def compute_qr_factorization(mat: Matrix) -> (Matrix, Matrix):
# Do not overwrite original matrix
mat = mat.copy()
householders = [] # store householder transformations
iterations = min(mat.num_rows(), mat.num_cols())
for iteration in range(iterations):
col = mat.get_col(iteration)
# Zero out the entries below the diagonal
hh = Householder(col[iteration:])
householders.append((iteration, hh))
mat = hh.multiply_left(mat, pad_top=iteration)
# Accumulate the householder transformations
q_mat = Matrix.identity(mat.num_rows())
for iteration, hh in householders[::-1]:
q_mat = hh.multiply_left(q_mat, pad_top=iteration)
return (q_mat, mat)
def reduce_to_bidiagonal(
mat: Matrix) -> (Matrix, List[Householder], List[Householder]):
mat = mat.copy()
if mat.num_rows() != mat.num_cols():
raise ValueError("Matrix should be square")
iterations = mat.num_rows() - 1
acc_left = []
acc_right = []
for iteration in range(iterations):
# clear zeroes below diagonal
col = mat.get_col(iteration)[iteration:]
householder_left = Householder(col)
mat = householder_left.multiply_left(mat, pad_top=iteration)
acc_left.append(householder_left)
if iteration != iterations - 1:
# clear zeroes above superdiagonal
row = mat.get_row(iteration)[iteration + 1:]
householder_right = Householder(row)
mat = householder_right.multiply_right(mat, pad_top=iteration + 1)
acc_right.append(householder_right)
return mat, acc_left, acc_right