def test_bidiagonal_recreate_2(self):
mat = Matrix.from_cols([[1, 2, 3], [2, 5, 1], [-1, 3, -2]])
b, left, right = reduce_to_bidiagonal(mat)
for index, hh in list(enumerate(left))[::-1]:
b = hh.multiply_left(b, index)
for index, hh in list(enumerate(right))[::-1]:
b = hh.multiply_right(b, index + 1)
utils.assert_matrix_equal(mat, b)
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_householder_inverse(self):
vec = [5, 4, 3, 2, 1]
householder = Householder(vec)
householder_mat = householder.to_matrix()
product = householder_mat.multiply(householder_mat)
utils.assert_matrix_equal(product, Matrix.identity(5))
def test_householder_symmetric(self):
vec = [5, 4, 3, 2, 1]
householder = Householder(vec)
householder_mat = householder.to_matrix()
utils.assert_matrix_equal(householder_mat, householder_mat.transpose())
def test_givens_inverse(self):
givens = Givens(1, 1).to_matrix()
product = givens.transpose().multiply(givens)
utils.assert_matrix_equal(product, Matrix.identity(2))