SciPy

scipy.linalg.sqrtm

scipy.linalg.sqrtm(A, disp=True, blocksize=64)[source]

Matrix square root.

Parameters:

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)

Returns:

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

References

[R91]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.

Examples

>>> 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.]])

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