def decompose(self, matrix):
orthogonal_matrix = MatrixFactory.identity(size=matrix.row_count)
for j in range(matrix.column_count - 1):
e = numpy.zeros((matrix.column_count - j, 1))
e[0, 0] = 1
e = Matrix(e)
h = self.create_householder_reflection(
matrix.get_column_vector(j, j), e)
h = MatrixFactory.build_block_matrix(
d=h,
row_count=orthogonal_matrix.row_count,
col_count=orthogonal_matrix.row_count)
for i in range(j):
h.matrix_vectors[i, i] = 1
matrix = h * matrix
orthogonal_matrix = h * orthogonal_matrix
return orthogonal_matrix.transpose(), matrix
def test_create_identity(self):
for matrix in MatrixCollection.complete:
matrix = Matrix(matrix)
self.assertEqual(matrix,
MatrixFactory.identity(matrix.row_count) * matrix)