BUG: NumPy's `random` module should not be in the `scipy` namespace.

Describe your issue.

Currently, scipy.random is an alias for numpy.random:

In [12]: import numpy as np

In [13]: import scipy

In [14]: scipy.__version__
Out[14]: '1.8.0.dev0+1859.14341ea'

In [15]: scipy.random
Out[15]: <module 'numpy.random' from '/home/warren/mc39scipy/lib/python3.9/site-packages/numpy/random/__init__.py'>

In [16]: scipy.random is np.random
Out[16]: True

We have already deprecated other names in scipy that come from numpy, e.g.

In [17]: scipy.array([1, 2, 3])
<ipython-input-17-773c09c10413>:1: DeprecationWarning: scipy.array is deprecated and will be removed in SciPy 2.0.0, use numpy.array instead
  scipy.array([1, 2, 3])
Out[17]: array([1, 2, 3])

We should do the same for random, so a call such as the following generates a deprecation warning:

In [18]: scipy.random.randint(10, size=3)
Out[18]: array([8, 5, 5])

Reproducing Code Example

See above.

Error message

See above.

SciPy/NumPy/Python version information

1.8.0.dev0+1859.14341ea 1.21.2 sys.version_info(major=3, minor=9, micro=5, releaselevel=‘final’, serial=0)

[ilayn]

Not really an API break but actually fixes something that should have not happened anyways but just a missed star import. So it’s not really a big deal. And it didn’t create any noise so let’s close it and deal when it becomes an issue.

[WarrenWeckesser]

@andyfaff, according to the deprecation warning, the other numpy names are scheduled to be removed from SciPy 2.0.0. random should follow the same schedule.