Description

sq_rsp(...) is an ancient diagonalizer function from Psi3 with many issues. While its innards could be improved, the function signature is horrid. It should be deprecated and replaced with something better.
Stemming from the awful interface, users of sq_rsp(...) never check if the diagonalization failed, because they cannot. This is now rectified by adding failure checks wherever the new DSYEV wrappers are called.
Checks against non-square matrices are also added where there is both a row and column count at the call site.

Some of the call sites would be dfocc territory, this PR does not include them to avoid conflicts with the dfocc overhaul.
This is another shard of the #2642 mega-PR that can be merged after PR #2678 and #2738 are in.

Todos

• Implement two new wrapper functions around DSYEV to replace sq_rsp(...) with. The new wrappers have a much cleaner interface, and no longer require the allocation of an eigenvector array if the caller only needs eigenvalues. They also no longer swallow the return value of DSYEV, in fact their return value is marked as [[nodiscard]]. In short, checking for diagonalization failure went from impossible to mandatory.
  Please note that unlike sq_rsp(...), the new functions do not take a "tolarence" value, but this is actually a null change as that parameter has been set-but-unused in sq_rsp(...) since ~forever ago when sq_rsp(...) switched to calling DSYEV internally.
• Replace sq_rsp(...) calls in mcscf (mcscf::SCF::energy and mcscf::MatrixBase::diagonalize) with new wrapper. Add checks for diagonalization failure and guard against non-square matrices.
• Replace sq_rsp(...) calls in detci (detci/h0block.cc, detci/sem.cc and detci/sem_test.cc) with new wrapper. Add checks for diagonalization failure.
• Replace sq_rsp(...) call in libmints/matrix.cc (Matrix::diagonalize) with new wrapper. Add checks for diagonalization failure. Add a sanity checks for non-square matrices and illegal values of "diagonalization order".
• Replace sq_rsp(...) calls in ccenergy (ccenergy/d1diag.cc, ccenergy/d2diag.cc and ccenergy/new_d1diag.cc) with new wrapper. Add checks for diagonalization failure. This allows the removal of the eigenvector array, and the code that allocates/deallocates it.
• Replace sq_rsp(...) calls in the libqt Davidson solver with new wrapper. Add checks for diagonalization failure.
• Replace sq_rsp(...) call in the RHF and ROHF stability checks with new wrapper. Add checks for diagonalization failure.
• Replace sq_rsp(...) calls in libsapt_solver/sapt2.cc with new wrapper. Add checks for diagonalization failure.

Questions

• Is libciomr a good place for the new wrappers to live in? The one they are replacing is there, so it seemed like as good of a place as any.

Checklist

• No new features
• 503/503 ctests are passing

Status

• Ready for review
• Ready for merge