linalg._matfuncs_sqrtm

Matrix square root for general matrices and for upper triangular matrices.

This module exists to avoid cyclic imports.

Module Contents

Classes

SqrtmError()

Functions

_sqrtm_triu(T,blocksize=64) Matrix square root of an upper triangular matrix.
sqrtm(A,disp=True,blocksize=64) Matrix square root.
class SqrtmError
_sqrtm_triu(T, blocksize=64)

Matrix square root of an upper triangular matrix.

This is a helper function for sqrtm and logm.

T : (N, N) array_like upper triangular
Matrix whose square root to evaluate
blocksize : int, optional
If the blocksize is not degenerate with respect to the size of the input array, then use a blocked algorithm. (Default: 64)
sqrtm : (N, N) ndarray
Value of the sqrt function at T
[1]Edvin Deadman, Nicholas J. Higham, Rui Ralha (2013) “Blocked Schur Algorithms for Computing the Matrix Square Root, Lecture Notes in Computer Science, 7782. pp. 171-182.
sqrtm(A, disp=True, blocksize=64)

Matrix square root.

A : (N, N) array_like
Matrix whose square root to evaluate
disp : bool, optional
Print warning if error in the result is estimated large instead of returning estimated error. (Default: True)
blocksize : integer, optional
If the blocksize is not degenerate with respect to the size of the input array, then use a blocked algorithm. (Default: 64)
sqrtm : (N, N) ndarray
Value of the sqrt function at A
errest : float

(if disp == False)

Frobenius norm of the estimated error, ||err||_F / ||A||_F

[1]Edvin Deadman, Nicholas J. Higham, Rui Ralha (2013) “Blocked Schur Algorithms for Computing the Matrix Square Root, Lecture Notes in Computer Science, 7782. pp. 171-182.
>>> from scipy.linalg import sqrtm
>>> a = np.array([[1.0, 3.0], [1.0, 4.0]])
>>> r = sqrtm(a)
>>> r
array([[ 0.75592895,  1.13389342],
       [ 0.37796447,  1.88982237]])
>>> r.dot(r)
array([[ 1.,  3.],
       [ 1.,  4.]])