# jax.scipy.linalg.sqrtm#

jax.scipy.linalg.sqrtm(A, blocksize=1)[source]#

Matrix square root.

LAX-backend implementation of `scipy.linalg._matfuncs_sqrtm.sqrtm()`.

This differs from `scipy.linalg.sqrtm` in that the return type of `jax.scipy.linalg.sqrtm` is always `complex64` for 32-bit input, and `complex128` for 64-bit input.

This function implements the complex Schur method described in [A]. It does not use recursive blocking to speed up computations as a Sylvester Equation solver is not available yet in JAX.

[A] Björck, Å., & Hammarling, S. (1983).

“A Schur method for the square root of a matrix”. Linear algebra and its applications, 52, 127-140.

Original docstring below.

Parameters:
• A ((N, N) array_like) – Matrix whose square root to evaluate

• 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)

Return type:

`Array`

Returns:

• sqrtm ((N, N) ndarray) – Value of the sqrt function at A. The dtype is float or complex. The precision (data size) is determined based on the precision of input A. When the dtype is float, the precision is the same as A. When the dtype is complex, the precision is double that of A. The precision might be clipped by each dtype precision range.

• errest (float) – (if disp == False)

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

References