def test_Matrix_toFile_fromFile():
matrix = Matrix([[1, 2.5],
[4, 5.5],
])
matrix.toFile("output.txt")
newMatrix = Matrix.fromFile("output.txt")
assert newMatrix == matrix
def test_Matrix_LU():
list = [[2,3,1,5],
[6,13,5,19],
[2,19,10,23],
[4,10,11,31],
]
LU = [[2,3,1,5],
[3,4,2,4],
[1,4,1,2],
[2,1,7,3],
]
LTrue = [[1,0,0,0],
[3,1,0,0],
[1,4,1,0],
[2,1,7,1],
]
UTrue = [[2,3,1,5],
[0,4,2,4],
[0,0,1,2],
[0,0,0,3],
]
matrix = Matrix(list)
L, U = Matrix.LU(matrix)
assert matrix == Matrix(list)
#assert matrix == Matrix(LU)
assert L == Matrix(LTrue)
assert U == Matrix(UTrue)
def test_Matrix_solveAxbWithLUP(Matrix120):
b = Matrix([[0.1],
[12.5],
[10.3]])
x, y = Matrix.solveAxbWithLUP(Matrix120, b)
assert y == Matrix([[10.3], [6.319999], [-5.571428]])
assert x == Matrix([[0.5], [-0.2], [3]])
def TryToSolveATask(path):
A, b = CreateMatricies(path)
if (path == "Tasks/Task_6Y.txt"):
for i in range(0, A.n_rows):
A._matrix[0][i] /= float(10**9)
A._matrix[2][i] *= float(10**10)
b._matrix[0][0] /= float(10**9)
b._matrix[2][0] *= float(10**10)
print "-.-.- Applied special transformations -.-.-"
try:
print "-.-.- solveAxbWithLU -.-.-"
x, y = Matrix.solveAxbWithLU(A, b)
PrintResults(x, y)
except ZeroDivisionError:
print u"Cannot solve with LU"
print
try:
print "-.-.- solveAxbWithLUP -.-.-"
x, y = Matrix.solveAxbWithLUP(A, b)
PrintResults(x, y)
except ZeroDivisionError:
print u"Cannot solve with LUP"
print
def test_Matrix_solveAxbWithLU(Matrix120):
b = Matrix([[0.1],
[12.5],
[10.3]])
x, y = Matrix.solveAxbWithLU(Matrix120, b)
assert y == Matrix([[0.1], [12.2], [-39]])
assert x == Matrix([[0.5], [-0.2], [3]])
def test_Matrix_LUP(Matrix120):
list = [[1, 2, 0],
[3, 5, 4],
[5, 6, 3],
]
LUP = [[5, 6, 3],
[3/5., 7/5., 11/5.],
[1/5., 4/7., -13/7.],
]
LTrue = [[1, 0, 0],
[3/5., 1, 0],
[1/5., 4/7., 1],
]
UTrue = [[5, 6, 3],
[0, 7/5., 11/5.],
[0, 0, -13/7.],
]
PTrue = [[0, 0, 1],
[0, 1, 0],
[1, 0, 0],
]
L, U, P = Matrix.LUP(Matrix120)
assert Matrix120 == Matrix(list)
#assert Matrix120 == Matrix(LUP)
assert L == Matrix(LTrue)
assert U == Matrix(UTrue)
assert P == Matrix(PTrue)
def test_Matrix_inverse():
A = Matrix([[1, 2],
[3, 4],
])
result = Matrix([[-2, 1],
[3/2., -1/2.],
])
A.inverse()
assert A == result
def test_Matrix_solveUxy(Matrix120):
b = Matrix([[0.1],
[12.5],
[10.3]])
L, U, P = Matrix.LUP(Matrix120)
y = Matrix120._solveLyPb(L, P, b)
assert y == Matrix([[10.3], [6.319999], [-5.571428]])
x = Matrix120._solveUxy(U, y)
assert x == Matrix([[0.5], [-0.2], [3]])
def test_Matrix_solveLyPb(Matrix120):
b = Matrix([[0.1],
[12.5],
[10.3]])
L, U = Matrix.LU(Matrix120)
P = Matrix120._CreateI()
y = Matrix120._solveLyPb(L, P, b)
assert y == Matrix([[0.1], [12.2], [-39]])
x = Matrix120._solveUxy(U, y)
assert x == Matrix([[0.5], [-0.2], [3]])
def Matrix120():
matrix = Matrix([[1, 2, 0],
[3, 5, 4],
[5, 6, 3],
])
return matrix
def Matrix2468():
matrix = Matrix([[2, 4],
[6, 8],
])
return matrix
def test_Matrix__init__Dimensions(): matrix = Matrix(3,3) assert matrix[(3,3)] == 0
def test_Matrix__eq__F(MatrixDull):
newMatrix = Matrix([[1, 2],
[3,4],
[5,6]
])
assert (MatrixDull == newMatrix) == False
def test_Matrix__eq__(MatrixDull):
newMatrix = Matrix([[1.000001, 22],
[333, 4444],
[55555,666666]
])
assert (MatrixDull == newMatrix) == True
def Matrix1234():
matrix = Matrix([[1, 2],
[3, 4],
])
return matrix
def test_Matrix__mul__Huge(): matrixManyRows = Matrix([[1], [2], [3], [4], [5]]) matrixManyColumns = Matrix([[1,2,3,4,5]]) hugeMatrix = matrixManyRows * matrixManyColumns assert hugeMatrix[5,5] == 25
def test_Matrix__mul__SingleValue(): matrixManyRows = Matrix([[1], [2], [3], [4], [5]]) matrixManyColumns = Matrix([[1,2,3,4,5]]) singleValueMatrix = matrixManyColumns * matrixManyRows assert singleValueMatrix[(1,1)] == 55
def MatrixDull():
matrix = Matrix([[1, 22],
[333, 4444],
[55555,666666]
])
return matrix
def CreateMatricies(path):
A = Matrix.fromFile(path.replace("Y", "A"))
b = Matrix.fromFile(path.replace("Y", "b"))
PrintLoaded(A, b)
return A, b