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from visma.functions.constant import Constant
from visma.functions.operator import Multiply
from visma.functions.operator import Minus
from visma.functions.operator import Plus
from visma.functions.constant import Zero
from visma.functions.structure import Expression
import numpy as np
from visma.functions.operator import Binary
class Matrix(object):
"""Class for matrix type
The elements in the matrix are function tokens.
Example:
[ 1 , 2xy^2 ;
4xy , x+y ]
is tokenized to
[[ [Constant] , [Variable] ],
[ [Variable] , [Variable, Binary, Variable]]]
and stored in matrix.value.
"""
def __init__(self, value=None, coefficient=None, power=None, dim=None, scope=None):
self.scope = None
if value is not None:
self.value = value
else:
self.value = []
if coefficient is not None:
self.coefficient = coefficient
else:
self.coefficient = 1
if power is not None:
self.power = power
else:
self.power = 1
if dim is not None:
self.dim = dim
else:
self.dim = [0, 0]
def convertMatrixToString(self, Latex=False):
from visma.io.parser import tokensToString
MatrixString = ''
self.dim[0] = len(self.value)
self.dim[1] = len(self.value[0])
for i in range(self.dim[0]):
for j in range(self.dim[1]):
if not Latex:
MatrixString += tokensToString(self.value[i][j]) + '\t'
else:
MatrixString += tokensToString(self.value[i][j]) + ' '
MatrixString += '\n'
return MatrixString
def __add__(self, other):
"""Adds two matrices
Arguments:
self {visma.matrix.structure.Matrix} -- matrix token
other {visma.matrix.structure.Matrix} -- matrix token
Returns:
matSum {visma.matrix.structure.Matrix} -- sum matrix token
Note:
Make dimCheck before calling addMatrix
"""
matSum = Matrix()
matSum.empty(self.dim)
for i in range(self.dim[0]):
for j in range(self.dim[1]):
matSum.value[i][j].extend(self.value[i][j])
matSum.value[i][j].append(Binary('+'))
matSum.value[i][j].extend(other.value[i][j])
from visma.matrix.operations import simplifyMatrix
matSum = simplifyMatrix(matSum)
return matSum
def __sub__(self, other):
"""Subtracts two matrices
Arguments:
self {visma.matrix.structure.Matrix} -- matrix token
other {visma.matrix.structure.Matrix} -- matrix token
Returns:
matSub {visma.matrix.structure.Matrix} -- subtracted matrix token
Note:
Make dimCheck before calling subMatrix
"""
matSub = Matrix()
matSub.empty(self.dim)
for i in range(self.dim[0]):
for j in range(self.dim[1]):
matSub.value[i][j].extend(self.value[i][j])
matSub.value[i][j].append(Binary('-'))
matSub.value[i][j].extend(other.value[i][j])
from visma.matrix.operations import simplifyMatrix
matSub = simplifyMatrix(matSub)
return matSub
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 __str__(self):
represent = "["
for i in range(self.dim[0]):
for j in range(self.dim[1]):
for tok in self.value[i][j]:
represent += tok.__str__()
represent += ","
represent = represent[:-1] + ";"
represent = represent[:-1] + "]"
return represent
def empty(self, dim=None):
"""Empties the matrix into a matrix of dimension dim
Keyword Arguments:
dim {list} -- dimension of matrix (default: {None})
"""
if dim is not None:
self.dim = dim
self.value = [[[] for _ in range(self.dim[1])] for _ in range(self.dim[0])]
def prop(self, scope=None, value=None, coeff=None, power=None, operand=None, operator=None):
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
def isSquare(self):
"""Checks if matrix is square
Returns:
bool -- if square matrix or not
"""
if self.dim[0] == self.dim[1]:
self.__class__ = SquareMat
return True
else:
return False
def isIdentity(self):
"""Checks if matrix is identity
Returns:
bool -- if identity matrix or not
"""
if self.isDiagonal():
for i in range(0, self.dim[0]):
if self.value[i][i][0].value != 1:
return False
self.__class__ = IdenMat
return True
else:
return False
def isDiagonal(self):
"""Checks if matrix is diagonal
Returns:
bool -- if diagonal matrix or not
"""
if self.isSquare():
for i in range(0, self.dim[0]):
for j in range(0, self.dim[1]):
if i != j and (self.value[i][j][0].value != 0 or len(self.value[i][j]) > 1):
return False
self.__class__ = DiagMat
return True
else:
return False
def dimension(self):
"""Gets the dimension of the matrix
dim[0] -- number of rows
dim[1] -- number of columns
"""
self.dim[0] = len(self.value)
self.dim[1] = len(self.value[0])
def transposeMat(self):
"""Returns Transpose of Matrix
Returns:
matRes {visma.matrix.structure.Matrix} -- result matrix token
"""
matRes = Matrix()
matRes.empty([self.dim[1], self.dim[0]])
for i in range(self.dim[0]):
for j in range(self.dim[1]):
matRes.value[j][i] = self.value[i][j]
return matRes
class SquareMat(Matrix):
"""Class for Square matrix
Square matrix is a matrix with equal dimensions.
Extends:
Matrix
"""
def determinant(self, mat=None):
"""Calculates square matrices' determinant
Returns:
list of tokens forming the determinant
"""
from visma.simplify.simplify import simplify
if mat is None:
self.dimension()
mat = np.array(self.value)
if(mat.shape[0] > 2):
ans = []
for i in range(mat.shape[0]):
mat1 = SquareMat()
mat1.value = np.concatenate((mat[1:, :i], mat[1:, i+1:]), axis=1).tolist()
a, _, _, _, _ = simplify(mat1.determinant())
if(a[0].value != 0 and a != []):
a, _, _, _, _ = simplify(a + [Multiply()] + mat[0][i].tolist())
if(i % 2 == 0):
if(ans != []):
ans, _, _, _, _ = simplify(ans + [Plus()] + a)
else:
ans = a
else:
ans, _, _, _, _ = simplify(ans + [Minus()] + a)
elif(mat.shape[0] == 2):
a = Multiply()
b = Minus()
mat = mat.tolist()
a1, _, _, _, _ = simplify(mat[0][0] + [a] + mat[1][1])
a2, _, _, _, _ = simplify(mat[0][1] + [a] + mat[1][0])
ans, _, _, _, _ = simplify([a1[0], b, a2[0]])
if (isinstance(ans[0], Minus) or isinstance(ans[0], Plus)) and ans[0].value not in ['+', '-']:
ans[0] = Constant(ans[0].value)
else:
ans, _, _, _, _ = simplify(mat[0][0])
if not ans:
ans = Zero()
return ans
def traceMat(self):
"""Returns the trace of a square matrix (sum of diagonal elements)
Arguments:
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
trace {visma.matrix.structure.Matrix} -- string token
"""
from visma.simplify.simplify import simplify
trace = []
self.dim[0] = len(self.value)
self.dim[1] = len(self.value[0])
for i in range(self.dim[0]):
trace.extend(self.value[i][i])
trace.append(Binary('+'))
trace.pop()
trace, _, _, _, _ = simplify(trace)
return trace
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
def cofactor(self):
"""Calculates cofactors matrix of the Square Matrix
Returns:
An object of type SquareMat
"""
mat1 = SquareMat()
mat1.value = []
for i in range(self.dim[0]):
if(i % 2 == 0):
coeff = -1
else:
coeff = 1
mat1.value.append([])
for j in range(self.dim[1]):
coeff *= -1
mat = SquareMat()
temp = np.array(self.value)
mat.value = np.concatenate((np.concatenate((temp[:i, :j], temp[i+1:, :j])), np.concatenate((temp[:i, j+1:], temp[i+1:, j+1:]))), axis=1).tolist()
val = mat.determinant()[0]
val.value *= coeff
mat1.value[i].append([val])
mat1.dimension()
return mat1
class DiagMat(SquareMat):
"""Class for Diagonal matrix
Diagonal matrix is a square matrix with all elements as 0 except for the diagonal elements.
Extends:
SquareMat
"""
def __init__(self, dim, diagElem):
"""
dim {list} -- dimension of matrix
diagElem {list} -- list of tokens list
"""
super().__init__()
self.dim = dim
for i in range(0, dim[0]):
row = []
for j in range(0, dim[1]):
if i == j:
row.append(diagElem[i])
else:
row.append([Constant(0)])
self.value.append(row)
class IdenMat(DiagMat):
"""Class for identity matrix
Identity matrix is a diagonal matrix with all elements as 0 except for the diagonal elements which are 1.
Extends:
DiagMat
"""
def __init__(self, dim):
super().__init__(dim, [[Constant(1)]]*dim[0])
for i in range(0, dim[0]):
self.value[i][i] = Constant(1)
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