+ 4 * w2 * (R31 * x21 + R32 * x22 + R33 * x23 - y23) * x23
)
# w3
J_w[:, 0, 2] = (
-(
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* (
2 * R31 * w3 * x31**2
+ 2 * R32 * w3 * x31 * x32
+ 2 * R33 * w3 * x31 * x33
- 2 * w3 * x31 * y33
)
)
/ denom_w
+ 4 * w3 * (R11 * x31 + R12 * x32 + R13 * x33 - y31) * x31
)
J_w[:, 1, 2] = (
-(
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* (
2 * R31 * w3 * x31**2
+ 2 * R32 * w3 * x31 * x32
+ 2 * R33 * w3 * x31 * x33
- 2 * w3 * x31 * y33
)
)
/ denom_w
+ 4 * w3 * (R11 * x31 + R12 * x32 + R13 * x33 - y31) * x32
)
J_w[:, 2, 2] = (
-(
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* (
2 * R31 * w3 * x31**2
+ 2 * R32 * w3 * x31 * x32
+ 2 * R33 * w3 * x31 * x33
- 2 * w3 * x31 * y33
)
)
/ denom_w
+ 4 * w3 * (R11 * x31 + R12 * x32 + R13 * x33 - y31) * x33
)
J_w[:, 3, 2] = (
-(
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* (
2 * R31 * w3 * x31**2
+ 2 * R32 * w3 * x31 * x32
+ 2 * R33 * w3 * x31 * x33
- 2 * w3 * x31 * y33
)
)
/ denom_w
+ 4 * w3 * (R21 * x31 + R22 * x32 + R23 * x33 - y32) * x31
)
J_w[:, 4, 2] = (
-(
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* (
2 * R31 * w3 * x31**2
+ 2 * R32 * w3 * x31 * x32
+ 2 * R33 * w3 * x31 * x33
- 2 * w3 * x31 * y33
)
)
/ denom_w
+ 4 * w3 * (R21 * x31 + R22 * x32 + R23 * x33 - y32) * x32
)
J_w[:, 5, 2] = (
-(
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* (
2 * R31 * w3 * x31**2
+ 2 * R32 * w3 * x31 * x32
+ 2 * R33 * w3 * x31 * x33
- 2 * w3 * x31 * y33
)
)
/ denom_w
+ 4 * w3 * (R21 * x31 + R22 * x32 + R23 * x33 - y32) * x33
)
J_w[:, 6, 2] = (
-(
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* (
2 * R31 * w3 * x31**2
+ 2 * R32 * w3 * x31 * x32
+ 2 * R33 * w3 * x31 * x33
- 2 * w3 * x31 * y33
)
)
/ denom_w
+ 4 * w3 * (R31 * x31 + R32 * x32 + R33 * x33 - y33) * x31
)
J_w[:, 7, 2] = (
-(
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* (
2 * R31 * w3 * x31**2
+ 2 * R32 * w3 * x31 * x32
+ 2 * R33 * w3 * x31 * x33
- 2 * w3 * x31 * y33
)
)
/ denom_w
+ 4 * w3 * (R31 * x31 + R32 * x32 + R33 * x33 - y33) * x32
)
J_w[:, 8, 2] = (
-(
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* (
2 * R31 * w3 * x31**2
+ 2 * R32 * w3 * x31 * x32
+ 2 * R33 * w3 * x31 * x33
- 2 * w3 * x31 * y33
)
)
/ denom_w
+ 4 * w3 * (R31 * x31 + R32 * x32 + R33 * x33 - y33) * x33
)
# w4
J_w[:, 0, 3] = (
-(
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R11
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R12
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R13
)
* (
2 * R31 * w4 * x41**2
+ 2 * R32 * w4 * x41 * x42
+ 2 * R33 * w4 * x41 * x43
- 2 * w4 * x41 * y43
)
)
/ denom_w
+ 4 * w4 * (R11 * x41 + R12 * x42 + R13 * x43 - y41) * x41
)
J_w[:, 1, 3] = (
-(
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R11
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R12
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R13
)
* (
2 * R31 * w4 * x41**2
+ 2 * R32 * w4 * x41 * x42
+ 2 * R33 * w4 * x41 * x43
- 2 * w4 * x41 * y43
)
)
/ denom_w
+ 4 * w4 * (R11 * x41 + R12 * x42 + R13 * x43 - y41) * x42
)
J_w[:, 2, 3] = (
-(
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R11
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R12
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R13
)
* (
2 * R31 * w4 * x41**2
+ 2 * R32 * w4 * x41 * x42
+ 2 * R33 * w4 * x41 * x43
- 2 * w4 * x41 * y43
)
)
/ denom_w
+ 4 * w4 * (R11 * x41 + R12 * x42 + R13 * x43 - y41) * x43
)
J_w[:, 3, 3] = (
-(
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R21
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R22
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R23
)
* (
2 * R31 * w4 * x41**2
+ 2 * R32 * w4 * x41 * x42
+ 2 * R33 * w4 * x41 * x43
- 2 * w4 * x41 * y43
)
)
/ denom_w
+ 4 * w4 * (R21 * x41 + R22 * x42 + R23 * x43 - y42) * x41
)
J_w[:, 4, 3] = (
-(
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R21
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R22
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R23
)
* (
2 * R31 * w4 * x41**2
+ 2 * R32 * w4 * x41 * x42
+ 2 * R33 * w4 * x41 * x43
- 2 * w4 * x41 * y43
)
)
/ denom_w
+ 4 * w4 * (R21 * x41 + R22 * x42 + R23 * x43 - y42) * x42
)
J_w[:, 5, 3] = (
-(
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R21
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R22
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R23
)
* (
2 * R31 * w4 * x41**2
+ 2 * R32 * w4 * x41 * x42
+ 2 * R33 * w4 * x41 * x43
- 2 * w4 * x41 * y43
)
)
/ denom_w
+ 4 * w4 * (R21 * x41 + R22 * x42 + R23 * x43 - y42) * x43
)
J_w[:, 6, 3] = (
-(
(
4 * (R11**2 + R21**2 + R31**2 - 1) * R31
+ 4 * (R11 * R12 + R21 * R22 + R31 * R32) * R32
+ 4 * (R11 * R13 + R21 * R23 + R31 * R33) * R33
)
* (
2 * R31 * w4 * x41**2
+ 2 * R32 * w4 * x41 * x42
+ 2 * R33 * w4 * x41 * x43
- 2 * w4 * x41 * y43
)
)
/ denom_w
+ 4 * w4 * (R31 * x41 + R32 * x42 + R33 * x43 - y43) * x41
)
J_w[:, 7, 3] = (
-(
(
4 * (R11 * R12 + R21 * R22 + R31 * R32) * R31
+ 4 * (R12**2 + R22**2 + R32**2 - 1) * R32
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R33
)
* (
2 * R31 * w4 * x41**2
+ 2 * R32 * w4 * x41 * x42
+ 2 * R33 * w4 * x41 * x43
- 2 * w4 * x41 * y43
)
)
/ denom_w
+ 4 * w4 * (R31 * x41 + R32 * x42 + R33 * x43 - y43) * x42
)
J_w[:, 8, 3] = (
-(
(
4 * (R11 * R13 + R21 * R23 + R31 * R33) * R31
+ 4 * (R12 * R13 + R22 * R23 + R32 * R33) * R32
+ 4 * (R13**2 + R23**2 + R33**2 - 1) * R33
)
* (
2 * R31 * w4 * x41**2
+ 2 * R32 * w4 * x41 * x42
+ 2 * R33 * w4 * x41 * x43
- 2 * w4 * x41 * y43
)
)
/ denom_w
+ 4 * w4 * (R31 * x41 + R32 * x42 + R33 * x43 - y43) * x43
)
J_Rw = torch.zeros((b, 9, 4), device=R.device)
tmp = torch.eye(9, 9, dtype=torch.float, device=R.device)
for i in range(b):
try:
J_Rw[i, :, :] = -torch.inverse(J_R[i, :, :]).mm(J_w[i, :, :])
tmp = J_R[i, :, :]
except Exception as e:
J_Rw[i, :, :] = -torch.inverse(tmp).mm(J_w[i, :, :])
return J_Rw
| 72,996 | Python | .py | 2,360 | 19.849153 | 82 | 0.30036 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,697 | losses.py | disungatullina_MinBackProp/toy_examples/rotation/losses.py | import torch
def angle_error(R_true, R):
"""Pytorch inplementation of (0.5 * trace(R^(-1)R) - 1)"""
max_dot_product = 1.0 - 1e-8
error_rotation = (
(0.5 * ((R * R_true).sum(dim=(-2, -1)) - 1.0))
# .clamp_(-max_dot_product, max_dot_product)
.clamp_(-max_dot_product, max_dot_product).acos()
)
return error_rotation
def frobenius_norm(R_true, R):
return ((R - R_true) ** 2).sum(dim=(-2, -1))
| 442 | Python | .py | 12 | 31.5 | 62 | 0.565728 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,698 | msac_score.py | disungatullina_MinBackProp/scorings/msac_score.py | import torch
class MSACScore(object):
def __init__(self, device="cuda"):
# self.threshold = (3 / 2 * threshold)**2
# self.th = (3 / 2) * threshold
self.device = device
self.provides_inliers = True
def score(self, matches, models, threshold=0.75):
"""Rewrite from Graph-cut Ransac github.com/danini/graph-cut-ransac calculate the Sampson distance between
a point correspondence and essential/ fundamental matrix.
Sampson distance is the first order approximation of geometric distance, calculated from the closest correspondence
who satisfy the F matrix.
:param: x1: x, y, 1; x2: x', y', 1;
M: F/E matrix
"""
squared_threshold = (3 / 2 * threshold) ** 2
pts1 = matches[:, 0:2]
pts2 = matches[:, 2:4]
num_pts = pts1.shape[0]
# get homogeneous coordinates
hom_pts1 = torch.cat(
(pts1, torch.ones((num_pts, 1), device=pts1.device)), dim=-1
)
hom_pts2 = torch.cat(
(pts2, torch.ones((num_pts, 1), device=pts2.device)), dim=-1
)
# calculate the sampson distance and msac scores
try:
M_x1_ = models.matmul(hom_pts1.transpose(-1, -2))
except:
print()
M_x2_ = models.transpose(-1, -2).matmul(hom_pts2.transpose(-1, -2))
JJ_T_ = (
M_x1_[:, 0] ** 2 + M_x1_[:, 1] ** 2 + M_x2_[:, 0] ** 2 + M_x2_[:, 1] ** 2
)
x1_M_x2_ = hom_pts1.T.unsqueeze(0).mul(M_x2_).sum(-2)
try:
squared_distances = x1_M_x2_.square().div(JJ_T_)
except Exception as e:
print("wrong", e)
masks = squared_distances < squared_threshold
# soft inliers, sum of the squared distance, while transforming the negative ones to zero by torch.clamp()
msac_scores = torch.sum(
torch.clamp(1 - squared_distances / squared_threshold, min=0.0), dim=-1
)
# following c++
# squared_residuals = torch.sum(torch.where(squared_distances>=self.threshold, torch.zeros_like(squared_distances), squared_distances), dim=-1)
# inlier_number = torch.sum(squared_distances.squeeze(0) < self.threshold, dim=-1)
# score = (-squared_residuals + inlier_number * self.threshold)/self.threshold
return msac_scores, masks
| 2,366 | Python | .py | 50 | 37.92 | 151 | 0.59158 | disungatullina/MinBackProp | 8 | 0 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
2,288,699 | gen_data.py | XintSong_RMSF-net/gen_data.py | import numpy as np
import torch
import mrcfile
from scipy import ndimage
import subprocess
import sys
from moleculekit.molecule import Molecule
import os
def parse_map(map_file, r=1.5):
mrc = mrcfile.open(map_file, 'r')
voxel_size = np.asarray(
[mrc.voxel_size.x, mrc.voxel_size.y, mrc.voxel_size.z], dtype=np.float32)
cella = (mrc.header.cella.x, mrc.header.cella.y, mrc.header.cella.z)
origin = np.asarray([mrc.header.origin.x, mrc.header.origin.y,
mrc.header.origin.z], dtype=np.float32)
start_xyz = np.asarray(
[mrc.header.nxstart, mrc.header.nystart, mrc.header.nzstart], dtype=np.float32)
ncrs = (mrc.header.nx, mrc.header.ny, mrc.header.nz)
angle = np.asarray([mrc.header.cellb.alpha, mrc.header.cellb.beta,
mrc.header.cellb.gamma], dtype=np.float32)
map = np.asfarray(mrc.data.copy(), dtype=np.float32)
assert (angle[0] == angle[1] == angle[2] == 90.0)
mapcrs = np.subtract(
[mrc.header.mapc, mrc.header.mapr, mrc.header.maps], 1)
sort = np.asarray([0, 1, 2], dtype=np.int32)
for i in range(3):
sort[mapcrs[i]] = i
xyz_start = np.asarray([start_xyz[i] for i in sort])
nxyz = np.asarray([ncrs[i] for i in sort])
map = np.transpose(map, axes=2-sort[::-1])
mrc.close()
zoomFactor = np.divide(voxel_size, np.asarray([r, r, r], dtype=np.float32))
map2 = ndimage.zoom(map, zoom=zoomFactor)
nxyz = np.asarray([map2.shape[0], map2.shape[1],
map2.shape[2]], dtype=np.int32)
info = dict()
info['cella'] = cella
info['xyz_start'] = xyz_start
info['voxel_size'] = voxel_size
info['nxyz'] = nxyz
info['origin'] = origin
return map2, info
def parse_map2(map):
mrc = mrcfile.open(map, 'r')
voxel_size = np.asarray(
[mrc.voxel_size.x, mrc.voxel_size.y, mrc.voxel_size.z], dtype=np.float32)
cella = (mrc.header.cella.x, mrc.header.cella.y, mrc.header.cella.z)
origin = np.asarray([mrc.header.origin.x, mrc.header.origin.y,
mrc.header.origin.z], dtype=np.float32)
start_xyz = np.asarray(
[mrc.header.nxstart, mrc.header.nystart, mrc.header.nzstart], dtype=np.float32)
ncrs = (mrc.header.nx, mrc.header.ny, mrc.header.nz)
angle = np.asarray([mrc.header.cellb.alpha, mrc.header.cellb.beta,
mrc.header.cellb.gamma], dtype=np.float32)
map2 = np.asfarray(mrc.data.copy(), dtype=np.float32)
assert (angle[0] == angle[1] == angle[2] == 90.0)
mapcrs = np.subtract(
[mrc.header.mapc, mrc.header.mapr, mrc.header.maps], 1)
sort = np.asarray([0, 1, 2], dtype=np.int32)
if (mapcrs == sort).all():
changed = False
xyz_start = np.asarray([start_xyz[i] for i in sort])
nxyz = np.asarray([ncrs[i] for i in sort])
mrc.close()
else:
changed = True
for i in range(3):
sort[mapcrs[i]] = i
xyz_start = np.asarray([start_xyz[i] for i in sort])
nxyz = np.asarray([ncrs[i] for i in sort])
map2 = np.transpose(map2, axes=2-sort[::-1])
mrc.close()
info = dict()
info['cella'] = cella
info['xyz_start'] = xyz_start
info['voxel_size'] = voxel_size
info['nxyz'] = nxyz
info['origin'] = origin
info['changed'] = changed
return map2, info
def get_atom_map(pdb_file, shape, map_info, r=1.5):
atom_map = np.full((shape[0], shape[1], shape[2]), 0, dtype=np.int8)
pdb = Molecule(pdb_file)
pdb.filter('protein')
xyz = pdb.get('coords')-map_info['origin']
xyz_norm = ((xyz-map_info['voxel_size']*map_info['xyz_start'])/r)
for coord in xyz_norm:
atom_map[int(coord[2]), int(coord[1]), int(coord[0])] = 1
return atom_map
def split_map_and_select_item(map, atom_map, contour_level, box_size=40, core_size=10):
map_size = np.shape(map)
pad_map = np.full((map_size[0]+2*box_size, map_size[1] +
2*box_size, map_size[2]+2*box_size), 0, dtype=np.float32)
pad_map[box_size:-box_size, box_size:-box_size, box_size:-box_size] = map
pad_atom_map = np.full(
(map_size[0]+2*box_size, map_size[1]+2*box_size, map_size[2]+2*box_size), 0, dtype=np.int8)
pad_atom_map[box_size:-box_size, box_size:-
box_size, box_size:-box_size] = atom_map
start_point = box_size - int((box_size - core_size) / 2)
cur_x, cur_y, cur_z = start_point, start_point, start_point
box_list = list()
length = [int(np.ceil(map_size[0]/core_size)),
int(np.ceil(map_size[1]/core_size)), int(np.ceil(map_size[2]/core_size))]
print(
f"the total box of this map is {length[0]}*{length[1]}*{length[2]}={length[0]*length[1]*length[2]}")
keep_list = []
total_list = []
i = 0
while (cur_z + (box_size - core_size) / 2 < map_size[2] + box_size):
next_box = pad_map[cur_x:cur_x + box_size,
cur_y:cur_y + box_size, cur_z:cur_z + box_size]
next_atom_box_center = pad_atom_map[cur_x+15:cur_x + box_size -
15, cur_y+15:cur_y + box_size-15, cur_z+15:cur_z + box_size-15]
cur_x += core_size
if (cur_x + (box_size - core_size) / 2 >= map_size[0] + box_size):
cur_y += core_size
cur_x = start_point
if (cur_y + (box_size - core_size) / 2 >= map_size[1] + box_size):
cur_z += core_size
cur_y = start_point
cur_x = start_point
if (np.sum(next_atom_box_center) > 0):
box_list.append(next_box)
keep_list.append(i)
total_list.append(i)
i = i+1
print(f"the selected maps: {len(keep_list)}")
print(f"the total maps: {len(total_list)}")
return np.asarray(box_list), np.asarray(keep_list), np.asarray(total_list)
def get_smi_map(pdb_file, res, out_file, chimera_path=None, number=0.1, r=1.5):
chimera_script = open('./chimera_exe.cmd', 'w')
chimera_script.write('open ' + pdb_file + '\n'
'molmap #0 '+str(res)+' gridSpacing ' + str(r)+'\n'
'volume #'+str(number) + ' save ' +
str(out_file) + '\n'
'close all'
)
chimera_script.close()
print(f'chimera_path:{chimera_path}')
output = subprocess.check_output(
[chimera_path, '--nogui', chimera_script.name])
return output
def sim_map_ot(pdb_file, res, out_file, number=0.1, r=1.5, chimera_path=None):
output = get_smi_map(pdb_file, res,
out_file, chimera_path=chimera_path, r=r)
s = output.decode('utf-8').splitlines()
if "Wrote file" not in s[-1]:
output = get_smi_map(pdb_file, res,
out_file, r=r, number=1, chimera_path=chimera_path)
s = output.decode('utf-8').splitlines()
if "Wrote file" not in s[-1]:
return False
return True
class exp_2_sim:
def __init__(self, exp_map_file, sim_map_file, keep_list, total_list):
self.sim_map, self.sim_info = parse_map2(sim_map_file)
self.exp_map, self.exp_info = parse_map(exp_map_file)
self.keep_list = keep_list
self.total_list = total_list
@staticmethod
def convert_to_n_base(number, n_3):
result = []
i = 0
while number > 0:
remainder = number % n_3[i]
result.append(remainder)
number = number // n_3[i]
i = i+1
if len(result) != 3:
if len(result) == 2:
result.append(0)
elif len(result) == 1:
result.extend([0, 0])
elif len(result) == 0:
result.extend([0, 0, 0])
else:
print(f"too big,bigger than 3 digits")
assert (len(result) == 3)
result.reverse()
return result
def index_start(self, index, box_size=40, core_size=10, step_size=40):
start_point = box_size - int((box_size - core_size) / 2)
cur_box_num = self.keep_list[index]
exp_shape = self.exp_map.shape
num_per_dim = [(exp_shape[0]+9)//10, (exp_shape[1]+9) //
10, (exp_shape[2]+9)//10]
box_num_zyx = self.convert_to_n_base(int(cur_box_num), num_per_dim)
x11, y11, z11 = box_num_zyx[2]*core_size+start_point-box_size, box_num_zyx[1]*core_size+start_point-box_size,\
box_num_zyx[0]*core_size+start_point-box_size
add_center = int((box_size-step_size)/2)
x11, y11, z11 = x11+add_center, y11+add_center, z11+add_center
exp_index = [x11, y11, z11]
return exp_index
def trans_index_exp2sim(self, exp_index):
''' convert indices on the experimental map to indices on the simulated map.'''
x, y, z = exp_index[0], exp_index[1], exp_index[2]
x_coord, y_coord, z_coord = self.exp_info['origin'] + \
self.exp_info['xyz_start'] * \
self.exp_info['voxel_size']+np.array([z, y, x])*1.5
xyz_sim_index = [round(i) for i in reversed((np.array([x_coord, y_coord, z_coord]) -
self.sim_info['origin']-self.sim_info['voxel_size']*self.sim_info['xyz_start'])/1.5)]
return xyz_sim_index
def range2range_axis(self, x_left, x_right, i=0):
if x_left < 0 and x_right < 0:
print("out of sim_map,no overlap")
return 0, 0, 0, 0
if x_left > self.sim_info['nxyz'][i] and x_right > self.sim_info['nxyz'][i]:
print("out of sim_map,no overlap")
return 0, 0, 0, 0
if x_left >= 0 and x_right < self.sim_info['nxyz'][i]:
x_to_left, x_to_right = 0, x_right-x_left
elif x_left < 0 and x_right < self.sim_info['nxyz'][i]:
x_to_left, x_to_right = -x_left, x_right-x_left
x_left = 0
elif x_left >= 0 and x_right >= self.sim_info['nxyz'][i]:
x_to_left, x_to_right = 0, self.sim_info['nxyz'][i]-x_left
x_right = self.sim_info['nxyz'][i]
elif x_left < 0 and x_right >= self.sim_info['nxyz'][i]:
x_to_left, x_to_right = -x_left, self.sim_info['nxyz'][i]-x_left
x_left = 0
x_right = self.sim_info['nxyz'][i]
return x_left, x_right, x_to_left, x_to_right
def trans_range2range(self, xyz_sim_index, box_size=40, pad=0.):
x_left, x_right, x_to_left, x_to_right = self.range2range_axis(
xyz_sim_index[0], xyz_sim_index[0]+box_size, i=2)
y_left, y_right, y_to_left, y_to_right = self.range2range_axis(
xyz_sim_index[1], xyz_sim_index[1]+box_size, i=1)
z_left, z_right, z_to_left, z_to_right = self.range2range_axis(
xyz_sim_index[2], xyz_sim_index[2]+box_size, i=0)
return [x_left, x_right], [y_left, y_right], [z_left, z_right], [x_to_left, x_to_right], [y_to_left, y_to_right], [z_to_left, z_to_right]
def gene_boxs(self, box_size=40, pad=0.):
sim_box_list = []
for index in range(len(self.keep_list)):
exp_index = self.index_start(index)
xyz_sim_index = self.trans_index_exp2sim(exp_index)
sim_x_lr, sim_y_lr, sim_z_lr, box_x_lr, box_y_lr, box_z_lr = self.trans_range2range(
xyz_sim_index)
sim_box = np.full([box_size, box_size, box_size],
pad, dtype=np.float32)
sim_box[box_x_lr[0]:box_x_lr[1], box_y_lr[0]:box_y_lr[1], box_z_lr[0]:box_z_lr[1]
] = self.sim_map[sim_x_lr[0]:sim_x_lr[1], sim_y_lr[0]:sim_y_lr[1], sim_z_lr[0]:sim_z_lr[1]]
sim_box_list.append(sim_box)
sim_box_list = np.array(sim_box_list)
return sim_box_list
class gen_data:
def __init__(self, exp_map_file, pdb_file, output_dir, contour_level, chimera_path=None) -> None:
self.exp_map_file = exp_map_file
self.pdb_file = pdb_file
self.output_dir = output_dir
self.contour_level = contour_level
self.chimera_path = chimera_path
def get_data(self, r=1.5):
sim_map_file = f"{self.output_dir}/sim_map.mrc"
map, info = parse_map(self.exp_map_file, r=r)
atom_map = get_atom_map(self.pdb_file, map.shape, info)
intensity_list, keep_list, total_list = split_map_and_select_item(
map, atom_map, self.contour_level, box_size=40, core_size=10)
sim_yes = sim_map_ot(self.pdb_file, 4, sim_map_file,
r=r, chimera_path=self.chimera_path)
if not sim_yes:
print(" sim map not succeed")
sys.exit()
expsim = exp_2_sim(self.exp_map_file, sim_map_file,
keep_list, total_list)
sim_box_list = expsim.gene_boxs()
data_file = f"{self.output_dir}/data.pth"
torch.save({'intensity': torch.from_numpy(intensity_list).unsqueeze_(1), 'sim_intensity': torch.from_numpy(sim_box_list).unsqueeze_(1),
'keep_list': torch.from_numpy(keep_list), 'total_list': torch.from_numpy(total_list)}, data_file)
print(f"tensor datafile saved at {data_file}")
return data_file
| 13,295 | Python | .py | 270 | 39.285185 | 145 | 0.572743 | XintSong/RMSF-net | 8 | 1 | 0 | GPL-3.0 | 9/5/2024, 10:48:34 PM (Europe/Amsterdam) |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.