Description
Description
Right now we assume the inputs to solve_triangular are always consistent with the settings passed to the function. For example, if one sets lower, we assume that the incoming matrix really is lower triangular. If you set unit_diag, we assume there are ones on the diag, and so on.
This isn't actually how the function works. If you set unit_diag for instead, the main diagonal is simply ignored in computation; the function doesn't care whether it literally is unit diagonal or not. This is useful when working with LU factors for example. Instead of storing L (lower with unit diagonal) and U (upper) separately, it is common to store LU = tril(L, k=-1) + triu(U). Then solve_triangular(LU, b, lower=True, unit_diagonal=True) is exactly equivalent to doing solve(L, b) -- no need rebuild the individual matrices.
At the moment the analytical gradients don't take this into account, so setting unit_diag=True on a non-unit-diagonal matrix will have non-zero diagonal sensitivites, which is wrong.
Gradients are also incorrect when trans != "N", because we have no special logic in SolveBase.L_op to handle the transpose argument (see #1229)