Description

A number of PRs have gone in recently to handle corner cases concerning size 0 inputs that were discovered through the new autodiff test framework, authored in the most part by me.

A couple of comment #1452 ( #1452 (comment) and #1452 (comment)) made me look again at these corner cases, and I realised that things could be handled a bit better.

In particular:

• the current checks mishandle matrices of size 0 x N (or N x 0), as we may return an empty square matrix instead of a rectangular one: affects mdivide_left_ldlt, mdivide_right_ldlt and matrix_exp_multiply
• we should check for the input matrix being square before returning anything: affects matrix_exp_pade and scale_matrix_exp_multiply, for which we currently we return an empty matrix when we should instead throw
• for trace_inv_quad_form_ldlt if the input matrix is 0xN we should return 0, but we currently throw