Support generalized universal functions

Cupy does not offer generalized universal functions. I would like to discuss how should we proceed and implement this feature.

https://docs.scipy.org/doc/numpy/reference/c-api.generalized-ufuncs.html

TODOs

• Parse gufuncs signatures to retrieve the core dimensions.
• Modify core.pyx::ndarray::__array_ufunc__ to remove the signature check.
• Given the signature, modify _kernel.pyx::ufunc::__call__ to call the function sub-arraywise. Ufunc class relies on elementwise kernels when calling _get_ufunc_kernel. GUfuncs can also call kernels operating on regular vectors.
• Convert cupy inner1d, matmat, vecmat, matvec, matmul, outer_inner to actual gufuncs
• Add features such as axes, order, etc.

List of numpy gufuncs (thanks to @asi1024)

(n?,k),(k,m?)->(n?,m?)
         matmul
(m,m)->(),()
         slogdet
(m,m)->()
         det
(m,m)->(m),(m,m)
         eigh_lo
         eigh_up
         eig
(m,m)->(m)
         eigvalsh_up
         eigvalsh_lo
         eigvals
(m,m),(m,n)->(m,n)
         solve
(m,m),(m)->(m)
         solve1
(m, m)->(m, m)
         inv
(m,m)->(m,m)
         cholesky_lo
(m,n)->(m)
         svd_m
(m,n)->(n)
         svd_n
(m,n)->(m,m),(m),(m,n)
         svd_m_s
(m,n)->(m,n),(n),(n,n)
         svd_n_s
(m,n)->(m,m),(m),(n,n)
         svd_m_f
(m,n)->(m,m),(n),(n,n)
         svd_n_f
(m,n),(m,nrhs),()->(n,nrhs),(nrhs),(),(m)
         lstsq_m
(m,n),(m,nrhs),()->(n,nrhs),(nrhs),(),(n)
         lstsq_n

[rgommers]

+1 for this feature:)

Actually there’s people on the NumPy team who know much more about this than I do - I’ll ping @mattip and @seberg here for input.

[rushabh-v]

I am interested to work on this project under GSoC '20 and I am currently writing the proposal for it. Understood all the concepts quite nicely accept the feature order? Can you please elaborate a bit more on that @emcastillo ?