scipy: BUG: linalg.sqrtm results different between version 1.11.1 and 1.11.2/1.11.3

Describe your issue.

There is a difference in the result of scipy.linalg.sqrtm between version 1.11.1 and the following versions (to date: 1.11.2 and 1.11.3) for specific matrices. In the following code example, the error when calculating the square root of the matrix is infinitesimal in 1.11.1, but gigantic in 1.11.2 and 1.11.3. It seems that sqrtm either produced a wrong result in earlier versions, or newer versions fail to calculate the square root correctly.

I could not create an example with a random matrix, which is why I made a repository with some data that produces the error: https://github.com/akug/mwe_scipy_sqrtm_bug

Thank you for your time and effort maintaining scipy, it’s a great library!

Reproducing Code Example

# See the repository at https://github.com/akug/mwe_scipy_sqrtm_bug for sample data
import numpy as np
from scipy.linalg import sqrtm

data = np.load("./sample_sqrtm_fails.npz")["array"]
out, error = sqrtm(data, disp=False)
print(error)  # error in 1.11.2 and 1.11.3 is about 2.3e+24, but in 1.11.1 is 2.1e-28

Error message

# There is no error message, it just produces different results between versions

SciPy/NumPy/Python version and system information

1.11.3 1.26.0 sys.version_info(major=3, minor=11, micro=5, releaselevel='final', serial=0)
Build Dependencies:
  blas:
    detection method: pkgconfig
    found: true
    include directory: /usr/local/include
    lib directory: /usr/local/lib
    name: openblas
    openblas configuration: USE_64BITINT= DYNAMIC_ARCH=1 DYNAMIC_OLDER= NO_CBLAS=
      NO_LAPACK= NO_LAPACKE= NO_AFFINITY=1 USE_OPENMP= HASWELL MAX_THREADS=2
    pc file directory: /usr/local/lib/pkgconfig
    version: 0.3.21.dev
  lapack:
    detection method: pkgconfig
    found: true
    include directory: /usr/local/include
    lib directory: /usr/local/lib
    name: openblas
    openblas configuration: USE_64BITINT= DYNAMIC_ARCH=1 DYNAMIC_OLDER= NO_CBLAS=
      NO_LAPACK= NO_LAPACKE= NO_AFFINITY=1 USE_OPENMP= HASWELL MAX_THREADS=2
    pc file directory: /usr/local/lib/pkgconfig
    version: 0.3.21.dev
  pybind11:
    detection method: config-tool
    include directory: unknown
    name: pybind11
    version: 2.11.0
Compilers:
  c:
    commands: cc
    linker: ld.bfd
    name: gcc
    version: 10.2.1
  c++:
    commands: c++
    linker: ld.bfd
    name: gcc
    version: 10.2.1
  cython:
    commands: cython
    linker: cython
    name: cython
    version: 0.29.36
  fortran:
    commands: gfortran
    linker: ld.bfd
    name: gcc
    version: 10.2.1
  pythran:
    include directory: ../../tmp/pip-build-env-358nkn7q/overlay/lib/python3.11/site-packages/pythran
    version: 0.14.0
Machine Information:
  build:
    cpu: x86_64
    endian: little
    family: x86_64
    system: linux
  cross-compiled: false
  host:
    cpu: x86_64
    endian: little
    family: x86_64
    system: linux
Python Information:
  path: /opt/python/cp311-cp311/bin/python
  version: '3.11'