def test_reduce_to_bidiagonal(self):
mat = Matrix.from_cols([[1, 2, 3], [4, 5, 6], [7, 8, 10]])
b, _, _ = reduce_to_bidiagonal(mat)
utils.assert_upper_triangular(b)
truncated = MatrixView.with_size(
b, (0, 1), (mat.num_rows() - 1, mat.num_cols() - 1)).to_matrix()
utils.assert_lower_triangular(truncated)
def test_lu(self):
matrix = Matrix.from_cols([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
mat_l, mat_u = compute_lu_factorization(matrix)
utils.assert_lower_triangular(mat_l)
utils.assert_upper_triangular(mat_u)
assert self.vector_all(utils.extract_diagonal(mat_l), 1)
product = mat_l.multiply(mat_u)
assert product.all_cols() == matrix.all_cols()
def test_lu_more_rows(self):
mat_l = Matrix.from_cols([[1, 2, 3, 4, 5], [0, 1, 2, 3, 4],
[0, 0, 1, 2, 3], [0, 0, 0, 1, 2],
[0, 0, 0, 0, 1]])
mat_u = Matrix.from_cols([[5, 1, 2, 3, 4], [0, 4, 3, 2, 1],
[0, 0, 2, 1, 0]])
matrix = mat_l.multiply(mat_u)
mat_l, mat_u = compute_lu_factorization(matrix)
# note LU factorization is not unique therefore we are not comparing L and U
utils.assert_lower_triangular(mat_l)
utils.assert_upper_triangular(mat_u)
assert self.vector_all(utils.extract_diagonal(mat_l), 1)
product = mat_l.multiply(mat_u)
assert product.all_cols() == matrix.all_cols()
def check_svd(self, u, s, v, mat):
utils.assert_orthonormal(u)
utils.assert_orthonormal(v)
utils.assert_lower_triangular(s)
utils.assert_upper_triangular(s)
diagonal = utils.extract_diagonal(s)
for i in range(len(diagonal) - 1):
assert diagonal[i] >= diagonal[i + 1]
for elem in diagonal:
assert elem >= 0
product = u.multiply(s).multiply(v.transpose())
product.print_full()
mat.print_full()
utils.assert_matrix_equal(product, mat)
def test_rectangular_triangular(self):
utils.assert_upper_triangular(
Matrix.from_cols([[4, 0], [1, 2], [3, 4]]))
def test_identity_triangular(self):
identity = Matrix.identity(3)
utils.assert_upper_triangular(identity)
utils.assert_lower_triangular(identity)
def test_upper_triangular(self):
mat = Matrix.from_cols([[1, 0, 0], [2, 3, 0], [4, 5, 6]])
utils.assert_upper_triangular(mat)
with pytest.raises(AssertionError):
utils.assert_upper_triangular(mat.transpose())