`scipy.linalg._decomp:hessenberg`

source: /scipy/linalg/_decomp.py :1405

Signature

   def     hessenberg (    a    ,    calc_q    =  False   ,    overwrite_a    =  False   ,    check_finite    =  True     )

Summary

Compute Hessenberg form of a matrix.

Extended Summary

The Hessenberg decomposition is

A = Q H Q^H

where Q is unitary/orthogonal and H has only zero elements below the first sub-diagonal.

The documentation is written assuming array arguments are of specified "core" shapes. However, array argument(s) of this function may have additional "batch" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see linalg_batch for details. Note that calls with zero-size batches are unsupported and will raise a ValueError.

Parameters

a : (M, M) array_like: Matrix to bring into Hessenberg form.
calc_q : bool, optional: Whether to compute the transformation matrix. Default is False.
overwrite_a : bool, optional: Whether to overwrite a; may improve performance. Default is False.
check_finite : bool, optional: Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns

H : (M, M) ndarray: Hessenberg form of a.
Q : (M, M) ndarray: Unitary/orthogonal similarity transformation matrix A = Q H Q^H. Only returned if calc_q=True.

Examples

import numpy as np
from scipy.linalg import hessenberg
A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]])
H, Q = hessenberg(A, calc_q=True)

✓

✗

np.allclose(Q @ H @ Q.conj().T - A, np.zeros((4, 4)))

✓

Aliases

scipy.linalg.hessenberg