File size: 10,456 Bytes
389d072 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 |
import copy
class Function(object):
"""Basis function class for all functions
The Function class forms the basis for the functions tokens of all types.
"""
def __init__(self):
self.tid = None
self.scope = None
self.value = None
self.coefficient = 1
self.power = 1
self.operand = None
self.operator = None
self.before = None
self.after = None
self.beforeScope = None
self.afterScope = None
def __str__(self, nv=None, np=None, nc=None):
"""Equation token to string
Coverts equation tokens to string for text and LaTeX rendering
Keyword Arguments:
nv {int} -- number of values (default: {None})
np {int} -- number of powers (default: {None})
nc {int} -- number of coefficients (default: {None})
Returns:
represent {string} -- string/latex representation of equation
"""
# OPTIMIZE: Works but a mess. Organize and add comments
represent = ""
if np is None and nv is None and nc is None:
if self.coefficient != 1:
represent += str(self.coefficient)
elif nc is not None:
if self.coefficient[nc] != 1:
represent += str(self.coefficient[nc])
if isinstance(self.value, list):
if nv is None and np is None:
for eachValue, eachPower in zip(self.value, self.power):
represent += "{" + str(eachValue) + "}"
if eachPower != 1:
represent += "^" + "{" + str(eachPower) + "}"
elif nc is None:
represent += "{" + str(self.value[nv]) + "}"
if self.power[np] != 1:
represent += "^" + "{" + str(self.power[np]) + "}"
elif nc is not None:
for i, val in enumerate(self.value):
represent += "{" + str(val) + "}"
if self.power[np][i] != 1:
represent += "^" + "{" + str(self.power[np][i]) + "}"
elif self.operand is not None:
represent += "\\" + self.value
if self.power != 1:
represent += "^" + "{" + str(self.power) + "}"
represent += "({" + self.operand.__str__() + "})"
else:
represent += "{" + str(self.value) + "}"
if self.power != 1:
represent += "^" + "{" + str(self.power) + "}"
return represent
def prop(self, tid=None, scope=None, value=None, coeff=None, power=None, operand=None, operator=None):
"""Set function token properties
Keyword Arguments:
tid {[type]} -- Token ID (default: {None})
scope {int} -- Scope (default: {None})
value {int or list} -- Value (default: {None})
coeff {int} -- Coefficient (default: {None})
power {int or list} -- Power (default: {None})
operand {visma.functions.structure.Function} -- Operand (default: {None})
operator {visma.functions.structure.Function} -- Operator (default: {None})
"""
if tid is not None:
self.tid = tid
if scope is not None:
self.scope = scope
if value is not None:
self.value = value
if coeff is not None:
self.coefficient = coeff
if power is not None:
self.power = power
if operand is not None:
self.operand = operand
if operator is not None:
self.operator = operator
def differentiate(self):
"""Differentiate function token
"""
self.power = 1
self.coefficient = 1
def level(self):
"""Level of function token
"""
return (int((len(self.tid)) / 2)), 5
def functionOf(self):
inst = copy.deepcopy(self)
while inst.operand is not None:
inst = inst.operand
return inst.value
def isZero(self):
"""
It checks if the Function is equal to Zero or not, to decide it should be Added, Subtracted,...etc. or not.
:returns: bool
"""
if (self.value == 0 and self.power != 0) or self.coefficient == 0:
return True
return False
##########
# FuncOp #
##########
class FuncOp(Function):
"""Defined for functions of form sin(...), log(...), exp(...) etc which take a function(operand) as argument
"""
def __init__(self, operand=None):
super().__init__()
if operand is not None:
self.operand = operand
def __str__(self):
represent = ""
represent += "\\" + self.value
if self.power != 1:
represent += "^" + "{" + str(self.power) + "}"
if self.operand is not None:
represent += "{(" + str(self.operand) + ")}"
return represent
def inverse(self, rToken, wrtVar, inverseFunction):
"""Returns inverse of function
Applies inverse of function to RHS and LHS.
Arguments:
rToken {visma.functions.structure.Function} -- RHS token
wrtVar {string} -- with respect to variable
inverseFunction {visma.functions.structure.Function} -- inverse of the function itself
Returns:
self {visma.functions.structure.Function} -- function itself(operand before inverse)
rToken {visma.functions.structure.Function} -- new RHS token
comment {string} -- steps comment
"""
rToken.coefficient /= self.coefficient
rToken.power /= self.power
invFunc = copy.deepcopy(inverseFunction)
invFunc.operand = rToken
self = self.operand
comment = "Applying inverse function on LHS and RHS"
return self, rToken, comment
###################
# Mixed Functions #
###################
# For example: sec(x)*tan(x) or sin(x)*log(x) or e^(x)*cot(x)
# Will be taken care by function Expression
class Expression(Function):
"""Class for expression type
"""
def __init__(self, tokens=None, coefficient=None, power=None):
super().__init__()
if coefficient is not None:
self.coefficient = coefficient
else:
self.coefficient = 1
if power is not None:
self.power = power
else:
self.power = 1
self.tokens = []
if tokens is not None:
self.tokens.extend(tokens)
def __str__(self):
represent = ""
if self.coefficient != 1:
represent += str(self.coefficient) + "*"
represent += "{("
for token in self.tokens:
represent += token.__str__()
represent += ")}"
if self.power != 1:
represent += "^" + "{" + str(self.power) + "}"
if self.operand is not None:
represent += "{(" + str(self.operand) + ")}"
return represent
def __mul__(self, other):
from visma.functions.constant import Constant
from visma.functions.variable import Variable
if isinstance(other, Expression):
result = Expression()
for i, _ in enumerate(self.tokens):
c = copy.deepcopy(self)
d = copy.deepcopy(other)
if isinstance(c.tokens[i], Constant) or isinstance(c.tokens[i], Variable):
result.tokens.extend([c.tokens[i] * d])
else:
result.tokens.extend([c.tokens[i]])
return result
def __add__(self, other):
from visma.functions.constant import Constant
from visma.functions.variable import Variable
from visma.functions.operator import Plus
if isinstance(other, Expression):
result = Expression()
for tok1 in self.tokens:
result.tokens.append(tok1)
result.tokens.append(Plus())
if (other.tokens[0], Constant):
if (other.tokens[0].value < 0):
result.tokens.pop()
elif (other.tokens[0], Variable):
if (other.tokens[0].coefficient < 0):
result.tokens.pop()
for tok2 in other.tokens:
result.tokens.append(tok2)
return result
elif isinstance(other, Constant):
result = self
constFound = False
for i, _ in enumerate(self.tokens):
if isinstance(self.tokens[i], Constant):
self.tokens[i] += other
constFound = True
if constFound:
return result
else:
result.tokens += other
return result
elif isinstance(other, Variable):
result = Expression()
result = other + self
return result
def __sub__(self, other):
from visma.functions.constant import Constant
from visma.functions.variable import Variable
from visma.functions.operator import Plus, Minus
if isinstance(other, Expression):
result = Expression()
for tok1 in self.tokens:
result.tokens.append(tok1)
for _, x in enumerate(other.tokens):
if x.value == '+':
x.value = '-'
elif x.value == '-':
x.value = '+'
result.tokens.append(Minus())
if (isinstance(other.tokens[0], Constant)):
if (other.tokens[0].value < 0):
result.tokens[-1] = Plus()
other.tokens[0].value = abs(other.tokens[0].value)
elif (isinstance(other.tokens[0], Variable)):
if (other.tokens[0].coefficient < 0):
result.tokens[-1] = Plus()
other.tokens[0].coefficient = abs(other.tokens[0].coefficient)
return result
elif isinstance(other, Constant):
result = self
result += (Constant(0) - other)
return result
elif isinstance(other, Variable):
result = self
a = Constant(0) - other
result = a + result
return result
class Equation(Expression):
"""Class for equation type
"""
def __init__(self):
super().__init__()
self.tokens = None
|