BUG: linalg.solve_{sylvester, continuous_lyapunov}: empty array support

[redha2404]

Reference issue

Check the boxes solve_sylvester and solve_continuous_lyapunov Linalg empty array support #20372

What does this implement/fix?

The functions now support empty array and return outputs of the same dtype of the non empty array
The function solve_sylvester now raises a value error if the shape of the inputs are not correct

Additional information

[ilayn]

Here you can write the following

    tdict = {'s': np.float32, 'd': np.float64, 'c': np.complex64, 'z': np.complex128}
    func = get_lapack_funcs(('trsyl',), arrays=(a, b, q))
    return np.empty(q.shape, dtype=tdict[func.typecode])

First line creates the mapping from lapack types to numpy types, second line searches for the suitable type given the arrays (uses an example array of 'trsyl' but can be anything). Third line uses the resulting lapack type to get the numpy type of q.

[redha2404]

Thanks. Done 👍