def __mul__(self, other):
"""Multiplies two matrices
Arguments:
self {visma.matrix.structure.Matrix} -- matrix token
other {visma.matrix.structure.Matrix} -- matrix token
Returns:
matPro {visma.matrix.structure.Matrix} -- product matrix token
Note:
Make mulitplyCheck before calling multiplyMatrix
Not commutative
"""
matPro = Matrix()
matPro.empty([self.dim[0], other.dim[1]])
for i in range(self.dim[0]):
for j in range(other.dim[1]):
for k in range(self.dim[1]):
if matPro.value[i][j] != []:
matPro.value[i][j].append(Binary('+'))
if len(self.value[i][k]) != 1:
matPro.value[i][j].append(Expression(self.value[i][k]))
else:
matPro.value[i][j].extend(self.value[i][k])
matPro.value[i][j].append(Binary('*'))
if len(other.value[k][j]) != 1:
matPro.value[i][j].append(Expression(
other.value[k][j]))
else:
matPro.value[i][j].extend(other.value[k][j])
from visma.matrix.operations import simplifyMatrix
matPro = simplifyMatrix(matPro)
return matPro
def multiplyMatrix(matA, matB):
"""Multiplies two matrices
Arguments:
matA {visma.matrix.structure.Matrix} -- matrix token
matB {visma.matrix.structure.Matrix} -- matrix token
Returns:
matPro {visma.matrix.structure.Matrix} -- product matrix token
Note:
Make mulitplyCheck before calling multiplyMatrix
Not commutative
"""
matPro = Matrix()
matPro.empty([matA.dim[0], matB.dim[1]])
for i in range(matA.dim[0]):
for j in range(matB.dim[1]):
for k in range(matA.dim[1]):
if matPro.value[i][j] != []:
matPro.value[i][j].append(Binary('+'))
if len(matA.value[i][k]) != 1:
matPro.value[i][j].append(Expression(matA.value[i][k]))
else:
matPro.value[i][j].extend(matA.value[i][k])
matPro.value[i][j].append(Binary('*'))
if len(matB.value[k][j]) != 1:
matPro.value[i][j].append(Expression(matB.value[k][j]))
else:
matPro.value[i][j].extend(matB.value[k][j])
matPro = simplifyMatrix(matPro)
return matPro
def __mul__(self, other):
if isinstance(other, Cotangent):
result = Expression()
result.coefficient = self.coefficient * other.coefficient
c = copy.deepcopy(self)
d = copy.deepcopy(other)
result.tokens.extend([c, Multiply(), d])
return result
def differentiate(self, wrtVar):
term1 = Constant(-1, 1, 1)
term2 = copy.deepcopy(self)
term2.__class__ = Sine
term2.value = 'sin'
result = Expression()
result.tokens = [term1, Multiply(), term2]
return result
def integrate(self, wrtVar=None):
term1 = Constant(-1, 1, 1)
term2 = copy.deepcopy(self)
term2.__class__ = Cosine
term2.value = 'cos'
term2.coefficient = 1
result = Expression()
result.tokens = [term1, Multiply(), term2]
return result
def differentiate(self, wrtVar):
term1 = Constant(-1, 1, 1)
term2 = copy.deepcopy(self)
term2.__class__ = Cosecant
term2.value = 'csc'
term2.coefficient = 1
term2.power = 2
result = Expression()
result.tokens = [term1, Multiply(), term2]
return result
def integrate(self, wrtVar):
term1 = Constant(-1, 1, 1)
term2 = NaturalLog()
term3 = Cosine()
term3.operand = self.operand
term2.operand = term3
term2.power = 1
term2.coefficient = 1
result = Expression()
result.tokens = [term1, Multiply(), term2]
return result
def differentiate(self, wrtVar):
term1 = Constant(-1, 1, 1)
term2 = Cosecant()
term2.operand = self.operand
term2.coefficient = 1
term3 = Cotangent()
term3.operand = self.operand
term3.coefficient = 1
result = Expression()
result.tokens = [term1, Multiply(), term2, Multiply(), term3]
return result
def integrate(self, wrtVar):
resultTerm = NaturalLog()
term3 = Secant()
term3.operand = self.operand
term4 = Tangent()
term4.operand = self.operand
inExpression = Expression()
inExpression.tokens = [term3, Plus(), term4]
resultTerm.operand = inExpression
resultTerm.power = 1
resultTerm.coefficient = 1
return resultTerm
def factorizeTokens(tokens):
coeffs, var = getPolyCoeffs(tokens)
gcf, roots, polynomial = factor(coeffs)
if roots != []:
tokens = []
comment = "The real roots of the above polynomial are "
for root in roots:
comment += r"$" + str(root) + "\ ,\ " + r"$"
if gcf != 1:
tokens.append(Constant(float(gcf)))
tokens.append(Multiply())
for root in roots:
expression = Expression()
expression.tokens.append(Variable(1, var, 1))
if root > 0:
expression.tokens.append(Minus())
expression.tokens.append(Constant(float(root)))
elif root < 0:
expression.tokens.append(Plus())
expression.tokens.append(Constant(float(-root)))
tokens.append(expression)
tokens.append(Multiply())
if polynomial != [1]:
expression = Expression()
degree = len(polynomial) - 1
for i, coeff in enumerate(polynomial):
if i == degree:
if coeff > 0:
expression.tokens.append(Plus())
expression.tokens.append(Constant(float(coeff)))
elif coeff < 0:
expression.tokens.append(Minus())
expression.tokens.append(Constant(float(-coeff)))
elif coeff > 0:
expression.tokens.append(Plus())
expression.tokens.append(Variable(coeff, var, degree - i))
elif coeff < 0:
expression.tokens.append(Minus())
expression.tokens.append(Variable(-coeff, var, degree - i))
if isinstance(expression.tokens[0], Plus):
expression.tokens.pop(0)
tokens.append(expression)
else:
tokens.pop()
else:
comment = None
animation = [tokens]
comments = [comment]
return tokens, animation, comments
def __truediv__(self, other):
from visma.functions.constant import Constant
if isinstance(other, Variable) or isinstance(other, Constant):
self = self * (other**Constant(-1, 1, 1))
return self
elif isinstance(other, Expression):
expression = Expression()
self.coefficient /= other.coefficient
other.power *= -1
expression.tokens = [self]
expression.tokens.extend([Multiply(), other])
self = expression
return expression
def __sub__(self, other):
from visma.functions.constant import Constant
if isinstance(other, Variable):
otherValueSorted = sorted(other.value)
selfValueSorted = sorted(self.value)
if (other.power == self.power) & (selfValueSorted
== otherValueSorted):
self = self + Constant(-1, 1, 1) * other
return self
else:
expression = Expression()
expression.tokens = [self]
expression.tokens.extend([Minus(), other])
self = expression
return expression
elif isinstance(other, Constant):
if other.isZero():
return self
expression = Expression()
expression.tokens = [self]
expression.tokens.extend([Minus(), other])
self = expression
return expression
elif isinstance(other, Expression):
expression = Expression()
expression.tokens = [self]
for i, token in enumerate(other.tokens):
if isinstance(token, Variable):
tokenValueSorted = sorted(token.value)
selfValueSorted = sorted(self.value)
if (token.power == self.power) & (tokenValueSorted
== selfValueSorted):
if other.tokens[i - 1].value == '+' or (i == 0):
self.coefficient -= other.tokens[i].coefficient
elif other.tokens[i - 1].value == '-':
self.coefficient += other.tokens[i].coefficient
else:
if other.tokens[i - 1].value == '+' or i == 0:
expression.tokens.extend([Plus(), Variable(token)])
elif other.tokens[i - 1].value == '-':
expression.tokens.extend(
[Minus(), Variable(token)])
elif not isinstance(token, Binary):
if other.tokens[i - 1].value == '+' or (i == 0):
expression.tokens.extend([Minus(), token])
elif other.tokens[i - 1].value == '-':
expression.tokens.extend([Plus(), token])
expression.tokens[0] = self
self = expression
return expression
def __sub__(self, other):
if isinstance(other, Constant):
self = self + Constant(-1, 1, 1) * other
return self
elif isinstance(other, Variable):
if self.value == 0:
other.coefficient *= -1
return other
expression = Expression()
expression.tokens = [self]
expression.tokens.extend([Minus(), other])
elif isinstance(other, Expression):
expression = Expression()
expression.tokens = [self]
if other.power == 1:
coeff = other.coefficient
for i, token in enumerate(other.tokens):
print(expression, " ", type(token), other.tokens[i-1])
if isinstance(token, Constant):
if other.tokens[i-1].value == '+' or i == 0:
expression.tokens[0] = Constant(self.calculate() - token.calculate()*coeff)
elif other.tokens[i-1].value == '-':
expression.tokens[0] = Constant(self.calculate() + token.calculate()*coeff)
elif isinstance(token, Variable):
if other.tokens[i-1].value == '+' or i == 0:
expression.tokens.extend([Minus(), Variable(token)])
elif other.tokens[i-1].value == '-':
expression.tokens.extend([Plus(), Variable(token)])
else:
expression.tokens.extend([Minus(), other])
self = expression
return expression
def differentiationProductRule(tokens, wrtVar):
resultTokens = []
for i in range(0, len(tokens), 2):
currentDiff = Expression()
currentDiffTokens, _, _, _, _ = differentiate([tokens[i]], wrtVar)
currentDiff.tokens = currentDiffTokens
tempTokens = copy.deepcopy(tokens)
tempTokens[i] = currentDiff
resultTokens.extend(tempTokens)
resultTokens.append(Plus())
resultTokens.pop()
token_string = tokensToString(resultTokens)
# TODO: Make simplify module to simplify expressions involving Trigonometric Expressions (to some extent)
# resultTokens, _, token_string, _, _ = simplify(resultTokens)
return tokens, [], token_string, [], []
def test_substitute():
init_tok = getTokens("x")
subs_tok = getTokens("2")
tok_list = getTokens("3zx^2 + x^3 + 5x")
assert tokensToString(substitute(init_tok, subs_tok, tok_list)) == "12.0z + 8.0 + 10.0"
init_tok = getTokens("2x")
subs_tok = getTokens("4yz^2")
tok_list = getTokens("3 + 2x + zx^4 + 3xyz")
assert tokensToString(substitute(init_tok, subs_tok, tok_list)) == "3.0 + 4.0yz^(2.0) + 16.0z^(9.0)y^(4.0) + 6.0y^(2.0)z^(3.0)"
init_tok = getTokens("4x^2")
subs_tok = getTokens("9yz")
tok_list = getTokens("2x + zx^3 + 3xyz")
assert tokensToString(substitute(init_tok, subs_tok, tok_list)) == "3.0y^(0.5)z^(0.5) + 3.375z^(2.5)y^(1.5) + 4.5y^(1.5)z^(1.5)"
init_tok = getTokens("2xy^3")
subs_tok = getTokens("4z")
tok_list = getTokens("3 + 2xy^3 + z + 3x^(2)y^(6)z")
assert tokensToString(substitute(init_tok, subs_tok, tok_list)) == "3.0 + 4.0z + z + 12.0z^(3.0)"
init_tok = getTokens("5x")
subs_tok = Expression(getTokens("y + 2"))
tok_list = getTokens("3 + 4x + 2xy^3 + 3x^(2)y^(3)z")
assert tokensToString(substitute(init_tok, subs_tok, tok_list)) == "3.0 + 0.8*(y + 2.0) + (0.4y^(3.0) * (y + 2.0)) + (0.12y^(3.0)z * (y + 2.0)^(2.0))"
def scalarSub(const, mat):
"""
Subtracts constant terms with Matrix
Arguments:
const {string}--- constant value
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
matRes {visma.matrix.structure.Matrix} -- subtracted matrix token
Note:
This scalar addition follows the following equation
{mat} - {lambda}{identity mat}
"""
matRes = Matrix()
matRes.empty([mat.dim[0], mat.dim[1]])
for i in range(mat.dim[0]):
for j in range(mat.dim[1]):
if i != j:
matRes.value[i][j].extend(mat.value[i][j])
else:
if len(mat.value[i][j]) != 1:
matRes.value[i][j].append(Expression(mat.value[i][j]))
else:
matRes.value[i][j].extend(mat.value[i][j])
matRes.value[i][j].append(Binary('-'))
matRes.value[i][j].append(Constant(int(const)))
matRes = simplifyMatrix(matRes)
return matRes
def scalarDiv(const, mat):
"""Divides constant terms with Matrix
Arguments:
const {string}--- constant value
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
matRes {visma.matrix.structure.Matrix} -- result matrix token
"""
if const != 0:
matRes = Matrix()
matRes.empty([mat.dim[0], mat.dim[1]])
for i in range(mat.dim[0]):
for j in range(mat.dim[1]):
if len(mat.value[i][j]) != 1:
matRes.value[i][j].append(Expression(mat.value[i][j]))
else:
matRes.value[i][j].extend(mat.value[i][j])
matRes.value[i][j].append(Binary('/'))
matRes.value[i][j].append(Constant(int(const)))
matRes = simplifyMatrix(matRes)
return matRes
else:
logger.error("ZeroDivisionError: Cannot divide matrix by zero")
def differentiateTokens(funclist, wrtVar):
"""Differentiates given tokens wrt given variable
Arguments:
funclist {list} -- list of function tokens
wrtVar {string} -- with respect to variable
Returns:
diffFunc {list} -- list of differentiated tokens
animNew {list} -- equation tokens for step-by-step
commentsNew {list} -- comments for step-by-step
"""
diffFunc = []
animNew = []
commentsNew = ["Differentiating with respect to " + r"$" + wrtVar + r"$" + "\n"]
for func in funclist:
if isinstance(func, Operator):
diffFunc.append(func)
else:
newExpression = Expression()
newfunc = []
while(isinstance(func, Function)):
commentsNew[0] += r"$" + "\\frac{d}{d" + wrtVar + "} ( " + func.__str__() + ")" + r"$"
funcCopy = copy.deepcopy(func)
if wrtVar in funcCopy.functionOf():
if isinstance(funcCopy, Trigonometric) or isinstance(funcCopy, Logarithm) or isinstance(funcCopy, Variable) or isinstance(funcCopy, Exponential):
funcCopy = funcCopy.differentiate(wrtVar)
newfunc.append(funcCopy)
commentsNew[0] += r"$" + r"= " + funcCopy.__str__() + r"\ ;\ " + r"$"
else:
funcCopy = Zero()
newfunc.append(funcCopy)
commentsNew[0] += r"$" + r"= " + funcCopy.__str__() + r"\ ;\ " + r"$"
newfunc.append(Multiply())
if func.operand is None:
break
else:
func = func.operand
if isinstance(func, Constant):
diffFunc = Zero()
break
newfunc.pop()
newExpression.tokens = newfunc
diffFunc.extend([newExpression])
animNew.extend(diffFunc)
return diffFunc, animNew, commentsNew
def test_isTokenInToken():
varA = getTokens("x^3")
varB = getTokens("xy^2")
varC = Expression(getTokens("1 + w + x"))
varD = Expression(getTokens("w + y"))
assert isTokenInToken(varA, varB)
assert isTokenInToken(varA, varC)
assert not isTokenInToken(varA, varD)
varA = getTokens("xy^2")
varB = getTokens("x^(2)y^(4)z")
varC = getTokens("yx^0.5")
varD = getTokens("xy^(3)z")
varE = getTokens("2")
assert isTokenInToken(varA, varB)
assert isTokenInToken(varA, varC)
assert not isTokenInToken(varA, varD)
assert not isTokenInToken(varA, varE)
def integrate(self, wrtVar):
if wrtVar not in self.value:
self.value.append(wrtVar)
self.power.append(1)
else:
for i, val in enumerate(self.value):
if val == 'wrtVar':
break
if self.power[i] == -1:
self.power.pop(i)
self.value.pop(i)
expression = Expression()
expression.tokens = [self]
variable = Variable(1, 'wrtVar', 1)
expression.tokens.append(Logarithm(variable))
self.__class__ = Expression
self = expression
else:
self.coefficient /= self.power[i] + 1
self.power[i] += 1
def inverse(self, rToken, wrtVar):
l2rVar = Variable()
for i, var in enumerate(self.value):
if var != wrtVar:
l2rVar.value.append(self.value.pop(i))
l2rVar.power.append(self.power.pop(i))
if l2rVar.value != []:
rToken = Expression([rToken, Divide(), l2rVar])
rToken.coefficient /= (self.coefficient)**(1 / self.power[0])
rToken.power /= self.power[0]
self.coefficient = 1
self.power[0] = 1
comment = "Therefore, " + r"$" + wrtVar + r"$" + " can be written as:"
return self, rToken, comment
def substituteTokens(initTok, subsTok, givenTok):
"""Substitute initTok with subsTok in a givenTok.
For example: substitute x(initTok) with wyz^2(subsTok) in xyz(givenTok)
i.e. final_tok will be wy^2z^3
Arguments:
initTok {functions.structure.Function} -- token to be substituted
subsTok {functions.structure.Function} -- substitute token
givenTok {functions.structure.Function} -- given token
Returns:
givenTok {functions.structure.Function} -- given token after substitution
"""
if isinstance(givenTok, Variable):
if isinstance(initTok, Variable):
power = getPowerRatio(initTok, givenTok)
if isinstance(subsTok, Constant):
givenTok = removeValues(initTok, givenTok)
if len(givenTok.value) == 0:
givenTok = Constant(
(subsTok.value**power) * givenTok.coefficient)
else:
givenTok.coefficient *= subsTok.value**power
elif isinstance(subsTok, Variable):
givenTok.coefficient /= initTok.coefficient**power
givenTok.coefficient *= subsTok.coefficient**power
givenTok = replaceValues(initTok, subsTok, givenTok, power)
elif isinstance(subsTok, Expression):
subs_copy = copy.deepcopy(subsTok)
givenTok.coefficient /= initTok.coefficient**power
givenTok.coefficient *= subs_copy.coefficient**power
subs_copy.coefficient = 1
subs_copy.power = power
givenTok = removeValues(initTok, givenTok)
if len(givenTok.value) == 0:
subs_copy.coefficient = givenTok.coefficient
givenTok = subs_copy
else:
givenTok = Expression([givenTok, Multiply(), subs_copy])
elif isinstance(givenTok, Expression):
substitute(initTok, subsTok, Expression.toklist)
return givenTok
def __mul__(self, other):
from visma.io.checks import isNumber
from visma.functions.constant import Constant
if isinstance(other, Variable):
for j, var in enumerate(other.value):
found = False
for k, var2 in enumerate(self.value):
self.coefficient *= other.coefficient
if var == var2:
if isNumber(other.power[j]) and isNumber(
self.power[k]):
self.power[k] += other.power[j]
if self.power[k] == 0:
del self.power[k]
del self.value[k]
found = True
break
if not found:
self.value.append(other.value[j])
self.power.append(other.power[j])
if len(self.value) == 0:
result = Constant(self.coefficient)
result.scope = self.scope
result.power = 1
result.value = self.coefficient
self = result
return self
elif isinstance(other, Constant):
self.coefficient *= other.calculate()
return self
elif isinstance(other, Expression):
result = Expression()
for _, token in enumerate(other.tokens):
if isinstance(token, Variable) or isinstance(token, Constant):
c = copy.deepcopy(self)
result.tokens.extend([c * token])
else:
result.tokens.extend([token])
return result
def integrate(self, wrtVar):
term1 = Constant(-1, 1, 1)
term2 = NaturalLog()
result = Expression()
term3 = Cosecant()
term3.operand = self.operand
term4 = Cotangent()
term4.operand = self.operand
inExpression = Expression()
inExpression.tokens = [term3, Plus(), term4]
term2.operand = inExpression
term2.power = 1
term2.coefficient = 1
result.tokens = [term1, Multiply(), term2]
return result
def funcInverse(lTokens, rTokens, wrtVar):
"""Applies inverse of funtion of wrtVar to RHS
Arguments:
lTokens {list} -- LHS tokens list
rTokens {list} -- RHS tokens list
wrtVar {string} -- variable to be solved
Returns:
lTokens {list} -- LHS tokens list
rTokens {list} -- RHS tokens list
animation {list} -- list of equation solving progress
comments {list} -- list of solution steps
"""
if len(lTokens) == 1:
rExpr = Expression()
rExpr.tokens.extend(rTokens)
lToken, rToken, comment = lTokens[0].inverse(rExpr, wrtVar)
animation = copy.deepcopy(lTokens)
animation.append(EqualTo())
animation.append(rToken)
return [lToken], [rToken], animation, [comment]
def __add__(self, other):
if isinstance(other, Constant):
if self.before == '-':
result = Constant(self.calculate() - other.calculate(), self.power)
else:
result = Constant(self.calculate() + other.calculate(), self.power)
self.value = result.value
if result.value == 0 and result.power == 0:
result.value = 1
result.power = 1
result.scope = self.scope
result.value = result.calculate()
return result
elif self.isZero():
return other
elif other.isZero():
return self
elif isinstance(other, Expression):
if other.power == 1 and other.coefficient == 1:
constFound = False
for i, var in enumerate(other.tokens):
if isinstance(var, Constant):
if other.tokens[i-1].value == '+' or i == 0:
other.tokens[i] = self + var
elif other.tokens[i-1].value == '-':
other.tokens[i-1] = self - var
constFound = True
break
if not constFound:
other.tokens.extend([Plus(), self])
return other
else:
pass
self.value = self.calculate()
self.power = 1
self.coefficient = 1
exprAdd = Expression([self, Plus(), other]) # Make an Expression and assign the Tokens attribute with the Constant and the Other Variable, Trig. function,...etc.
return exprAdd
def scalarMult(const, mat):
"""Multiplies constant terms with Matrix
Arguments:
const {string}--- constant value
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
matRes {visma.matrix.structure.Matrix} -- product matrix token
"""
matRes = Matrix()
matRes.empty([mat.dim[0], mat.dim[1]])
for i in range(mat.dim[0]):
for j in range(mat.dim[1]):
if len(mat.value[i][j]) != 1:
matRes.value[i][j].append(Expression(mat.value[i][j]))
else:
matRes.value[i][j].extend(mat.value[i][j])
matRes.value[i][j].append(Binary('*'))
matRes.value[i][j].append(Constant(int(const)))
matRes = simplifyMatrix(matRes)
return matRes
def test_Constant():
# Tests for Calculus operations for Constant Class.
constant1 = Constant(10)
assert constant1.__str__() == "{10}"
constant1.differentiate()
assert constant1.value == 0
constant2 = Constant(5, 2)
constant2.integrate('x')
assert isinstance(constant2, Variable)
assert constant2.__str__() == "25{x}"
# Tests for Add/Sub operations (using Overloading) for Constant Class.
constant4 = Constant(2, 2)
constant5 = Constant(7)
constant3 = constant4 - constant5
assert constant3.__str__() == "{-3}"
constant4 = Constant(7, 2)
constant0 = Constant(5)
constant6 = constant4 - constant3 - constant5 + constant0
assert constant6.__str__() == "{50}"
constant0 = Constant(5, 2, 2)
constant2 = constant0
variable0 = Variable(5, 'X', 3)
summation0 = constant0 - variable0 + constant2
assert summation0.__str__() == "{({100}-5{X}^{3})}"
constant0 = Constant(5, 2, 2)
constant2 = constant0
variable0 = Variable(5, 'X', 3)
summation0 = constant0 + variable0 + constant2
assert summation0.__str__() == "{({100}+5{X}^{3})}"
var1 = Variable(3, 'x', 3)
const1 = Constant(5)
expr1 = Expression([var1, Minus(), const1])
constant2 = Constant(2, 2)
sub1 = constant2 - expr1
assert sub1.__str__() == "{({9}-3{x}^{3})}"
constant1 = Constant(2)
constant2 = Constant(7)
constant3 = constant1 + constant2
assert constant3.__str__() == "{9}"
constant1 = Constant(2)
constant2 = Constant(7)
constant3 = constant1 - constant2
assert constant3.__str__() == "{-5}"
constant1 = Constant(5)
variable1 = Variable(5, 'x', 3)
summation = constant1 + variable1
assert summation.__str__() == "{({5}+5{x}^{3})}"
constant1 = Constant(5)
variable1 = Variable(5, 'x', 3)
summation = constant1 - variable1
assert summation.__str__() == "{({5}-5{x}^{3})}"
# Tests for Add/Sub operations (using Overloading) for Constant Class.
constant0 = Constant(0, 2)
constant1 = Constant(5)
mul1 = constant0 * constant1
assert mul1.calculate() == 0
mul1 = constant1 * constant0
assert mul1.calculate() == 0
mul1 = constant1 * constant1 + constant0 * constant1 + constant0 * constant1
assert mul1.calculate() == 25
constant1 = Constant(5, 2)
constant2 = Constant(4, 2)
variable0 = Variable(3, 'X', 3)
mul3 = constant1 * (constant2 + variable0)
assert mul3.__str__() == "{({400}+75{X}^{3})}"
constant1 = Constant(5, 2)
constant2 = Constant(4, 2)
variable0 = Variable(3, 'X', 3)
mul3 = constant1 / (constant2 + variable0)
assert mul3.__str__() == "{25}*{({16}+3{X}^{3})}^{-1}"
constant1 = Constant(5)
constant2 = Constant(4)
div1 = constant1 / constant2
assert div1.__str__() == "{1.25}"
constant1 = Constant(3, 2)
constant2 = Constant(4, 2)
variable0 = Variable(3, 'X', 3)
mul3 = constant1 - constant1 / (constant2 / variable0 + constant1)
assert mul3.__str__(
) == "{({9}-{9}*{(5.333333333333333{X}^{-3}+{9})}^{-1})}"
constant1 = Constant(2, 2)
constant2 = Constant(2, 2)
mul3 = constant1**constant2
assert mul3.__str__() == "{256}"
constant1 = Constant(5)
constant2 = Constant(5)
summation = constant1 * constant2
assert summation.__str__() == "{25}"
constant1 = Constant(5)
variable1 = Variable(5, 'x', 3)
exp1 = Expression([constant1, Plus(), variable1])
constant2 = Constant(10)
summation = constant2 + exp1
assert summation.__str__() == "{({15}+5{x}^{3})}"
constant1 = Constant(5)
variable1 = Variable(5, 'x', 3)
exp1 = Expression([constant1, Plus(), variable1])
constant2 = Constant(10)
summation = constant2 - exp1
assert summation.__str__() == "{({5}-5{x}^{3})}"
constant1 = Constant(5)
variable1 = Variable(5, 'x', 3)
exp1 = Expression([constant1, Plus(), variable1])
constant2 = Constant(10)
summation = exp1 - constant2
assert summation.__str__() == "{({-5}+5{x}^{3})}"
constant1 = Constant(5)
variable1 = Variable(5, 'x', 3)
summation = constant1 * variable1
assert summation.__str__() == "25{x}^{3}"
constant1 = Constant(5)
variable1 = Variable(5, 'x', 3)
exp1 = Expression([constant1, Plus(), variable1])
constant2 = Constant(10)
summation = constant2 * exp1
assert summation.__str__() == "{({50}+50{x}^{3})}"
constant1 = Constant(5)
constant2 = Constant(5)
summation = constant1 / constant2
assert summation.__str__() == "{1.0}"
constant1 = Constant(5)
variable1 = Variable(5, 'x', 3)
summation = constant1 / variable1
assert summation.__str__() == "{x}^{-3}"
constant1 = Constant(5)
variable1 = Variable(5, 'x', 3)
exp1 = Expression([constant1, Plus(), variable1])
constant2 = Constant(10)
summation = constant2 / exp1
assert summation.__str__() == "{10}*{({5}+5{x}^{3})}^{-1}"
constant1 = Constant(5)
variable1 = Variable(5, 'x', 3)
exp1 = Expression([constant1, Plus(), variable1])
constant2 = Constant(10)
summation = exp1 / constant2
assert summation.__str__() == "{({0.5}+0.5{x}^{3})}"
def test_Variable():
variable1 = Variable(2, 'x', 3)
assert variable1.__str__() == "2{x}^{3}"
variable1, _ = variable1.integrate('x')
assert variable1.__str__() == "0.5{x}^{4}"
constant = Constant(3)
variable = Variable(2, 'x', 3)
add = variable + constant
assert add.__str__() == "{(2{x}^{3}+{3})}"
variable1 = Variable(2, 'x', 3)
variable2 = Variable(4, 'x', 3)
add1 = variable1 + variable2
assert add1.__str__() == "6{x}^{3}"
variable1 = Variable(2, 'x', 3)
constant = Constant(3)
exp1 = Expression([variable1, Plus(), constant])
variable2 = Variable(4, 'x', 3)
add2 = variable2 + exp1
assert add2.__str__() == "{(6{x}^{3}+{3})}"
variable1 = Variable(2, 'x', 3)
constant = Constant(3)
exp1 = variable1 + constant
variable2 = Variable(4, 'x', 3)
add2 = variable2 - exp1
assert add2.__str__() == "{(2{x}^{3}-{3})}"
variable1 = Variable(2, 'x', 3)
constant = Constant(3)
exp1 = Expression([variable1, Plus(), constant])
variable2 = Variable(4, 'x', 3)
add2 = exp1 - variable2
assert add2.__str__() == "{(-2{x}^{3}+{3})}"
constant = Constant(3)
variable = Variable(2, 'x', 3)
add = variable - constant
assert add.__str__() == "{(2{x}^{3}-{3})}"
variable1 = Variable(2, 'x', 3)
variable2 = Variable(4, 'x', 3)
variable3 = Variable(2, 'x', 4)
variable4 = Variable(2, 'x', 3)
add1 = variable1 - variable2
add2 = variable3 - variable4
assert add1.__str__() == "-2{x}^{3}"
assert add2.__str__() == "{(2{x}^{4}-2{x}^{3})}"
constant = Constant(3)
variable = Variable(2, 'x', 3)
add = variable * constant
assert add.__str__() == "6{x}^{3}"
variable1 = Variable(2, 'x', 3)
variable2 = Variable(4, 'x', 3)
add2 = variable1 * variable2
assert add2.__str__() == "8{x}^{6}"
variable1 = Variable(2, 'x', 3)
variable2 = Variable(4, 'y', 3)
add2 = variable1 * variable2
assert add2.__str__() == "8{x}^{3}{y}^{3}"
variable1 = Variable(2, 'x', 3)
variable2 = Variable(4, 'y', 4)
add1 = variable1 / variable2
assert add1.__str__() == "0.5{x}^{3}{y}^{-4}"
variable1 = Variable(2, 'x', 3)
constant = Constant(3)
exp1 = variable1 - constant
variable2 = Variable(4, 'x', 3)
add2 = variable2 / exp1
assert add2.__str__() == "{(4.0{x}^{3}*{(2{x}^{3}-{3})}^{-1})}"
variable1 = Variable(2, 'x', 3)
constant = Constant(3)
exp1 = variable1 - constant
variable2 = Variable(4, 'x', 3)
add2 = variable2 * exp1
assert add2.__str__() == "{(8{x}^{6}-12{x}^{3})}"
variable1 = Variable(2, 'x', 3)
constant1 = Constant(3)
exp1 = variable1 - constant1
variable2 = Variable(4, 'x', 3)
constant2 = Constant(4)
exp2 = variable2 - constant2
add2 = exp1 * exp2
assert add2.__str__() == "{({(8{x}^{6}-8{x}^{3})}-{(12{x}^{3}-{12})})}"
variable2 = Variable(3, 'x', -1)
variable2, _ = variable2.integrate('x')
assert tokensToString(variable2) == '3 * log(x)'
def inverse(self):
"""Calculates the inverse of the matrix using Gauss-Jordan Elimination
Arguments:
matrix {visma.matrix.structure.Matrix} -- matrix token
Returns:
inv {visma.matrix.structure.Matrix} -- result matrix token
"""
from visma.simplify.simplify import simplify
from visma.io.tokenize import tokenizer
from visma.io.parser import tokensToString
if tokensToString(self.determinant()) == "0":
return -1
self.dim[0] = len(self.value)
self.dim[1] = len(self.value[0])
n = self.dim[0]
mat = Matrix()
mat.empty([n, 2 * n])
for i in range(0, n):
for j in range(0, 2 * n):
if j < n:
mat.value[i][j] = self.value[i][j]
else:
mat.value[i][j] = []
for i in range(0, n):
for j in range(n, 2 * n):
if j == (i + n):
mat.value[i][j].extend(tokenizer('1'))
else:
mat.value[i][j].extend(tokenizer("0"))
for i in range(n - 1, 0, -1):
if mat.value[i - 1][0][0].value < mat.value[i][0][0].value:
for j in range(0, 2 * n):
temp = mat.value[i][j]
mat.value[i][j] = mat.value[i - 1][j]
mat.value[i - 1][j] = temp
for i in range(0, n):
for j in range(0, n):
if j != i:
temp = []
if len(mat.value[j][i]) != 1:
temp.append(Expression(mat.value[j][i]))
else:
temp.extend(mat.value[j][i])
temp.append(Binary('/'))
if len(mat.value[i][i]) != 1:
temp.append(Expression(mat.value[i][i]))
else:
temp.extend(mat.value[i][i])
temp, _, _, _, _ = simplify(temp)
for k in range(0, 2 * n):
t = []
if mat.value[i][k][0].value != 0:
if len(mat.value[i][k]) != 1:
t.append(Expression(mat.value[i][k]))
else:
t.extend(mat.value[i][k])
t.append(Binary('*'))
if len(temp) != 1:
t.append(Expression(temp))
else:
t.extend(temp)
t, _, _, _, _ = simplify(t)
mat.value[j][k].append(Binary('-'))
if len(t) != 1:
mat.value[j][k].append(Expression(t))
else:
mat.value[j][k].extend(t)
mat.value[j][k], _, _, _, _ = simplify(
mat.value[j][k])
for i in range(0, n):
temp = []
temp.extend(mat.value[i][i])
for j in range(0, 2 * n):
if mat.value[i][j][0].value != 0:
mat.value[i][j].append(Binary('/'))
mat.value[i][j].extend(temp)
mat.value[i][j], _, _, _, _ = simplify(mat.value[i][j])
inv = SquareMat()
inv.empty([n, n])
for i in range(0, n):
for j in range(n, 2 * n):
inv.value[i][j - n] = mat.value[i][j]
return inv