def test_plu_factorization(self):
matrix = Matrix([[1, 5, 4], [3, 6, 4], [8, 2, 3]], fraction=True)
permuted, lower, upper = plu_factorization(matrix)
self.assertEqual(
repr(permuted),
"Matrix([['1', '0', '0'], ['0', '1', '0'], ['0', '0', '1']])")
self.assertEqual(
repr(lower),
"Matrix([['1', '0', '0'], ['3', '1', '0'], ['8', '38/9', '1']])")
self.assertEqual(
repr(upper),
"Matrix([['1', '5', '4'], ['0', '-9', '-8'], ['0', '0', '43/9']])")
self.assertEqual(repr(lower * upper), repr(permuted * matrix))
matrix = Matrix([[0, 5, 4], [3, 0, 4], [8, 2, 3]], fraction=True)
permuted, lower, upper = plu_factorization(matrix)
self.assertEqual(
repr(permuted),
"Matrix([['0', '1', '0'], ['1', '0', '0'], ['0', '0', '1']])")
self.assertEqual(
repr(lower),
"Matrix([['1', '0', '0'], ['0', '1', '0'], ['8/3', '2/5', '1']])")
self.assertEqual(
repr(upper),
"Matrix([['3', '0', '4'], ['0', '5', '4'], ['0', '0', '-139/15']])"
)
self.assertEqual(repr(lower * upper), repr(permuted * matrix))
matrix = fill_matrix(2, 3, 1)
with self.assertRaises(DimensionError) as c:
permuted, lower, upper = plu_factorization(matrix)
self.assertTrue("Matrix must be a square matrix." in str(c.exception))
def test_gaussian_elimination(self):
matrix = Matrix([[1, 2, 3], [4, 5, 6]], fraction=True)
c_matrix, traceback, inverse_traceback = gaussian_elimination(matrix)
self.assertEqual(repr(c_matrix),
"Matrix([['1', '0', '-1'], ['0', '1', '2']])")
self.assertEqual(repr(traceback), "[]")
self.assertEqual(repr(inverse_traceback), "[]")
matrix = Matrix([[4, 7], [2, 6]], fraction=True)
c_matrix, traceback, inverse_traceback = gaussian_elimination(
matrix, history=True)
self.assertEqual(repr(c_matrix), "Matrix([['1', '0'], ['0', '1']])")
self.assertEqual(
repr(traceback), "[Matrix([['1/4', '0'], ['0', '1']]), " +
"Matrix([['1', '0'], ['-2', '1']]), " +
"Matrix([['1', '0'], ['0', '2/5']]), " +
"Matrix([['1', '-7/4'], ['0', '1']])]")
self.assertEqual(repr(inverse_traceback), "[]")
matrix = Matrix([[4, 7], [2, 6]], fraction=True)
c_matrix, traceback, inverse_traceback = gaussian_elimination(
matrix, inverse_history=True)
self.assertEqual(repr(c_matrix), "Matrix([['1', '0'], ['0', '1']])")
self.assertEqual(repr(traceback), "[]")
self.assertEqual(
repr(inverse_traceback), "[Matrix([['4', '0'], ['0', '1']]), " +
"Matrix([['1', '0'], ['2', '1']]), " +
"Matrix([['1', '0'], ['0', '5/2']]), " +
"Matrix([['1', '7/4'], ['0', '1']])]")
matrix = Matrix([[0, 0, 0], [3, 2, 1]], fraction=True)
c_matrix, traceback, inverse_traceback = gaussian_elimination(
matrix, history=True, inverse_history=True)
self.assertEqual(repr(c_matrix),
"Matrix([['1', '2/3', '1/3'], ['0', '0', '0']])")
def test_inverse(self):
matrix = Matrix([[1, 2], [3, 4]], fraction=True)
inverted = inverse(matrix)
self.assertEqual(repr(inverted),
"Matrix([['-2', '1'], ['3/2', '-1/2']])")
self.assertEqual(repr(is_identity(matrix * inverted)), "True")
matrix = Matrix([[1, 1], [2, 2]], fraction=True)
inverted = inverse(matrix)
self.assertEqual(repr(inverted), "None")
def test_ref(self):
matrix = Matrix([[1, 2, 3], [4, 5, 6]], fraction=True)
c_matrix, traceback, inverse_traceback = ref(matrix)
self.assertEqual(repr(c_matrix),
"Matrix([['1', '2', '3'], ['0', '1', '2']])")
self.assertEqual(repr(traceback), "[]")
self.assertEqual(repr(inverse_traceback), "[]")
def test_el_matrix_add(self):
matrix = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
el_matrix = el_matrix_add(matrix, 1, 2, 2)
self.assertEqual(repr(el_matrix),
"Matrix([['1', '0', '0'], ['0', '1', '2'], ['0', '0', '1']])")
self.assertEqual(repr(el_matrix * matrix),
"Matrix([['1', '2', '3'], ['18', '21', '24'], ['7', '8', '9']])")
def test_permute_matrix(self):
matrix = Matrix([[1, 1, 1], [1, 1, 1], [1, 1, 1]])
permute = permute_matrix(matrix)
self.assertEqual(
repr(permute),
"Matrix([['1', '0', '0'], ['0', '1', '0'], ['0', '0', '1']])")
matrix = Matrix([[0, 1, 1], [1, 2, 1], [2, 7, 9]])
permute = permute_matrix(matrix)
self.assertEqual(
repr(permute),
"Matrix([['0', '1', '0'], ['1', '0', '0'], ['0', '0', '1']])")
matrix = fill_matrix(2, 3, 1)
with self.assertRaises(DimensionError) as c:
permute = permute_matrix(matrix)
self.assertTrue("Matrix must be a square matrix." in str(c.exception))
def test_rank(self):
matrix = Matrix([[1, 2, 3], [4, 5, 6]], fraction=True)
matrix_rank = rank(matrix)
self.assertEqual(repr(matrix_rank), "2")
matrix = fill_matrix(3, 3, 2)
matrix_rank = rank(matrix)
self.assertEqual(repr(matrix_rank), "1")
def test_lu_factorization(self):
matrix = Matrix([[2, 1], [6, 8]], fraction=True)
lower, upper = lu_factorization(matrix)
self.assertEqual(repr(lower), "Matrix([['1', '0'], ['3', '1']])")
self.assertEqual(repr(upper), "Matrix([['2', '1'], ['0', '5']])")
self.assertEqual(repr(lower * upper), repr(matrix))
matrix = fill_matrix(2, 3, 1)
with self.assertRaises(DimensionError) as c:
lower, upper = lu_factorization(matrix)
self.assertTrue("Matrix must be a square matrix." in str(c.exception))
def test_upper_triangular(self):
matrix = Matrix([[2, 1], [6, 8]], fraction=True)
upper, history, inverse_history = \
upper_triangular(matrix, history=True, inverse_history=True)
self.assertEqual(repr(upper), "Matrix([['2', '1'], ['0', '5']])")
self.assertEqual(repr(history), "[Matrix([['1', '0'], ['-3', '1']])]")
self.assertEqual(repr(inverse_history),
"[Matrix([['1', '0'], ['3', '1']])]")
matrix = fill_matrix(2, 3, 1)
with self.assertRaises(DimensionError) as c:
upper = upper_triangular(matrix)
self.assertTrue("Matrix must be a square matrix." in str(c.exception))
def test_lower_triangular(self):
matrix = Matrix([[2, 1], [6, 8]], fraction=True)
lower, history, inverse_history = \
lower_triangular(matrix, history=True, inverse_history=True)
self.assertEqual(repr(lower), "Matrix([['5/4', '0'], ['6', '8']])")
self.assertEqual(repr(history),
"[Matrix([['1', '-1/8'], ['0', '1']])]")
self.assertEqual(repr(inverse_history),
"[Matrix([['1', '1/8'], ['0', '1']])]")
matrix = fill_matrix(2, 3, 1)
with self.assertRaises(DimensionError) as c:
lower = lower_triangular(matrix)
self.assertTrue("Matrix must be a square matrix." in str(c.exception))
def test_ldlt_factorization(self):
matrix = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]], fraction=True)
lower, diag, lower_t = ldlt_factorization(matrix)
self.assertEqual(repr(lower), "None")
self.assertEqual(repr(diag), "None")
self.assertEqual(repr(lower_t), "None")
matrix = Matrix([[1, 2, 3], [2, 1, 4], [3, 4, 1]], fraction=True)
lower, diag, lower_t = ldlt_factorization(matrix)
self.assertEqual(
repr(lower),
"Matrix([['1', '0', '0'], ['2', '1', '0'], ['3', '2/3', '1']])")
self.assertEqual(
repr(diag),
"Matrix([['1', '0', '0'], ['0', '-3', '0'], ['0', '0', '-20/3']])")
self.assertEqual(
repr(lower_t),
"Matrix([['1', '2', '3'], ['0', '1', '2/3'], ['0', '0', '1']])")
self.assertEqual(repr(lower * diag * lower_t), repr(matrix))
matrix = fill_matrix(2, 3, 1)
with self.assertRaises(DimensionError) as c:
lower, diag, lower_t = ldlt_factorization(matrix)
self.assertTrue("Matrix must be a square matrix." in str(c.exception))
def test_ldu_factorization(self):
matrix = Matrix([[1, 5, 4], [3, 6, 4], [8, 2, 3]], fraction=True)
lower, diag, upper = ldu_factorization(matrix)
self.assertEqual(
repr(lower),
"Matrix([['1', '0', '0'], ['3', '1', '0'], ['8', '38/9', '1']])")
self.assertEqual(
repr(diag),
"Matrix([['1', '0', '0'], ['0', '-9', '0'], ['0', '0', '43/9']])")
self.assertEqual(
repr(upper),
"Matrix([['1', '5', '4'], ['0', '1', '8/9'], ['0', '0', '1']])")
self.assertEqual(repr(lower * diag * upper), repr(matrix))
matrix = fill_matrix(2, 3, 1)
with self.assertRaises(DimensionError) as c:
lower, diag, upper = ldu_factorization(matrix)
self.assertTrue("Matrix must be a square matrix." in str(c.exception))