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QUESTION 3 | import numpy as np
A = np.array([2,7,4])
B = np.array([3,9,8])
cross = np.cross(A,B)
print(cross) | [20 -4 -3]
| Apache-2.0 | PRELIM_EXAM.ipynb | Singko25/Linear-Algebra-58020 |
from google.colab import drive
drive.mount('/content/drive')
import torch
import torch.nn as nn
import torch.optim as optim
import torch.nn.functional as F
import torchvision.datasets as dset
import torchvision.transforms as T
from torch.utils.data import TensorDataset
from torch.utils.data import DataLoader
from torch.utils.data import sampler
import numpy as np
import pandas as pd
from PIL import Image
from sklearn import preprocessing, metrics, model_selection
USE_GPU = True
dtype = torch.float # we will be using float throughout this tutorial
if USE_GPU and torch.cuda.is_available():
device = torch.device('cuda')
else:
device = torch.device('cpu')
# Constant to control how frequently we print train loss
print_every = 100
print('using device:', device)
train_mean = 0.0
train_std = 0.0
val_mean = 0.0
val_std = 0.0
district_list = ['villages_towns_Sanxia', 'villages_towns_Sanzhi',
'villages_towns_Sanchong', 'villages_towns_Zhonghe',
'villages_towns_Zhongshan', 'villages_towns_Zhongzheng',
'villages_towns_Wugu', 'villages_towns_Xinyi', 'villages_towns_Neihu',
'villages_towns_Bali', 'villages_towns_Beitou',
'villages_towns_Nangang', 'villages_towns_Tucheng',
'villages_towns_Shilin', 'villages_towns_Datong', 'villages_towns_Daan',
'villages_towns_Wenshan', 'villages_towns_Xindian',
'villages_towns_Xinzhuang', 'villages_towns_Songshan',
'villages_towns_Banqiao', 'villages_towns_Linkou',
'villages_towns_Shulin', 'villages_towns_Yonghe',
'villages_towns_Xizhi', 'villages_towns_Taishan',
'villages_towns_Tamsui', 'villages_towns_Shenkeng',
'villages_towns_Ruifang', 'villages_towns_Wanhua',
'villages_towns_Wanli', 'villages_towns_Luzhou',
'villages_towns_Gongliao', 'villages_towns_Jinshan',
'villages_towns_Shuangxi', 'villages_towns_Yingge']
building_material = ['building_materials_RC', 'building_materials_RB',
'building_materials_brick', 'building_materials_steel',
'building_materials_SRC', 'building_materials_PRX',
'building_materials_other_material']
FILE = '/content/drive/MyDrive/SC201_Final_Project/Data/final_data_taipei.csv'
# standardize data
# train_mean = 154170.694
# train_std = 79570.40139
data = pd.read_csv(FILE)
data = data[data.unit_price != 0]
data = data[data.unit_price != 2211457]
print(data.count())
sd = {}
mean = {}
columns = ['zoning', 'total_floors', 'floors_area', 'unit_price', 'unit_berth_price', 'total_berth_price', 'main_building_area', 'auxiliary_building_area', 'balcony_area', 'building_age']
for column in columns:
print(column)
sd_each = data[column].std()
# sd[column] = sd_each
mean_each = data[column].mean()
# mean[column] = mean_each
data[column] = (data[column] - mean_each)/sd_each
data.to_csv('/content/drive/MyDrive/SC201_Final_Project/Data/new_data_taipei.csv', encoding="utf_8_sig", index=False)
| _____no_output_____ | MIT | Mean & SD.ipynb | sharlenechen0113/Real-Estate-Price-Prediction |
|
Install Python. jupyter --no-browserIn the favorite browser, typehttp://localhost:8888 (or the port that is assigned)Basic usage of jupyter notebooks.- create a newdocument by clicking the New Notebook- start typing code in the shaded textbox- execute the code |
x = 0.1
N = 3
a = 1
b = 0
c = -1
print('f(' + str(x) + ') = ' + str(a*x**2 + b*x + c))
a = 1
b = 1
print(a*b,a*(b+1),a*(b+2),a*(b+3))
a = 2
print(a*b,a*(b+1),a*(b+2),a*(b+3))
a = 3
print(a*b,a*(b+1),a*(b+2),a*(b+3))
a = 4
print(a*b,a*(b+1),a*(b+2),a*(b+3))
| (1, 2, 3, 4)
(2, 4, 6, 8)
(3, 6, 9, 12)
(4, 8, 12, 16)
| MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Fibionacci Series | N = 0
a_1 = 1
a_2 = 0
x = 1
if N>0:
print('x_' + str(0) + ' = ' + str(x) )
for i in range(1,N):
x = a_1 + a_2
print('x_' + str(i) + ' = ' + str(x) )
a_2 = a_1
a_1 = x
l = -1
r = 1
delta = 0.1
steps = (r-l)/delta+1
print '-'*20
print('| '),
print('x'),
print('| '),
print('3*x**2 + 2*x + 3'),
print('| ')
for i in range(0,int(steps)):
x = l+i*delta
print '-'*20
print('| '),
print(x),
print('| '),
print(3*x**2 + 2*x + 3),
print('| ')
def f(x):
return 3*x**2 + 2*x + 3
l = -1
r = 1
delta = 0.1
steps = (r-l)/delta
for i in range(0,int(steps)):
x = l+i*delta
print x,
print f(x)
def f(r, T, S_0):
return S_0*(1+r)**T
interest_rate = 0.12
T = 10
S_0 = 100
l = 1
r = T
delta = 1
steps = (r-l)/delta
for i in range(0,int(steps)):
T = l+i*delta
print T,
print f(interest_rate, T, S_0) | 1 112.0
2 125.44
3 140.4928
4 157.351936
5 176.23416832
6 197.382268518
7 221.068140741
8 247.596317629
9 277.307875745
| MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Arrays, lists | a = [1,2,5,7,5, 3.2, 7]
names = ['Ali','Veli','Fatma','Asli']
#for s in names:
# print(s)
print(names[3])
print(len(names))
for i in range(len(names)-1,-1,-1):
print(names[i])
for i in range(len(names)):
print(names[len(names)-i])
for n in reversed(names):
print(n) | Asli
Fatma
Veli
Ali
| MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Average and standard deviation | #x = [0.1,3,-2.1,5,12,3,17]
x = [1,-1,0]
s1 = 0.0
for a in x:
s1 += a
mean = s1/len(x)
s2 = 0.0
for a in x:
s2 += (a-mean)**2
variance = s2/len(x)
print('mean = '),
print(mean)
print('variance = '),
print(variance)
| mean = 0.0
variance = 0.666666666667
| MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Find the minimum in an array | a = [2,5,1.2, 0,-4, 3]
mn = a[0]
for i in range(1,len(a)):
if a[i]<mn:
mn = a[i]
print(mn)
a.sort()
a.append(-7)
v = a.pop()
a.reverse()
v = a.pop(0)
a.sort
a = 5
a.bit_length | _____no_output_____ | MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Homework: Value counts given an array of integers | a = [5, 3, 1, 1, 6, 3, 2]
ua = []
for j in a:
found = False
for i in ua:
if j==i:
found = True;
break;
if not found:
ua.append(j)
print(ua)
for i in ua:
s = 0
for j in a:
if i==j:
s = s+1
print(i, s)
a = [5, 3, 1, 1, 6, 3, 2]
ca = []
sum = 0
for j in a:
ca.append(sum)
sum += j
ca.append(sum)
print(ca)
#ca = [0, 5, 8, 9, 10, 16, 19, 21]
a = [3, 6, 7, 2]
#oa = [3, 6, 7, 2, 2, 7, 6, 3]
oa = a
for i in reversed(a):
oa.append(i)
oa
oa = a
for i in range()
a = [3, 4, 6]
oa = list(a)
oa = a
print(a)
for i in range(1,len(a)+1):
# print(a[-i])
oa.append(a[-i])
oa
a+list(reversed(a))
a0 = 0
a = [2, 6, 3, 1, 4, 8, 3, 5, 5]
prev = a0
Inc = []
Dec = []
for i in a:
Inc.append(i>prev)
Dec.append(i<prev)
prev = i
print(Inc)
print(Dec)
#Inc = [True, True, False, False, True, True, False, True, False]
#Dec = [False, False, True, True,False, False, True, False, False]
| [True, True, False, False, True, True, False, True, False]
[False, False, True, True, False, False, True, False, False]
| MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Generate random walk in an array | import random
N = 10
mu = 0
sig = 1
x = 0
a = [x]
for i in range(N):
w = random.gauss(mu, sig)
x = x + w
a.append(x)
print(a)
len(a) | [0, 0.07173293905450501, -0.3652340160453349, -0.07610430577230803, -1.4172015782500376, -0.31469586619290335, -1.4458834127459201, -0.7189045208807692, 0.9895551731951309, 0.1012103597338051, -1.0353093339238497]
| MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
List Comprehension |
N = 100
mu = 0
sig = 1
a = [random.gauss(mu, sig) for i in range(N)]
for i in range(len(a)-1):
a[i+1] = a[i] + a[i+1]
%matplotlib inline
import matplotlib.pylab as plt
plt.plot(a)
plt.show() | /Users/cemgil/anaconda/envs/py27/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.
warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')
| MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Moving Average | # Window Lenght
W = 20
y = []
for i in range(len(a)):
s = 0
n = 0
for j in range(W):
if i-j < 0:
break;
s = s + a[i-j]
n = n + 1
y.append(s/n)
plt.plot(a)
plt.plot(y)
plt.show()
| _____no_output_____ | MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Moving average, second version | # Window Lenght
W = 20
y = []
s = 0
n = 0
for i in range(len(a)):
s = s + a[i]
if i>=W:
s = s - a[i-W]
else:
n = n + 1
y.append(s/n)
plt.plot(a)
plt.plot(y)
plt.show()
def mean(a):
s = 0
for x in a:
s = s+x
return s/float(len(a))
def var(a):
mu = mean(a)
s = 0
for i in range(len(a)):
s = s+ (a[i]-mu)**2
return float(s)/len(a)
a = [3,4,1,2]
print(mean(a))
print(var(a))
| 2.5
1.25
| MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Mean and Variance, online calculation | def mean(a):
mu = 0.0
for i in range(len(a)):
mu = i/(i+1.0)*mu + 1.0/(i+1.0)*a[i]
return mu
a = [3,4,1,2]
#print(a)
print(mean(a)) | 2.5
| MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Implement the recursive formula for the variance | for i in range(1,len(a)+1):
print(i)
a = [i**2 for i in range(10)]
a
st = 'if'
if st == 'if':
print('if')
elif st == 'elif':
print('elif')
else:
print('not elif')
if x<10 and x>3:
for i in range(10):
if i%2:
continue
print i
x
del x
from math import exp
import math as m
x = 3
exp(x)
m.sin(x)
if x == 3:
print 'x'
i = 0
while i<10:
i+=1
print(i*10)
%matplotlib inline
import matplotlib.pylab as plt
x = [z/10. for z in range(-20,21)]
x2 = [z**2 for z in x]
x3 = [z**3 for z in x]
sinx = [math.sin(z) for z in x]
plt.plot(x,x)
plt.plot(x,x2)
plt.plot(x,sinx)
plt.show()
import numpy as np
x = [z for z in np.arange(-2,2,0.1)]
x
x = [2,3]
y = (2,3)
x[0] = 3
y = (z for z in range(5))
for i in y:
print(i)
import random
math.pi*(2*random.random()-1)
def unif():
return 2*random.random() - 1
N = 100
# Generate N points in the square and store in a list
points = [[unif(), unif()] for i in range(N) ]
# For each point check if it is in the circle and count the total number
# plot points in the circle as blue
# plot points outside as red
count = 0
px_in = []
py_in = []
px_out = []
py_out = []
for x in points:
if x[0]**2 + x[1]**2< 1:
count += 1
px_in.append(x[0])
py_in.append(x[1])
else:
px_out.append(x[0])
py_out.append(x[1])
print(4.0*count/N)
plt.plot(px_in, py_in,'.b')
plt.plot(px_out, py_out,'.r')
plt.show()
def unif():
return 2*random.random() - 1
N = 1000000
count = 0
for i in range(N):
x = [unif(), unif(), unif()]
if x[0]**2 + x[1]**2 + x[2]**2 < 1:
count += 1
print(8*float(count)/N)
print(4.0/3.0*math.pi)
for x in points:
print(x)
y = [3,4,5]
x = ['a','b','d']
for u,v in zip(x, y):
print(u,v)
import sys
sys.stdout
a = [3,4,5]
a = map(lambda x: x**2, a)
reduce(lambda a,b: a*b, a)
ln = 'twinkle tinkle little star'
ln.split()
lst = [1,3,4]
lst.insert(2,4)
lst
import sys
N = int(raw_input().strip())
lst = []
for line in sys.stdin:
tok = line.split()
if tok[0] == 'insert':
i = int(tok[1])
val = int(tok[2])
lst.insert(i,val)
elif tok[0] == 'print':
print(lst)
elif tok[0] == 'remove':
val = int(tok[1])
lst.remove(val)
elif tok[0] == 'append':
val = int(tok[1])
lst.append(val)
elif tok[0] == 'sort':
lst.sort()
elif tok[0] == 'pop':
lst.pop()
elif tok[0] == 'reverse':
lst.reverse()
else:
print('none')
p = raw_input('Enter Price ')
C = raw_input('Enter Capital ')
print 'Number of Items'
print float(C)/int(p)
c = {'A': 3, 'B': 7, 'C': [2,3], 'D': 'Adana'}
#print(c)
c['D']
| _____no_output_____ | MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Catalog | def fun(x, par):
print(x, par['volatility'])
params = {'volatility': 0.1, 'interest_rate': 0.08}
sig = params['volatility']
r = params['interest_rate']
fun(3, params)
plate = {'Istanbul':34}
city = 'Istanbul'
print 'the number plate for', city,'is', plate[city]
plate = {'Istanbul':34, 'Adana': '01', 'Ankara': '06', 'Izmir': 35, 'Hannover': 'H'}
cities = ['Adana', 'Ankara','Istanbul','Izmir','Hannover']
for city in cities:
print('the number plate for', city,'is', plate[city])
for i in plate.keys():
print i
plate.has_key('Balikesir')
plate['Eskisehir'] = 26
for i in sorted(plate.keys()):
print i, plate[i]
students = {273: {'Name': 'Ali', 'Surname': 'Yasar', 'Gender': 'M'}}
students[395] = {'Name': 'Ayse', 'Surname': 'Oz', 'Gender': 'F'}
students[398] = {'Name': 'Ayse', 'Surname': 'Atik', 'Gender': 'F'}
students[112] = {'Name': 'Ahmet', 'Surname': 'Uz', 'Gender': 'M'}
students[450] = {'Name': 'Veli', 'Surname': 'Gez', 'Gender': 'M'}
students[451] = {'Name': 'Taylan', 'Surname': 'Cemgil', 'Gender': 'U'}
for i in students:
if students[i]['Gender'] is 'F':
print students[i]['Name']
counts = {'M': 0, 'F': 0}
for i in students:
G = students[i]['Gender']
if counts.has_key(G):
counts[G] += 1
else:
counts[G] = 1
counts
counts = {}
for i in students:
G = students[i]['Name']
if counts.has_key(G):
counts[G] += 1
else:
counts[G] = 1
counts
| _____no_output_____ | MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Tuples (Immutable Arrays, no change possible after creation) | a = ('Ankara', '06')
a.count('Istanbul')
%matplotlib inline
import numpy as np
import matplotlib.pylab as plt
x = np.arange(-2,2,0.1)
plt.plot(x,x)
plt.plot(x,x**2)
plt.plot(x,np.sin(x))
plt.show()
| _____no_output_____ | MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Numpy arrays versus matrices | A = np.random.rand(3,5)
x = np.random.rand(5,1)
print(A.dot(x))
A = np.mat(A)
x = np.mat(x)
print(A*x)
a = np.mat(np.random.rand(3,1))
b = np.mat(np.random.rand(3,1))
print(a)
print(b)
a.T*b
N = 1000
D = 3
X = np.random.rand(N, D)
mu = X.mean(axis=0, keepdims=True)
#print(mu)
print((X - mu).T.dot(X-mu)/(N-1.))
np.cov(X.T)
print(np.mat(np.arange(1,11)).T*np.mat(np.arange(1,11))) | [[ 1 2 3 4 5 6 7 8 9 10]
[ 2 4 6 8 10 12 14 16 18 20]
[ 3 6 9 12 15 18 21 24 27 30]
[ 4 8 12 16 20 24 28 32 36 40]
[ 5 10 15 20 25 30 35 40 45 50]
[ 6 12 18 24 30 36 42 48 54 60]
[ 7 14 21 28 35 42 49 56 63 70]
[ 8 16 24 32 40 48 56 64 72 80]
[ 9 18 27 36 45 54 63 72 81 90]
[ 10 20 30 40 50 60 70 80 90 100]]
| MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
B&S with Monte Carlo Call and Put pricing, use a catalog and numpy, avoid using for loops | import numpy as np
def European(Param, S0=1., T=1., Strike=1.,N=10000 ):
'''
Price_Call, Price_Put = European(Param, S0, T, Strike,N)
Param: Market parameters, a catalog with fields
Param['InterestRate'] : Yearly risk free interest rate
Param['Volatility'] :
S0 : Initial asset price
T : Time Period (in Years)
Strike: Strike Price
N : Number of Monte Carlo Samples
'''
W = np.sqrt(T)*np.random.standard_normal(N)
ST = S0*np.exp(T*(Param['InterestRate']-0.5*Param['Volatility']**2) + Param['Volatility']*W)
CT = np.maximum(ST-Strike, 0)
PT = np.maximum(Strike-ST, 0)
Price_C = CT.mean()*np.exp(-Param['InterestRate']*T)
Price_P = PT.mean()*np.exp(-Param['InterestRate']*T)
return Price_C, Price_P
def Lookback(Param, S0=1., T=1., Strike=1., Steps=12, N=10000 ):
'''
Price_Call, Price_Put = Lookback(Param, S0, T, Strike, Steps, N)
Param: Market parameters, a catalog with fields
Param['InterestRate'] : Yearly risk free interest rate
Param['Volatility'] :
S0 : Initial asset price
T : Time Period (in Years)
Strike: Strike Price
Steps : Number of steps to monitor the stock price
N : Number of Monte Carlo Samples
'''
Tstep = T/Steps
Smax = S0*np.ones(N)
Smin = S0*np.ones(N)
St = S0*np.ones(N)
for t in range(Steps):
W = np.sqrt(Tstep)*np.random.standard_normal(N)
St = St*np.exp(Tstep*(Param['InterestRate']-0.5*Param['Volatility']**2) + Param['Volatility']*W)
Smax = np.maximum(St, Smax)
Smin = np.minimum(St, Smin)
CT = np.maximum(Smax-Strike, 0)
PT = np.maximum(Strike-Smin, 0)
Price_C = CT.mean()*np.exp(-Param['InterestRate']*T)
Price_P = PT.mean()*np.exp(-Param['InterestRate']*T)
return Price_C, Price_P
def Asian(Param, S0=1., T=1., Strike=1., Steps=12, N=10000 ):
'''
Price_Call, Price_Put = Asian(Param, S0, T, Strike, Steps, N)
Param: Market parameters, a catalog with fields
Param['InterestRate'] : Yearly risk free interest rate
Param['Volatility'] :
S0 : Initial asset price
T : Time Period (in Years)
Strike: Strike Price
Steps : Number of steps to monitor the stock price
N : Number of Monte Carlo Samples
'''
Tstep = T/Steps
Smean = np.zeros(N)
St = S0*np.ones(N)
for t in range(Steps):
W = np.sqrt(Tstep)*np.random.standard_normal(N)
St = St*np.exp(Tstep*(Param['InterestRate']-0.5*Param['Volatility']**2) + Param['Volatility']*W)
i = t+1
Smean = (i-1)*Smean/i + St/i
CT = np.maximum(Smean-Strike, 0)
PT = np.maximum(Strike-Smean, 0)
Price_C = CT.mean()*np.exp(-Param['InterestRate']*T)
Price_P = PT.mean()*np.exp(-Param['InterestRate']*T)
return Price_C, Price_P
def FloatingLookback(Param, S0=1., T=1., Steps=12, N=10000 ):
'''
Price_Call, Price_Put = FloatingLookback(Param, S0, T, Steps, N)
Param: Market parameters, a catalog with fields
Param['InterestRate'] : Yearly risk free interest rate
Param['Volatility'] :
S0 : Initial asset price
T : Time Period (in Years)
Steps : Number of steps to monitor the stock price
N : Number of Monte Carlo Samples
'''
Tstep = T/Steps
Smax = S0*np.ones(N)
Smin = S0*np.ones(N)
St = S0*np.ones(N)
for t in range(Steps):
W = np.sqrt(Tstep)*np.random.standard_normal(N)
St = St*np.exp(Tstep*(Param['InterestRate']-0.5*Param['Volatility']**2) + Param['Volatility']*W)
Smax = np.maximum(St, Smax)
Smin = np.minimum(St, Smin)
CT = np.maximum(St-Smin, 0)
PT = np.maximum(Smax-St, 0)
Price_C = CT.mean()*np.exp(-Param['InterestRate']*T)
Price_P = PT.mean()*np.exp(-Param['InterestRate']*T)
return Price_C, Price_P
Param = {'Volatility': 0.25, 'InterestRate': 0.11}
Price_C, Price_P = European(Param, S0=100, T=1.0, Strike=100)
print 'European\nCall= ', Price_C,'\n','Put = ', Price_P
Price_C, Price_P = Asian(Param, S0=100, T=1.0, Strike=100, Steps=1000)
print 'Asian\nCall= ', Price_C,'\n','Put = ', Price_P
Price_C, Price_P = Lookback(Param, S0=100, T=1.0, Strike=100, Steps=1000)
print 'Lookback\nCall= ', Price_C,'\n','Put = ', Price_P
Price_C, Price_P = FloatingLookback(Param, S0=100, T=1.0, Steps=1000)
print 'FloatingLookback\nCall= ', Price_C,'\n','Put = ', Price_P
| European
Call= 15.5726197769
Put = 5.13556380233
Asian
Call= 8.16477817074
Put = 3.17271035914
Lookback
Call= 25.6819276647
Put = 12.5838549789
FloatingLookback
Call= 23.0385882044
Put = 15.3296952253
| MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Next week Assignment:Consolidate all pricing methods into one single function avoiding code repetitions. | def OptionPricer(type_of_option, Params):
'''
Price_Call, Price_Put = OptionPricer(type_of_option, Param, S0, T, Strike, Steps, N)
type_of_option = 'European'
'Asian', 'Lookback', 'FloatingLookback'
Param: Parameter catalog with fields
Param['InterestRate'] : Yearly risk free interest rate (default: 0.11)
Param['Volatility'] : scalar or array of length steps (default: 0.11)
Param['S0'] : Initial asset price (default: 1)
Param['T '] : Time Period (in Years) (default: 1)
Param['Strike']: Strike Price (default: 1)
Param['Steps'] : Number of steps to monitor the stock price (default: 12)
Param['N'] : Number of Monte Carlo Samples (default: 1000)
'''
# Some test cases
par = {'Volatility': [0.01,0.01,0.01,0.03,0.03], 'InterestRate': 0.11}
OptionPricer('Asian', par) | _____no_output_____ | MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Next week: Kalman Filtering (Learn Numpy and matplotlib) | th = 0.5
A = np.mat([[np.cos(th), np.sin(th)],[-np.sin(th), np.cos(th)]])
x = np.mat([1,0]).T
x = np.mat([[1],[0]])
for t in range(10):
x = A*x + 0*np.random.randn(2,1)
print(x)
name = raw_input("What is your name? ")
print name
def fun(x):
print x,
x = map(fun,range(1,10+1))
x = map(fun,range(1,10+1))
def myfun(x,y):
return x*y
def myfun2(x,y):
return x+y
def funn(f, x, y):
return f(x,y)
print funn(myfun2, 3, 5)
l = [1,2,3,4]
def power(x):
return 2**x
r = sum(map(power, l))
print(r)
s = 'insert 0 5'
u = s.split(' ')
print(u)
l = [1,2,3]
l.pop
N = int(raw_input())
l = []
for i in range(N):
s = raw_input()
items = s.split(' ')
cmd = items[0]
if cmd == 'insert':
pos = int(items[1])
num = int(items[2])
l.insert(pos, num)
if cmd == 'print':
print l
if cmd == 'remove':
num = int(items[1])
l.remove(num)
if cmd == 'append':
num = int(items[1])
l.append(num)
if cmd == 'sort':
l.sort()
if cmd == 'pop':
l.pop()
if cmd == 'reverse':
l.reverse()
N = 2
l = '1 2'.split(' ')
l2 = [int(i) for i in l[0:N+1]]
c = tuple(l2)
print hash(c)
48*21 | _____no_output_____ | MIT | fe588/fe588_introduction.ipynb | bkoyuncu/notes |
Importing classes from the `tcalc` module | from TCalc.tcalc import eyepiece, telescope, barlow_lens, focal_reducer | _____no_output_____ | MIT | docs/tutorials/TCalc_tutorial.ipynb | Bhavesh012/Telescope-Calculator |
To quickly access the docstring, run `help(classname)` | help(eyepiece) | Help on class eyepiece in module TCalc.tcalc:
class eyepiece(builtins.object)
| eyepiece(f_e, fov_e=50)
|
| Class representing a single eyepiece
| Args:
| f_e: focal length of the eyepiece (mm)
| fov_e: field of view of the eyepiece (deg). Defaults to 50 degrees.
|
| Methods defined here:
|
| __init__(self, f_e, fov_e=50)
| Initialize self. See help(type(self)) for accurate signature.
|
| ----------------------------------------------------------------------
| Data descriptors defined here:
|
| __dict__
| dictionary for instance variables (if defined)
|
| __weakref__
| list of weak references to the object (if defined)
| MIT | docs/tutorials/TCalc_tutorial.ipynb | Bhavesh012/Telescope-Calculator |
For an example, let's try to have estimate the specifications of Celestron's 8 SE telescope. | c8 = telescope(D_o=203.2, f_o=2032, user_D_eye=None, user_age=22) # adding configuration of 8in scope
omni_40 = eyepiece(40, 52) # defining 40 mm eyepiece
omni_25 = eyepiece(25, 52) # defining 25 mm eyepiece
# adding eyepiece to the telescope
c8.add_eyepiece(omni_40, id='omni_40', select=True)
c8.add_eyepiece(omni_25, id='omni_25', select=True)
# listing all the added eyepieces in a table format
c8.list_eyepiece()
# listing overall configuration of the telescope
c8.say_configuration() # remember this with 25 mm eyepiece
# selecting different eyepiece
c8.select_eyepiece('omni_40')
c8.say_configuration()
# calling individual functions
c8._compute_focal_ratio()
# adding additional optical parts
reducer = focal_reducer(.5) # defining focal reducer of 0.5x
barlow = barlow_lens(2) # defining barlow lens of 2x
c8.add_optic(reducer,'reducer 1', select=True) # adding reducer to the telescope
c8.add_optic(barlow,'barlow 1', select=False) # adding barlow to the telescope
#if the magnifications limits get reached then warning will be printed.
c8.add_optic(reducer,'reducer 1', select=False)
c8.add_optic(barlow,'barlow 1', select=True)
# printing configuration again with barlow lens
c8.say_configuration() |
The telescope has the following layout:
Aperture diameter: 203.2 mm
Focal length: 2032 mm, corresponding to a focal ratio of 10.0
'barlow 1', a Barlow lens, has been added to the optical path. This increases the focal length by 2
This results in
Focal length: 4064 mm, corresponding to a focal ratio of 20.0
In good atmospheric conditions, the resolution of the telescope (Dawes limit) is 0.6 arcseconds
By wavelength, the resolution is
400 nm (blue): 0.5 arcsec
550 nm (green): 0.7 arcsec
700 nm (red): 0.9 arcsec
The maximum possible magnification factor is 406.4
This means the minimum compatible eyepiece focal length is 10.0 mm
The minimum magnification factor and corresponding maximum eyepiece focal length depend on the diameter of the observer's eye.
For a telescope user with an eye diameter of 7 mm (apropriate for an age around 25 years):
The minimum magnification factor is 29.0
This means the maximum compatible eyepiece focal length is 406.4 mm
The faintest star that can be seen by this telescope is 13.5 mag
The currently selected eyepiece is 'omni_40', which has the following layout:
Focal length: 40 mm
Field of view: 52 degrees
With this eyepiece:
The magnification factor is 101.6. This is compatible with the telescope limits.
The true field of view is 1 degrees
The exit pupil diameter is 2.0 mm
The faintest surface brightness that can be seen by this telescope is 8.00
| MIT | docs/tutorials/TCalc_tutorial.ipynb | Bhavesh012/Telescope-Calculator |
You can notice that if used a *2x barlow lens* on a *40mm eyepiece*, the brightness of the object will be decresead by **4 times!**This way you can simulate different scenarios and find out which accesories are optimal for your purpose. This will save you both time and money on costly accesories! For advanced users, the plot functionality provides the plots of `resolution performance`, `maginfication_limits` and `eyepiece_limits`. | c8.show_resolving_power()
c8.show_magnification_limits()
c8.show_eyepiece_limits() | _____no_output_____ | MIT | docs/tutorials/TCalc_tutorial.ipynb | Bhavesh012/Telescope-Calculator |
Week 6 - SMM695Matteo DevigiliJune, 28th 2021[_PySpark_](https://spark.apache.org/docs/latest/api/python/index.html): during this lecture, we will approach Spark through Python **Agenda**:1. Introduction to Spark1. Installing PySpark1. PySpark Basics1. PySpark and Pandas1. PySpark and SQL1. Load data from your DBMS Introduction to Spark**Big Data Challenge**:* Cost of storing data has dropped* The need for parallel computation has increased**Note**: [IBM Blue Gen\L](https://www.ibm.com/ibm/history/ibm100/us/en/icons/bluegene/) **What is [Apache Spark](https://spark.apache.org)**?> "Apache Spark is a unified computing engine and a set of libraries for parallel data processing on computer clusters"[Chambers and Zaharia 2018](references) **Programming Languages Supported**: **Spark's philosophy**:* *Unified*: Spark offers a large variety of data analytics tools* *Computing Engine*: Spark focuses on computing, not on storage* *Libraries*: Spark has different libraries to perform several tasks **Apache Spark Libraries**:* *Spark SQL** *Spark Streaming** *Spark MLlib** *Spark GraphX*[Third-party projects](https://spark.apache.org/third-party-projects.html) **Spark Application**:| Component ||Role ||----|----|---|| *Spark Driver*| | Execute user-defined tasks || *Cluster Manager* | | Manage workers nodes|| *Executors* | | Execute tasks | **From Python to Spark code and back**:Source: _Bill Chambers, Matei Zaharia 2018_ (p. 23) Installing PySparkThere are several ways to set-up PySpark on your local machine. Here, two methods are discussed:* Pure-python users: ```pythonpip install pyspark```* Conda users:```pythonconda install pyspark```Further info at [Spark Download page](https://spark.apache.org/downloads.html). RequirementsPay attention to the following:>Spark runs on Java 8/11Check java version running on your machine. Type the following on your terminal:```pythonjava -version```If you are running a different Java version, install java 8/11! Check out [Spark Downloading info](https://spark.apache.org/docs/latest/downloading). PySpark - Basics Libraries | #to create a spark session object
from pyspark.sql import SparkSession
# functions
import pyspark.sql.functions as F
# data types
from pyspark.sql.types import *
# import datetime
from datetime import date as dt | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
* More info on **Functions** at these [link-1](https://spark.apache.org/docs/latest/api/python/pyspark.sql.htmlmodule-pyspark.sql.functions) & [link-2](https://spark.apache.org/docs/2.3.0/api/sql/index.htmlyear)* More info on **Data Types** at this [link](https://spark.apache.org/docs/latest/sql-ref-datatypes.html) Opening a SessionThe **SparkSession** is a driver process that enables:* to control our Spark Application* to execute user-defined manipulationsCheck this [link](https://spark.apache.org/docs/latest/api/python/pyspark.sql.htmlpyspark.sql.SparkSession) for further reference. | # to open a Session
spark = SparkSession.builder.appName('last_dance').getOrCreate() | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
**Spark UI**The spark UI is useful to monitor your application. You have the following tabs:* *Jobs*: info concerning Spark jobs* *Stages*: info on individual stages and their tasks* *Storage*: info on data that is currently in our spark application* *Environment*: info on configurations and current settings of our application* *Executors*: info on the executors that run our application* *SQL*: refers to both SQL and DataFrames | spark | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
Create DataframeIn order to create a dataframe from scratch, we need to:1. Create a schema, passing: * Column names * Data types1. Pass values as an array of tuples | # Here, I define a schema
# .add(field, data_type=None, nullable=True, metadata=None)
schema = StructType().add("id", "integer", True).add("first_name", "string", True).add(
"last_name", "string", True).add("dob", "date", True)
'''
schema = StructType().add("id", IntegerType(), True).add("first_name", StringType(), True).add(
"last_name", StringType(), True).add("dob", DateType(), True)
'''
# Then, I can pass some values
df = spark.createDataFrame([(1, 'Michael', "Jordan", dt(1963, 2, 17)),
(2, 'Scottie', "Pippen", dt(1965, 9, 25)),
(3, 'Dennis', "Rodman", dt(1961, 5, 16))],
schema=schema)
# Let's explore Schema structure
df.printSchema()
# We can also leverage on functions to create a new column
df=df.withColumn('age', F.year(F.current_date()) - F.year(df.dob))
df.show() | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
**Transformations*** Immutability: once created, data structures can not be changed* Lazy evaluation: computational instructions will be executed at the very last **Actions*** view data* collect data* write to output data sources PySpark and Pandas Load a csv Loading a csv file from you computer, you need to type:* Pands: * db = pd.read_csv('path/to/movies.csv')* Pyspark: * df = spark.read.csv('path/to/movies.csv', header=True, inferSchema=True)Here, we will import a csv directly from GitHub. Data are provided by [FiveThirtyEight](https://github.com/fivethirtyeight)[](https://fivethirtyeight.com/features/the-dollar-and-cents-case-against-hollywoods-exclusion-of-women/) | # import pandas
import pandas as pd
# import SparkFiles
from pyspark import SparkFiles
# target dataset
url = 'https://raw.githubusercontent.com/fivethirtyeight/data/master/bechdel/movies.csv'
# loading data with pandas
db = pd.read_csv(url)
# loading data with pyspark
spark.sparkContext.addFile(url)
df = spark.read.csv(SparkFiles.get('movies.csv'), header=True, inferSchema=True) | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
Inspecting dataframes | # pandas info
db.info()
# pyspark schema
df.printSchema()
# pandas fetch 5
db.head(5)
# pyspark fetch 5
df.show(5)
df.take(5)
# pandas filtering:
db[db.year == 1970]
# pyspark filtering:
df[df.year == 1970].show()
# get columns and data types
print("""
Pandas db.columns:
===================
{}
PySpark df.columns:
===================
{}
Pandas db.dtype:
===================
{}
PySpark df.dtypes:
===================
{}
""".format(db.columns, df.columns, db.dtypes, df.dtypes), flush = True) | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
Columns | # pandas add a column
db['newcol'] = db.domgross/db.intgross
# pyspark add a column
df=df.withColumn('newcol', df.domgross/df.intgross)
# pandas rename columns
db.rename(columns={'newcol': 'dgs/igs'}, inplace=True)
# pyspark rename columns
df=df.withColumnRenamed('newcol', 'dgs/igs') | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
Drop | # pandas drop `code' column
db.drop('code', axis=1, inplace=True)
# pyspark drop `code' column
df=df.drop('code')
# pandas dropna()
db.dropna(subset=['domgross'], inplace=True)
# pyspark dropna()
df=df.dropna(subset='domgross') | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
Stats | # pandas describe
db.describe()
# pyspark describe
df.describe(['year', 'budget']).show() | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
Pyspark and SQL | # pyspark rename 'budget_2013$'
df=df.withColumnRenamed('budget_2013$', 'budget_2013')
# Create a temporary table
df.createOrReplaceTempView('bechdel')
# Run a simple SQL command
sql = spark.sql("""SELECT imdb, year, title, budget FROM bechdel LIMIT(5)""")
sql.show()
# AVG budget differences
sql_avg = spark.sql(
"""
SELECT
binary,
COUNT(*) AS count,
format_number(AVG(budget),2) AS avg_budget,
format_number((SELECT AVG(budget) FROM bechdel),2) AS avg_budget_samp,
format_number(AVG(budget_2013),2) AS avg_budget2013,
format_number((SELECT AVG(budget_2013) FROM bechdel),2) AS avg_budget2013_samp
FROM bechdel GROUP BY binary
"""
)
sql_avg.show() | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
Load data from DBMS To run the following you need to restart the notebook. | # to create a spark session object
from pyspark.sql import SparkSession | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
PostgreSQL To interact with postgre you need to: * Download the *postgresql-42.2.22.jar file* [here](https://jdbc.postgresql.org/download.html)* Include the path to the downloaded jar file into SparkSession() | # Open a session running data from PostgreSQL
spark_postgre = SparkSession \
.builder \
.appName("last_dance_postgre") \
.config("spark.jars", "/Users/matteodevigili/py3venv/dms695/share/py4j/postgresql-42.2.22.jar") \
.getOrCreate()
spark_postgre
# Read data from PostgreSQL running at localhost
df = spark_postgre.read \
.format("jdbc") \
.option("url", "jdbc:postgresql://localhost:5432/pagila") \
.option("dbtable", "film") \
.option("user", "dms695") \
.option("password", "smm695") \
.option("driver", "org.postgresql.Driver") \
.load()
df.printSchema()
# get some stats
df.describe(['release_year', 'rental_rate', 'rental_duration']).show()
# Create a temporary table
df.createOrReplaceTempView('film')
# Run a simple SQL command
sql = spark_postgre.sql("""SELECT title, release_year, length, rating FROM film LIMIT(1)""")
sql.show() | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
MongoDB For further reference check the [Python Guide provided by Mongo](https://docs.mongodb.com/spark-connector/current/python-api/) or the [website for the mongo-spark connector](https://spark-packages.org/package/mongodb/mongo-spark). | # add path to Mongo
spark_mongo = SparkSession \
.builder \
.appName("last_dance_mongo") \
.config("spark.mongodb.input.uri", "mongodb://127.0.0.1/amazon.music") \
.config("spark.mongodb.output.uri", "mongodb://127.0.0.1/amazon.music") \
.config('spark.jars.packages', 'org.mongodb.spark:mongo-spark-connector_2.12:3.0.1') \
.getOrCreate()
spark_mongo
# load data from MongoDB
df = spark_mongo.read.format("mongo").load()
df.printSchema()
# get some stats
df.describe(['overall', 'unixReviewTime']).show()
# Create a temporary table
df.createOrReplaceTempView('music')
# Run a simple SQL command
sql = spark_mongo.sql("""SELECT asin, date, helpful, overall, unixReviewTime FROM music LIMIT(1)""")
sql.show() | _____no_output_____ | MIT | week-6/sc_6.ipynb | mattDevigili/dms-smm695 |
______Universidad Tecnológica Nacional, Buenos Aires__\__Ingeniería Industrial__\__Cátedra de Investigación Operativa__\__Autor: Rodrigo Maranzana______ Ejercicio 3 Un agente comercial realiza su trabajo en tres ciudades A, B y C. Para evitar desplazamientos innecesarios está todo el día en la misma ciudad y allí pernocta, desplazándose a otra ciudad al día siguiente, si no tiene suficiente trabajo. Después de estar trabajando un día en C, la probabilidad de tener que seguir trabajando en ella al día siguiente es 0,4, la de tener que viajar a B es 0,4 y la de tener que ir a A es 0,2. Si el viajante duerme un día en B, con probabilidad de un 20% tendrá que seguir trabajando en la misma ciudad al día siguiente, en el 60% de los casos viajará a C, mientras que irá a A con probabilidad 0,2. Por último si el agente comercial trabaja todo un día en A, permanecerá en esa misma ciudad, al día siguiente, con una probabilidad 0,1, irá a B con una probabilidad de 0,3 y a C con una probabilidad de 0,6.* Ejercicio A: Si hoy el viajante está en C, ¿cuál es la probabilidad de que también tenga que trabajar en C al cabo de cuatro días?* Ejercicio B: ¿Cuáles son los porcentajes de días en los que el agente comercial está en cada una de las tres ciudades? Índice1 Datos Iniciales2 Ejercicio A2.1 Forma alternativa de resolución:3 Ejercicio B3.1 Forma alternativa: usando una matriz no cuadrada3.2 Cálculo auxiliar: partiendo directamente de la matriz de transición Datos Iniciales Importamos las librerías necesarias. | import numpy as np | _____no_output_____ | Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Ingresamos los datos de la matriz de transición en una matriz numpy: | # Matriz de transición como numpy array:
T = np.array([[0.1, 0.3, 0.6],
[0.2, 0.2, 0.6],
[0.2, 0.4, 0.4]])
# Printeamos T
print(f'Matriz de transición: \n{T}') | Matriz de transición:
[[0.1 0.3 0.6]
[0.2 0.2 0.6]
[0.2 0.4 0.4]]
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Ejercicio A En primer lugar, calculamos la matriz de transición habiendo pasado 4 días: elevamos la matriz a la cuarta usando el método de la potencia de álgebra lineal de la librería Numpy. | # Cálculo de la matriz de transición a tiempo 4:
T4 = np.linalg.matrix_power(T, 4)
# printeamos la matriz de transicion de 4 pasos:
print(f'Matriz de transición a tiempo 4: \n{T4}\n') | Matriz de transición a tiempo 4:
[[0.1819 0.3189 0.4992]
[0.1818 0.319 0.4992]
[0.1818 0.3174 0.5008]]
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Sabiendo que $p_0$ considera que el agente está en el nodo C:$ p_0 = (0, 0, 1) $ | # Generación del vector inicial p_0:
p_0 = np.array([0, 0, 1])
# printeamos el vector inicial:
print(f'Vector de estado a tiempo 0: \n{p_0}\n') | Vector de estado a tiempo 0:
[0 0 1]
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Calculamos: $ p_0 T^4 = p_4 $ | # Cálculo del estado a tiempo 4, p_4:
p_4 = np.dot(p_0, T4)
# printeamos p4:
print(f'Vector de estado a tiempo 4: \n{p_4}\n') | Vector de estado a tiempo 4:
[0.1818 0.3174 0.5008]
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Dado el vector $ p_4 $, nos quedamos con el componente perteneciente al estado C. | # Componente del nodo C:
p_4_c = p_4[2]
# printeamos lo obtenido:
print(f'Probabilidad de estar en c habiendo iniciado en c: \n{p_4_c}\n') | Probabilidad de estar en c habiendo iniciado en c:
0.5008
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Forma alternativa de resolución:El resultado es el mismo si consideramos que la componente ${T^4}_{cc}$ es la probabilidad de transición del nodo c al mismo nodo habiendo pasado 4 ciclos.Veamos cómo se obtiene esa componente: | # Componente de cc de la matriz de transición a tiempo 4:
T4cc = T4[2,2]
print('\n ** Probabilidad de estar en c habiendo iniciado en c: \n %.5f' % T4cc) |
** Probabilidad de estar en c habiendo iniciado en c:
0.50080
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Ejercicio B Dada una matriz $A$ proveniente del sistema de ecuaciones que resuelve $\pi T = \pi$ | # Matriz A:
A = np.array([[-0.9, 0.2, 0.2],
[ 0.3, -0.8, 0.4],
[ 0.6, 0.6, -0.6],
[1, 1, 1]])
# Printeamos A:
print(f'Matriz asociada al sistema lineal de ecuaciones: \n{A}') | Matriz asociada al sistema lineal de ecuaciones:
[[-0.9 0.2 0.2]
[ 0.3 -0.8 0.4]
[ 0.6 0.6 -0.6]
[ 1. 1. 1. ]]
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Y dado un vector $B$ relacionado con los términos independientes del sistema de ecuaciones anteriormente mencionado. | # Vector B:
B = np.array([0, 0, 0, 1])
# Printeamos B:
print(f'Vector de términos independientes: \n{B}') | Vector de términos independientes:
[0 0 0 1]
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Dado que el solver de numpy solamente admite sistemas lineales cuadrados por el algoritmo que usa para la resolución [1], debemos eliminar una de las filas (cualquiera) de la matriz homogénea y quedarnos con la fila relacionada a la ecuación $ \sum_i{\pi_i} = 1$.Hacemos lo mismo para el vector de términos independientes B.Para hacer esto usamos la función el método delete de numpy, indicando la posición a eliminar y el eje (axis) al que pertenece.[1] https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.linalg.solve.html | # Copio la matriz A original, para que no se modifique.
A_s = A.copy()
# Eliminamos la primer fila de la matriz A:
A_s = np.delete(A_s, 0, 0)
# Printeamos:
print(f'Matriz asociada al sistema lineal de ecuaciones: \n{A_s}')
print(f'\n -> Dimensión: {A_s.shape}')
# Copio el vector B original, para que no se modifique.
B_s = B.copy()
# Eliminamos la primera componente del vector B:
B_s = np.delete(B_s, 0, 0)
print(f'\nVector de términos independientes: \n{B_s}')
print(f'\n -> Dimensión: {B_s.shape}') |
Vector de términos independientes:
[0 0 1]
-> Dimensión: (3,)
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Cumpliendo con un sistema cuadrado, usamos el método solve de numpy para obtener $x$ del sistema $Ax = B$ | x = np.linalg.solve(A_s, B_s)
print('\n ** Vector solución de estado estable: \n %s' % x) |
** Vector solución de estado estable:
[0.18181818 0.31818182 0.5 ]
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Forma alternativa: usando una matriz no cuadradaComo explicamos anteriormente no podemos usar el método $solve$ en matrices no cuadradas. En su lugar podemos usar el método de los mínimos cuadrados para aproximar la solución[2]. Este método no tiene restricciones en cuanto a la dimensión de la matriz.El desarrollo del método no forma parte de la materia, siendo contenido de Análisis Numérico y Cálculo Avanzado.[2] https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.lstsq.html | x_lstsq, _, _, _ = np.linalg.lstsq(A, B, rcond=None)
print('\n ** Vector solución de estado estable: \n %s' % x_lstsq) |
** Vector solución de estado estable:
[0.18181818 0.31818182 0.5 ]
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Cálculo auxiliar: partiendo directamente de la matriz de transiciónEn la resolución original, usamos una matriz A relacionada al sistema lineal de ecuaciones que resolvimos a mano. Ahora veremos otra forma de llegar a la solución solamente con los datos dados y tratamiento de matrices.Partiendo del sistema original: $\pi T = \pi$Despejando $\pi$ obtenemos:$(T^T - I) \pi^T = 0 $Podemos transformar lo anterior en la notación que usamos más arriba para que tenga consistencia:$A = (T^T - I)$$X = \pi^T$$B = 0$Por lo tanto, llegamos a la misma expresión $Ax = B$ Entonces, comenzamos calculando: $A = (T^T - I)$ | # Primero calculamos la traspuesta de la matriz de transición:
Tt = np.transpose(T)
print(f'\nT traspuesta: \n{Tt}')
# Luego con calculamos la matriz A, sabiendo que es la traspuesta de T menos la identidad.
A1 = Tt - np.identity(Tt.shape[0])
print(f'\nMatriz A: \n{A1}') |
T traspuesta:
[[0.1 0.2 0.2]
[0.3 0.2 0.4]
[0.6 0.6 0.4]]
Matriz A:
[[-0.9 0.2 0.2]
[ 0.3 -0.8 0.4]
[ 0.6 0.6 -0.6]]
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Seguimos con: $B = 0$ | # El vector B, es un vector de ceros:
B1 = np.zeros(3)
print(f'\nVector B: \n{B1}') |
Vector B:
[0. 0. 0.]
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
A partir de aca, simplemente aplicamos el método que ya sabemos. Agregamos la información correspondiente a: $\sum_i{\pi_i} = 1$. | # Copio la matriz A1 original, para que no se modifique.
A1_s = A1.copy()
# Agregamos las probabilidades a la matriz A
eq_suma_p = np.array([[1, 1, 1]])
A1_s = np.concatenate((A1_s, eq_suma_p), axis=0)
# Printeamos:
print(f'Matriz A: \n{A1_s}')
# Copio el vector B1 original, para que no se modifique.
B1_s = B1.copy()
# Agregamos 1 al vector B:
B1_s = np.append(B1_s, 1)
# Printeamos:
print(f'\nVector B: \n{B1_s}') |
Vector B:
[0. 0. 0. 1.]
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Resolvemos por mínimos cuadrados: | # Resolvemos con método de mínimos cuadrados:
x_lstsq, _, _, _ = np.linalg.lstsq(A1_s, B1_s, rcond=None)
# Printeamos la solucion:
print(f'\nVector solución de estado estable: {x_lstsq}') |
Vector solución de estado estable: [0.18181818 0.31818182 0.5 ]
| Apache-2.0 | 04_markov/.ipynb_checkpoints/ejercicio_3-checkpoint.ipynb | juanntripaldi/pyOperativ |
Wavefront set inpainting real phantom In this notebook we are implementing a Wavefront set inpainting algorithm based on a hallucination network | %matplotlib inline
import os
os.environ["CUDA_VISIBLE_DEVICES"]="0"
# Import the needed modules
from data.data_factory import generate_realphantom_WFinpaint, DataGenerator_realphantom_WFinpaint
from ellipse.ellipseWF_factory import plot_WF
import matplotlib.pyplot as plt
import numpy.random as rnd
import numpy as np
import odl
import matplotlib.pyplot as plt | /store/kepler/datastore/andrade/GitHub_repos/Joint_CTWF_Recon/WF_inpaint/data/data_factory.py:7: UserWarning:
This call to matplotlib.use() has no effect because the backend has already
been chosen; matplotlib.use() must be called *before* pylab, matplotlib.pyplot,
or matplotlib.backends is imported for the first time.
The backend was *originally* set to 'module://ipykernel.pylab.backend_inline' by the following code:
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/runpy.py", line 193, in _run_module_as_main
"__main__", mod_spec)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/runpy.py", line 85, in _run_code
exec(code, run_globals)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel_launcher.py", line 16, in <module>
app.launch_new_instance()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/traitlets/config/application.py", line 658, in launch_instance
app.start()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/kernelapp.py", line 505, in start
self.io_loop.start()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/platform/asyncio.py", line 132, in start
self.asyncio_loop.run_forever()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/asyncio/base_events.py", line 438, in run_forever
self._run_once()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/asyncio/base_events.py", line 1451, in _run_once
handle._run()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/asyncio/events.py", line 145, in _run
self._callback(*self._args)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/ioloop.py", line 758, in _run_callback
ret = callback()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/stack_context.py", line 300, in null_wrapper
return fn(*args, **kwargs)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/gen.py", line 1233, in inner
self.run()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/gen.py", line 1147, in run
yielded = self.gen.send(value)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/kernelbase.py", line 357, in process_one
yield gen.maybe_future(dispatch(*args))
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/gen.py", line 326, in wrapper
yielded = next(result)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/kernelbase.py", line 267, in dispatch_shell
yield gen.maybe_future(handler(stream, idents, msg))
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/gen.py", line 326, in wrapper
yielded = next(result)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/kernelbase.py", line 534, in execute_request
user_expressions, allow_stdin,
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/gen.py", line 326, in wrapper
yielded = next(result)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/ipkernel.py", line 294, in do_execute
res = shell.run_cell(code, store_history=store_history, silent=silent)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/zmqshell.py", line 536, in run_cell
return super(ZMQInteractiveShell, self).run_cell(*args, **kwargs)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/IPython/core/interactiveshell.py", line 2823, in run_cell
self.events.trigger('post_run_cell', result)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/IPython/core/events.py", line 88, in trigger
func(*args, **kwargs)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/pylab/backend_inline.py", line 164, in configure_once
activate_matplotlib(backend)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/IPython/core/pylabtools.py", line 314, in activate_matplotlib
matplotlib.pyplot.switch_backend(backend)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/matplotlib/pyplot.py", line 231, in switch_backend
matplotlib.use(newbackend, warn=False, force=True)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/matplotlib/__init__.py", line 1410, in use
reload(sys.modules['matplotlib.backends'])
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/importlib/__init__.py", line 166, in reload
_bootstrap._exec(spec, module)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/matplotlib/backends/__init__.py", line 16, in <module>
line for line in traceback.format_stack()
matplotlib.use('Agg')
/store/kepler/datastore/andrade/GitHub_repos/Joint_CTWF_Recon/WF_inpaint/ellipse/ellipseWF_factory.py:9: UserWarning:
This call to matplotlib.use() has no effect because the backend has already
been chosen; matplotlib.use() must be called *before* pylab, matplotlib.pyplot,
or matplotlib.backends is imported for the first time.
The backend was *originally* set to 'module://ipykernel.pylab.backend_inline' by the following code:
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/runpy.py", line 193, in _run_module_as_main
"__main__", mod_spec)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/runpy.py", line 85, in _run_code
exec(code, run_globals)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel_launcher.py", line 16, in <module>
app.launch_new_instance()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/traitlets/config/application.py", line 658, in launch_instance
app.start()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/kernelapp.py", line 505, in start
self.io_loop.start()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/platform/asyncio.py", line 132, in start
self.asyncio_loop.run_forever()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/asyncio/base_events.py", line 438, in run_forever
self._run_once()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/asyncio/base_events.py", line 1451, in _run_once
handle._run()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/asyncio/events.py", line 145, in _run
self._callback(*self._args)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/ioloop.py", line 758, in _run_callback
ret = callback()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/stack_context.py", line 300, in null_wrapper
return fn(*args, **kwargs)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/gen.py", line 1233, in inner
self.run()
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/gen.py", line 1147, in run
yielded = self.gen.send(value)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/kernelbase.py", line 357, in process_one
yield gen.maybe_future(dispatch(*args))
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/gen.py", line 326, in wrapper
yielded = next(result)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/kernelbase.py", line 267, in dispatch_shell
yield gen.maybe_future(handler(stream, idents, msg))
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/gen.py", line 326, in wrapper
yielded = next(result)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/kernelbase.py", line 534, in execute_request
user_expressions, allow_stdin,
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/tornado/gen.py", line 326, in wrapper
yielded = next(result)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/ipkernel.py", line 294, in do_execute
res = shell.run_cell(code, store_history=store_history, silent=silent)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/zmqshell.py", line 536, in run_cell
return super(ZMQInteractiveShell, self).run_cell(*args, **kwargs)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/IPython/core/interactiveshell.py", line 2823, in run_cell
self.events.trigger('post_run_cell', result)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/IPython/core/events.py", line 88, in trigger
func(*args, **kwargs)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/ipykernel/pylab/backend_inline.py", line 164, in configure_once
activate_matplotlib(backend)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/IPython/core/pylabtools.py", line 314, in activate_matplotlib
matplotlib.pyplot.switch_backend(backend)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/matplotlib/pyplot.py", line 231, in switch_backend
matplotlib.use(newbackend, warn=False, force=True)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/matplotlib/__init__.py", line 1410, in use
reload(sys.modules['matplotlib.backends'])
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/importlib/__init__.py", line 166, in reload
_bootstrap._exec(spec, module)
File "/homes/extern/andrade/store/miniconda3/envs/tf_gpu/lib/python3.6/site-packages/matplotlib/backends/__init__.py", line 16, in <module>
line for line in traceback.format_stack()
matplotlib.use('Agg')
| MIT | WF_inpaint/WF_inpaint_realphantom_unet_train.ipynb | arsenal9971/DeeMicrolocalReconstruction |
Data generator | batch_size = 1
size = 256
nClasses = 180
lowd = 40
y_arr, x_true_arr =generate_realphantom_WFinpaint(batch_size, size, nClasses, lowd)
plt.figure(figsize=(6,6))
plt.axis('off')
plot_WF(y_arr[0,:,:,0])
plt.figure(figsize=(6,6))
plt.axis('off')
plot_WF(x_true_arr[0,:,:,0]) | _____no_output_____ | MIT | WF_inpaint/WF_inpaint_realphantom_unet_train.ipynb | arsenal9971/DeeMicrolocalReconstruction |
Load the model | # Tensorflow and seed
seed_value = 0
import random
random.seed(seed_value)
import tensorflow as tf
tf.set_random_seed(seed_value)
# Importing relevant keras modules
from tensorflow.keras.callbacks import ModelCheckpoint, CSVLogger
from tensorflow.keras.models import load_model
from shared.shared import create_increasing_dir
import pickle
# Import model and custom losses
from models.unet import UNet
from models.losses import CUSTOM_OBJECTS
# Parameters for the training
learning_rate = 1e-3
loss = 'mae'
batch_size = 50
epoches = 10000
pretrained = 1
path_to_model_dir = './models/unets_realphantom_WFinpaint/training_5'
# Data generator
size = 256
nClasses = 180
lowd = 40
train_gen = DataGenerator_realphantom_WFinpaint(batch_size, size, nClasses, lowd)
val_gen = DataGenerator_realphantom_WFinpaint(batch_size, size, nClasses, lowd)
if pretrained==0:
# Create a fresh model
print("Create a fresh model")
unet = UNet()
model = unet.create_model( img_shape = (size, size, 1) , loss = loss, learning_rate = learning_rate)
path_to_training = create_increasing_dir('./models/unets_realphantom_WFinpaint', 'training')
print("Save training in {}".format(path_to_training))
path_to_model_dir = path_to_training
else:
print("Use trained model as initialization:")
print(path_to_model_dir+"/weights.hdf5")
model = load_model(path_to_model_dir+"/weights.hdf5",
custom_objects=CUSTOM_OBJECTS)
path_to_training = path_to_model_dir
# Callbacks for saving model
context = {
"loss": loss,
"batch_size": batch_size,
"learning_rate": learning_rate,
"path_to_model_dir": path_to_model_dir,
}
path_to_context = path_to_training+'/context.log'
with open(path_to_context, 'wb') as dict_items_save:
pickle.dump(context, dict_items_save)
print("Save training context to {}".format(path_to_context))
# Save architecture
model_json = model.to_json()
path_to_architecture = path_to_training + "/model.json"
with open(path_to_architecture, "w") as json_file:
json_file.write(model_json)
print("Save model architecture to {}".format(path_to_architecture))
# Checkpoint for trained model
checkpoint = ModelCheckpoint(
path_to_training+'/weights.hdf5',
monitor='val_loss', verbose=1, save_best_only=True)
csv_logger = CSVLogger(path_to_training+'/training.log')
callbacks_list = [checkpoint, csv_logger]
model.fit_generator(train_gen,epochs=epoches, steps_per_epoch=5600 // batch_size,
callbacks=callbacks_list, validation_data=val_gen, validation_steps= 2000// batch_size) | Epoch 1/10000
111/112 [============================>.] - ETA: 13s - loss: 0.9985 - my_mean_squared_error: 111.1464 - mean_squared_error: 111.1464 - mean_absolute_error: 0.9985 - l2_on_wedge: 107.8654 - my_psnr: -5.8870 | MIT | WF_inpaint/WF_inpaint_realphantom_unet_train.ipynb | arsenal9971/DeeMicrolocalReconstruction |
7. Vertical Vibration of Quarter Car ModelThis notebook introduces the base excitation system by examning the behavior of a quarter car model.After the completion of this assignment students will be able to:- excite a system with a sinusoidal input- understand the difference in transient and steady state solutions- create a frequency response plot- define resonance and determine the parameters that cause resonance | import numpy as np
import matplotlib.pyplot as plt
%matplotlib notebook
from resonance.linear_systems import SimpleQuarterCarSystem
sys = SimpleQuarterCarSystem() | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
The simple quarter car model has a suspension stiffness and damping, along with the sprung car mass in kilograms, and a travel speed parameter in meters per second. | sys.constants
sys.coordinates
sys.speeds | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
A sinusoidal roadThe road is described as:$$y(t) = Ysin\omega_b t$$where $Y$ is the amplitude of the sinusoidal road undulations and $\omega_b$ is the frequency of the a function of the car's speed. If the distance between the peaks (amplitude 0.01 meters) of the sinusoidal road is 6 meters and the car is traveling at 7.5 m/s calculate what the frequency will be. | Y = 0.01 # m
v = sys.constants['travel_speed']
bump_distance = 6 # m
wb = v / bump_distance * 2 * np.pi # rad /s
print(wb) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Now with the amplitude and frequency set you can use the `sinusoidal_base_displacing_response()` function to simulate the system. | traj = sys.sinusoidal_base_displacing_response(Y, wb, 20.0)
traj.head()
traj.plot(subplots=True); | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
We've written an animation for you. You can play it with: | sys.animate_configuration(fps=20) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
**Exercise**Try different travel speeds and see what kind of behavior you can observe. Make sure to set the `travel_speed` constant and the frequency value for `sinusoidal_base_displacing_response()` to be consistent. TransmissibilityWhen designing a car the designer wants the riders to feel comfortable and to isolate them from the road's bumps. There are two important aspects to investigate. The first is called *displacement transmissibility* and is a ratio between the ampitude of the steady state motion and the ampitude of the sinusoidal base displacement. So in our case this would be:$$ \frac{X}{Y}(\omega_b) = \frac{\textrm{Steady State Amplitude}}{\textrm{Base Displacement Amplitude}} $$This can be plotted as a function of the base displacement frequency. A car suspension designer may want this ratio to be an optimal value for rider comfort. Maybe they'd like to make the ratio 1 or maybe even less than one if possible.**Exercise**Use the curve fitting technique from the previous notebook to plot $X/Y$ for a range of frequencies. Your code should look something like:```pythonfrom scipy.optimize import curve_fitdef cosine_func(times, amp, freq, phase_angle): return amp * np.cos(freq * times - phase_angle)frequencies = np.linspace(1.0, 20.0, num=100) amplitudes = [] for omega in frequencies: your code hereamplitudes = np.array(amplitudes)fig, ax = plt.subplots(1, 1, sharex=True)ax.set_xlabel('$\omega_b$ [rad/s]')ax.set_ylabel('Displacement Transmissibility') ax.axvline(, color='black') natural frequencyax.plot()?ax.grid();``` | from scipy.optimize import curve_fit
def cosine_func(times, amp, freq, phase_angle):
return amp * np.cos(freq * times - phase_angle)
frequencies = np.linspace(1.0, 20.0, num=100)
amplitudes = []
for omega in frequencies:
traj = sys.sinusoidal_base_displacing_response(Y, omega, 20.0)
popt, pcov = curve_fit(cosine_func,
traj[10:].index, traj[10:].car_vertical_position,
p0=(Y, omega, 0.05))
amplitudes.append(abs(popt[0]))
amplitudes = np.array(amplitudes)
fig, ax = plt.subplots(1, 1, sharex=True)
ax.set_xlabel('$\omega_b$ [rad/s]')
ax.set_ylabel('Displacement Transmissibility')
ax.axvline(np.sqrt(sys.constants['suspension_stiffness'] / sys.constants['sprung_mass']), color='black')
ax.plot(frequencies, amplitudes / Y)
ax.grid();
# write you answer here | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
The second thing to investigate is the *force transmissibility*. This is the ratio of the force applied by the suspension to the sprung car. Riders will feel this force when the car travels over bumps. Reducing this is also preferrable. The force applied to the car can be compared to the **Excersice**Create a measurement to calculate the force applied to the car by the suspension. Simulate the system with $Y=0.01$ m, $v = 10$ m/s, and the distance between bump peaks as $6$ m. Plot the trajectories.```pythondef force_on_car(suspension_damping, suspension_stiffness, car_vertical_position, car_vertical_velocity, travel_speed, time): write this codesys.add_measurement('force_on_car', force_on_car) write code for Y and omega_b, etc``` | Y = 0.01 # m
bump_distance = 6 # m
def force_on_car(suspension_damping, suspension_stiffness,
car_vertical_position, car_vertical_velocity,
travel_speed, time):
wb = travel_speed / bump_distance * 2 * np.pi
y = Y * np.sin(wb * time)
yd = Y * wb * np.cos(wb * time)
return (suspension_damping * (car_vertical_velocity - yd) +
suspension_stiffness * (car_vertical_position - y))
sys.add_measurement('force_on_car', force_on_car)
v = 10.0
sys.constants['travel_speed'] = v
wb = v / bump_distance * 2 * np.pi # rad /s
traj = sys.sinusoidal_base_displacing_response(Y, wb, 10.0)
traj[['car_vertical_position', 'car_vertical_velocity', 'force_on_car']].plot(subplots=True)
# write your answer here
sys.animate_configuration(fps=30) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Force transmissibility will be visited more in your next homework. Arbitrary Periodic Forcing (Fourier Series)Fourier discovered that any periodic function with a period $T$ can be described by an infinite series of sums of sines and cosines. See the wikipedia article for more info (https://en.wikipedia.org/wiki/Fourier_series). The key equation is this:$$ F(t) = \frac{a_0}{2} + \sum_{n=1}^\infty (a_n \cos n\omega_T t + b_n \sin n \omega_T t)$$The terms $a_0, a_n, b_n$ are called the Fourier coefficients and are defined as such:$$ a_0 = \frac{2}{T} \int_0^T F(t) dt$$$$ a_n = \frac{2}{T} \int_0^T F(t) \cos n \omega_T t dt \quad \textrm{for} \quad n = 1, 2, \ldots $$$$ b_n = \frac{2}{T} \int_0^T F(t) \sin n \omega_T t dt \quad \textrm{for} \quad n = 1, 2, \ldots $$ Introduction to SymPySymPy is a Python package for symbolic computing. It can do many symbolic operations, for instance, integration, differentiation, linear algebra, etc. See http://sympy.org for more details of the features and the documentation. Today we will cover how to do integrals using SymPy and use it to find the Fourier series that represents a sawtooth function. | import sympy as sm | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
The function `init_printing()` enables LaTeX based rendering in the Jupyter notebook of all SymPy objects. | sm.init_printing() | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Symbols can be created by using the `symbols()` function. | x, y, z = sm.symbols('x, y, z')
x, y, z | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
The `integrate()` function allows you to do symbolic indefinite or definite integrals. Note that the constants of integration are not included in indefinite integrals. | sm.integrate(x * y, x) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
The `Integral` class creates and unevaluated integral, where as the `integrate()` function automatically evaluates the integral. | expr = sm.Integral(x * y, x)
expr | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
To evaluate the unevaluated form you call the `.doit()` method. Note that all unevaluated SymPy objects have this method. | expr.doit() | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
This shows how to create an unevaluated definite integral, store it in a variable, and then evaluate it. | expr = sm.Integral(x * y, (x, 0, 5))
expr
expr.doit() | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Fourier Coefficients for the Sawtooth functionNow let's compute the Fourier coefficients for a saw tooth function. The function that describes the saw tooth is:$$F(t) = \begin{cases} A \left( \frac{4t}{T} - 1 \right) & 0 \leq t \leq T/2 \\ A \left( 3 - \frac{4t}{t} \right) & T/2 \leq t \leq T \end{cases}$$where:- $A$ is the amplitude of the saw tooth- $T$ is the period of the saw tooth- $\omega_T$ is the frequency of the saw tooth, i.e. $\omega_T = \frac{2\pi}{T}$- $t$ is timeThis is a piecewise function with two parts from $t=0$ to $t=T$. | A, T, wT, t = sm.symbols('A, T, omega_T, t', real=True, positive=True)
A, T, wT, t | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
The first Fourier coefficient $a_0$ describes the average value of the periodic function. and is:$$a_0 = \frac{2}{T} \int_0^T F(t) dt$$This integral will have to be done in two parts:$$a_0 = a_{01} + a_{02} = \frac{2}{T} \int_0^{T/2} F(t) dt + \frac{2}{T} \int_{T/2}^T F(t) dt$$These two integrals are evaluated below. Note that $a_0$ evaluates to zero. This is because the average of our function is 0. | ao_1 = 2 / T * sm.Integral(A * (4 * t / T - 1), (t, 0, T / 2))
ao_1
ao_1.doit()
ao_2 = 2 / T * sm.Integral(A * (3 - 4 * t / T), (t, T / 2, T))
ao_2
ao_2.doit() | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
But SymPy can also handle piecewise directly. The following shows how to define a piecewise function. | F_1 = A * (4 * t / T - 1)
F_2 = A * (3 - 4 * t / T)
F = sm.Piecewise((F_1, t<=T/2),
(F_2, T/2<t))
F
F_of_t_only = F.xreplace({A: 0.01, T: 2 * sm.pi / wb})
F_of_t_only
sm.plot(F_of_t_only, (t, 0, 2 * np.pi / wb)) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
The integral can be taken of the entire piecewise function in one call. | sm.integrate(F, (t, 0, T)) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Now the Fourier coefficients $a_n$ and $b_n$ can be computed.$$a_n = \frac{2}{T}\int_0^T F(t) \cos n\omega_Tt dt \\b_n = \frac{2}{T}\int_0^T F(t) \sin n\omega_Tt dt$$ | n = sm.symbols('n', real=True, positive=True) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
For $a_n$: | an = 2 / T * sm.Integral(F * sm.cos(n * wT * t), (t, 0, T))
an
an.doit() | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
This can be simplified: | an = an.doit().simplify()
an | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Now substitute the $2\pi/T$ for $\omega_T$. | an = an.subs({wT: 2 * sm.pi / T})
an | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Let's see how this function varies with increasing $n$. We will use a loop but the SymPy expressions will not automatically display because they are inside a loop. So we need to use SymPy's `latex()` function and the IPython display tools. SymPy's `latex()` function transforms the SymPy expression into a string of matching LaTeX commands. | sm.latex(an, mode='inline') | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
The `display()` and `LaTeX()` functions then turn the LaTeX string in to a displayed version. | from IPython.display import display, Latex | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Now we can see how $a_n$ varies with $n=1,2,\ldots$. | for n_i in range(1, 6):
ans = an.subs({n: n_i})
display(Latex('$a_{} = $'.format(n_i) + sm.latex(ans, mode='inline'))) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
For even $n$ values the coefficient is zero and for even values it varies with the inverse of $n^2$. More precisely:$$a_n =\begin{cases}0 & \textrm{if }n\textrm{ is even} \\-\frac{8A}{n^2\pi^2} & \textrm{if }n\textrm{ is odd}\end{cases}$$SymPy can actually reduce this further if your set the assumption that $n$ is an integer. | n = sm.symbols('n', real=True, positive=True, integer=True)
an = 2 / T * sm.Integral(F * sm.cos(n * wT * t), (t, 0, T))
an = an.doit().simplify()
an.subs({wT: 2 * sm.pi / T}) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
The odd and even versions can be computed by setting the respective assumptions. | n = sm.symbols('n', real=True, positive=True, integer=True, odd=True)
an = 2 / T * sm.Integral(F * sm.cos(n * wT * t), (t, 0, T))
an = an.doit().simplify()
an.subs({wT: 2 * sm.pi / T}) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Note that $b_n$ is always zero: | bn = 2 / T * sm.Integral(F * sm.sin(n * wT * t), (t, 0, T))
bn
bn.doit().simplify().subs({wT: 2 * sm.pi / T}) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Numerical evalution of the Fourier SeriesNow the Fourier coefficients can be used to plot the approximation of the saw tooth forcing function. | import numpy as np | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
The following function plots the actual sawtooth function. It does it all in one line by cleverly using the absolute value and the modulo functions. | def sawtooth(A, T, t):
return (4 * A / T) * (T / 2 - np.abs(t % T - T / 2) ) - A
A = 1
T = 2
t = np.linspace(0, 5, num=500)
plt.figure()
plt.plot(t, sawtooth(A, T, t)); | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
ExerciseWrite a function that computes the Fourier approximation of the sawtooth function for a given value of $n$, i.e. using a finite number of terms. Then plot it for $n=2, 4, 6, 8, 10$ on top of the actual sawtooth function. How many terms of the infinite series are needed to get a good sawtooth?```pythondef sawtooth_approximation(n, A, T, t): code here return f plot sawtoothf = sawtooth(A, T, t)plt.figure()plt.plot(t, f, color='k', label='true sawtooth')for n in np.arange(2, 12, 2): f_approx = sawtooth_approximation(n, A, T, t) plt.plot(t, f_approx, label='n = {}'.format(n))plt.legend() zoom in a bit on the interesting bitplt.xlim(0, T)``` | def sawtooth_approximation(n, A, T, t):
# odd values of indexing variable up to n
n = np.arange(1, n+1)[:, np.newaxis]
# cos coefficients
an = A *(8 * (-1)**n - 8) / 2 / np.pi**2 / n**2
# sawtooth frequency
wT = 2 * np.pi / T
# sum of n cos functions
f = np.sum(an * np.cos(n * wT * t), axis=0)
return f
# plot sawtooth
f = sawtooth(A, T, t)
plt.figure()
plt.plot(t, f, color='k', label='true sawtooth')
for n in np.arange(2, 12, 2):
f_approx = sawtooth_approximation(n, A, T, t)
plt.plot(t, f_approx, label='n = {}'.format(n))
plt.legend()
# zoom in a bit on the interesting bit
plt.xlim(0, T)
# write answer here | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Below is a interactive plot that shows the same thing as above. | A = 1
T = 2
t = np.linspace(0, 5, num=500)
fig, ax = plt.subplots(1, 1)
f = sawtooth(A, T, t)
saw_tooth_lines = ax.plot(t, f, color='k')
n = 2
f_approx = sawtooth_approximation(n, A, T, t)
approx_lines = ax.plot(t, f_approx)
leg = ax.legend(['true', 'approx, n = {}'.format(n)])
# zoom in a bit on the interesting bit
plt.xlim(0, 2 * T)
def update(n=0):
f_approx = sawtooth_approximation(n, A, T, t)
approx_lines[0].set_ydata(f_approx)
leg.get_texts()[1].set_text('approx, n = {}'.format(n))
from ipywidgets import interact
interact(update, n=(0, 20, 2)) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Apply the sawtooth to the quarter carNow that you know the Fourier series coefficients. Calculate them for a suitable number of terms and simulate them with the `sys.periodic_base_displacing_response()` function.Your code should look something like:```pythondef fourier_coeffs(A, T, N): write your code herea0, an, bn = fourier_coeffs(?)traj = sys.periodic_base_displacing_response(?)``` | def fourier_coeffs(A, T, N):
n = np.arange(1, N+1)
an = A *(8 * (-1)**n - 8) / 2 / np.pi**2 / n**2
return 0, an, np.zeros_like(an)
a0, an, bn = fourier_coeffs(0.01, 2 * np.pi / wb, 100)
traj = sys.periodic_base_displacing_response(a0, an, bn, wb, 20.0)
traj.plot(subplots=True)
sys.animate_configuration(fps=30) | _____no_output_____ | MIT | notebooks/07/07_vertical_vibration_of_a_quarter_car.ipynb | gbrault/resonance |
Define the data_directory of preprocessed data | data_directory = "C:/Users/kwokp/OneDrive/Desktop/Study/zzz_application project/Final/data_after_preprocessing.csv" | _____no_output_____ | MIT | Codes/2.2 Remove redundant words - SVM,KNN,Kmeans_v2.ipynb | matchlesswei/application_project_nlp_company_description |
We devide the data into 3 groups:* Group 1: full data* Group 2: data with four large categories which have more than 1000 companies each* Group 3: seven categories of data, number of companies in each category is same but small In the function selectGroup, giving 1, 2 or 3 as input parameter to selet the relevant data for experiment | # read the data from directory, then select the group
# of data we want to process.
def selectGroup(directory, group_nr):
data = pd.read_csv(directory, sep='\t')
if group_nr == 1:
return data
if group_nr == 2:
df_healthcare_group=data[data['Category'] == 'HEALTHCARE GROUP'].sample(n=1041,replace=False)
df_business_financial_services=data[data['Category'] == 'BUSINESS & FINANCIAL SERVICES'].sample(n=1041,replace=False)
df_consumer_service_group=data[data['Category'] == 'CONSUMER SERVICES GROUP'].sample(n=1041,replace=False)
df_information_technology_group=data[data['Category'] == 'INFORMATION TECHNOLOGY GROUP'].sample(n=1041,replace=False)
df_clean = pd.concat([df_healthcare_group, df_business_financial_services,df_consumer_service_group,df_information_technology_group])
return df_clean.sample(frac=1)
if group_nr == 3:
df_healthcare_group=data[data['Category'] == 'HEALTHCARE GROUP'].sample(n=219,replace=False)
df_business_financial_services=data[data['Category'] == 'BUSINESS & FINANCIAL SERVICES'].sample(n=219,replace=False)
df_consumer_service_group=data[data['Category'] == 'CONSUMER SERVICES GROUP'].sample(n=219,replace=False)
df_information_technology_group=data[data['Category'] == 'INFORMATION TECHNOLOGY GROUP'].sample(n=219,replace=False)
df_industry_goods=data[data['Category'] == 'INDUSTRIAL GOODS & MATERIALS GROUP'].sample(n=219,replace=False)
df_consumer_goods=data[data['Category'] == 'CONSUMER GOODS GROUP'].sample(n=219,replace=False)
df_energy=data[data['Category'] == 'ENERGY & UTILITIES GROUP'].sample(n=219,replace=False)
df_clean = pd.concat([df_healthcare_group, df_business_financial_services,df_consumer_service_group,df_information_technology_group,df_industry_goods,df_consumer_goods,df_energy])
return df_clean.sample(frac=1)
# use tf-idf methode to generate scores for each company
def tf_idf_func(df_document, max_features):
feature_extraction = TfidfVectorizer(max_features = max_features, stop_words = 'english')
score_matrix = feature_extraction.fit_transform(df_document.values)
return score_matrix, feature_extraction
# get the top_n words
def get_top_keywords(scores_matrix, clusters, labels, n_terms):
df = pd.DataFrame(scores_matrix.todense()).groupby(clusters).mean()
for i,r in df.iterrows():
print('\nCluster {}'.format(i))
print(','.join([labels[t] for t in np.argsort(r)[-n_terms:]]))
# get the top_n words with highest tf-idf scores in each category, and count the word occurence
def get_top_keywords_with_frequence(Top_N, score_matrix, df_data, feature_extraction):
df = pd.DataFrame(score_matrix.todense()) #read tf-idf score-matrix, each line is vectors for each company, each column matches each word
df['Category'] = df_data['Category'] #assign the category for each line(company) in score-matrix
dfg = df.groupby(['Category']).mean() #calculate the mean score of each word in each cateogry
labels = feature_extraction.get_feature_names()
categories = df_data['Category'].unique()
col_names = ['Category', 'Top_N', 'Score']
df_top = pd.DataFrame(columns = col_names)
Dict = {}
for i,r in dfg.iterrows(): #i-index(category), r-row, iterate the average score matrix of each category
category = i
top_series = np.argsort(r)[-Top_N:]#find the location of top_n words
label_series = top_series.apply(lambda x: labels[x]) #find top_n words with best scores in each category
top_scores = np.sort(r)[-Top_N:] #find the scores corresponding with top_n words
df_each = pd.DataFrame({'Category':category,'Top_N':label_series,'Score':top_scores})
df_top = df_top.append(df_each, ignore_index = True)
for key in label_series: #count how often each word appears in the top_n
if key in Dict:
Dict[key] = Dict[key]+1
else:
Dict[key] = 1
df_reshape = df_top.pivot(index='Top_N', columns='Category') #reformat the top-n score matrix
sortedDict = sorted(Dict.items(), key=lambda x: x[1]) #sort the dictionary
return sortedDict
# convert the input of the top_n words with their occurence in each category, to a list of stopwords,
# if the occurence is larger than the given occurence
def get_word_occurence_stopwordslist(max_occurence, dict_list):
word = []
occurence = []
frequent_stopwords = []
for key, value in dict_list:
word.append(key)
occurence.append(value)
if value > max_occurence: # if the occurence is larger than the given occurence
frequent_stopwords.append(key) # store to a list of stopwords
return word, occurence, frequent_stopwords
#remove the words from a sentence, which is in the stopwords
def remove_frequent_stopwords(sentences, frequent_stopwords):
splitted_string = sentences.split()
remove_stopwords = [w for w in splitted_string if not w in frequent_stopwords]
return ' '.join(remove_stopwords)
#remove the words from the website content, which is in the stopwords
#update the tf-idf score matrix for the whole corpus
def remove_frequent_stopwords_and_get_updated_tfidfscore(data, feature_extraction, top_n, frequent_stopwords):
df_update = data['clean'].apply(lambda x: remove_frequent_stopwords(x, frequent_stopwords))
score_matrix_update = feature_extraction.fit_transform(df_update.values)
return score_matrix_update | _____no_output_____ | MIT | Codes/2.2 Remove redundant words - SVM,KNN,Kmeans_v2.ipynb | matchlesswei/application_project_nlp_company_description |
List Occurence of words in Top 50 Keywords in Categories | #visualize top_n words with occurence
def visulaze_topwords_occurence(top_n, word_list, occurence_list):
objects = word_list
y_pos = np.arange(len(word_list))
performance = occurence_list
plt.figure(figsize=(10,24))
plt.barh(y_pos, performance, align='center', alpha=0.5)
plt.yticks(y_pos, objects)
plt.xlabel('Occurence')
plt.title('Occurence of words in Top ' + str(top_n) + ' Keywords in categories')
plt.show()
data = selectGroup(data_directory, 1)
score_matrix, feature_extraction = tf_idf_func(data['clean'], 8000)
sortedDict = get_top_keywords_with_frequence(50, score_matrix, data, feature_extraction)
word, occurence, _ = get_word_occurence_stopwordslist(1, sortedDict)
visulaze_topwords_occurence(50, word, occurence) | _____no_output_____ | MIT | Codes/2.2 Remove redundant words - SVM,KNN,Kmeans_v2.ipynb | matchlesswei/application_project_nlp_company_description |
We remove the redundunt words which appears in multiple category . Main steps are as follows:1. select the group of data to do the test2. generate TF-IDF score matrix3. get the top 50 words in each category4. find the words which appears in more than one category's top-50 words, set them as stopwords5. remove these stopwords and update the tf-idf score matrix6. count and calculate the word occurences in each company's website7. plot the number of valid words in each website8. remove the website which has less than 200 words We may notice there are quite a few companies which has less than 200 words. These websites could be useless. And the category distrubtion after processing is shown as the reuslt of the cell. | #get the data, remove the frequent words which appear in more than one category, and update the tf-idf score matrix
data = selectGroup(data_directory, 1)
score_matrix, feature_extraction = tf_idf_func(data['clean'], 8000)
sortedDict = get_top_keywords_with_frequence(50, score_matrix, data, feature_extraction)
_, _, frequent_stopwords = get_word_occurence_stopwordslist(1, sortedDict)
score_matrix_update = remove_frequent_stopwords_and_get_updated_tfidfscore(data, feature_extraction, 10, frequent_stopwords)
#show the top keywords of the rest words after removing the frequent words which appear in more than one category
get_top_keywords(score_matrix_update, data['Category'].values, feature_extraction.get_feature_names(), 10)
# count the non-zero words from updated tf-idf score matrix and display the non-zero word count in each company website
score_value = score_matrix_update.todense()
website_word_count=np.asarray(np.count_nonzero(score_value, axis=1)).reshape(-1)
plt.hist(website_word_count, bins = 30)
plt.xlabel('number of words in the whole website')
plt.ylabel('number of websites')
plt.title('Distribution of number of words in the websites')
df_score=pd.DataFrame(score_value)
df_score.columns=feature_extraction.get_feature_names()
df_score['Keep']=website_word_count>200
df_score['Category'] = data['Category'].reset_index(drop=True)
df_score_valid = df_score[df_score['Keep']]
df_score_valid['Category'].value_counts() |
Cluster BUSINESS & FINANCIAL SERVICES
learn,agreement,need,insurance,media,experience,financial,companies,clients,marketing
Cluster CONSUMER GOODS GROUP
read,sites,address,brand,organic,home,shipping,ingredients,foods,food
Cluster CONSUMER SERVICES GROUP
experience,media,sites,world,address,parties,people,day,agreement,agree
Cluster ENERGY & UTILITIES GROUP
llc,basin,electricity,wind,drilling,renewable,fuel,power,oil,solar
Cluster HEALTHCARE GROUP
dr,treatment,cancer,healthcare,patient,care,health,clinical,patients,medical
Cluster INDUSTRIAL GOODS & MATERIALS GROUP
industries,process,range,industrial,parts,aerospace,materials,steel,packaging,manufacturing
Cluster INFORMATION TECHNOLOGY GROUP
application,world,performance,experience,need,learn,enterprise,domain,solution,network
| MIT | Codes/2.2 Remove redundant words - SVM,KNN,Kmeans_v2.ipynb | matchlesswei/application_project_nlp_company_description |
Split the data 80% for training and 20% for testing | df_final = df_score_valid[df_score_valid.columns.difference(['Keep', 'Category'])] #remove columns'Keep' and 'Category'
df_category = df_score_valid['Category'].reset_index(drop=True)
msk = np.random.rand(len(df_final)) < 0.8
train_x = np.nan_to_num(df_final[msk])
test_x = np.nan_to_num(df_final[~msk])
train_y = df_category[msk].to_numpy()
test_y = df_category[~msk].to_numpy() | _____no_output_____ | MIT | Codes/2.2 Remove redundant words - SVM,KNN,Kmeans_v2.ipynb | matchlesswei/application_project_nlp_company_description |
Perform Linear SVM | from sklearn.metrics import classification_report, confusion_matrix, accuracy_score
#use svm classifier to classify TF-IDF of each website
def linear_svc_classifier(train_x, train_y, test_x, test_y):
print("start svm")
classifier_svm = svm.LinearSVC()
classifier_svm.fit(train_x, train_y)
predictions = classifier_svm.predict(test_x)
print(confusion_matrix(test_y, predictions))
print(classification_report(test_y, predictions))
print(accuracy_score(test_y, predictions))
array = confusion_matrix(test_y, predictions)
y_true = ["BUSINESS & FINANCIAL SERVICES", "CONSUMER GOODS GROUP", "CONSUMER SERVICES GROUP", "ENERGY & UTILITIES GROUP","HEALTHCARE GROUP", "INDUSTRIAL GOODS & MATERIALS GROUP","INFORMATION TECHNOLOGY GROUP"]
y_pred = y_true
df_cm = pd.DataFrame(array, y_true, y_pred)
df_cm.index.name = 'Actual'
df_cm.columns.name = 'Predicted'
plt.figure(figsize = (10,7))
#sn.set(font_scale=1.4)#for label size
ax=sn.heatmap(df_cm, cmap="Blues", annot=True, fmt='d',annot_kws={"size": 16})# font size
bottom, top=ax.get_ylim()
ax.set_ylim(bottom+0.5, top-0.5)
ax.tick_params(labelsize=10)
plt.show()
return confusion_matrix(test_y, predictions),predictions
confusion_matrix, predictions = linear_svc_classifier(train_x, train_y, test_x, test_y) | start svm
[[145 4 24 2 3 5 66]
[ 4 28 16 0 3 7 5]
[ 24 7 115 1 8 2 30]
[ 6 0 0 21 0 2 3]
[ 8 5 6 1 135 4 15]
[ 15 3 6 3 1 45 9]
[ 68 4 32 1 6 9 225]]
precision recall f1-score support
BUSINESS & FINANCIAL SERVICES 0.54 0.58 0.56 249
CONSUMER GOODS GROUP 0.55 0.44 0.49 63
CONSUMER SERVICES GROUP 0.58 0.61 0.60 187
ENERGY & UTILITIES GROUP 0.72 0.66 0.69 32
HEALTHCARE GROUP 0.87 0.78 0.82 174
INDUSTRIAL GOODS & MATERIALS GROUP 0.61 0.55 0.58 82
INFORMATION TECHNOLOGY GROUP 0.64 0.65 0.64 345
accuracy 0.63 1132
macro avg 0.64 0.61 0.62 1132
weighted avg 0.64 0.63 0.63 1132
0.6307420494699647
| MIT | Codes/2.2 Remove redundant words - SVM,KNN,Kmeans_v2.ipynb | matchlesswei/application_project_nlp_company_description |
Perform KNN with 5 Neighbours | from sklearn.metrics import classification_report, confusion_matrix, accuracy_score
#use knn classifier to classify TF-IDF of each website
def knn_classifier(x_train, y_train, x_test, y_test):
print("start knn")
modelknn = KNeighborsClassifier(n_neighbors=5)
modelknn.fit(x_train, y_train)
predictions = modelknn.predict(x_test)
print(confusion_matrix(y_test, predictions))
print(classification_report(y_test, predictions))
print(accuracy_score(y_test, predictions))
array = confusion_matrix(y_test, predictions)
y_true = ["INDUSTRIAL GOODS & MATERIALS GROUP", "CONSUMER SERVICES GROUP","CONSUMER GOODS GROUP","INFORMATION TECHNOLOGY GROUP","ENERGY & UTILITIES GROUP","BUSINESS & FINANCIAL SERVICES", "HEALTHCARE GROUP"]
y_pred = y_true
df_cm = pd.DataFrame(array, y_true, y_pred)
df_cm.index.name = 'Actual'
df_cm.columns.name = 'Predicted'
plt.figure(figsize = (10,7))
#sn.set(font_scale=1.4)#for label size
ax=sn.heatmap(df_cm, cmap="Greens", annot=True, fmt='d',annot_kws={"size": 16})# font size
bottom, top=ax.get_ylim()
ax.set_ylim(bottom+0.5, top-0.5)
ax.tick_params(labelsize=10)
plt.show()
return confusion_matrix(test_y, predictions),predictions
confusion_matrix, predictions = knn_classifier(train_x, train_y, test_x, test_y) | start knn
[[153 7 22 4 5 4 54]
[ 8 25 19 1 3 2 5]
[ 33 17 89 1 12 2 33]
[ 10 1 0 16 2 0 3]
[ 18 5 8 0 133 3 7]
[ 21 4 4 4 2 34 13]
[106 6 40 2 8 7 176]]
precision recall f1-score support
BUSINESS & FINANCIAL SERVICES 0.44 0.61 0.51 249
CONSUMER GOODS GROUP 0.38 0.40 0.39 63
CONSUMER SERVICES GROUP 0.49 0.48 0.48 187
ENERGY & UTILITIES GROUP 0.57 0.50 0.53 32
HEALTHCARE GROUP 0.81 0.76 0.78 174
INDUSTRIAL GOODS & MATERIALS GROUP 0.65 0.41 0.51 82
INFORMATION TECHNOLOGY GROUP 0.60 0.51 0.55 345
accuracy 0.55 1132
macro avg 0.56 0.53 0.54 1132
weighted avg 0.57 0.55 0.56 1132
0.5530035335689046
| MIT | Codes/2.2 Remove redundant words - SVM,KNN,Kmeans_v2.ipynb | matchlesswei/application_project_nlp_company_description |
Perform K means and Plot SSE, PCA and TSNE | from sklearn.cluster import MiniBatchKMeans
from sklearn.feature_extraction.text import TfidfVectorizer
from sklearn.decomposition import PCA
from sklearn.manifold import TSNE
import matplotlib.cm as cm
import itertools
#Find the optimal clusters from 2 to maximum of clusters of data group, plot respective SSE.
def find_optimal_clusters(data, max_k):
iters = range(2, max_k+1, 2)
sse = []
for k in iters:
sse.append(MiniBatchKMeans(n_clusters=k, init_size=512, batch_size=1024, random_state=20).fit(data).inertia_)
print('Fit {} clusters'.format(k))
f, ax = plt.subplots(1, 1)
ax.plot(iters, sse, marker='o')
ax.set_xlabel('Cluster Centers')
ax.set_xticks(iters)
ax.set_xticklabels(iters)
ax.set_ylabel('SSE')
ax.set_title('SSE by Cluster Center Plot')
#Plot TSNE and PCA for the clusters
def plot_tsne_pca(data, labels):
max_label = max(labels+1)
max_items = np.random.choice(range(data.shape[0]), size=3000, replace=False)
pca = PCA(n_components=2).fit_transform(data[max_items,:].todense())
tsne = TSNE().fit_transform(PCA(n_components=50).fit_transform(data[max_items,:].todense()))
idx = np.random.choice(range(pca.shape[0]), size=300, replace=False)
label_subset = labels[max_items]
label_subset = [cm.hsv(i/max_label) for i in label_subset[idx]]
f, ax = plt.subplots(1, 2, figsize=(14, 6))
ax[0].scatter(pca[idx, 0], pca[idx, 1], c=label_subset)
ax[0].set_title('PCA Cluster Plot')
ax[1].scatter(tsne[idx, 0], tsne[idx, 1], c=label_subset)
ax[1].set_title('TSNE Cluster Plot')
#Calculate the accuracy of the clustered data and actual label
def Calculate_accuracy(clusters, actual_label):
count = 0
for index, cluster in enumerate(clusters):
if cluster==actual_label[index]:
count+=1
accuracy = count/len(clusters)*1.0
return accuracy
#Assign clisters for the clustered data
def assign_clusters(original_label, permu, nr_group):
if nr_group == 2:
categories = ["BUSINESS & FINANCIAL SERVICES", "CONSUMER SERVICES GROUP", "HEALTHCARE GROUP", "INFORMATION TECHNOLOGY GROUP"]
else:
categories = ["INDUSTRIAL GOODS & MATERIALS GROUP", "CONSUMER SERVICES GROUP","CONSUMER GOODS GROUP","INFORMATION TECHNOLOGY GROUP","ENERGY & UTILITIES GROUP","BUSINESS & FINANCIAL SERVICES", "HEALTHCARE GROUP"]
mydict=dict(zip(categories, permu))
actual_label = np.zeros(len(original_label))
for index, label in enumerate(original_label):
actual_label[index] = mydict[label]
return actual_label
#Perform Kmeans and Plot
def kmeans_classifier(score_matrix_update, nr_group):
if nr_group == 2:
nr_cluster = 4
else:
nr_cluster = 7
find_optimal_clusters(score_matrix_update, nr_cluster)
clusters = MiniBatchKMeans(n_clusters=nr_cluster, init_size=512, batch_size=1024, random_state=20).fit_predict(score_matrix_update)
plot_tsne_pca(score_matrix_update, clusters)
get_top_keywords(score_matrix_update, clusters, feature_extraction.get_feature_names(), 10)
if nr_group == 2:
numbers=[0,1,2,3]
else:
numbers = [0,1,2,3,4,5,6]
permu = list(itertools.permutations(numbers))
best_accuracy = 0
for i in range(len(permu)):
actual_label = assign_clusters(data['Category'].values, permu[i], nr_group)
accuracy = Calculate_accuracy(clusters, actual_label)
if best_accuracy<accuracy:
best_accuracy=accuracy
final_label = actual_label
category = permu[i]
else:
best_accuracy=best_accuracy
print(category)
#print(final_label)
print("The Accuracy is " + str(round(best_accuracy,2)))
kmeans_classifier(score_matrix_update, 1) | Fit 2 clusters
Fit 4 clusters
Fit 6 clusters
Cluster 0
devices,storage,application,performance,networks,infrastructure,enterprise,solution,wireless,network
Cluster 1
reserved,click,read,learn,world,copyright,need,home,wordpress,domain
Cluster 2
dr,healthcare,treatment,cancer,care,health,patient,medical,clinical,patients
Cluster 3
meal,day,fresh,coffee,delicious,cheese,restaurant,foods,ingredients,food
Cluster 4
http,window,archive,width,function,document,gform,jquery,px,var
Cluster 5
people,group,market,global,years,financial,companies,experience,marketing,clients
Cluster 6
address,provided,applicable,sites,websites,law,collect,parties,agree,agreement
(4, 6, 3, 1, 0, 5, 2)
The Accuracy is 0.34
| MIT | Codes/2.2 Remove redundant words - SVM,KNN,Kmeans_v2.ipynb | matchlesswei/application_project_nlp_company_description |
Carpetplots | import opengrid as og
from opengrid.library import plotting as og_plot
import pandas as pd
from joule import meta, filter_meta
plt = og.plot_style()
#%matplotlib notebook
#%matplotlib notebook
for building in meta['RecordNumber'].unique():
ts = pd.read_pickle('data/Electricity_{}.pkl'.format(building)).sum(axis=1)*60
if not ts.empty:
for i in range(1,13):
df_month = ts[ts.index.month == i]
if len(df_month) > 1:
og_plot.carpet(df_month, title=building, )
fig = plt.gcf()
fig.savefig("figures/carpet_electricity_month{}_{}.png".format(i, building))
plt.show()
| _____no_output_____ | Apache-2.0 | Carpet.ipynb | saroele/jouleboulevard |
Zbozinek TD, Perez OD, Wise T, Fanselow M, & Mobbs D | import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from theano import scan
import theano.tensor as T
import pymc3 as pm
import theano
import seaborn as sns
import os, sys, subprocess | _____no_output_____ | Apache-2.0 | modeling/modeling code/Experiment_2_Direct_Associations.ipynb | tzbozinek/2nd-order-occasion-setting |
Load Data | data = pd.read_csv(os.path.join('../data/', "2nd_POS_Modeling_Data_Direct_Associations.csv"))
data['DV'] = ((data['DV'].values - 1) / 2) - 1
observed_R = data.pivot(columns = 'ID', index = 'trialseq', values = 'DV').values[:, np.newaxis, :] #values.T transposes the data, so you can make trials the first dimension or participants first | _____no_output_____ | Apache-2.0 | modeling/modeling code/Experiment_2_Direct_Associations.ipynb | tzbozinek/2nd-order-occasion-setting |
Subsets and Splits