def test_copy(self):
mat = SquareMatrix.copy(self.matF1)
self.assertTrue(mat == self.matF1)
mat = SquareMatrix.copy(self.matF5)
self.assertTrue(mat == self.matF5)
def test_creation_from_list(self):
mat= SquareMatrix.from_list(self.lsF1size[0],self.lsF1)
self.is_matrix_equal(self.matF1, mat)
mat= SquareMatrix.from_list(self.lsF2size[0] ,self.lsF2)
self.is_matrix_equal(self.matF2, mat)
def test_creation_from_list(self):
mat = SquareMatrix.from_list(self.lsF1size[0], self.lsF1)
self.is_matrix_equal(self.matF1, mat)
mat = SquareMatrix.from_list(self.lsF2size[0], self.lsF2)
self.is_matrix_equal(self.matF2, mat)
def test_copy(self):
mat = SquareMatrix.copy(self.matF1)
self.assertTrue(mat == self.matF1)
mat = SquareMatrix.copy(self.matF5)
self.assertTrue(mat == self.matF5)
def setUp(self):
#setting up some fixtures
self.lsF1 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
self.lsF1size = (4, 4)
self.lsF2 = [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4]
self.lsF2size = (4, 4)
self.lsF3 = [3, 1, 4, 5, 2, 3, 2, 1, 2]
self.lsF3size = (3, 3)
self.lsF4 = [i for i in range(6)]
self.lsF4size = (3, 2)
self.lsF5 = [i for i in range(12)]
self.lsF5size = (3, 4)
self.lsF6 = [4, 6, 2, 3, 8, 1, 0, 5, 1]
self.lsF6size = (3, 3)
self.lsF7 = [1, 3, 5, 7, 0, 0, 1, 2, 2, 6, 8, 8]
self.lsF7size = (4, 3)
self.lsF8 = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]
self.lsF8size = (4, 4)
self.lsF9 = [1, 0, 0, 0, 1, 2, 0, 0, 1, 2, 3, 0, 1, 2, 3, 4]
self.lsF9size = (4, 4)
self.lsF10 = [3, 0, 0, 5, 2, 0, 2, 1, 2]
self.lsF10size = (3, 3)
self.lsF11 = [1, 2, 3, 4, 0, 2, 3, 4, 0, 0, 3, 4, 0, 0, 0, 4]
self.lsF11size = (4, 4)
self.lsF12 = [3, 1, 4, 0, 2, 3, 0, 0, 2]
self.lsF12size = (3, 3)
self.matF1 = Matrix.from_list(self.lsF1size[0], self.lsF1size[1],
self.lsF1)
self.matF2 = Matrix.from_list(self.lsF2size[0], self.lsF2size[1],
self.lsF2)
self.matF3 = Matrix.from_list(self.lsF3size[0], self.lsF3size[1],
self.lsF3)
self.matF4 = Matrix.from_list(self.lsF4size[0], self.lsF4size[1],
self.lsF4)
self.matF5 = Matrix.from_list(self.lsF5size[0], self.lsF5size[1],
self.lsF5)
self.matF6 = Matrix.from_list(self.lsF6size[0], self.lsF6size[1],
self.lsF6)
self.matF7 = Matrix.from_list(self.lsF7size[0], self.lsF7size[1],
self.lsF7)
self.matF8 = Matrix.from_list(self.lsF8size[0], self.lsF8size[1],
self.lsF8)
self.matF9 = SquareMatrix.from_list(self.lsF9size[0], self.lsF9)
self.matF10 = SquareMatrix.from_list(self.lsF10size[0], self.lsF10)
self.matF11 = SquareMatrix.from_list(self.lsF11size[0], self.lsF11)
self.matF12 = SquareMatrix.from_list(self.lsF12size[0], self.lsF12)
def test_set_lower_triangular(self):
mat = SquareMatrix.copy(self.matF2)
mat.set_lower_triangular()
self.is_matrix_equal_to_list(mat, self.lsF11)
mat = SquareMatrix.copy(self.matF3)
mat.set_lower_triangular()
self.is_matrix_equal_to_list(mat, self.lsF12)
def test_set_lower_symmetry(self):
mat = SquareMatrix.copy(self.matF1)
mat.set_lower_simmetry()
self.is_matrix_equal_to_list(mat, self.lsF1)
mat = SquareMatrix.copy(self.matF2)
mat.set_lower_simmetry()
self.is_matrix_equal_to_list(mat, [1,1,1,1,1,2,2,2,1,2,3,3,1,2,3,4])
def test_set_transpose(self):
mat = SquareMatrix.copy(self.matF1)
mat.set_transpose()
self.is_matrix_equal_to_list(mat, self.lsF1)
mat = SquareMatrix.copy(self.matF2)
mat.set_transpose()
self.is_matrix_equal_to_list(mat, [1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4])
def test_set_unit_lower_triangular(self):
mat = SquareMatrix.copy(self.matF2)
mat.set_unit_lower_triangular()
self.is_matrix_equal_to_list(mat, [1,2,3,4, 0,1,3,4,0,0,1,4,0,0,0,1])
mat = SquareMatrix.copy(self.matF3)
mat.set_unit_lower_triangular()
self.is_matrix_equal_to_list(mat, [1,1,4,0,1,3,0,0,1])
def test_set_strictly_lower_triangular(self):
mat = SquareMatrix.copy(self.matF2)
mat.set_strictly_lower_triangular()
self.is_matrix_equal_to_list(mat, [0,2,3,4, 0,0,3,4,0,0,0,4,0,0,0,0])
mat = SquareMatrix.copy(self.matF3)
mat.set_strictly_lower_triangular()
self.is_matrix_equal_to_list(mat, [0,1,4,0,0,3,0,0,0])
def test_set_lower_triangular(self):
mat = SquareMatrix.copy(self.matF2)
mat.set_lower_triangular()
self.is_matrix_equal_to_list(mat, self.lsF11)
mat = SquareMatrix.copy(self.matF3)
mat.set_lower_triangular()
self.is_matrix_equal_to_list(mat, self.lsF12)
def test_identity(self):
mat = SquareMatrix.from_list(self.lsF1size[0], self.lsF1)
self.is_matrix_equal_to_list(mat, self.lsF1)
mat = SquareMatrix.from_list(self.lsF2size[0], self.lsF2)
self.is_matrix_equal_to_list(mat, self.lsF2)
mat = SquareMatrix.from_list(self.lsF3size[0], self.lsF3)
self.is_matrix_equal_to_list(mat, self.lsF3)
def test_set_unit_lower_triangular(self):
mat = SquareMatrix.copy(self.matF2)
mat.set_unit_lower_triangular()
self.is_matrix_equal_to_list(
mat, [1, 2, 3, 4, 0, 1, 3, 4, 0, 0, 1, 4, 0, 0, 0, 1])
mat = SquareMatrix.copy(self.matF3)
mat.set_unit_lower_triangular()
self.is_matrix_equal_to_list(mat, [1, 1, 4, 0, 1, 3, 0, 0, 1])
def test_set_lower_symmetry(self):
mat = SquareMatrix.copy(self.matF1)
mat.set_lower_simmetry()
self.is_matrix_equal_to_list(mat, self.lsF1)
mat = SquareMatrix.copy(self.matF2)
mat.set_lower_simmetry()
self.is_matrix_equal_to_list(
mat, [1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 3, 3, 1, 2, 3, 4])
def test_set_strictly_lower_triangular(self):
mat = SquareMatrix.copy(self.matF2)
mat.set_strictly_lower_triangular()
self.is_matrix_equal_to_list(
mat, [0, 2, 3, 4, 0, 0, 3, 4, 0, 0, 0, 4, 0, 0, 0, 0])
mat = SquareMatrix.copy(self.matF3)
mat.set_strictly_lower_triangular()
self.is_matrix_equal_to_list(mat, [0, 1, 4, 0, 0, 3, 0, 0, 0])
def test_identity(self):
mat = SquareMatrix.from_list(self.lsF1size[0], self.lsF1)
self.is_matrix_equal_to_list(mat , self.lsF1)
mat = SquareMatrix.from_list(self.lsF2size[0], self.lsF2)
self.is_matrix_equal_to_list(mat , self.lsF2)
mat = SquareMatrix.from_list(self.lsF3size[0], self.lsF3)
self.is_matrix_equal_to_list(mat , self.lsF3)
def test_set_transpose(self):
mat = SquareMatrix.copy(self.matF1)
mat.set_transpose()
self.is_matrix_equal_to_list(mat, self.lsF1)
mat = SquareMatrix.copy(self.matF2)
mat.set_transpose()
self.is_matrix_equal_to_list(
mat, [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4])
def test_creation(self):
mat = SquareMatrix(4, None, True)
self.is_matrix_equal(self.matF8, mat)
mat = SquareMatrix(4, [
Vector([1, 0, 0, 0]),
Vector([0, 1, 0, 0]),
Vector([0, 0, 1, 0]),
Vector([0, 0, 0, 1])
], False)
self.is_matrix_equal(self.matF8, mat)
def test_lu_factorization(self):
mat = SquareMatrix.from_list(3, [2, 4, 6, 4, -2, -4, -2, 6, 2])
L, U = mat.lu_factorization()
self.is_matrix_equal_to_matrix(L.mult_matrix_update_by_column(U), mat)
#ensuring A - (LU) = zero matrix
mat.set_add(-(L.mult_matrix_update_by_column(U)))
self.is_matrix_equal_to_matrix(mat, SquareMatrix.copy(self.matF1))
mat = SquareMatrix.from_list(3, [1, 5, -2, -2, -15, -11, 2, 8, -11])
L, U = mat.lu_factorization()
self.is_matrix_equal_to_list(L, [1, 5, -2, 0, 1, 3, 0, 0, 1])
self.is_matrix_equal_to_list(U, [1, 0, 0, -2, -5, 0, 2, -2, -1])
def test_solve_lower_triangular_system(self):
mat = SquareMatrix.from_list(3, [2, 4, 6, 4, -2, -4, -2, 6, 2])
L, U = mat.lu_factorization()
vec = Vector([-10, 20, 18])
res = L.solve_lower_triangular_system(vec)
self.is_vector_equal_to_list(res, [-10, 40, -16])
def test_solve_linear_system(self):
mat = SquareMatrix.from_list(4, [2,-2,4,-4,0,-1,-1,1,1,1,5,-3,2,-1,4,-8])
vec = Vector([2,2,11,-3])
res = mat.solve_linear_system(vec)
self.is_vector_equal_to_list(res,[1,-1,2,-1])
def test_gaussian_appended_reduction_upper_triangular(self):
mat = SquareMatrix.from_list(3, [2,4,6,4, -2,-4,-2,6,2])
res = mat.gaussian_reduction_upper_triangular(True)
vec = Vector([-10,20,18])
res= res.gaussian_appended_reduction_upper_triangular( vec)
self.is_vector_equal_to_list(res, [-10,40,-16])
def test_solve_lower_triangular_system(self):
mat = SquareMatrix.from_list(3, [2,4,6,4, -2,-4,-2,6,2])
L, U = mat.lu_factorization()
vec = Vector([-10,20,18])
res= L.solve_lower_triangular_system( vec)
self.is_vector_equal_to_list(res, [-10,40,-16])
def test_lu_factorization_compact(self):
mat = SquareMatrix.from_list(3, [2,4,6,4, -2,-4,-2,6,2])
lu_res = mat.lu_factorization_compact()
gres = mat.gaussian_reduction_upper_triangular(True)
self.is_matrix_equal_to_list(lu_res, [2,2,3,4,-10,1.6,-2,10,-8])
self.is_matrix_equal_to_matrix(lu_res,gres)
def test_solve_linear_system(self):
mat = SquareMatrix.from_list(
4, [2, -2, 4, -4, 0, -1, -1, 1, 1, 1, 5, -3, 2, -1, 4, -8])
vec = Vector([2, 2, 11, -3])
res = mat.solve_linear_system(vec)
self.is_vector_equal_to_list(res, [1, -1, 2, -1])
def test_gaussian_appended_reduction_upper_triangular(self):
mat = SquareMatrix.from_list(3, [2, 4, 6, 4, -2, -4, -2, 6, 2])
res = mat.gaussian_reduction_upper_triangular(True)
vec = Vector([-10, 20, 18])
res = res.gaussian_appended_reduction_upper_triangular(vec)
self.is_vector_equal_to_list(res, [-10, 40, -16])
def test_gaussian_reduction_upper_triangular(self):
mat = SquareMatrix.from_list(3, [2, 4, 6, 4, -2, -4, -2, 6, 2])
res = mat.gaussian_reduction_upper_triangular()
self.is_matrix_equal_to_list(res, [2, 0, 0, 4, -10, 0, -2, 10, -8])
res = mat.gaussian_reduction_upper_triangular(True)
self.is_matrix_equal_to_list(res, [2, 2, 3, 4, -10, 1.6, -2, 10, -8])
vec = Vector([-10, 20, 18])
res = mat.gaussian_reduction_upper_triangular(True, vec)
self.is_matrix_equal_to_list(res, [2, 2, 3, 4, -10, 1.6, -2, 10, -8])
self.is_vector_equal_to_list(vec, [-10, 40, -16])
mat = SquareMatrix.from_list(3, [1, -3, 1, 1, 0, 13, 2, -3, 20])
res = mat.gaussian_reduction_upper_triangular()
self.is_matrix_equal_to_list(res, [1, 0, 0, 1, 3, 0, 2, 3, 6])
def test_solve_upper_triangular_system(self):
mat = SquareMatrix.from_list(3, [-2, 0, 0, -1, -3, 0, 1, -2, 1])
vec = Vector([6, 9, 3])
it = vec.vector_iterator(True)
res = mat.solve_upper_triangular_system(vec)
self.is_vector_equal_to_list(res, [1, -5, 3])
def test_gaussian_reduction_upper_triangular(self):
mat = SquareMatrix.from_list(3, [2,4,6,4, -2,-4,-2,6,2])
res = mat.gaussian_reduction_upper_triangular()
self.is_matrix_equal_to_list(res, [2,0,0,4,-10,0,-2,10,-8])
res = mat.gaussian_reduction_upper_triangular(True)
self.is_matrix_equal_to_list(res, [2,2,3,4,-10,1.6,-2,10,-8])
vec = Vector([-10,20,18])
res = mat.gaussian_reduction_upper_triangular(True, vec)
self.is_matrix_equal_to_list(res, [2,2,3,4,-10,1.6,-2,10,-8])
self.is_vector_equal_to_list(vec, [-10,40,-16])
mat = SquareMatrix.from_list(3, [1,-3,1,1,0,13,2,-3,20])
res = mat.gaussian_reduction_upper_triangular()
self.is_matrix_equal_to_list(res, [1,0,0,1,3,0,2,3,6])
def test_lu_factorization_compact(self):
mat = SquareMatrix.from_list(3, [2, 4, 6, 4, -2, -4, -2, 6, 2])
lu_res = mat.lu_factorization_compact()
gres = mat.gaussian_reduction_upper_triangular(True)
self.is_matrix_equal_to_list(lu_res,
[2, 2, 3, 4, -10, 1.6, -2, 10, -8])
self.is_matrix_equal_to_matrix(lu_res, gres)
def test_lu_factorization(self):
mat = SquareMatrix.from_list(3, [2,4,6,4, -2,-4,-2,6,2])
L, U = mat.lu_factorization()
self.is_matrix_equal_to_matrix(L.mult_matrix_update_by_column(U),mat)
#ensuring A - (LU) = zero matrix
mat.set_add (-(L.mult_matrix_update_by_column(U)))
self.is_matrix_equal_to_matrix(mat,
SquareMatrix.copy(self.matF1))
mat = SquareMatrix.from_list(3,[1,5,-2,-2,-15,-11,2,8,-11])
L,U = mat.lu_factorization()
self.is_matrix_equal_to_list(L, [1,5,-2,0,1,3,0,0,1])
self.is_matrix_equal_to_list(U, [1,0,0,-2,-5,0,2,-2,-1])
def test_solve_upper_triangular_system(self):
mat = SquareMatrix.from_list(3, [-2,0,0,-1,-3,0,1,-2,1])
vec = Vector([6,9,3])
it = vec.vector_iterator(True)
res = mat.solve_upper_triangular_system(vec)
self.is_vector_equal_to_list(res,[1,-5,3])
def setUp(self):
#setting up some fixtures
self.lsF1 = [0,0,0,0,
0,0,0,0,
0,0,0,0,
0,0,0,0]
self.lsF1size = (4,4)
self.lsF2 = [1,2,3,4,
1,2,3,4,
1,2,3,4,
1,2,3,4]
self.lsF2size = (4,4)
self.lsF3 = [3,1,4,
5,2,3,
2,1,2]
self.lsF3size = (3,3)
self.lsF4 = [ i for i in range(6)]
self.lsF4size = (3,2)
self.lsF5 = [ i for i in range(12)]
self.lsF5size = (3,4)
self.lsF6 = [4,6,2,
3,8,1,
0,5,1]
self.lsF6size= (3,3)
self.lsF7 = [1,3,5,7,
0,0,1,2,
2,6,8,8]
self.lsF7size = (4,3)
self.lsF8 = [1,0,0,0,
0,1,0,0,
0,0,1,0,
0,0,0,1]
self.lsF8size = (4,4)
self.lsF9 = [1,0,0,0,
1,2,0,0,
1,2,3,0,
1,2,3,4]
self.lsF9size = (4,4)
self.lsF10 = [3,0,0,
5,2,0,
2,1,2]
self.lsF10size = (3,3)
self.lsF11 = [1,2,3,4,
0,2,3,4,
0,0,3,4,
0,0,0,4]
self.lsF11size = (4,4)
self.lsF12 = [3,1,4,
0,2,3,
0,0,2]
self.lsF12size = (3,3)
self.matF1 = Matrix.from_list(self.lsF1size[0], self.lsF1size[1],self.lsF1)
self.matF2 = Matrix.from_list(self.lsF2size[0], self.lsF2size[1],self.lsF2)
self.matF3 = Matrix.from_list(self.lsF3size[0], self.lsF3size[1],self.lsF3)
self.matF4 = Matrix.from_list(self.lsF4size[0], self.lsF4size[1],self.lsF4)
self.matF5 = Matrix.from_list(self.lsF5size[0], self.lsF5size[1],self.lsF5)
self.matF6 = Matrix.from_list(self.lsF6size[0], self.lsF6size[1],self.lsF6)
self.matF7 = Matrix.from_list(self.lsF7size[0], self.lsF7size[1],self.lsF7)
self.matF8 = Matrix.from_list(self.lsF8size[0], self.lsF8size[1],self.lsF8)
self.matF9 = SquareMatrix.from_list(self.lsF9size[0] ,self.lsF9)
self.matF10 = SquareMatrix.from_list(self.lsF10size[0],self.lsF10)
self.matF11 = SquareMatrix.from_list(self.lsF11size[0],self.lsF11)
self.matF12 = SquareMatrix.from_list(self.lsF12size[0],self.lsF12)
def test_set_to_diagonal(self):
self.matF2 = SquareMatrix.copy(self.matF2)
self.matF2.set_to_diagonal([1,1,1,1])
self.is_matrix_equal_to_list(self.matF2,self.lsF8)
def test_set_to_diagonal(self):
self.matF2 = SquareMatrix.copy(self.matF2)
self.matF2.set_to_diagonal([1, 1, 1, 1])
self.is_matrix_equal_to_list(self.matF2, self.lsF8)