batched - dense: Testing and fixing Serial QR

[lucbv]

The serial QR algorithms does not have unit-tests and is failing for non square matrices. See issue #2328.
This first commit fixes the issue with rectangular matrices and adds a basic test for that use case.
Next will work on adding a test that exercises the interfaces on multiple matrices of different sizes within a parallel_for. Finally equivalent tests will be added for the square case as well.

Tasks:

• analytical test on rectangular matrix (SerialQR, ApplyQ, FormQ, Q*Q^t=I)
  • SerialQR
  • ApplyQ
  • FormQ
• multiple variable size rectangular matrices (same API as above)
  • SerialQR
  • ApplyQ
  • FormQ
• analytical test on square matrix
  • SerialQR
  • ApplyQ
  • FormQ
• multiple variable size square matrices
  • SerialQR
  • ApplyQ
  • FormQ

[cwpearson]

edit - duplicated comment

[yasahi-hpc]

I requested small changes. I also have three additional points.

1. It seems that Side::Right specialization of KokkosBatched::SerialApplyQ is not tested. Is it possible to add a test case for this specialization?
2. Could you also consider to add docstrings in APIs under KokkosBatched_ApplyQ_Decl.hpp and KokkosBatched_QR_Decl.hpp? It would be helpful to generate API reference
3. Could you also add static_assertion to check the template argument is valid, e.g., check if ArgTrans is NoTranspose or Transpose.

[lucbv]

I addressed 1. and 3. however for the documentation I will delay until we have it setup in the repo for batched algorithms.
This should not take too long as I am in the process of writing the main page for that and then we will be able to add the APIs one by one as we get to them.

[yasahi-hpc]

LGTM.
As for the documentation, I can contribute if needed.
Let me know if you decided how to implement.

[ndellingwood]

@lucbv some of these changes were incompatible with usage in Trilinos (intrepid2), this is showing in the nightly integration builds:

17:53:53 [ 66%] Building CXX object packages/intrepid2/unit-test/Projection/CMakeFiles/Intrepid2_unit-test_Projection_test_project_fields_Serial_DOUBLE.dir/test_project_fields_Serial_DOUBLE.cpp.o
17:53:56 In file included from /home/jenkins/blake-new/workspace/KokkosEco_Trilinos_Blake_OneAPI2023_2_0_ICPX_Serial/Build/packages/intrepid2/unit-test/Projection/test_project_fields_Serial_DOUBLE.cpp:15:
17:53:56 In file included from /home/jenkins/blake-new/workspace/KokkosEco_Trilinos_Blake_OneAPI2023_2_0_ICPX_Serial/Trilinos/packages/intrepid2/unit-test/Projection/test_project_fields.hpp:34:
17:53:56 /home/jenkins/blake-new/workspace/KokkosEco_Trilinos_Blake_OneAPI2023_2_0_ICPX_Serial/Trilinos/packages/intrepid2/src/Projection/Intrepid2_ProjectionTools.hpp:527:9: error: no member named 'SerialQR_Internal' in namespace 'KokkosBatched'; did you mean 'KokkosBatched::Impl::SerialQR_Internal'?
17:53:56         KokkosBatched::SerialQR_Internal::invoke(A0_host.extent(0), A0_host.extent(1),
17:53:56         ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
17:53:56         KokkosBatched::Impl::SerialQR_Internal
17:53:56 /home/jenkins/blake-new/workspace/KokkosEco_Trilinos_Blake_OneAPI2023_2_0_ICPX_Serial/Trilinos/kokkos-kernels/batched/dense/impl/KokkosBatched_QR_Serial_Internal.hpp:34:8: note: 'KokkosBatched::Impl::SerialQR_Internal' declared here
17:53:56 struct SerialQR_Internal {
17:53:56        ^
17:53:56 In file included from /home/jenkins/blake-new/workspace/KokkosEco_Trilinos_Blake_OneAPI2023_2_0_ICPX_Serial/Build/packages/intrepid2/unit-test/Projection/test_project_fields_Serial_DOUBLE.cpp:15:
17:53:56 In file included from /home/jenkins/blake-new/workspace/KokkosEco_Trilinos_Blake_OneAPI2023_2_0_ICPX_Serial/Trilinos/packages/intrepid2/unit-test/Projection/test_project_fields.hpp:34:
17:53:56 /home/jenkins/blake-new/workspace/KokkosEco_Trilinos_Blake_OneAPI2023_2_0_ICPX_Serial/Trilinos/packages/intrepid2/src/Projection/Intrepid2_ProjectionTools.hpp:583:11: error: no member named 'SerialQR_Internal' in namespace 'KokkosBatched'; did you mean 'KokkosBatched::Impl::SerialQR_Internal'?
17:53:56           KokkosBatched::SerialQR_Internal::invoke(A.extent(0), A.extent(1),
17:53:56           ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
17:53:56           KokkosBatched::Impl::SerialQR_Internal
17:53:56 /home/jenkins/blake-new/workspace/KokkosEco_Trilinos_Blake_OneAPI2023_2_0_ICPX_Serial/Trilinos/kokkos-kernels/batched/dense/impl/KokkosBatched_QR_Serial_Internal.hpp:34:8: note: 'KokkosBatched::Impl::SerialQR_Internal' declared here
17:53:56 struct SerialQR_Internal {

Should I be able to add a guard on version and include updates to include the Impl namespace to resolve?

[ndellingwood]

Yeah, simple namespace update was all that was needed, PR up trilinos/Trilinos#13876