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from visma.functions.operator import Binary
from visma.functions.structure import Expression
from visma.functions.constant import Constant
from visma.simplify.simplify import simplify
from visma.matrix.structure import Matrix
from visma.gui import logger
def simplifyMatrix(mat):
"""Simplifies each element in the matrix
Arguments:
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
mat {visma.matrix.structure.Matrix} -- simplified matrix token
"""
mat.dim[0] = len(mat.value)
mat.dim[1] = len(mat.value[0])
for i in range(mat.dim[0]):
for j in range(mat.dim[1]):
mat.value[i][j], _, _, _, _ = simplify(mat.value[i][j])
return mat
def addMatrix(matA, matB):
"""Adds two matrices
Arguments:
matA {visma.matrix.structure.Matrix} -- matrix token
matB {visma.matrix.structure.Matrix} -- matrix token
Returns:
matSum {visma.matrix.structure.Matrix} -- sum matrix token
Note:
Make dimCheck before calling addMatrix
"""
matSum = Matrix()
matA.dim[0] = len(matA.value)
matA.dim[1] = len(matA.value[0])
matSum.empty(matA.dim)
for i in range(matA.dim[0]):
for j in range(matA.dim[1]):
matSum.value[i][j].extend(matA.value[i][j])
matSum.value[i][j].append(Binary('+'))
matSum.value[i][j].extend(matB.value[i][j])
matSum = simplifyMatrix(matSum)
return matSum
def subMatrix(matA, matB):
"""Subtracts two matrices
Arguments:
matA {visma.matrix.structure.Matrix} -- matrix token
matB {visma.matrix.structure.Matrix} -- matrix token
Returns:
matSub {visma.matrix.structure.Matrix} -- subtracted matrix token
Note:
Make dimCheck before calling subMatrix
"""
matSub = Matrix()
matA.dim[0] = len(matA.value)
matA.dim[1] = len(matA.value[0])
matSub.empty(matA.dim)
for i in range(matA.dim[0]):
for j in range(matA.dim[1]):
matSub.value[i][j].extend(matA.value[i][j])
matSub.value[i][j].append(Binary('-'))
matSub.value[i][j].extend(matB.value[i][j])
matSub = simplifyMatrix(matSub)
return matSub
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()
matA.dim[0] = len(matA.value)
matA.dim[1] = len(matA.value[0])
matB.dim[0] = len(matB.value)
matB.dim[1] = len(matB.value[0])
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 scalarAdd(const, mat):
"""
Adds constant terms with Matrix
Arguments:
const {string}--- constant value
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
matRes {visma.matrix.structure.Matrix} -- sum matrix token
Note:
This scalar addition follows the following equation
{mat} + {lambda}{identity mat}
"""
matRes = Matrix()
mat.dim[0] = len(mat.value)
mat.dim[1] = len(mat.value[0])
matRes.empty(mat.dim)
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 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 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 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 row_echelon(mat):
"""
Returns the row echelon form of the given matrix
Arguments:
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
row_echelon {visma.matrix.structure.Matrix} -- result matrix token
"""
N = mat.dim[0]
M = mat.dim[1]
for k in range(0, N):
if abs(mat.value[k][k][0].value) == 0.0:
if k == N-1:
return simplifyMatrix(mat)
else:
for i in range(0, N):
t = mat.value[k][i]
mat.value[k][i] = mat.value[k+1][i]
mat.value[k+1][i] = t
else:
for i in range(k+1, N):
temp = []
temp.extend(mat.value[i][k])
temp.append(Binary('/'))
temp.extend(mat.value[k][k])
temp, _, _, _, _ = simplify(temp)
for j in range(k+1, M):
temp2 = []
temp2.extend(mat.value[k][j])
temp2.append(Binary('*'))
temp2.extend(temp)
temp2, _, _, _, _ = simplify(temp2)
mat.value[i][j].append(Binary('-'))
mat.value[i][j].extend(temp2)
mat.value[i][k].append(Binary('*'))
mat.value[i][k].append(Constant(0))
mat = simplifyMatrix(mat)
return simplifyMatrix(mat)
def gauss_elim(mat):
"""
Returns calculated values of unknown variables
Arguments:
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
result {visma.matrix.structure.Matrix} -- result matrix token
Note: result is a Nx1 matrix
"""
echelon = Matrix()
echelon = row_echelon(mat)
result = Matrix()
result.empty([mat.dim[0], 1])
N = mat.dim[0]
M = mat.dim[1]
index = N-1
for i in range(N-1, -1, -1):
sum_ = []
temp = []
if echelon.value[i][i][0].value == 0.0: # no unique solution for this case
return -1
for j in range(i+1, M-1):
temp = []
temp.extend(echelon.value[i][j])
temp.append(Binary('*'))
temp.extend(result.value[j][0])
temp, _, _, _, _ = simplify(temp)
sum_.extend(temp)
if j != M-2:
sum_.append(Binary('+'))
sum_, _, _, _, _ = simplify(sum_)
result.value[index][0].extend(echelon.value[i][M-1])
if sum_:
if sum_[0].value < 0:
result.value[index][0].append(Binary('-')) # negative sign makes the negative sign in value positive
else:
result.value[index][0].append(Binary('-'))
result.value[index][0].extend(sum_)
result.value[index][0], _, _, _, _ = simplify(result.value[index][0])
result.value[index][0].append(Binary('/'))
result.value[index][0].extend(echelon.value[i][i])
result.value[index][0], _, _, _, _ = simplify(result.value[index][0])
index -= 1
return result
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