Ifpack2_BlockTriDiContainer_impl.hpp

// @HEADER
// *****************************************************************************
//       Ifpack2: Templated Object-Oriented Algebraic Preconditioner Package
//
// Copyright 2009 NTESS and the Ifpack2 contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER

#ifndef IFPACK2_BLOCKTRIDICONTAINER_IMPL_HPP
#define IFPACK2_BLOCKTRIDICONTAINER_IMPL_HPP

// #define IFPACK2_BLOCKTRIDICONTAINER_WRITE_MM
// #define IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF

#include <Teuchos_Details_MpiTypeTraits.hpp>

#include <Tpetra_Details_extractMpiCommFromTeuchos.hpp>
#include <Tpetra_Distributor.hpp>
#include <Tpetra_BlockMultiVector.hpp>

#if KOKKOS_VERSION >= 40799
#include <KokkosKernels_ArithTraits.hpp>
#else
#include <Kokkos_ArithTraits.hpp>
#endif
#include <KokkosBatched_Util.hpp>
#include <KokkosBatched_Vector.hpp>
#include <KokkosBatched_Copy_Decl.hpp>
#include <KokkosBatched_Copy_Impl.hpp>
#include <KokkosBatched_AddRadial_Decl.hpp>
#include <KokkosBatched_AddRadial_Impl.hpp>
#include <KokkosBatched_SetIdentity_Decl.hpp>
#include <KokkosBatched_SetIdentity_Impl.hpp>
#include <KokkosBatched_Gemm_Decl.hpp>
#include <KokkosBatched_Gemm_Serial_Impl.hpp>
#include <KokkosBatched_Gemm_Team_Impl.hpp>
#include <KokkosBatched_Gemv_Decl.hpp>
#include <KokkosBatched_Gemv_Team_Impl.hpp>
#include <KokkosBatched_Trsm_Decl.hpp>
#include <KokkosBatched_Trsm_Serial_Impl.hpp>
#include <KokkosBatched_Trsm_Team_Impl.hpp>
#include <KokkosBatched_Trsv_Decl.hpp>
#include <KokkosBatched_Trsv_Serial_Impl.hpp>
#include <KokkosBatched_Trsv_Team_Impl.hpp>
#include <KokkosBatched_LU_Decl.hpp>
#include <KokkosBatched_LU_Serial_Impl.hpp>
#include <KokkosBatched_LU_Team_Impl.hpp>

#include <KokkosBlas1_nrm1.hpp>
#include <KokkosBlas1_nrm2.hpp>

#include <memory>

#include "Ifpack2_BlockHelper.hpp"
#include "Ifpack2_BlockComputeResidualVector.hpp"
#include "Ifpack2_BlockComputeResidualAndSolve.hpp"

// need to interface this into cmake variable (or only use this flag when it is necessary)
// #define IFPACK2_BLOCKTRIDICONTAINER_ENABLE_PROFILE
// #undef  IFPACK2_BLOCKTRIDICONTAINER_ENABLE_PROFILE
#if defined(KOKKOS_ENABLE_CUDA) && defined(IFPACK2_BLOCKTRIDICONTAINER_ENABLE_PROFILE)
#include "cuda_profiler_api.h"
#endif

// I am not 100% sure about the mpi 3 on cuda
#if MPI_VERSION >= 3
#define IFPACK2_BLOCKTRIDICONTAINER_USE_MPI_3
#endif

// ::: Experiments :::
// define either pinned memory or cudamemory for mpi
// if both macros are disabled, it will use tpetra memory space which is uvm space for cuda
// if defined, this use pinned memory instead of device pointer
// by default, we enable pinned memory
#define IFPACK2_BLOCKTRIDICONTAINER_USE_PINNED_MEMORY_FOR_MPI
// #define IFPACK2_BLOCKTRIDICONTAINER_USE_CUDA_MEMORY_FOR_MPI

// if defined, all views are allocated on cuda space intead of cuda uvm space
#define IFPACK2_BLOCKTRIDICONTAINER_USE_CUDA_SPACE

// if defined, btdm_scalar_type is used (if impl_scala_type is double, btdm_scalar_type is float)
#if defined(HAVE_IFPACK2_BLOCKTRIDICONTAINER_SMALL_SCALAR)
#define IFPACK2_BLOCKTRIDICONTAINER_USE_SMALL_SCALAR_FOR_BLOCKTRIDIAG
#endif

// if defined, it uses multiple execution spaces
#define IFPACK2_BLOCKTRIDICONTAINER_USE_EXEC_SPACE_INSTANCES

namespace Ifpack2 {

namespace BlockTriDiContainerDetails {

namespace KB = KokkosBatched;

using do_not_initialize_tag = Kokkos::ViewAllocateWithoutInitializing;

template <typename MemoryTraitsType, Kokkos::MemoryTraitsFlags flag>
using MemoryTraits = Kokkos::MemoryTraits<MemoryTraitsType::is_unmanaged |
                                          MemoryTraitsType::is_random_access |
                                          flag>;

template <typename ViewType>
using Unmanaged = Kokkos::View<typename ViewType::data_type,
                               typename ViewType::array_layout,
                               typename ViewType::device_type,
                               MemoryTraits<typename ViewType::memory_traits, Kokkos::Unmanaged>>;
template <typename ViewType>
using Atomic = Kokkos::View<typename ViewType::data_type,
                            typename ViewType::array_layout,
                            typename ViewType::device_type,
                            MemoryTraits<typename ViewType::memory_traits, Kokkos::Atomic>>;
template <typename ViewType>
using Const = Kokkos::View<typename ViewType::const_data_type,
                           typename ViewType::array_layout,
                           typename ViewType::device_type,
                           typename ViewType::memory_traits>;
template <typename ViewType>
using ConstUnmanaged = Const<Unmanaged<ViewType>>;

template <typename ViewType>
using AtomicUnmanaged = Atomic<Unmanaged<ViewType>>;

template <typename ViewType>
using Unmanaged = Kokkos::View<typename ViewType::data_type,
                               typename ViewType::array_layout,
                               typename ViewType::device_type,
                               MemoryTraits<typename ViewType::memory_traits, Kokkos::Unmanaged>>;

template <typename ViewType>
using Scratch = Kokkos::View<typename ViewType::data_type,
                             typename ViewType::array_layout,
                             typename ViewType::execution_space::scratch_memory_space,
                             MemoryTraits<typename ViewType::memory_traits, Kokkos::Unmanaged>>;

template <typename T>
struct BlockTridiagScalarType {
  typedef T type;
};
#if defined(IFPACK2_BLOCKTRIDICONTAINER_USE_SMALL_SCALAR_FOR_BLOCKTRIDIAG)
template <>
struct BlockTridiagScalarType<double> {
  typedef float type;
};
// template<> struct SmallScalarType<Kokkos::complex<double> > { typedef Kokkos::complex<float> type; };
#endif

#if defined(KOKKOS_ENABLE_CUDA) && defined(IFPACK2_BLOCKTRIDICONTAINER_ENABLE_PROFILE)
#define IFPACK2_BLOCKTRIDICONTAINER_PROFILER_REGION_BEGIN \
  KOKKOS_IMPL_CUDA_SAFE_CALL(cudaProfilerStart());

#define IFPACK2_BLOCKTRIDICONTAINER_PROFILER_REGION_END \
  { KOKKOS_IMPL_CUDA_SAFE_CALL(cudaProfilerStop()); }
#else
#define IFPACK2_BLOCKTRIDICONTAINER_PROFILER_REGION_BEGIN
#define IFPACK2_BLOCKTRIDICONTAINER_PROFILER_REGION_END
#endif

template <typename MatrixType>
typename Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_import_type>
createBlockCrsTpetraImporter(const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_row_matrix_type> &A) {
  IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::CreateBlockCrsTpetraImporter", CreateBlockCrsTpetraImporter);
  using impl_type             = BlockHelperDetails::ImplType<MatrixType>;
  using tpetra_map_type       = typename impl_type::tpetra_map_type;
  using tpetra_mv_type        = typename impl_type::tpetra_block_multivector_type;
  using tpetra_import_type    = typename impl_type::tpetra_import_type;
  using crs_matrix_type       = typename impl_type::tpetra_crs_matrix_type;
  using block_crs_matrix_type = typename impl_type::tpetra_block_crs_matrix_type;

  auto A_crs  = Teuchos::rcp_dynamic_cast<const crs_matrix_type>(A);
  auto A_bcrs = Teuchos::rcp_dynamic_cast<const block_crs_matrix_type>(A);

  bool hasBlockCrsMatrix = !A_bcrs.is_null();

  // This is OK here to use the graph of the A_crs matrix and a block size of 1
  const auto g = hasBlockCrsMatrix ? A_bcrs->getCrsGraph() : *(A_crs->getCrsGraph());  // tpetra crs graph object

  const auto blocksize = hasBlockCrsMatrix ? A_bcrs->getBlockSize() : 1;
  const auto src       = Teuchos::rcp(new tpetra_map_type(tpetra_mv_type::makePointMap(*g.getDomainMap(), blocksize)));
  const auto tgt       = Teuchos::rcp(new tpetra_map_type(tpetra_mv_type::makePointMap(*g.getColMap(), blocksize)));
  IFPACK2_BLOCKHELPER_TIMER_FENCE(typename BlockHelperDetails::ImplType<MatrixType>::execution_space)
  return Teuchos::rcp(new tpetra_import_type(src, tgt));
}

// Partial replacement for forward-mode MultiVector::doImport.
// Permits overlapped communication and computation, but also supports sync'ed.
// I'm finding that overlapped comm/comp can give quite poor performance on some
// platforms, so we can't just use it straightforwardly always.

template <typename MatrixType>
struct AsyncableImport {
 public:
  using impl_type = BlockHelperDetails::ImplType<MatrixType>;

 private:
#if !defined(HAVE_IFPACK2_MPI)
  typedef int MPI_Request;
  typedef int MPI_Comm;
#endif
  using scalar_type = typename impl_type::scalar_type;

  static int isend(const MPI_Comm comm, const char *buf, int count, int dest, int tag, MPI_Request *ireq) {
#ifdef HAVE_IFPACK2_MPI
    MPI_Request ureq;
    int ret = MPI_Isend(const_cast<char *>(buf), count, MPI_CHAR, dest, tag, comm, ireq == NULL ? &ureq : ireq);
    if (ireq == NULL) MPI_Request_free(&ureq);
    return ret;
#else
    return 0;
#endif
  }

  static int irecv(const MPI_Comm comm, char *buf, int count, int src, int tag, MPI_Request *ireq) {
#ifdef HAVE_IFPACK2_MPI
    MPI_Request ureq;
    int ret = MPI_Irecv(buf, count, MPI_CHAR, src, tag, comm, ireq == NULL ? &ureq : ireq);
    if (ireq == NULL) MPI_Request_free(&ureq);
    return ret;
#else
    return 0;
#endif
  }

  static int waitany(int count, MPI_Request *reqs, int *index) {
#ifdef HAVE_IFPACK2_MPI
    return MPI_Waitany(count, reqs, index, MPI_STATUS_IGNORE);
#else
    return 0;
#endif
  }

  static int waitall(int count, MPI_Request *reqs) {
#ifdef HAVE_IFPACK2_MPI
    return MPI_Waitall(count, reqs, MPI_STATUS_IGNORE);
#else
    return 0;
#endif
  }

 public:
  using tpetra_map_type    = typename impl_type::tpetra_map_type;
  using tpetra_import_type = typename impl_type::tpetra_import_type;

  using local_ordinal_type  = typename impl_type::local_ordinal_type;
  using global_ordinal_type = typename impl_type::global_ordinal_type;
  using size_type           = typename impl_type::size_type;
  using impl_scalar_type    = typename impl_type::impl_scalar_type;

  using int_1d_view_host                = Kokkos::View<int *, Kokkos::HostSpace>;
  using local_ordinal_type_1d_view_host = Kokkos::View<local_ordinal_type *, Kokkos::HostSpace>;

  using execution_space            = typename impl_type::execution_space;
  using memory_space               = typename impl_type::memory_space;
  using local_ordinal_type_1d_view = typename impl_type::local_ordinal_type_1d_view;
  using size_type_1d_view          = typename impl_type::size_type_1d_view;
  using size_type_1d_view_host     = Kokkos::View<size_type *, Kokkos::HostSpace>;

#if defined(KOKKOS_ENABLE_CUDA)
  using impl_scalar_type_1d_view =
      typename std::conditional<std::is_same<execution_space, Kokkos::Cuda>::value,
#if defined(IFPACK2_BLOCKTRIDICONTAINER_USE_PINNED_MEMORY_FOR_MPI)
                                Kokkos::View<impl_scalar_type *, Kokkos::CudaHostPinnedSpace>,
#elif defined(IFPACK2_BLOCKTRIDICONTAINER_USE_CUDA_MEMORY_FOR_MPI)
                                Kokkos::View<impl_scalar_type *, Kokkos::CudaSpace>,
#else   // no experimental macros are defined
                                typename impl_type::impl_scalar_type_1d_view,
#endif  
                                typename impl_type::impl_scalar_type_1d_view>::type;
#else
  using impl_scalar_type_1d_view = typename impl_type::impl_scalar_type_1d_view;
#endif
  using impl_scalar_type_1d_view_host   = Kokkos::View<impl_scalar_type *, Kokkos::HostSpace>;
  using impl_scalar_type_2d_view        = typename impl_type::impl_scalar_type_2d_view;
  using impl_scalar_type_2d_view_tpetra = typename impl_type::impl_scalar_type_2d_view_tpetra;

#ifdef HAVE_IFPACK2_MPI
  MPI_Comm comm;
#endif

  impl_scalar_type_2d_view_tpetra remote_multivector;
  local_ordinal_type blocksize;

  template <typename T>
  struct SendRecvPair {
    T send, recv;
  };

  // (s)end and (r)eceive data:
  SendRecvPair<int_1d_view_host> pids;                      // mpi ranks
  SendRecvPair<std::vector<MPI_Request>> reqs;              // MPI_Request is pointer, cannot use kokkos view
  SendRecvPair<size_type_1d_view> offset;                   // offsets to local id list and data buffer
  SendRecvPair<size_type_1d_view_host> offset_host;         // offsets to local id list and data buffer
  SendRecvPair<local_ordinal_type_1d_view> lids;            // local id list
  SendRecvPair<impl_scalar_type_1d_view> buffer;            // data buffer
  SendRecvPair<impl_scalar_type_1d_view_host> buffer_host;  // data buffer

  local_ordinal_type_1d_view dm2cm;  // permutation

#if defined(KOKKOS_ENABLE_CUDA) || defined(KOKKOS_ENABLE_HIP) || defined(KOKKOS_ENABLE_SYCL)
  using exec_instance_1d_std_vector = std::vector<execution_space>;
  exec_instance_1d_std_vector exec_instances;
#endif

  // for cuda
 public:
  void setOffsetValues(const Teuchos::ArrayView<const size_t> &lens,
                       const size_type_1d_view &offs) {
    // wrap lens to kokkos view and deep copy to device
    Kokkos::View<size_t *, Kokkos::HostSpace> lens_host(const_cast<size_t *>(lens.getRawPtr()), lens.size());
    const auto lens_device = Kokkos::create_mirror_view_and_copy(memory_space(), lens_host);

    // exclusive scan
    const Kokkos::RangePolicy<execution_space> policy(0, offs.extent(0));
    const local_ordinal_type lens_size = lens_device.extent(0);
    Kokkos::parallel_scan(
        "AsyncableImport::RangePolicy::setOffsetValues",
        policy, KOKKOS_LAMBDA(const local_ordinal_type &i, size_type &update, const bool &final) {
          if (final)
            offs(i) = update;
          update += (i < lens_size ? lens_device[i] : 0);
        });
  }

  void setOffsetValuesHost(const Teuchos::ArrayView<const size_t> &lens,
                           const size_type_1d_view_host &offs) {
    // wrap lens to kokkos view and deep copy to device
    Kokkos::View<size_t *, Kokkos::HostSpace> lens_host(const_cast<size_t *>(lens.getRawPtr()), lens.size());
    const auto lens_device = Kokkos::create_mirror_view_and_copy(memory_space(), lens_host);

    // exclusive scan
    offs(0) = 0;
    for (local_ordinal_type i = 1, iend = offs.extent(0); i < iend; ++i) {
      offs(i) = offs(i - 1) + lens[i - 1];
    }
  }

 private:
  void createMpiRequests(const tpetra_import_type &import) {
    Tpetra::Distributor &distributor = import.getDistributor();

    // copy pids from distributor
    const auto pids_from = distributor.getProcsFrom();
    pids.recv            = int_1d_view_host(do_not_initialize_tag("pids recv"), pids_from.size());
    memcpy(pids.recv.data(), pids_from.getRawPtr(), sizeof(int) * pids.recv.extent(0));

    const auto pids_to = distributor.getProcsTo();
    pids.send          = int_1d_view_host(do_not_initialize_tag("pids send"), pids_to.size());
    memcpy(pids.send.data(), pids_to.getRawPtr(), sizeof(int) * pids.send.extent(0));

    // mpi requests
    reqs.recv.resize(pids.recv.extent(0));
    memset(reqs.recv.data(), 0, reqs.recv.size() * sizeof(MPI_Request));
    reqs.send.resize(pids.send.extent(0));
    memset(reqs.send.data(), 0, reqs.send.size() * sizeof(MPI_Request));

    // construct offsets
#if 0
        const auto lengths_to = distributor.getLengthsTo();
        offset.send = size_type_1d_view(do_not_initialize_tag("offset send"), lengths_to.size() + 1);

        const auto lengths_from = distributor.getLengthsFrom();
        offset.recv = size_type_1d_view(do_not_initialize_tag("offset recv"), lengths_from.size() + 1);

        setOffsetValues(lengths_to,   offset.send);
        offset_host.send = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), offset.send);

        setOffsetValues(lengths_from, offset.recv);
        offset_host.recv = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), offset.recv);
#else
    const auto lengths_to = distributor.getLengthsTo();
    offset_host.send      = size_type_1d_view_host(do_not_initialize_tag("offset send"), lengths_to.size() + 1);

    const auto lengths_from = distributor.getLengthsFrom();
    offset_host.recv        = size_type_1d_view_host(do_not_initialize_tag("offset recv"), lengths_from.size() + 1);

    setOffsetValuesHost(lengths_to, offset_host.send);
    // offset.send = Kokkos::create_mirror_view_and_copy(memory_space(), offset_host.send);

    setOffsetValuesHost(lengths_from, offset_host.recv);
    // offset.recv = Kokkos::create_mirror_view_and_copy(memory_space(), offset_host.recv);
#endif
  }

  void createSendRecvIDs(const tpetra_import_type &import) {
    // For each remote PID, the list of LIDs to receive.
    const auto remote_lids = import.getRemoteLIDs();
    const local_ordinal_type_1d_view_host
        remote_lids_view_host(const_cast<local_ordinal_type *>(remote_lids.getRawPtr()), remote_lids.size());
    lids.recv = local_ordinal_type_1d_view(do_not_initialize_tag("lids recv"), remote_lids.size());
    Kokkos::deep_copy(lids.recv, remote_lids_view_host);

    // For each export PID, the list of LIDs to send.
    auto epids = import.getExportPIDs();
    auto elids = import.getExportLIDs();
    TEUCHOS_ASSERT(epids.size() == elids.size());
    lids.send           = local_ordinal_type_1d_view(do_not_initialize_tag("lids send"), elids.size());
    auto lids_send_host = Kokkos::create_mirror_view(lids.send);

    // naive search (not sure if pids or epids are sorted)
    for (local_ordinal_type cnt = 0, i = 0, iend = pids.send.extent(0); i < iend; ++i) {
      const auto pid_send_value = pids.send[i];
      for (local_ordinal_type j = 0, jend = epids.size(); j < jend; ++j)
        if (epids[j] == pid_send_value) lids_send_host[cnt++] = elids[j];
      TEUCHOS_ASSERT(static_cast<size_t>(cnt) == offset_host.send[i + 1]);
    }
    Kokkos::deep_copy(lids.send, lids_send_host);
  }

  void createExecutionSpaceInstances() {
#if defined(KOKKOS_ENABLE_CUDA) || defined(KOKKOS_ENABLE_HIP) || defined(KOKKOS_ENABLE_SYCL)
    // The following line creates 8 streams:
#if KOKKOS_VERSION >= 40699
    exec_instances =
        Kokkos::Experimental::partition_space(execution_space(), std::vector<int>(8, 1));
#else
    exec_instances =
        Kokkos::Experimental::partition_space(execution_space(), 1, 1, 1, 1, 1, 1, 1, 1);
#endif
#endif
  }

 public:
  // for cuda, all tag types are public
  struct ToBuffer {};
  struct ToMultiVector {};

  AsyncableImport(const Teuchos::RCP<const tpetra_map_type> &src_map,
                  const Teuchos::RCP<const tpetra_map_type> &tgt_map,
                  const local_ordinal_type blocksize_,
                  const local_ordinal_type_1d_view dm2cm_) {
    blocksize = blocksize_;
    dm2cm     = dm2cm_;

#ifdef HAVE_IFPACK2_MPI
    comm = Tpetra::Details::extractMpiCommFromTeuchos(*tgt_map->getComm());
#endif
    const tpetra_import_type import(src_map, tgt_map);

    createMpiRequests(import);
    createSendRecvIDs(import);
    createExecutionSpaceInstances();
  }

  void createDataBuffer(const local_ordinal_type &num_vectors) {
    const size_type extent_0 = lids.recv.extent(0) * blocksize;
    const size_type extent_1 = num_vectors;
    if (remote_multivector.extent(0) == extent_0 &&
        remote_multivector.extent(1) == extent_1) {
      // skip
    } else {
      remote_multivector =
          impl_scalar_type_2d_view_tpetra(do_not_initialize_tag("remote multivector"), extent_0, extent_1);

      const auto send_buffer_size = offset_host.send[offset_host.send.extent(0) - 1] * blocksize * num_vectors;
      const auto recv_buffer_size = offset_host.recv[offset_host.recv.extent(0) - 1] * blocksize * num_vectors;

      buffer.send = impl_scalar_type_1d_view(do_not_initialize_tag("buffer send"), send_buffer_size);
      buffer.recv = impl_scalar_type_1d_view(do_not_initialize_tag("buffer recv"), recv_buffer_size);

      if (!Tpetra::Details::Behavior::assumeMpiIsGPUAware()) {
        buffer_host.send = impl_scalar_type_1d_view_host(do_not_initialize_tag("buffer send"), send_buffer_size);
        buffer_host.recv = impl_scalar_type_1d_view_host(do_not_initialize_tag("buffer recv"), recv_buffer_size);
      }
    }
  }

  void cancel() {
#ifdef HAVE_IFPACK2_MPI
    waitall(reqs.recv.size(), reqs.recv.data());
    waitall(reqs.send.size(), reqs.send.data());
#endif
  }

  // ======================================================================
  // Async version using execution space instances
  // ======================================================================

#if defined(KOKKOS_ENABLE_CUDA) || defined(KOKKOS_ENABLE_HIP) || defined(KOKKOS_ENABLE_SYCL)
  template <typename PackTag>
  static void copy(const local_ordinal_type_1d_view &lids_,
                   const impl_scalar_type_1d_view &buffer_,
                   const local_ordinal_type ibeg_,
                   const local_ordinal_type iend_,
                   const impl_scalar_type_2d_view_tpetra &multivector_,
                   const local_ordinal_type blocksize_,
                   const execution_space &exec_instance_) {
    const local_ordinal_type num_vectors  = multivector_.extent(1);
    const local_ordinal_type mv_blocksize = blocksize_ * num_vectors;
    const local_ordinal_type idiff        = iend_ - ibeg_;
    const auto abase                      = buffer_.data() + mv_blocksize * ibeg_;

    using team_policy_type = Kokkos::TeamPolicy<execution_space>;
    local_ordinal_type vector_size(0);
    if (blocksize_ <= 4)
      vector_size = 4;
    else if (blocksize_ <= 8)
      vector_size = 8;
    else if (blocksize_ <= 16)
      vector_size = 16;
    else
      vector_size = 32;

    const auto work_item_property = Kokkos::Experimental::WorkItemProperty::HintLightWeight;
    const team_policy_type policy(exec_instance_, idiff, 1, vector_size);
    Kokkos::parallel_for(  //"AsyncableImport::TeamPolicy::copyViaCudaStream",
        Kokkos::Experimental::require(policy, work_item_property),
        KOKKOS_LAMBDA(const typename team_policy_type::member_type &member) {
          const local_ordinal_type i = member.league_rank();
          Kokkos::parallel_for(Kokkos::TeamThreadRange(member, num_vectors), [&](const local_ordinal_type &j) {
            auto aptr = abase + blocksize_ * (i + idiff * j);
            auto bptr = &multivector_(blocksize_ * lids_(i + ibeg_), j);
            if (std::is_same<PackTag, ToBuffer>::value)
              Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, blocksize_), [&](const local_ordinal_type &k) {
                aptr[k] = bptr[k];
              });
            else
              Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, blocksize_), [&](const local_ordinal_type &k) {
                bptr[k] = aptr[k];
              });
          });
        });
  }

  void asyncSendRecvVar1(const impl_scalar_type_2d_view_tpetra &mv) {
    IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::AsyncableImport::AsyncSendRecv", AsyncSendRecv);

#ifdef HAVE_IFPACK2_MPI
    // constants and reallocate data buffers if necessary
    const local_ordinal_type num_vectors  = mv.extent(1);
    const local_ordinal_type mv_blocksize = blocksize * num_vectors;

    // 0. post receive async
    for (local_ordinal_type i = 0, iend = pids.recv.extent(0); i < iend; ++i) {
      if (Tpetra::Details::Behavior::assumeMpiIsGPUAware()) {
        irecv(comm,
              reinterpret_cast<char *>(buffer.recv.data() + offset_host.recv[i] * mv_blocksize),
              (offset_host.recv[i + 1] - offset_host.recv[i]) * mv_blocksize * sizeof(impl_scalar_type),
              pids.recv[i],
              42,
              &reqs.recv[i]);
      } else {
        irecv(comm,
              reinterpret_cast<char *>(buffer_host.recv.data() + offset_host.recv[i] * mv_blocksize),
              (offset_host.recv[i + 1] - offset_host.recv[i]) * mv_blocksize * sizeof(impl_scalar_type),
              pids.recv[i],
              42,
              &reqs.recv[i]);
      }
    }

    execution_space().fence();

    // 1. async memcpy
    for (local_ordinal_type i = 0; i < static_cast<local_ordinal_type>(pids.send.extent(0)); ++i) {
      // 1.0. enqueue pack buffer
      if (i < 8) exec_instances[i % 8].fence();
      copy<ToBuffer>(lids.send, buffer.send,
                     offset_host.send(i), offset_host.send(i + 1),
                     mv, blocksize,
                     // execution_space());
                     exec_instances[i % 8]);
      if (!Tpetra::Details::Behavior::assumeMpiIsGPUAware()) {
        // if (i<8)  exec_instances[i%8].fence();
        const local_ordinal_type num_vectors  = mv.extent(1);
        const local_ordinal_type mv_blocksize = blocksize * num_vectors;

        Kokkos::deep_copy(exec_instances[i % 8],
                          Kokkos::subview(buffer_host.send,
                                          Kokkos::pair<local_ordinal_type, local_ordinal_type>(
                                              offset_host.send(i) * mv_blocksize,
                                              offset_host.send(i + 1) * mv_blocksize)),
                          Kokkos::subview(buffer.send,
                                          Kokkos::pair<local_ordinal_type, local_ordinal_type>(
                                              offset_host.send(i) * mv_blocksize,
                                              offset_host.send(i + 1) * mv_blocksize)));
      }
    }
    // execution_space().fence();
    for (local_ordinal_type i = 0; i < static_cast<local_ordinal_type>(pids.send.extent(0)); ++i) {
      // 1.1. sync the stream and isend
      if (i < 8) exec_instances[i % 8].fence();
      if (Tpetra::Details::Behavior::assumeMpiIsGPUAware()) {
        isend(comm,
              reinterpret_cast<const char *>(buffer.send.data() + offset_host.send[i] * mv_blocksize),
              (offset_host.send[i + 1] - offset_host.send[i]) * mv_blocksize * sizeof(impl_scalar_type),
              pids.send[i],
              42,
              &reqs.send[i]);
      } else {
        isend(comm,
              reinterpret_cast<const char *>(buffer_host.send.data() + offset_host.send[i] * mv_blocksize),
              (offset_host.send[i + 1] - offset_host.send[i]) * mv_blocksize * sizeof(impl_scalar_type),
              pids.send[i],
              42,
              &reqs.send[i]);
      }
    }

    // 2. poke communication
    for (local_ordinal_type i = 0, iend = pids.recv.extent(0); i < iend; ++i) {
      int flag;
      MPI_Status stat;
      MPI_Iprobe(pids.recv[i], 42, comm, &flag, &stat);
    }
#endif  // HAVE_IFPACK2_MPI
    IFPACK2_BLOCKHELPER_TIMER_FENCE(execution_space)
  }

  void syncRecvVar1() {
    IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::AsyncableImport::SyncRecv", SyncRecv);
#ifdef HAVE_IFPACK2_MPI
    // 0. wait for receive async.
    for (local_ordinal_type i = 0; i < static_cast<local_ordinal_type>(pids.recv.extent(0)); ++i) {
      local_ordinal_type idx = i;

      // 0.0. wait any
      waitany(pids.recv.extent(0), reqs.recv.data(), &idx);

      if (!Tpetra::Details::Behavior::assumeMpiIsGPUAware()) {
        const local_ordinal_type num_vectors  = remote_multivector.extent(1);
        const local_ordinal_type mv_blocksize = blocksize * num_vectors;

        Kokkos::deep_copy(
            Kokkos::subview(buffer.recv,
                            Kokkos::pair<local_ordinal_type, local_ordinal_type>(
                                offset_host.recv(idx) * mv_blocksize,
                                offset_host.recv(idx + 1) * mv_blocksize)),
            Kokkos::subview(buffer_host.recv,
                            Kokkos::pair<local_ordinal_type, local_ordinal_type>(
                                offset_host.recv(idx) * mv_blocksize,
                                offset_host.recv(idx + 1) * mv_blocksize)));
      }

      // 0.1. unpack data after data is moved into a device
      copy<ToMultiVector>(lids.recv, buffer.recv,
                          offset_host.recv(idx), offset_host.recv(idx + 1),
                          remote_multivector, blocksize,
                          exec_instances[idx % 8]);
    }

    // 1. fire up all cuda events
    Kokkos::fence();

    // 2. cleanup all open comm
    waitall(reqs.send.size(), reqs.send.data());
#endif  // HAVE_IFPACK2_MPI
    IFPACK2_BLOCKHELPER_TIMER_FENCE(execution_space)
  }
#endif  // defined(KOKKOS_ENABLE_CUDA|HIP|SYCL)

  // ======================================================================
  // Generic version without using execution space instances
  // - only difference between device and host architecture is on using team
  //   or range policies.
  // ======================================================================
  template <typename PackTag>
  static void copy(const local_ordinal_type_1d_view &lids_,
                   const impl_scalar_type_1d_view &buffer_,
                   const local_ordinal_type &ibeg_,
                   const local_ordinal_type &iend_,
                   const impl_scalar_type_2d_view_tpetra &multivector_,
                   const local_ordinal_type blocksize_) {
    const local_ordinal_type num_vectors  = multivector_.extent(1);
    const local_ordinal_type mv_blocksize = blocksize_ * num_vectors;
    const local_ordinal_type idiff        = iend_ - ibeg_;
    const auto abase                      = buffer_.data() + mv_blocksize * ibeg_;
    if constexpr (BlockHelperDetails::is_device<execution_space>::value) {
      using team_policy_type = Kokkos::TeamPolicy<execution_space>;
      local_ordinal_type vector_size(0);
      if (blocksize_ <= 4)
        vector_size = 4;
      else if (blocksize_ <= 8)
        vector_size = 8;
      else if (blocksize_ <= 16)
        vector_size = 16;
      else
        vector_size = 32;
      const team_policy_type policy(idiff, 1, vector_size);
      Kokkos::parallel_for(
          "AsyncableImport::TeamPolicy::copy",
          policy, KOKKOS_LAMBDA(const typename team_policy_type::member_type &member) {
            const local_ordinal_type i = member.league_rank();
            Kokkos::parallel_for(Kokkos::TeamThreadRange(member, num_vectors), [&](const local_ordinal_type &j) {
              auto aptr = abase + blocksize_ * (i + idiff * j);
              auto bptr = &multivector_(blocksize_ * lids_(i + ibeg_), j);
              if (std::is_same<PackTag, ToBuffer>::value)
                Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, blocksize_), [&](const local_ordinal_type &k) {
                  aptr[k] = bptr[k];
                });
              else
                Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, blocksize_), [&](const local_ordinal_type &k) {
                  bptr[k] = aptr[k];
                });
            });
          });
    } else {
      const Kokkos::RangePolicy<execution_space> policy(0, idiff * num_vectors);
      Kokkos::parallel_for(
          "AsyncableImport::RangePolicy::copy",
          policy, KOKKOS_LAMBDA(const local_ordinal_type &ij) {
            const local_ordinal_type i = ij % idiff;
            const local_ordinal_type j = ij / idiff;
            auto aptr                  = abase + blocksize_ * (i + idiff * j);
            auto bptr                  = &multivector_(blocksize_ * lids_(i + ibeg_), j);
            auto from                  = std::is_same<PackTag, ToBuffer>::value ? bptr : aptr;
            auto to                    = std::is_same<PackTag, ToBuffer>::value ? aptr : bptr;
            memcpy(to, from, sizeof(impl_scalar_type) * blocksize_);
          });
    }
  }

  void asyncSendRecvVar0(const impl_scalar_type_2d_view_tpetra &mv) {
    IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::AsyncableImport::AsyncSendRecv", AsyncSendRecv);

#ifdef HAVE_IFPACK2_MPI
    // constants and reallocate data buffers if necessary
    const local_ordinal_type num_vectors  = mv.extent(1);
    const local_ordinal_type mv_blocksize = blocksize * num_vectors;

    // receive async
    for (local_ordinal_type i = 0, iend = pids.recv.extent(0); i < iend; ++i) {
      if (Tpetra::Details::Behavior::assumeMpiIsGPUAware()) {
        irecv(comm,
              reinterpret_cast<char *>(buffer.recv.data() + offset_host.recv[i] * mv_blocksize),
              (offset_host.recv[i + 1] - offset_host.recv[i]) * mv_blocksize * sizeof(impl_scalar_type),
              pids.recv[i],
              42,
              &reqs.recv[i]);
      } else {
        irecv(comm,
              reinterpret_cast<char *>(buffer_host.recv.data() + offset_host.recv[i] * mv_blocksize),
              (offset_host.recv[i + 1] - offset_host.recv[i]) * mv_blocksize * sizeof(impl_scalar_type),
              pids.recv[i],
              42,
              &reqs.recv[i]);
      }
    }

    // send async
    for (local_ordinal_type i = 0, iend = pids.send.extent(0); i < iend; ++i) {
      copy<ToBuffer>(lids.send, buffer.send, offset_host.send(i), offset_host.send(i + 1),
                     mv, blocksize);
      Kokkos::fence();
      if (Tpetra::Details::Behavior::assumeMpiIsGPUAware()) {
        isend(comm,
              reinterpret_cast<const char *>(buffer.send.data() + offset_host.send[i] * mv_blocksize),
              (offset_host.send[i + 1] - offset_host.send[i]) * mv_blocksize * sizeof(impl_scalar_type),
              pids.send[i],
              42,
              &reqs.send[i]);
      } else {
        Kokkos::deep_copy(
            Kokkos::subview(buffer_host.send,
                            Kokkos::pair<local_ordinal_type, local_ordinal_type>(
                                offset_host.send(i) * mv_blocksize,
                                offset_host.send(i + 1) * mv_blocksize)),
            Kokkos::subview(buffer.send,
                            Kokkos::pair<local_ordinal_type, local_ordinal_type>(
                                offset_host.send(i) * mv_blocksize,
                                offset_host.send(i + 1) * mv_blocksize)));
        isend(comm,
              reinterpret_cast<const char *>(buffer_host.send.data() + offset_host.send[i] * mv_blocksize),
              (offset_host.send[i + 1] - offset_host.send[i]) * mv_blocksize * sizeof(impl_scalar_type),
              pids.send[i],
              42,
              &reqs.send[i]);
      }
    }

    // I find that issuing an Iprobe seems to nudge some MPIs into action,
    // which helps with overlapped comm/comp performance.
    for (local_ordinal_type i = 0, iend = pids.recv.extent(0); i < iend; ++i) {
      int flag;
      MPI_Status stat;
      MPI_Iprobe(pids.recv[i], 42, comm, &flag, &stat);
    }
#endif
    IFPACK2_BLOCKHELPER_TIMER_FENCE(execution_space)
  }

  void syncRecvVar0() {
    IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::AsyncableImport::SyncRecv", SyncRecv);
#ifdef HAVE_IFPACK2_MPI
    // receive async.
    for (local_ordinal_type i = 0, iend = pids.recv.extent(0); i < iend; ++i) {
      local_ordinal_type idx = i;
      waitany(pids.recv.extent(0), reqs.recv.data(), &idx);
      if (!Tpetra::Details::Behavior::assumeMpiIsGPUAware()) {
        const local_ordinal_type num_vectors  = remote_multivector.extent(1);
        const local_ordinal_type mv_blocksize = blocksize * num_vectors;
        Kokkos::deep_copy(
            Kokkos::subview(buffer.recv,
                            Kokkos::pair<local_ordinal_type, local_ordinal_type>(
                                offset_host.recv(idx) * mv_blocksize,
                                offset_host.recv(idx + 1) * mv_blocksize)),
            Kokkos::subview(buffer_host.recv,
                            Kokkos::pair<local_ordinal_type, local_ordinal_type>(
                                offset_host.recv(idx) * mv_blocksize,
                                offset_host.recv(idx + 1) * mv_blocksize)));
      }
      copy<ToMultiVector>(lids.recv, buffer.recv, offset_host.recv(idx), offset_host.recv(idx + 1),
                          remote_multivector, blocksize);
    }
    // wait on the sends to match all Isends with a cleanup operation.
    waitall(reqs.send.size(), reqs.send.data());
#endif
    IFPACK2_BLOCKHELPER_TIMER_FENCE(execution_space)
  }

  void asyncSendRecv(const impl_scalar_type_2d_view_tpetra &mv) {
#if defined(KOKKOS_ENABLE_CUDA) || defined(KOKKOS_ENABLE_HIP) || defined(KOKKOS_ENABLE_SYCL)
#if defined(IFPACK2_BLOCKTRIDICONTAINER_USE_EXEC_SPACE_INSTANCES)
    asyncSendRecvVar1(mv);
#else
    asyncSendRecvVar0(mv);
#endif
#else
    asyncSendRecvVar0(mv);
#endif
  }
  void syncRecv() {
#if defined(KOKKOS_ENABLE_CUDA) || defined(KOKKOS_ENABLE_HIP) || defined(KOKKOS_ENABLE_SYCL)
#if defined(IFPACK2_BLOCKTRIDICONTAINER_USE_EXEC_SPACE_INSTANCES)
    syncRecvVar1();
#else
    syncRecvVar0();
#endif
#else
    syncRecvVar0();
#endif
  }

  void syncExchange(const impl_scalar_type_2d_view_tpetra &mv) {
    IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::AsyncableImport::SyncExchange", SyncExchange);
    asyncSendRecv(mv);
    syncRecv();
    IFPACK2_BLOCKHELPER_TIMER_FENCE(execution_space)
  }

  impl_scalar_type_2d_view_tpetra getRemoteMultiVectorLocalView() const { return remote_multivector; }
};

template <typename ViewType1, typename ViewType2>
struct are_same_struct {
  ViewType1 keys1;
  ViewType2 keys2;

  are_same_struct(ViewType1 keys1_, ViewType2 keys2_)
    : keys1(keys1_)
    , keys2(keys2_) {}
  KOKKOS_INLINE_FUNCTION
  void operator()(int i, unsigned int &count) const {
    if (keys1(i) != keys2(i)) count++;
  }
};

template <typename ViewType1, typename ViewType2>
bool are_same(ViewType1 keys1, ViewType2 keys2) {
  unsigned int are_same_ = 0;

  Kokkos::parallel_reduce(Kokkos::RangePolicy<typename ViewType1::execution_space>(0, keys1.extent(0)),
                          are_same_struct(keys1, keys2),
                          are_same_);
  return are_same_ == 0;
}

template <typename MatrixType>
Teuchos::RCP<AsyncableImport<MatrixType>>
createBlockCrsAsyncImporter(const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_row_matrix_type> &A) {
  IFPACK2_BLOCKHELPER_TIMER("createBlockCrsAsyncImporter", createBlockCrsAsyncImporter);
  using impl_type                        = BlockHelperDetails::ImplType<MatrixType>;
  using tpetra_map_type                  = typename impl_type::tpetra_map_type;
  using local_ordinal_type               = typename impl_type::local_ordinal_type;
  using global_ordinal_type              = typename impl_type::global_ordinal_type;
  using local_ordinal_type_1d_view       = typename impl_type::local_ordinal_type_1d_view;
  using crs_matrix_type                  = typename impl_type::tpetra_crs_matrix_type;
  using block_crs_matrix_type            = typename impl_type::tpetra_block_crs_matrix_type;
  using global_indices_array_device_type = Kokkos::View<const global_ordinal_type *, typename tpetra_map_type::device_type>;

  auto A_crs  = Teuchos::rcp_dynamic_cast<const crs_matrix_type>(A);
  auto A_bcrs = Teuchos::rcp_dynamic_cast<const block_crs_matrix_type>(A);

  bool hasBlockCrsMatrix = !A_bcrs.is_null();

  // This is OK here to use the graph of the A_crs matrix and a block size of 1
  const auto g = hasBlockCrsMatrix ? A_bcrs->getCrsGraph() : *(A_crs->getCrsGraph());  // tpetra crs graph object

  const auto blocksize  = hasBlockCrsMatrix ? A_bcrs->getBlockSize() : 1;
  const auto domain_map = g.getDomainMap();
  const auto column_map = g.getColMap();

  std::vector<global_ordinal_type> gids;

  Kokkos::Subview<global_indices_array_device_type, std::pair<int, int>> column_map_global_iD_last;

  bool separate_remotes = true, found_first = false, need_owned_permutation = false;
  {
    IFPACK2_BLOCKHELPER_TIMER("createBlockCrsAsyncImporter::loop_over_local_elements", loop_over_local_elements);

    global_indices_array_device_type column_map_global_iD = column_map->getMyGlobalIndicesDevice();
    global_indices_array_device_type domain_map_global_iD = domain_map->getMyGlobalIndicesDevice();

    if (are_same(domain_map_global_iD, column_map_global_iD)) {
      // this should be the most likely path
      separate_remotes       = true;
      need_owned_permutation = false;

      column_map_global_iD_last = Kokkos::subview(column_map_global_iD,
                                                  std::pair<int, int>(domain_map_global_iD.extent(0), column_map_global_iD.extent(0)));
    } else {
      // This loop is relatively expensive
      for (size_t i = 0; i < column_map->getLocalNumElements(); ++i) {
        const global_ordinal_type gid = column_map->getGlobalElement(i);
        if (!domain_map->isNodeGlobalElement(gid)) {
          found_first = true;
          gids.push_back(gid);
        } else if (found_first) {
          separate_remotes = false;
          break;
        }
        if (!found_first && !need_owned_permutation &&
            domain_map->getLocalElement(gid) != static_cast<local_ordinal_type>(i)) {
          // The owned part of the domain and column maps are different
          // orderings. We *could* do a super efficient impl of this case in the
          // num_sweeps > 1 case by adding complexity to PermuteAndRepack. But,
          // really, if a caller cares about speed, they wouldn't make different
          // local permutations like this. So we punt on the best impl and go for
          // a pretty good one: the permutation is done in place in
          // compute_b_minus_Rx for the pure-owned part of the MVP. The only cost
          // is the presumably worse memory access pattern of the input vector.
          need_owned_permutation = true;
        }
      }
    }
    IFPACK2_BLOCKHELPER_TIMER_FENCE(typename BlockHelperDetails::ImplType<MatrixType>::execution_space)
  }

  if (separate_remotes) {
    IFPACK2_BLOCKHELPER_TIMER("createBlockCrsAsyncImporter::separate_remotes", separate_remotes);
    const auto invalid              = Teuchos::OrdinalTraits<global_ordinal_type>::invalid();
    const auto parsimonious_col_map = need_owned_permutation ? Teuchos::rcp(new tpetra_map_type(invalid, gids.data(), gids.size(), 0, domain_map->getComm())) : Teuchos::rcp(new tpetra_map_type(invalid, column_map_global_iD_last, 0, domain_map->getComm()));
    if (parsimonious_col_map->getGlobalNumElements() > 0) {
      // make the importer only if needed.
      local_ordinal_type_1d_view dm2cm;
      if (need_owned_permutation) {
        dm2cm                 = local_ordinal_type_1d_view(do_not_initialize_tag("dm2cm"), domain_map->getLocalNumElements());
        const auto dm2cm_host = Kokkos::create_mirror_view(dm2cm);
        for (size_t i = 0; i < domain_map->getLocalNumElements(); ++i)
          dm2cm_host(i) = domain_map->getLocalElement(column_map->getGlobalElement(i));
        Kokkos::deep_copy(dm2cm, dm2cm_host);
      }
      IFPACK2_BLOCKHELPER_TIMER_FENCE(typename BlockHelperDetails::ImplType<MatrixType>::execution_space)
      return Teuchos::rcp(new AsyncableImport<MatrixType>(domain_map, parsimonious_col_map, blocksize, dm2cm));
    }
  }
  IFPACK2_BLOCKHELPER_TIMER_FENCE(typename BlockHelperDetails::ImplType<MatrixType>::execution_space)
  return Teuchos::null;
}

template <typename local_ordinal_type>
local_ordinal_type costTRSM(const local_ordinal_type block_size) {
  return block_size * block_size;
}

template <typename local_ordinal_type>
local_ordinal_type costGEMV(const local_ordinal_type block_size) {
  return 2 * block_size * block_size;
}

template <typename local_ordinal_type>
local_ordinal_type costTriDiagSolve(const local_ordinal_type subline_length, const local_ordinal_type block_size) {
  return 2 * subline_length * costTRSM(block_size) + 2 * (subline_length - 1) * costGEMV(block_size);
}

template <typename local_ordinal_type>
local_ordinal_type costSolveSchur(const local_ordinal_type num_parts,
                                  const local_ordinal_type num_teams,
                                  const local_ordinal_type line_length,
                                  const local_ordinal_type block_size,
                                  const local_ordinal_type n_subparts_per_part) {
  const local_ordinal_type subline_length = ceil(double(line_length - (n_subparts_per_part - 1) * 2) / n_subparts_per_part);
  if (subline_length < 1) {
    return INT_MAX;
  }

  const local_ordinal_type p_n_lines      = ceil(double(num_parts) / num_teams);
  const local_ordinal_type p_n_sublines   = ceil(double(n_subparts_per_part) * num_parts / num_teams);
  const local_ordinal_type p_n_sublines_2 = ceil(double(n_subparts_per_part - 1) * num_parts / num_teams);

  const local_ordinal_type p_costApplyE    = p_n_sublines_2 * subline_length * 2 * costGEMV(block_size);
  const local_ordinal_type p_costApplyS    = p_n_lines * costTriDiagSolve((n_subparts_per_part - 1) * 2, block_size);
  const local_ordinal_type p_costApplyAinv = p_n_sublines * costTriDiagSolve(subline_length, block_size);
  const local_ordinal_type p_costApplyC    = p_n_sublines_2 * 2 * costGEMV(block_size);

  if (n_subparts_per_part == 1) {
    return p_costApplyAinv;
  }
  return p_costApplyE + p_costApplyS + p_costApplyAinv + p_costApplyC;
}

template <typename local_ordinal_type>
local_ordinal_type getAutomaticNSubparts(const local_ordinal_type num_parts,
                                         const local_ordinal_type num_teams,
                                         const local_ordinal_type line_length,
                                         const local_ordinal_type block_size) {
  // BMK: replaced theoretical model with empirical model
  // This is a linear regression based on data from a grid search.
  // The independent terms in the regression are:
  // - "parallelism surplus" - smaller when problem has enough lines to saturate GPU, larger otherwise
  // - log2 of the line length
  // - block size
  double parallelismSurplus = Kokkos::sqrt((double)num_teams / num_parts);
  double logLineLength      = Kokkos::log2((double)line_length);
  (void)logLineLength;
  // Directly predict with linear model
#if defined(KOKKOS_ARCH_AMD_GFX942) || defined(KOKKOS_ARCH_AMD_GFX942_APU)
  // MI300-specific data
  double modeled = -9.2312 + 4.6946 * parallelismSurplus + 0.4095 * block_size + 0.966 * logLineLength;
  // Do not split lines if there is plenty of parallelism
  if (parallelismSurplus < 0.3)
    modeled = 1;
#elif defined(KOKKOS_ARCH_HOPPER) || defined(KOKKOS_ARCH_BLACKWELL)
  // Based on H100 data
  double modeled = -9.6053 + 4.7477 * parallelismSurplus + 0.2338 * block_size + 1.0794 * logLineLength;
  // On H100, performance degrades rapidly if small lines are split too many times
  double maxSplit = (double)line_length / 8;
  if (modeled > maxSplit)
    modeled = maxSplit;
#elif defined(KOKKOS_ENABLE_CUDA)
  // Based on V100 data, line splitting is profitable in fewer cases
  // (only when there are few, long lines)
  double modeled = 1;
  if (parallelismSurplus > 1 && line_length > 64)
    modeled = 4;
#elif defined(KOKKOS_ENABLE_HIP)
  // Based on MI250X data
  double modeled = -8.6214 + 7.3468 * parallelismSurplus + 0.3596 * block_size + 0.6673 * logLineLength;
#else
  // GPUs other than CUDA or HIP: default to simple model that works for V100
  double modeled = 1;
  if (parallelismSurplus > 1 && line_length > 64)
    modeled = 4;
#endif

  // Round to nearest integer
  local_ordinal_type n_subparts_per_part = 0.5 + modeled;
  // Do not split lines if there is plenty of parallelism available
  if (parallelismSurplus < 0.3)
    n_subparts_per_part = 1;
  // Clamp the result to valid range
  // Criteria for valid n_subparts_per_part (where connection_length is 2 for wide separators)
  //   line_length >= n_subparts_per_part + (n_subparts_per_part - 1) * connection_length
  // Equivalently:
  //   line_length >= n_subparts_per_part + n_subparts_per_part * 2 - 2
  //   line_length >= 3 * n_subparts_per_part - 2
  local_ordinal_type min_subparts_per_part = 1;
  local_ordinal_type max_subparts_per_part = (line_length + 2) / 3;
  // Limit memory usage from too many sublines
  if (max_subparts_per_part > 16)
    max_subparts_per_part = 16;
  if (n_subparts_per_part < min_subparts_per_part)
    n_subparts_per_part = min_subparts_per_part;
  if (n_subparts_per_part > max_subparts_per_part)
    n_subparts_per_part = max_subparts_per_part;
  return n_subparts_per_part;
}

template <typename ArgActiveExecutionMemorySpace>
struct SolveTridiagsDefaultModeAndAlgo;

template <typename MatrixType>
BlockHelperDetails::PartInterface<MatrixType>
createPartInterface(const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_row_matrix_type> &A,
                    const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_crs_graph_type> &G,
                    const Teuchos::Array<Teuchos::Array<typename BlockHelperDetails::ImplType<MatrixType>::local_ordinal_type>> &partitions,
                    const typename BlockHelperDetails::ImplType<MatrixType>::local_ordinal_type n_subparts_per_part_in) {
  IFPACK2_BLOCKHELPER_TIMER("createPartInterface", createPartInterface);
  using impl_type                  = BlockHelperDetails::ImplType<MatrixType>;
  using local_ordinal_type         = typename impl_type::local_ordinal_type;
  using local_ordinal_type_1d_view = typename impl_type::local_ordinal_type_1d_view;
  using local_ordinal_type_2d_view = typename impl_type::local_ordinal_type_2d_view;
  using size_type                  = typename impl_type::size_type;

  auto bA = Teuchos::rcp_dynamic_cast<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_block_crs_matrix_type>(A);

  TEUCHOS_ASSERT(!bA.is_null() || G->getLocalNumRows() != 0);
  const local_ordinal_type blocksize   = bA.is_null() ? A->getLocalNumRows() / G->getLocalNumRows() : A->getBlockSize();
  constexpr int vector_length          = impl_type::vector_length;
  constexpr int internal_vector_length = impl_type::internal_vector_length;

  const auto comm = A->getRowMap()->getComm();

  BlockHelperDetails::PartInterface<MatrixType> interf;

  const local_ordinal_type A_n_lclrows = G->getLocalNumRows();
  const bool jacobi                    = partitions.size() == 0 || partitions.size() == A_n_lclrows;
  const local_ordinal_type nparts      = jacobi ? A_n_lclrows : partitions.size();

  typedef std::pair<local_ordinal_type, local_ordinal_type> size_idx_pair_type;
  std::vector<size_idx_pair_type> partsz(nparts);

  if (!jacobi) {
    for (local_ordinal_type i = 0; i < nparts; ++i)
      partsz[i] = size_idx_pair_type(partitions[i].size(), i);
    std::sort(partsz.begin(), partsz.end(),
              [](const size_idx_pair_type &x, const size_idx_pair_type &y) {
                return x.first > y.first;
              });
  }

  local_ordinal_type n_subparts_per_part;
  if (jacobi) {
    n_subparts_per_part = 1;
  } else {
    if (n_subparts_per_part_in == -1) {
      // If the number of subparts is set to -1, the user let the algorithm
      // decides the value automatically
      using execution_space = typename impl_type::execution_space;

      // Line splitting only benefits GPUs
      if constexpr (impl_type::node_type::is_gpu) {
        const int line_length = partsz[0].first;

        const local_ordinal_type team_size =
            SolveTridiagsDefaultModeAndAlgo<typename execution_space::memory_space>::
                recommended_team_size(blocksize, vector_length, internal_vector_length);

        const local_ordinal_type num_teams = std::max(1, execution_space().concurrency() / (team_size * vector_length));
        n_subparts_per_part                = getAutomaticNSubparts(nparts, num_teams, line_length, blocksize);
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
        printf("Automatically chosen n_subparts_per_part = %d for nparts = %d, num_teams = %d, team_size = %d, line_length = %d, and blocksize = %d;\n", n_subparts_per_part, nparts, num_teams, team_size, line_length, blocksize);
#endif
      } else {
        n_subparts_per_part = 1;
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
        printf("Automatically chosen n_subparts_per_part = 1 for CPU backend\n");
#endif
      }
    } else {
      n_subparts_per_part = n_subparts_per_part_in;
    }
  }

  // Total number of sub lines:
  const local_ordinal_type n_sub_parts = nparts * n_subparts_per_part;
  // Total number of sub lines + the Schur complement blocks.
  // For a given live 2 sub lines implies one Schur complement, 3 sub lines implies two Schur complements etc.
  const local_ordinal_type n_sub_parts_and_schur = n_sub_parts + nparts * (n_subparts_per_part - 1);

#if defined(BLOCKTRIDICONTAINER_DEBUG)
  local_ordinal_type nrows = 0;
  if (jacobi)
    nrows = nparts;
  else
    for (local_ordinal_type i = 0; i < nparts; ++i) nrows += partitions[i].size();

  TEUCHOS_TEST_FOR_EXCEPT_MSG(nrows != A_n_lclrows, BlockHelperDetails::get_msg_prefix(comm) << "The #rows implied by the local partition is not "
                                                                                             << "the same as getLocalNumRows: " << nrows << " vs " << A_n_lclrows);
#endif

  // permutation vector
  std::vector<local_ordinal_type> p;
  if (jacobi) {
    interf.max_partsz          = 1;
    interf.max_subpartsz       = 0;
    interf.n_subparts_per_part = 1;
    interf.nparts              = nparts;
  } else {
    // reorder parts to maximize simd packing efficiency
    p.resize(nparts);

    for (local_ordinal_type i = 0; i < nparts; ++i)
      p[i] = partsz[i].second;

    interf.max_partsz = partsz[0].first;

    constexpr local_ordinal_type connection_length = 2;
    const local_ordinal_type sub_line_length       = (interf.max_partsz - (n_subparts_per_part - 1) * connection_length) / n_subparts_per_part;
    const local_ordinal_type last_sub_line_length  = interf.max_partsz - (n_subparts_per_part - 1) * (connection_length + sub_line_length);

    interf.max_subpartsz       = (sub_line_length > last_sub_line_length) ? sub_line_length : last_sub_line_length;
    interf.n_subparts_per_part = n_subparts_per_part;
    interf.nparts              = nparts;
  }

  // allocate parts
  interf.partptr          = local_ordinal_type_1d_view(do_not_initialize_tag("partptr"), nparts + 1);
  interf.lclrow           = local_ordinal_type_1d_view(do_not_initialize_tag("lclrow"), A_n_lclrows);
  interf.part2rowidx0     = local_ordinal_type_1d_view(do_not_initialize_tag("part2rowidx0"), nparts + 1);
  interf.part2packrowidx0 = local_ordinal_type_1d_view(do_not_initialize_tag("part2packrowidx0"), nparts + 1);
  interf.rowidx2part      = local_ordinal_type_1d_view(do_not_initialize_tag("rowidx2part"), A_n_lclrows);

  interf.part2rowidx0_sub     = local_ordinal_type_1d_view(do_not_initialize_tag("part2rowidx0_sub"), n_sub_parts_and_schur + 1);
  interf.part2packrowidx0_sub = local_ordinal_type_2d_view(do_not_initialize_tag("part2packrowidx0_sub"), nparts, 2 * n_subparts_per_part);
  interf.rowidx2part_sub      = local_ordinal_type_1d_view(do_not_initialize_tag("rowidx2part"), A_n_lclrows);

  interf.partptr_sub = local_ordinal_type_2d_view(do_not_initialize_tag("partptr_sub"), n_sub_parts_and_schur, 2);

  // mirror to host and compute on host execution space
  const auto partptr     = Kokkos::create_mirror_view(interf.partptr);
  const auto partptr_sub = Kokkos::create_mirror_view(interf.partptr_sub);

  const auto lclrow           = Kokkos::create_mirror_view(interf.lclrow);
  const auto part2rowidx0     = Kokkos::create_mirror_view(interf.part2rowidx0);
  const auto part2packrowidx0 = Kokkos::create_mirror_view(interf.part2packrowidx0);
  const auto rowidx2part      = Kokkos::create_mirror_view(interf.rowidx2part);

  const auto part2rowidx0_sub     = Kokkos::create_mirror_view(interf.part2rowidx0_sub);
  const auto part2packrowidx0_sub = Kokkos::create_mirror_view(Kokkos::HostSpace(), interf.part2packrowidx0_sub);
  const auto rowidx2part_sub      = Kokkos::create_mirror_view(interf.rowidx2part_sub);

  // Determine parts.
  interf.row_contiguous             = true;
  partptr(0)                        = 0;
  part2rowidx0(0)                   = 0;
  part2packrowidx0(0)               = 0;
  local_ordinal_type pack_nrows     = 0;
  local_ordinal_type pack_nrows_sub = 0;
  if (jacobi) {
    IFPACK2_BLOCKHELPER_TIMER("compute part indices (Jacobi)", Jacobi);
    // Jacobi (all lines have length 1) means that A_n_lclrows == nparts,
    // so the mapping between parts and rows is trivial.
    // Note: we can leave interf.row_contiguous = true, since for all i: lclrow(i) == i
    for (local_ordinal_type i = 0; i <= nparts; ++i) {
      part2rowidx0(i) = i;
      partptr(i)      = i;
    }
    for (local_ordinal_type i = 0; i < nparts; ++i) {
      rowidx2part(i) = i;
      lclrow(i)      = i;
    }
    for (local_ordinal_type ip = 0; ip < nparts; ++ip) {
      // assume No overlap.
      if (ip % vector_length == 0) pack_nrows = 1;
      part2packrowidx0(ip + 1) = part2packrowidx0(ip) + ((ip + 1) % vector_length == 0 || ip + 1 == nparts ? pack_nrows : 0);
    }
    part2rowidx0_sub(0) = 0;
    partptr_sub(0, 0)   = 0;

    for (local_ordinal_type ip = 0; ip < nparts; ++ip) {
      constexpr local_ordinal_type ipnrows      = 1;
      const local_ordinal_type full_line_length = partptr(ip + 1) - partptr(ip);

      TEUCHOS_TEST_FOR_EXCEPTION(full_line_length != ipnrows, std::logic_error,
                                 "In the part " << ip);

      constexpr local_ordinal_type connection_length = 2;

      if (full_line_length < n_subparts_per_part + (n_subparts_per_part - 1) * connection_length)
        TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error,
                                   "The part " << ip << " is too short to use " << n_subparts_per_part << " sub parts.");

      const local_ordinal_type sub_line_length      = (full_line_length - (n_subparts_per_part - 1) * connection_length) / n_subparts_per_part;
      const local_ordinal_type last_sub_line_length = full_line_length - (n_subparts_per_part - 1) * (connection_length + sub_line_length);

      if (ip % vector_length == 0) pack_nrows_sub = ipnrows;

      for (local_ordinal_type local_sub_ip = 0; local_sub_ip < n_subparts_per_part; ++local_sub_ip) {
        const local_ordinal_type sub_ip   = nparts * (2 * local_sub_ip) + ip;
        const local_ordinal_type schur_ip = nparts * (2 * local_sub_ip + 1) + ip;
        if (local_sub_ip != n_subparts_per_part - 1) {
          if (local_sub_ip != 0) {
            partptr_sub(sub_ip, 0) = partptr_sub(nparts * (2 * local_sub_ip - 1) + ip, 1);
          } else if (ip != 0) {
            partptr_sub(sub_ip, 0) = partptr_sub(nparts * 2 * (n_subparts_per_part - 1) + ip - 1, 1);
          }
          partptr_sub(sub_ip, 1)   = sub_line_length + partptr_sub(sub_ip, 0);
          partptr_sub(schur_ip, 0) = partptr_sub(sub_ip, 1);
          partptr_sub(schur_ip, 1) = connection_length + partptr_sub(schur_ip, 0);

          part2rowidx0_sub(sub_ip + 1) = part2rowidx0_sub(sub_ip) + sub_line_length;
          part2rowidx0_sub(sub_ip + 2) = part2rowidx0_sub(sub_ip + 1) + connection_length;

#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
          printf("Sub Part index = %d, first LID associated to the sub part = %d, sub part size = %d;\n", sub_ip, partptr_sub(ip, 2 * local_sub_ip), sub_line_length);
          printf("Sub Part index Schur = %d, first LID associated to the sub part = %d, sub part size = %d;\n", sub_ip + 1, partptr_sub(ip, 2 * local_sub_ip + 1), connection_length);
#endif
        } else {
          if (local_sub_ip != 0) {
            partptr_sub(sub_ip, 0) = partptr_sub(nparts * (2 * local_sub_ip - 1) + ip, 1);
          } else if (ip != 0) {
            partptr_sub(sub_ip, 0) = partptr_sub(nparts * 2 * (n_subparts_per_part - 1) + ip - 1, 1);
          }
          partptr_sub(sub_ip, 1) = last_sub_line_length + partptr_sub(sub_ip, 0);

          part2rowidx0_sub(sub_ip + 1) = part2rowidx0_sub(sub_ip) + last_sub_line_length;

#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
          printf("Sub Part index = %d, first LID associated to the sub part = %d, sub part size = %d;\n", sub_ip, partptr_sub(ip, 2 * local_sub_ip), last_sub_line_length);
#endif
        }
      }
    }

#ifdef IFPACK2_BLOCKTRIDICONTAINER_WRITE_MM
    std::cout << "partptr_sub = " << std::endl;
    for (size_type i = 0; i < partptr_sub.extent(0); ++i) {
      for (size_type j = 0; j < partptr_sub.extent(1); ++j) {
        std::cout << partptr_sub(i, j) << " ";
      }
      std::cout << std::endl;
    }
    std::cout << "partptr_sub end" << std::endl;
#endif

    {
      local_ordinal_type npacks = ceil(float(nparts) / vector_length);

      local_ordinal_type ip_max = nparts > vector_length ? vector_length : nparts;
      for (local_ordinal_type ip = 0; ip < ip_max; ++ip) {
        part2packrowidx0_sub(ip, 0) = 0;
      }
      for (local_ordinal_type ipack = 0; ipack < npacks; ++ipack) {
        if (ipack != 0) {
          local_ordinal_type ip_min = ipack * vector_length;
          ip_max                    = nparts > (ipack + 1) * vector_length ? (ipack + 1) * vector_length : nparts;
          for (local_ordinal_type ip = ip_min; ip < ip_max; ++ip) {
            part2packrowidx0_sub(ip, 0) = part2packrowidx0_sub(ip - vector_length, part2packrowidx0_sub.extent(1) - 1);
          }
        }

        for (size_type local_sub_ip = 0; local_sub_ip < part2packrowidx0_sub.extent(1) - 1; ++local_sub_ip) {
          local_ordinal_type ip_min = ipack * vector_length;
          ip_max                    = nparts > (ipack + 1) * vector_length ? (ipack + 1) * vector_length : nparts;

          const local_ordinal_type full_line_length = partptr(ip_min + 1) - partptr(ip_min);

          constexpr local_ordinal_type connection_length = 2;

          const local_ordinal_type sub_line_length      = (full_line_length - (n_subparts_per_part - 1) * connection_length) / n_subparts_per_part;
          const local_ordinal_type last_sub_line_length = full_line_length - (n_subparts_per_part - 1) * (connection_length + sub_line_length);

          if (local_sub_ip % 2 == 0) pack_nrows_sub = sub_line_length;
          if (local_sub_ip % 2 == 1) pack_nrows_sub = connection_length;
          if (local_sub_ip == part2packrowidx0_sub.extent(1) - 2) pack_nrows_sub = last_sub_line_length;

          part2packrowidx0_sub(ip_min, local_sub_ip + 1) = part2packrowidx0_sub(ip_min, local_sub_ip) + pack_nrows_sub;

          for (local_ordinal_type ip = ip_min + 1; ip < ip_max; ++ip) {
            part2packrowidx0_sub(ip, local_sub_ip + 1) = part2packrowidx0_sub(ip_min, local_sub_ip + 1);
          }
        }
      }

      Kokkos::deep_copy(interf.part2packrowidx0_sub, part2packrowidx0_sub);
    }
    IFPACK2_BLOCKHELPER_TIMER_FENCE(typename BlockHelperDetails::ImplType<MatrixType>::execution_space)
  } else {
    IFPACK2_BLOCKHELPER_TIMER("compute part indices", indices);
    for (local_ordinal_type ip = 0; ip < nparts; ++ip) {
      const auto *part                 = &partitions[p[ip]];
      const local_ordinal_type ipnrows = part->size();
      TEUCHOS_ASSERT(ip == 0 || (ipnrows <= static_cast<local_ordinal_type>(partitions[p[ip - 1]].size())));
      TEUCHOS_TEST_FOR_EXCEPT_MSG(ipnrows == 0,
                                  BlockHelperDetails::get_msg_prefix(comm)
                                      << "partition " << p[ip]
                                      << " is empty, which is not allowed.");
      // assume No overlap.
      part2rowidx0(ip + 1) = part2rowidx0(ip) + ipnrows;
      // Since parts are ordered in decreasing size, the size of the first
      // part in a pack is the size for all parts in the pack.
      if (ip % vector_length == 0) pack_nrows = ipnrows;
      part2packrowidx0(ip + 1)        = part2packrowidx0(ip) + ((ip + 1) % vector_length == 0 || ip + 1 == nparts ? pack_nrows : 0);
      const local_ordinal_type offset = partptr(ip);
      for (local_ordinal_type i = 0; i < ipnrows; ++i) {
        const auto lcl_row = (*part)[i];
        TEUCHOS_TEST_FOR_EXCEPT_MSG(lcl_row < 0 || lcl_row >= A_n_lclrows,
                                    BlockHelperDetails::get_msg_prefix(comm)
                                        << "partitions[" << p[ip] << "]["
                                        << i << "] = " << lcl_row
                                        << " but input matrix implies limits of [0, " << A_n_lclrows - 1
                                        << "].");
        lclrow(offset + i)      = lcl_row;
        rowidx2part(offset + i) = ip;
        if (interf.row_contiguous && offset + i > 0 && lclrow((offset + i) - 1) + 1 != lcl_row)
          interf.row_contiguous = false;
      }
      partptr(ip + 1) = offset + ipnrows;

#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
      printf("Part index = ip = %d, first LID associated to the part = partptr(ip) = offset = %d, part->size() = ipnrows = %d;\n", ip, offset, ipnrows);
      printf("partptr(%d+1) = %d\n", ip, partptr(ip + 1));
#endif
    }

    part2rowidx0_sub(0) = 0;
    partptr_sub(0, 0)   = 0;
    // const local_ordinal_type number_pack_per_sub_part = ceil(float(nparts)/vector_length);

    for (local_ordinal_type ip = 0; ip < nparts; ++ip) {
      const auto *part                          = &partitions[p[ip]];
      const local_ordinal_type ipnrows          = part->size();
      const local_ordinal_type full_line_length = partptr(ip + 1) - partptr(ip);

      TEUCHOS_TEST_FOR_EXCEPTION(full_line_length != ipnrows, std::logic_error,
                                 "In the part " << ip);

      constexpr local_ordinal_type connection_length = 2;

      if (full_line_length < n_subparts_per_part + (n_subparts_per_part - 1) * connection_length)
        TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error,
                                   "The part " << ip << " is too short to use " << n_subparts_per_part << " sub parts.");

      const local_ordinal_type sub_line_length      = (full_line_length - (n_subparts_per_part - 1) * connection_length) / n_subparts_per_part;
      const local_ordinal_type last_sub_line_length = full_line_length - (n_subparts_per_part - 1) * (connection_length + sub_line_length);

      if (ip % vector_length == 0) pack_nrows_sub = ipnrows;

      for (local_ordinal_type local_sub_ip = 0; local_sub_ip < n_subparts_per_part; ++local_sub_ip) {
        const local_ordinal_type sub_ip   = nparts * (2 * local_sub_ip) + ip;
        const local_ordinal_type schur_ip = nparts * (2 * local_sub_ip + 1) + ip;
        if (local_sub_ip != n_subparts_per_part - 1) {
          if (local_sub_ip != 0) {
            partptr_sub(sub_ip, 0) = partptr_sub(nparts * (2 * local_sub_ip - 1) + ip, 1);
          } else if (ip != 0) {
            partptr_sub(sub_ip, 0) = partptr_sub(nparts * 2 * (n_subparts_per_part - 1) + ip - 1, 1);
          }
          partptr_sub(sub_ip, 1)   = sub_line_length + partptr_sub(sub_ip, 0);
          partptr_sub(schur_ip, 0) = partptr_sub(sub_ip, 1);
          partptr_sub(schur_ip, 1) = connection_length + partptr_sub(schur_ip, 0);

          part2rowidx0_sub(sub_ip + 1) = part2rowidx0_sub(sub_ip) + sub_line_length;
          part2rowidx0_sub(sub_ip + 2) = part2rowidx0_sub(sub_ip + 1) + connection_length;

#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
          printf("Sub Part index = %d, first LID associated to the sub part = %d, sub part size = %d;\n", sub_ip, partptr_sub(sub_ip, 0), sub_line_length);
          printf("Sub Part index Schur = %d, first LID associated to the sub part = %d, sub part size = %d;\n", sub_ip + 1, partptr_sub(ip, 2 * local_sub_ip + 1), connection_length);
#endif
        } else {
          if (local_sub_ip != 0) {
            partptr_sub(sub_ip, 0) = partptr_sub(nparts * (2 * local_sub_ip - 1) + ip, 1);
          } else if (ip != 0) {
            partptr_sub(sub_ip, 0) = partptr_sub(nparts * 2 * (n_subparts_per_part - 1) + ip - 1, 1);
          }
          partptr_sub(sub_ip, 1) = last_sub_line_length + partptr_sub(sub_ip, 0);

          part2rowidx0_sub(sub_ip + 1) = part2rowidx0_sub(sub_ip) + last_sub_line_length;

#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
          printf("Sub Part index = %d, first LID associated to the sub part = %d, sub part size = %d;\n", sub_ip, partptr_sub(sub_ip, 0), last_sub_line_length);
#endif
        }
      }
    }

    {
      local_ordinal_type npacks = ceil(float(nparts) / vector_length);

      local_ordinal_type ip_max = nparts > vector_length ? vector_length : nparts;
      for (local_ordinal_type ip = 0; ip < ip_max; ++ip) {
        part2packrowidx0_sub(ip, 0) = 0;
      }
      for (local_ordinal_type ipack = 0; ipack < npacks; ++ipack) {
        if (ipack != 0) {
          local_ordinal_type ip_min = ipack * vector_length;
          ip_max                    = nparts > (ipack + 1) * vector_length ? (ipack + 1) * vector_length : nparts;
          for (local_ordinal_type ip = ip_min; ip < ip_max; ++ip) {
            part2packrowidx0_sub(ip, 0) = part2packrowidx0_sub(ip - vector_length, part2packrowidx0_sub.extent(1) - 1);
          }
        }

        for (size_type local_sub_ip = 0; local_sub_ip < part2packrowidx0_sub.extent(1) - 1; ++local_sub_ip) {
          local_ordinal_type ip_min = ipack * vector_length;
          ip_max                    = nparts > (ipack + 1) * vector_length ? (ipack + 1) * vector_length : nparts;

          const local_ordinal_type full_line_length = partptr(ip_min + 1) - partptr(ip_min);

          constexpr local_ordinal_type connection_length = 2;

          const local_ordinal_type sub_line_length      = (full_line_length - (n_subparts_per_part - 1) * connection_length) / n_subparts_per_part;
          const local_ordinal_type last_sub_line_length = full_line_length - (n_subparts_per_part - 1) * (connection_length + sub_line_length);

          if (local_sub_ip % 2 == 0) pack_nrows_sub = sub_line_length;
          if (local_sub_ip % 2 == 1) pack_nrows_sub = connection_length;
          if (local_sub_ip == part2packrowidx0_sub.extent(1) - 2) pack_nrows_sub = last_sub_line_length;

          part2packrowidx0_sub(ip_min, local_sub_ip + 1) = part2packrowidx0_sub(ip_min, local_sub_ip) + pack_nrows_sub;

          for (local_ordinal_type ip = ip_min + 1; ip < ip_max; ++ip) {
            part2packrowidx0_sub(ip, local_sub_ip + 1) = part2packrowidx0_sub(ip_min, local_sub_ip + 1);
          }
        }
      }

      Kokkos::deep_copy(interf.part2packrowidx0_sub, part2packrowidx0_sub);
    }
    IFPACK2_BLOCKHELPER_TIMER_FENCE(typename BlockHelperDetails::ImplType<MatrixType>::execution_space)
  }
#if defined(BLOCKTRIDICONTAINER_DEBUG)
  TEUCHOS_ASSERT(partptr(nparts) == nrows);
#endif
  if (lclrow(0) != 0) interf.row_contiguous = false;

  Kokkos::deep_copy(interf.partptr, partptr);
  Kokkos::deep_copy(interf.lclrow, lclrow);

  Kokkos::deep_copy(interf.partptr_sub, partptr_sub);

  // assume No overlap. Thus:
  interf.part2rowidx0 = interf.partptr;
  Kokkos::deep_copy(interf.part2packrowidx0, part2packrowidx0);

  interf.part2packrowidx0_back = part2packrowidx0_sub(part2packrowidx0_sub.extent(0) - 1, part2packrowidx0_sub.extent(1) - 1);
  Kokkos::deep_copy(interf.rowidx2part, rowidx2part);

  {  // Fill packptr.
    IFPACK2_BLOCKHELPER_TIMER("Fill packptr", packptr0);
    local_ordinal_type npacks = ceil(float(nparts) / vector_length) * (part2packrowidx0_sub.extent(1) - 1);
    npacks                    = 0;
    for (local_ordinal_type ip = 1; ip <= nparts; ++ip)  // n_sub_parts_and_schur
      if (part2packrowidx0(ip) != part2packrowidx0(ip - 1))
        ++npacks;

    interf.packptr     = local_ordinal_type_1d_view(do_not_initialize_tag("packptr"), npacks + 1);
    const auto packptr = Kokkos::create_mirror_view(interf.packptr);
    packptr(0)         = 0;
    for (local_ordinal_type ip = 1, k = 1; ip <= nparts; ++ip)
      if (part2packrowidx0(ip) != part2packrowidx0(ip - 1))
        packptr(k++) = ip;

    Kokkos::deep_copy(interf.packptr, packptr);

    local_ordinal_type npacks_per_subpart = ceil(float(nparts) / vector_length);
    npacks                                = ceil(float(nparts) / vector_length) * (part2packrowidx0_sub.extent(1) - 1);

    interf.packindices_sub   = local_ordinal_type_1d_view(do_not_initialize_tag("packindices_sub"), npacks_per_subpart * n_subparts_per_part);
    interf.packindices_schur = local_ordinal_type_2d_view(do_not_initialize_tag("packindices_schur"), npacks_per_subpart, n_subparts_per_part - 1);

    const auto packindices_sub   = Kokkos::create_mirror_view(interf.packindices_sub);
    const auto packindices_schur = Kokkos::create_mirror_view(interf.packindices_schur);

    // Fill packindices_sub and packindices_schur
    for (local_ordinal_type local_sub_ip = 0; local_sub_ip < n_subparts_per_part - 1; ++local_sub_ip) {
      for (local_ordinal_type local_pack_ip = 0; local_pack_ip < npacks_per_subpart; ++local_pack_ip) {
        packindices_sub(local_sub_ip * npacks_per_subpart + local_pack_ip) = 2 * local_sub_ip * npacks_per_subpart + local_pack_ip;
        packindices_schur(local_pack_ip, local_sub_ip)                     = 2 * local_sub_ip * npacks_per_subpart + local_pack_ip + npacks_per_subpart;
      }
    }

    for (local_ordinal_type local_pack_ip = 0; local_pack_ip < npacks_per_subpart; ++local_pack_ip) {
      packindices_sub((n_subparts_per_part - 1) * npacks_per_subpart + local_pack_ip) = 2 * (n_subparts_per_part - 1) * npacks_per_subpart + local_pack_ip;
    }

#ifdef IFPACK2_BLOCKTRIDICONTAINER_WRITE_MM
    std::cout << "packindices_sub = " << std::endl;
    for (size_type i = 0; i < packindices_sub.extent(0); ++i) {
      std::cout << packindices_sub(i) << " ";
    }
    std::cout << std::endl;
    std::cout << "packindices_sub end" << std::endl;

    std::cout << "packindices_schur = " << std::endl;
    for (size_type i = 0; i < packindices_schur.extent(0); ++i) {
      for (size_type j = 0; j < packindices_schur.extent(1); ++j) {
        std::cout << packindices_schur(i, j) << " ";
      }
      std::cout << std::endl;
    }

    std::cout << "packindices_schur end" << std::endl;
#endif

    Kokkos::deep_copy(interf.packindices_sub, packindices_sub);
    Kokkos::deep_copy(interf.packindices_schur, packindices_schur);

    interf.packptr_sub     = local_ordinal_type_1d_view(do_not_initialize_tag("packptr"), npacks + 1);
    const auto packptr_sub = Kokkos::create_mirror_view(interf.packptr_sub);
    packptr_sub(0)         = 0;
    for (local_ordinal_type k = 0; k < npacks + 1; ++k)
      packptr_sub(k) = packptr(k % npacks_per_subpart) + (k / npacks_per_subpart) * packptr(npacks_per_subpart);

    Kokkos::deep_copy(interf.packptr_sub, packptr_sub);
    IFPACK2_BLOCKHELPER_TIMER_FENCE(typename BlockHelperDetails::ImplType<MatrixType>::execution_space)
  }
  IFPACK2_BLOCKHELPER_TIMER_FENCE(typename BlockHelperDetails::ImplType<MatrixType>::execution_space)

  return interf;
}

template <typename MatrixType>
struct BlockTridiags {
  using impl_type                  = BlockHelperDetails::ImplType<MatrixType>;
  using local_ordinal_type_1d_view = typename impl_type::local_ordinal_type_1d_view;
  using size_type_1d_view          = typename impl_type::size_type_1d_view;
  using size_type_2d_view          = typename impl_type::size_type_2d_view;
  using vector_type_3d_view        = typename impl_type::vector_type_3d_view;
  using vector_type_4d_view        = typename impl_type::vector_type_4d_view;
  using btdm_scalar_type_3d_view   = typename impl_type::btdm_scalar_type_3d_view;

  // flat_td_ptr(i) is the index into flat-array values of the start of the
  // i'th tridiag. pack_td_ptr is the same, but for packs. If vector_length ==
  // 1, pack_td_ptr is the same as flat_td_ptr; if vector_length > 1, then i %
  // vector_length is the position in the pack.
  size_type_2d_view flat_td_ptr, pack_td_ptr, pack_td_ptr_schur;
  // List of local column indices into A from which to grab
  // data. flat_td_ptr(i) points to the start of the i'th tridiag's data.
  local_ordinal_type_1d_view A_colindsub;
  // Tridiag block values. pack_td_ptr(i) points to the start of the i'th
  // tridiag's pack, and i % vector_length gives the position in the pack.
  vector_type_3d_view values;
  // Schur block values. pack_td_ptr_schur(i) points to the start of the i'th
  // Schur's pack, and i % vector_length gives the position in the pack.
  vector_type_3d_view values_schur;
  // inv(A_00)*A_01 block values.
  vector_type_4d_view e_values;

  // The following are for fused block Jacobi only.
  // For block row i, diag_offset(i)...diag_offset(i + bs^2)
  // is the range of scalars for the diagonal block.
  size_type_1d_view diag_offsets;
  // For fused residual+solve block Jacobi case,
  // this contains the diagonal block inverses in flat, local row indexing:
  // d_inv(row, :, :) gives the row-major block for row.
  btdm_scalar_type_3d_view d_inv;

  bool is_diagonal_only;

  BlockTridiags()                       = default;
  BlockTridiags(const BlockTridiags &b) = default;

  // Index into row-major block of a tridiag.
  template <typename idx_type>
  static KOKKOS_FORCEINLINE_FUNCTION
      idx_type
      IndexToRow(const idx_type &ind) { return (ind + 1) / 3; }
  // Given a row of a row-major tridiag, return the index of the first block
  // in that row.
  template <typename idx_type>
  static KOKKOS_FORCEINLINE_FUNCTION
      idx_type
      RowToIndex(const idx_type &row) { return row > 0 ? 3 * row - 1 : 0; }
  // Number of blocks in a tridiag having a given number of rows.
  template <typename idx_type>
  static KOKKOS_FORCEINLINE_FUNCTION
      idx_type
      NumBlocks(const idx_type &nrows) { return nrows > 0 ? 3 * nrows - 2 : 0; }
  // Number of blocks associated to a Schur complement having a given number of rows.
  template <typename idx_type>
  static KOKKOS_FORCEINLINE_FUNCTION
      idx_type
      NumBlocksSchur(const idx_type &nrows) { return nrows > 0 ? 3 * nrows + 2 : 0; }
};

template <typename MatrixType>
BlockTridiags<MatrixType>
createBlockTridiags(const BlockHelperDetails::PartInterface<MatrixType> &interf) {
  IFPACK2_BLOCKHELPER_TIMER("createBlockTridiags", createBlockTridiags0);
  using impl_type          = BlockHelperDetails::ImplType<MatrixType>;
  using execution_space    = typename impl_type::execution_space;
  using local_ordinal_type = typename impl_type::local_ordinal_type;
  using size_type          = typename impl_type::size_type;
  using size_type_2d_view  = typename impl_type::size_type_2d_view;

  constexpr int vector_length = impl_type::vector_length;

  BlockTridiags<MatrixType> btdm;

  const local_ordinal_type ntridiags = interf.partptr_sub.extent(0);

  {  // construct the flat index pointers into the tridiag values array.
    btdm.flat_td_ptr = size_type_2d_view(do_not_initialize_tag("btdm.flat_td_ptr"), interf.nparts, 2 * interf.n_subparts_per_part);
    const Kokkos::RangePolicy<execution_space> policy(0, 2 * interf.nparts * interf.n_subparts_per_part);
    Kokkos::parallel_scan(
        "createBlockTridiags::RangePolicy::flat_td_ptr",
        policy, KOKKOS_LAMBDA(const local_ordinal_type &i, size_type &update, const bool &final) {
          const local_ordinal_type partidx          = i / (2 * interf.n_subparts_per_part);
          const local_ordinal_type local_subpartidx = i % (2 * interf.n_subparts_per_part);

          if (final) {
            btdm.flat_td_ptr(partidx, local_subpartidx) = update;
          }
          if (local_subpartidx != (2 * interf.n_subparts_per_part - 1)) {
            const local_ordinal_type nrows = interf.partptr_sub(interf.nparts * local_subpartidx + partidx, 1) - interf.partptr_sub(interf.nparts * local_subpartidx + partidx, 0);
            if (local_subpartidx % 2 == 0)
              update += btdm.NumBlocks(nrows);
            else
              update += btdm.NumBlocksSchur(nrows);
          }
        });

    const auto nblocks    = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), Kokkos::subview(btdm.flat_td_ptr, interf.nparts - 1, 2 * interf.n_subparts_per_part - 1));
    btdm.is_diagonal_only = (static_cast<local_ordinal_type>(nblocks()) == ntridiags);
  }

  // And the packed index pointers.
  if (vector_length == 1) {
    btdm.pack_td_ptr = btdm.flat_td_ptr;
  } else {
    // const local_ordinal_type npacks = interf.packptr_sub.extent(0) - 1;

    local_ordinal_type npacks_per_subpart = 0;
    const auto part2packrowidx0           = Kokkos::create_mirror_view(interf.part2packrowidx0);
    Kokkos::deep_copy(part2packrowidx0, interf.part2packrowidx0);
    for (local_ordinal_type ip = 1; ip <= interf.nparts; ++ip)  // n_sub_parts_and_schur
      if (part2packrowidx0(ip) != part2packrowidx0(ip - 1))
        ++npacks_per_subpart;

    btdm.pack_td_ptr = size_type_2d_view(do_not_initialize_tag("btdm.pack_td_ptr"), interf.nparts, 2 * interf.n_subparts_per_part);
    const Kokkos::RangePolicy<execution_space> policy(0, npacks_per_subpart);

    Kokkos::parallel_for(
        "createBlockTridiags::RangePolicy::pack_td_ptr",
        policy, KOKKOS_LAMBDA(const local_ordinal_type &i) {
          for (local_ordinal_type j = 0; j < 2 * interf.n_subparts_per_part; ++j) {
            const local_ordinal_type pack_id        = (j == 2 * interf.n_subparts_per_part - 1) ? i + (j - 1) * npacks_per_subpart : i + j * npacks_per_subpart;
            const local_ordinal_type nparts_in_pack = interf.packptr_sub(pack_id + 1) - interf.packptr_sub(pack_id);

            const local_ordinal_type parti   = interf.packptr_sub(pack_id);
            const local_ordinal_type partidx = parti % interf.nparts;

            for (local_ordinal_type pti = 0; pti < nparts_in_pack; ++pti) {
              btdm.pack_td_ptr(partidx + pti, j) = btdm.flat_td_ptr(i, j);
            }
          }
        });
  }

  btdm.pack_td_ptr_schur = size_type_2d_view(do_not_initialize_tag("btdm.pack_td_ptr_schur"), interf.nparts, interf.n_subparts_per_part);

  const auto host_pack_td_ptr_schur              = Kokkos::create_mirror_view(btdm.pack_td_ptr_schur);
  constexpr local_ordinal_type connection_length = 2;

  host_pack_td_ptr_schur(0, 0) = 0;
  for (local_ordinal_type i = 0; i < interf.nparts; ++i) {
    if (i % vector_length == 0) {
      if (i != 0)
        host_pack_td_ptr_schur(i, 0) = host_pack_td_ptr_schur(i - 1, host_pack_td_ptr_schur.extent(1) - 1);
      for (local_ordinal_type j = 0; j < interf.n_subparts_per_part - 1; ++j) {
        host_pack_td_ptr_schur(i, j + 1) = host_pack_td_ptr_schur(i, j) + btdm.NumBlocks(connection_length) + (j != 0 ? 1 : 0) + (j != interf.n_subparts_per_part - 2 ? 1 : 0);
      }
    } else {
      for (local_ordinal_type j = 0; j < interf.n_subparts_per_part; ++j) {
        host_pack_td_ptr_schur(i, j) = host_pack_td_ptr_schur(i - 1, j);
      }
    }
  }

  Kokkos::deep_copy(btdm.pack_td_ptr_schur, host_pack_td_ptr_schur);

#ifdef IFPACK2_BLOCKTRIDICONTAINER_WRITE_MM
  const auto host_flat_td_ptr = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), btdm.flat_td_ptr);
  std::cout << "flat_td_ptr = " << std::endl;
  for (size_type i = 0; i < host_flat_td_ptr.extent(0); ++i) {
    for (size_type j = 0; j < host_flat_td_ptr.extent(1); ++j) {
      std::cout << host_flat_td_ptr(i, j) << " ";
    }
    std::cout << std::endl;
  }
  std::cout << "flat_td_ptr end" << std::endl;

  const auto host_pack_td_ptr = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), btdm.pack_td_ptr);

  std::cout << "pack_td_ptr = " << std::endl;
  for (size_type i = 0; i < host_pack_td_ptr.extent(0); ++i) {
    for (size_type j = 0; j < host_pack_td_ptr.extent(1); ++j) {
      std::cout << host_pack_td_ptr(i, j) << " ";
    }
    std::cout << std::endl;
  }
  std::cout << "pack_td_ptr end" << std::endl;

  std::cout << "pack_td_ptr_schur = " << std::endl;
  for (size_type i = 0; i < host_pack_td_ptr_schur.extent(0); ++i) {
    for (size_type j = 0; j < host_pack_td_ptr_schur.extent(1); ++j) {
      std::cout << host_pack_td_ptr_schur(i, j) << " ";
    }
    std::cout << std::endl;
  }
  std::cout << "pack_td_ptr_schur end" << std::endl;
#endif

  // values and A_colindsub are created in the symbolic phase
  IFPACK2_BLOCKHELPER_TIMER_FENCE(typename BlockHelperDetails::ImplType<MatrixType>::execution_space)

  return btdm;
}

// Set the tridiags to be I to the full pack block size. That way, if a
// tridiag within a pack is shorter than the longest one, the extra blocks are
// processed in a safe way. Similarly, in the solve phase, if the extra blocks
// in the packed multvector are 0, and the tridiag LU reflects the extra I
// blocks, then the solve proceeds as though the extra blocks aren't
// present. Since this extra work is part of the SIMD calls, it's not actually
// extra work. Instead, it means we don't have to put checks or masks in, or
// quiet NaNs. This functor has to be called just once, in the symbolic phase,
// since the numeric phase fills in only the used entries, leaving these I
// blocks intact.
template <typename MatrixType>
void setTridiagsToIdentity(const BlockTridiags<MatrixType> &btdm,
                           const typename BlockHelperDetails::ImplType<MatrixType>::local_ordinal_type_1d_view &packptr) {
  using impl_type          = BlockHelperDetails::ImplType<MatrixType>;
  using execution_space    = typename impl_type::execution_space;
  using local_ordinal_type = typename impl_type::local_ordinal_type;
  using size_type_2d_view  = typename impl_type::size_type_2d_view;

  const ConstUnmanaged<size_type_2d_view> pack_td_ptr(btdm.pack_td_ptr);
  const local_ordinal_type blocksize = btdm.values.extent(1);

  {
    const int vector_length          = impl_type::vector_length;
    const int internal_vector_length = impl_type::internal_vector_length;

    using btdm_scalar_type     = typename impl_type::btdm_scalar_type;
    using internal_vector_type = typename impl_type::internal_vector_type;
    using internal_vector_type_4d_view =
        typename impl_type::internal_vector_type_4d_view;

    using team_policy_type = Kokkos::TeamPolicy<execution_space>;
    const internal_vector_type_4d_view values(reinterpret_cast<internal_vector_type *>(btdm.values.data()),
                                              btdm.values.extent(0),
                                              btdm.values.extent(1),
                                              btdm.values.extent(2),
                                              vector_length / internal_vector_length);
    const local_ordinal_type vector_loop_size = values.extent(3);
#if defined(KOKKOS_ENABLE_CUDA) && defined(__CUDA_ARCH__)
    local_ordinal_type total_team_size(0);
    if (blocksize <= 5)
      total_team_size = 32;
    else if (blocksize <= 9)
      total_team_size = 64;
    else if (blocksize <= 12)
      total_team_size = 96;
    else if (blocksize <= 16)
      total_team_size = 128;
    else if (blocksize <= 20)
      total_team_size = 160;
    else
      total_team_size = 160;
    const local_ordinal_type team_size = total_team_size / vector_loop_size;
    const team_policy_type policy(packptr.extent(0) - 1, team_size, vector_loop_size);
#elif defined(KOKKOS_ENABLE_HIP)
    // FIXME: HIP
    // These settings might be completely wrong
    // will have to do some experiments to decide
    // what makes sense on AMD GPUs
    local_ordinal_type total_team_size(0);
    if (blocksize <= 5)
      total_team_size = 32;
    else if (blocksize <= 9)
      total_team_size = 64;
    else if (blocksize <= 12)
      total_team_size = 96;
    else if (blocksize <= 16)
      total_team_size = 128;
    else if (blocksize <= 20)
      total_team_size = 160;
    else
      total_team_size = 160;
    const local_ordinal_type team_size = total_team_size / vector_loop_size;
    const team_policy_type policy(packptr.extent(0) - 1, team_size, vector_loop_size);
#elif defined(KOKKOS_ENABLE_SYCL)
    // SYCL: FIXME
    local_ordinal_type total_team_size(0);
    if (blocksize <= 5)
      total_team_size = 32;
    else if (blocksize <= 9)
      total_team_size = 64;
    else if (blocksize <= 12)
      total_team_size = 96;
    else if (blocksize <= 16)
      total_team_size = 128;
    else if (blocksize <= 20)
      total_team_size = 160;
    else
      total_team_size = 160;
    const local_ordinal_type team_size = total_team_size / vector_loop_size;
    const team_policy_type policy(packptr.extent(0) - 1, team_size, vector_loop_size);
#else
    // Host architecture: team size is always one
    const team_policy_type policy(packptr.extent(0) - 1, 1, 1);
#endif
    Kokkos::parallel_for(
        "setTridiagsToIdentity::TeamPolicy",
        policy, KOKKOS_LAMBDA(const typename team_policy_type::member_type &member) {
          const local_ordinal_type k    = member.league_rank();
          const local_ordinal_type ibeg = pack_td_ptr(packptr(k), 0);
          const local_ordinal_type iend = pack_td_ptr(packptr(k), pack_td_ptr.extent(1) - 1);

          const local_ordinal_type diff   = iend - ibeg;
          const local_ordinal_type icount = diff / 3 + (diff % 3 > 0);
          const btdm_scalar_type one(1);
          Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
            Kokkos::parallel_for(Kokkos::TeamThreadRange(member, icount), [&](const local_ordinal_type &ii) {
              const local_ordinal_type i = ibeg + ii * 3;
              for (local_ordinal_type j = 0; j < blocksize; ++j) {
                values(i, j, j, v) = one;
              }
            });
          });
        });
  }
}

template <typename MatrixType>
void performSymbolicPhase(const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_row_matrix_type> &A,
                          const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_crs_graph_type> &g,
                          const BlockHelperDetails::PartInterface<MatrixType> &interf,
                          BlockTridiags<MatrixType> &btdm,
                          BlockHelperDetails::AmD<MatrixType> &amd,
                          const bool overlap_communication_and_computation,
                          const Teuchos::RCP<AsyncableImport<MatrixType>> &async_importer,
                          bool useSeqMethod,
                          bool use_fused_jacobi) {
  IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::SymbolicPhase", SymbolicPhase);

  using impl_type = BlockHelperDetails::ImplType<MatrixType>;

  using execution_space      = typename impl_type::execution_space;
  using host_execution_space = typename impl_type::host_execution_space;

  using local_ordinal_type         = typename impl_type::local_ordinal_type;
  using global_ordinal_type        = typename impl_type::global_ordinal_type;
  using size_type                  = typename impl_type::size_type;
  using local_ordinal_type_1d_view = typename impl_type::local_ordinal_type_1d_view;
  using size_type_1d_view          = typename impl_type::size_type_1d_view;
  using vector_type_3d_view        = typename impl_type::vector_type_3d_view;
  using vector_type_4d_view        = typename impl_type::vector_type_4d_view;
  using crs_matrix_type            = typename impl_type::tpetra_crs_matrix_type;
  using block_crs_matrix_type      = typename impl_type::tpetra_block_crs_matrix_type;
  using btdm_scalar_type_3d_view   = typename impl_type::btdm_scalar_type_3d_view;

  constexpr int vector_length = impl_type::vector_length;

  const auto comm = A->getRowMap()->getComm();

  auto A_crs  = Teuchos::rcp_dynamic_cast<const crs_matrix_type>(A);
  auto A_bcrs = Teuchos::rcp_dynamic_cast<const block_crs_matrix_type>(A);

  bool hasBlockCrsMatrix = !A_bcrs.is_null();
  TEUCHOS_ASSERT(hasBlockCrsMatrix || g->getLocalNumRows() != 0);
  const local_ordinal_type blocksize = hasBlockCrsMatrix ? A->getBlockSize() : A->getLocalNumRows() / g->getLocalNumRows();

  // mirroring to host
  const auto partptr      = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), interf.partptr);
  const auto lclrow       = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), interf.lclrow);
  const auto rowidx2part  = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), interf.rowidx2part);
  const auto part2rowidx0 = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), interf.part2rowidx0);
  const auto packptr      = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), interf.packptr);

  const local_ordinal_type nrows = partptr(partptr.extent(0) - 1);

  Kokkos::View<local_ordinal_type *, host_execution_space> col2row("col2row", A->getLocalNumCols());

  // find column to row map on host

  Kokkos::deep_copy(col2row, Teuchos::OrdinalTraits<local_ordinal_type>::invalid());
  {
    const auto rowmap = g->getRowMap();
    const auto colmap = g->getColMap();
    const auto dommap = g->getDomainMap();
    TEUCHOS_ASSERT(!(rowmap.is_null() || colmap.is_null() || dommap.is_null()));
    rowmap->lazyPushToHost();
    colmap->lazyPushToHost();
    dommap->lazyPushToHost();

#if !defined(__CUDA_ARCH__) && !defined(__HIP_DEVICE_COMPILE__) && !defined(__SYCL_DEVICE_ONLY__)
    const Kokkos::RangePolicy<host_execution_space> policy(0, nrows);
    Kokkos::parallel_for(
        "performSymbolicPhase::RangePolicy::col2row",
        policy, KOKKOS_LAMBDA(const local_ordinal_type &lr) {
          const global_ordinal_type gid = rowmap->getGlobalElement(lr);
          TEUCHOS_ASSERT(gid != Teuchos::OrdinalTraits<global_ordinal_type>::invalid());
          if (dommap->isNodeGlobalElement(gid)) {
            const local_ordinal_type lc = colmap->getLocalElement(gid);
#if defined(BLOCKTRIDICONTAINER_DEBUG)
            TEUCHOS_TEST_FOR_EXCEPT_MSG(lc == Teuchos::OrdinalTraits<local_ordinal_type>::invalid(),
                                        BlockHelperDetails::get_msg_prefix(comm) << "GID " << gid
                                                                                 << " gives an invalid local column.");
#endif
            col2row(lc) = lr;
          }
        });
#endif
  }

  // construct the D and R graphs in A = D + R.
  {
    const auto local_graph        = g->getLocalGraphHost();
    const auto local_graph_rowptr = local_graph.row_map;
    TEUCHOS_ASSERT(local_graph_rowptr.size() == static_cast<size_t>(nrows + 1));
    const auto local_graph_colidx = local_graph.entries;

    // assume no overlap.

    Kokkos::View<local_ordinal_type *, host_execution_space> lclrow2idx("lclrow2idx", nrows);
    {
      const Kokkos::RangePolicy<host_execution_space> policy(0, nrows);
      Kokkos::parallel_for(
          "performSymbolicPhase::RangePolicy::lclrow2idx",
          policy, KOKKOS_LAMBDA(const local_ordinal_type &i) {
            lclrow2idx[lclrow(i)] = i;
          });
    }

    // count (block) nnzs in D and R.
    typedef BlockHelperDetails::SumReducer<size_type, 3, host_execution_space> sum_reducer_type;
    typename sum_reducer_type::value_type sum_reducer_value;
    {
      const Kokkos::RangePolicy<host_execution_space> policy(0, nrows);
      Kokkos::parallel_reduce
          // profiling interface does not work
          (  //"performSymbolicPhase::RangePolicy::count_nnz",
              policy, KOKKOS_LAMBDA(const local_ordinal_type &lr, typename sum_reducer_type::value_type &update) {
                // LID -> index.
                const local_ordinal_type ri0 = lclrow2idx[lr];
                const local_ordinal_type pi0 = rowidx2part(ri0);
                for (size_type j = local_graph_rowptr(lr); j < local_graph_rowptr(lr + 1); ++j) {
                  const local_ordinal_type lc   = local_graph_colidx(j);
                  const local_ordinal_type lc2r = col2row[lc];
                  bool incr_R                   = false;
                  do {  // breakable
                    if (lc2r == (local_ordinal_type)-1) {
                      incr_R = true;
                      break;
                    }
                    const local_ordinal_type ri = lclrow2idx[lc2r];
                    const local_ordinal_type pi = rowidx2part(ri);
                    if (pi != pi0) {
                      incr_R = true;
                      break;
                    }
                    // Test for being in the tridiag. This is done in index space. In
                    // LID space, tridiag LIDs in a row are not necessarily related by
                    // {-1, 0, 1}.
                    if (ri0 + 1 >= ri && ri0 <= ri + 1)
                      ++update.v[0];  // D_nnz
                    else
                      incr_R = true;
                  } while (0);
                  if (incr_R) {
                    if (lc < nrows)
                      ++update.v[1];  // R_nnz_owned
                    else
                      ++update.v[2];  // R_nnz_remote
                  }
                }
              },
              sum_reducer_type(sum_reducer_value));
    }
    size_type D_nnz        = sum_reducer_value.v[0];
    size_type R_nnz_owned  = sum_reducer_value.v[1];
    size_type R_nnz_remote = sum_reducer_value.v[2];

    if (!overlap_communication_and_computation) {
      R_nnz_owned += R_nnz_remote;
      R_nnz_remote = 0;
    }

    // construct the D_00 graph.
    {
      const auto flat_td_ptr = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), btdm.flat_td_ptr);

      btdm.A_colindsub         = local_ordinal_type_1d_view("btdm.A_colindsub", D_nnz);
      const auto D_A_colindsub = Kokkos::create_mirror_view(btdm.A_colindsub);

#if defined(BLOCKTRIDICONTAINER_DEBUG)
      Kokkos::deep_copy(D_A_colindsub, Teuchos::OrdinalTraits<local_ordinal_type>::invalid());
#endif

      const local_ordinal_type nparts = partptr.extent(0) - 1;

      {
        const Kokkos::RangePolicy<host_execution_space> policy(0, nparts);
        Kokkos::parallel_for(
            "performSymbolicPhase::RangePolicy<host_execution_space>::D_graph",
            policy, KOKKOS_LAMBDA(const local_ordinal_type &pi0) {
              const local_ordinal_type part_ri0 = part2rowidx0(pi0);
              local_ordinal_type offset         = 0;
              for (local_ordinal_type ri0 = partptr(pi0); ri0 < partptr(pi0 + 1); ++ri0) {
                const local_ordinal_type td_row_os = btdm.RowToIndex(ri0 - part_ri0) + offset;
                offset                             = 1;
                const local_ordinal_type lr0       = lclrow(ri0);
                const size_type j0                 = local_graph_rowptr(lr0);
                for (size_type j = j0; j < local_graph_rowptr(lr0 + 1); ++j) {
                  const local_ordinal_type lc   = local_graph_colidx(j);
                  const local_ordinal_type lc2r = col2row[lc];
                  if (lc2r == (local_ordinal_type)-1) continue;
                  const local_ordinal_type ri = lclrow2idx[lc2r];
                  const local_ordinal_type pi = rowidx2part(ri);
                  if (pi != pi0) continue;
                  if (ri + 1 < ri0 || ri > ri0 + 1) continue;
                  const local_ordinal_type row_entry                            = j - j0;
                  D_A_colindsub(flat_td_ptr(pi0, 0) + ((td_row_os + ri) - ri0)) = row_entry;
                }
              }
            });
      }
#if defined(BLOCKTRIDICONTAINER_DEBUG)
      for (size_t i = 0; i < D_A_colindsub.extent(0); ++i)
        TEUCHOS_ASSERT(D_A_colindsub(i) != Teuchos::OrdinalTraits<local_ordinal_type>::invalid());
#endif
      Kokkos::deep_copy(btdm.A_colindsub, D_A_colindsub);

      // Allocate values.
      {
        const auto pack_td_ptr_last  = Kokkos::subview(btdm.pack_td_ptr, btdm.pack_td_ptr.extent(0) - 1, btdm.pack_td_ptr.extent(1) - 1);
        const auto num_packed_blocks = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), pack_td_ptr_last);
        btdm.values                  = vector_type_3d_view("btdm.values", num_packed_blocks(), blocksize, blocksize);

        if (interf.n_subparts_per_part > 1) {
          const auto pack_td_ptr_schur_last  = Kokkos::subview(btdm.pack_td_ptr_schur, btdm.pack_td_ptr_schur.extent(0) - 1, btdm.pack_td_ptr_schur.extent(1) - 1);
          const auto num_packed_blocks_schur = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), pack_td_ptr_schur_last);
          btdm.values_schur                  = vector_type_3d_view("btdm.values_schur", num_packed_blocks_schur(), blocksize, blocksize);
        }

        if (vector_length > 1) setTridiagsToIdentity(btdm, interf.packptr);
      }
    }

    // Construct the R graph.
    {
      amd.rowptr      = size_type_1d_view("amd.rowptr", nrows + 1);
      amd.A_colindsub = local_ordinal_type_1d_view(do_not_initialize_tag("amd.A_colindsub"), R_nnz_owned);

      const auto R_rowptr      = Kokkos::create_mirror_view(amd.rowptr);
      const auto R_A_colindsub = Kokkos::create_mirror_view(amd.A_colindsub);

      amd.rowptr_remote      = size_type_1d_view("amd.rowptr_remote", overlap_communication_and_computation ? nrows + 1 : 0);
      amd.A_colindsub_remote = local_ordinal_type_1d_view(do_not_initialize_tag("amd.A_colindsub_remote"), R_nnz_remote);

      const auto R_rowptr_remote      = Kokkos::create_mirror_view(amd.rowptr_remote);
      const auto R_A_colindsub_remote = Kokkos::create_mirror_view(amd.A_colindsub_remote);

      {
        const Kokkos::RangePolicy<host_execution_space> policy(0, nrows);
        Kokkos::parallel_for(
            "performSymbolicPhase::RangePolicy<host_execution_space>::R_graph_count",
            policy, KOKKOS_LAMBDA(const local_ordinal_type &lr) {
              const local_ordinal_type ri0 = lclrow2idx[lr];
              const local_ordinal_type pi0 = rowidx2part(ri0);
              const size_type j0           = local_graph_rowptr(lr);
              for (size_type j = j0; j < local_graph_rowptr(lr + 1); ++j) {
                const local_ordinal_type lc   = local_graph_colidx(j);
                const local_ordinal_type lc2r = col2row[lc];
                if (lc2r != (local_ordinal_type)-1) {
                  const local_ordinal_type ri = lclrow2idx[lc2r];
                  const local_ordinal_type pi = rowidx2part(ri);
                  if (pi == pi0 && ri + 1 >= ri0 && ri <= ri0 + 1) {
                    continue;
                  }
                }
                // exclusive scan will be performed later
                if (!overlap_communication_and_computation || lc < nrows) {
                  ++R_rowptr(lr);
                } else {
                  ++R_rowptr_remote(lr);
                }
              }
            });
      }

      // exclusive scan
      typedef BlockHelperDetails::ArrayValueType<size_type, 2> update_type;
      {
        Kokkos::RangePolicy<host_execution_space> policy(0, nrows + 1);
        Kokkos::parallel_scan(
            "performSymbolicPhase::RangePolicy<host_execution_space>::R_graph_fill",
            policy, KOKKOS_LAMBDA(const local_ordinal_type &lr, update_type &update, const bool &final) {
              update_type val;
              val.v[0] = R_rowptr(lr);
              if (overlap_communication_and_computation)
                val.v[1] = R_rowptr_remote(lr);

              if (final) {
                R_rowptr(lr) = update.v[0];
                if (overlap_communication_and_computation)
                  R_rowptr_remote(lr) = update.v[1];

                if (lr < nrows) {
                  const local_ordinal_type ri0 = lclrow2idx[lr];
                  const local_ordinal_type pi0 = rowidx2part(ri0);

                  size_type cnt_rowptr        = R_rowptr(lr);
                  size_type cnt_rowptr_remote = overlap_communication_and_computation ? R_rowptr_remote(lr) : 0;  // when not overlap_communication_and_computation, this value is garbage

                  const size_type j0 = local_graph_rowptr(lr);
                  for (size_type j = j0; j < local_graph_rowptr(lr + 1); ++j) {
                    const local_ordinal_type lc   = local_graph_colidx(j);
                    const local_ordinal_type lc2r = col2row[lc];
                    if (lc2r != (local_ordinal_type)-1) {
                      const local_ordinal_type ri = lclrow2idx[lc2r];
                      const local_ordinal_type pi = rowidx2part(ri);
                      if (pi == pi0 && ri + 1 >= ri0 && ri <= ri0 + 1)
                        continue;
                    }
                    const local_ordinal_type row_entry = j - j0;
                    if (!overlap_communication_and_computation || lc < nrows)
                      R_A_colindsub(cnt_rowptr++) = row_entry;
                    else
                      R_A_colindsub_remote(cnt_rowptr_remote++) = row_entry;
                  }
                }
              }
              update += val;
            });
      }
      TEUCHOS_ASSERT(R_rowptr(nrows) == R_nnz_owned);
      Kokkos::deep_copy(amd.rowptr, R_rowptr);
      Kokkos::deep_copy(amd.A_colindsub, R_A_colindsub);
      if (overlap_communication_and_computation) {
        TEUCHOS_ASSERT(R_rowptr_remote(nrows) == R_nnz_remote);
        Kokkos::deep_copy(amd.rowptr_remote, R_rowptr_remote);
        Kokkos::deep_copy(amd.A_colindsub_remote, R_A_colindsub_remote);
      }

      // Allocate or view values.
      if (hasBlockCrsMatrix)
        amd.tpetra_values = (const_cast<block_crs_matrix_type *>(A_bcrs.get())->getValuesDeviceNonConst());
      else {
        amd.tpetra_values = (const_cast<crs_matrix_type *>(A_crs.get()))->getLocalValuesDevice(Tpetra::Access::ReadWrite);
      }
    }

    // Allocate view for E and initialize the values with B:

    if (interf.n_subparts_per_part > 1)
      btdm.e_values = vector_type_4d_view("btdm.e_values", 2, interf.part2packrowidx0_back, blocksize, blocksize);
  }
  // Precompute offsets of each A and x entry to speed up residual.
  // Applies if all of these are true:
  // - hasBlockCrsMatrix
  // - execution_space is a GPU
  // - !useSeqMethod (since this uses a different scheme for indexing A,x)
  //
  // Reading A, x take up to 4 and 6 levels of indirection respectively,
  // but precomputing the offsets reduces it to 2 for both (get index, then value)
  if (BlockHelperDetails::is_device<execution_space>::value && !useSeqMethod && hasBlockCrsMatrix) {
    bool is_async_importer_active    = !async_importer.is_null();
    local_ordinal_type_1d_view dm2cm = is_async_importer_active ? async_importer->dm2cm : local_ordinal_type_1d_view();
    bool ownedRemoteSeparate         = overlap_communication_and_computation || !is_async_importer_active;
    BlockHelperDetails::precompute_A_x_offsets<MatrixType>(amd, interf, g, dm2cm, blocksize, ownedRemoteSeparate);
  }

  // If using fused block Jacobi path, allocate diagonal inverses here (d_inv) and find diagonal offsets.
  if (use_fused_jacobi) {
    btdm.d_inv        = btdm_scalar_type_3d_view(do_not_initialize_tag("btdm.d_inv"), interf.nparts, blocksize, blocksize);
    auto rowptrs      = A_bcrs->getCrsGraph().getLocalRowPtrsDevice();
    auto entries      = A_bcrs->getCrsGraph().getLocalIndicesDevice();
    btdm.diag_offsets = BlockHelperDetails::findDiagOffsets<execution_space, size_type_1d_view>(rowptrs, entries, interf.nparts, blocksize);
  }
  IFPACK2_BLOCKHELPER_TIMER_FENCE(typename BlockHelperDetails::ImplType<MatrixType>::execution_space)
}

template <typename ArgActiveExecutionMemorySpace>
struct ExtractAndFactorizeTridiagsDefaultModeAndAlgo;

template <>
struct ExtractAndFactorizeTridiagsDefaultModeAndAlgo<Kokkos::HostSpace> {
  typedef KB::Mode::Serial mode_type;
#if defined(__KOKKOSBATCHED_INTEL_MKL_COMPACT_BATCHED__)
  typedef KB::Algo::Level3::CompactMKL algo_type;
#else
  typedef KB::Algo::Level3::Blocked algo_type;
#endif
  static int recommended_team_size(const int /* blksize */,
                                   const int /* vector_length */,
                                   const int /* internal_vector_length */) {
    return 1;
  }
};

#if defined(KOKKOS_ENABLE_CUDA)
static inline int ExtractAndFactorizeRecommendedCudaTeamSize(const int blksize,
                                                             const int vector_length,
                                                             const int internal_vector_length) {
  const int vector_size = vector_length / internal_vector_length;
  int total_team_size(0);
  if (blksize <= 5)
    total_team_size = 32;
  else if (blksize <= 9)
    total_team_size = 32;  // 64
  else if (blksize <= 12)
    total_team_size = 96;
  else if (blksize <= 16)
    total_team_size = 128;
  else if (blksize <= 20)
    total_team_size = 160;
  else
    total_team_size = 160;
  return 2 * total_team_size / vector_size;
}
template <>
struct ExtractAndFactorizeTridiagsDefaultModeAndAlgo<Kokkos::CudaSpace> {
  typedef KB::Mode::Team mode_type;
  typedef KB::Algo::Level3::Unblocked algo_type;
  static int recommended_team_size(const int blksize,
                                   const int vector_length,
                                   const int internal_vector_length) {
    return ExtractAndFactorizeRecommendedCudaTeamSize(blksize, vector_length, internal_vector_length);
  }
};
template <>
struct ExtractAndFactorizeTridiagsDefaultModeAndAlgo<Kokkos::CudaUVMSpace> {
  typedef KB::Mode::Team mode_type;
  typedef KB::Algo::Level3::Unblocked algo_type;
  static int recommended_team_size(const int blksize,
                                   const int vector_length,
                                   const int internal_vector_length) {
    return ExtractAndFactorizeRecommendedCudaTeamSize(blksize, vector_length, internal_vector_length);
  }
};
#endif

#if defined(KOKKOS_ENABLE_HIP)
static inline int ExtractAndFactorizeRecommendedHIPTeamSize(const int blksize,
                                                            const int vector_length,
                                                            const int internal_vector_length) {
  const int vector_size = vector_length / internal_vector_length;
  int total_team_size(0);
  if (blksize <= 5)
    total_team_size = 32;
  else if (blksize <= 9)
    total_team_size = 32;  // 64
  else if (blksize <= 12)
    total_team_size = 96;
  else if (blksize <= 16)
    total_team_size = 128;
  else if (blksize <= 20)
    total_team_size = 160;
  else
    total_team_size = 160;
  return 2 * total_team_size / vector_size;
}
template <>
struct ExtractAndFactorizeTridiagsDefaultModeAndAlgo<Kokkos::HIPSpace> {
  typedef KB::Mode::Team mode_type;
  typedef KB::Algo::Level3::Unblocked algo_type;
  static int recommended_team_size(const int blksize,
                                   const int vector_length,
                                   const int internal_vector_length) {
    return ExtractAndFactorizeRecommendedHIPTeamSize(blksize, vector_length, internal_vector_length);
  }
};
template <>
struct ExtractAndFactorizeTridiagsDefaultModeAndAlgo<Kokkos::HIPHostPinnedSpace> {
  typedef KB::Mode::Team mode_type;
  typedef KB::Algo::Level3::Unblocked algo_type;
  static int recommended_team_size(const int blksize,
                                   const int vector_length,
                                   const int internal_vector_length) {
    return ExtractAndFactorizeRecommendedHIPTeamSize(blksize, vector_length, internal_vector_length);
  }
};
#endif

#if defined(KOKKOS_ENABLE_SYCL)
static inline int ExtractAndFactorizeRecommendedSYCLTeamSize(const int blksize,
                                                             const int vector_length,
                                                             const int internal_vector_length) {
  const int vector_size = vector_length / internal_vector_length;
  int total_team_size(0);
  if (blksize <= 5)
    total_team_size = 32;
  else if (blksize <= 9)
    total_team_size = 32;  // 64
  else if (blksize <= 12)
    total_team_size = 96;
  else if (blksize <= 16)
    total_team_size = 128;
  else if (blksize <= 20)
    total_team_size = 160;
  else
    total_team_size = 160;
  return 2 * total_team_size / vector_size;
}
template <>
struct ExtractAndFactorizeTridiagsDefaultModeAndAlgo<Kokkos::Experimental::SYCLDeviceUSMSpace> {
  typedef KB::Mode::Team mode_type;
  typedef KB::Algo::Level3::Unblocked algo_type;
  static int recommended_team_size(const int blksize,
                                   const int vector_length,
                                   const int internal_vector_length) {
    return ExtractAndFactorizeRecommendedSYCLTeamSize(blksize, vector_length, internal_vector_length);
  }
};
template <>
struct ExtractAndFactorizeTridiagsDefaultModeAndAlgo<Kokkos::Experimental::SYCLSharedUSMSpace> {
  typedef KB::Mode::Team mode_type;
  typedef KB::Algo::Level3::Unblocked algo_type;
  static int recommended_team_size(const int blksize,
                                   const int vector_length,
                                   const int internal_vector_length) {
    return ExtractAndFactorizeRecommendedSYCLTeamSize(blksize, vector_length, internal_vector_length);
  }
};
#endif

template <typename impl_type, typename WWViewType>
KOKKOS_INLINE_FUNCTION void
solveMultiVector(const typename Kokkos::TeamPolicy<typename impl_type::execution_space>::member_type &member,
                 const typename impl_type::local_ordinal_type & /* blocksize */,
                 const typename impl_type::local_ordinal_type &i0,
                 const typename impl_type::local_ordinal_type &r0,
                 const typename impl_type::local_ordinal_type &nrows,
                 const typename impl_type::local_ordinal_type &v,
                 const ConstUnmanaged<typename impl_type::internal_vector_type_4d_view> D_internal_vector_values,
                 const Unmanaged<typename impl_type::internal_vector_type_4d_view> X_internal_vector_values,
                 const WWViewType &WW,
                 const bool skip_first_pass = false) {
  using execution_space    = typename impl_type::execution_space;
  using team_policy_type   = Kokkos::TeamPolicy<execution_space>;
  using member_type        = typename team_policy_type::member_type;
  using local_ordinal_type = typename impl_type::local_ordinal_type;

  typedef SolveTridiagsDefaultModeAndAlgo<typename execution_space::memory_space> default_mode_and_algo_type;

  typedef typename default_mode_and_algo_type::mode_type default_mode_type;
  typedef typename default_mode_and_algo_type::multi_vector_algo_type default_algo_type;

  using btdm_magnitude_type = typename impl_type::btdm_magnitude_type;

  // constant
#if KOKKOS_VERSION >= 40799
  const auto one = KokkosKernels::ArithTraits<btdm_magnitude_type>::one();
#else
  const auto one  = Kokkos::ArithTraits<btdm_magnitude_type>::one();
#endif
#if KOKKOS_VERSION >= 40799
  const auto zero = KokkosKernels::ArithTraits<btdm_magnitude_type>::zero();
#else
  const auto zero = Kokkos::ArithTraits<btdm_magnitude_type>::zero();
#endif

  // subview pattern
  auto A  = Kokkos::subview(D_internal_vector_values, i0, Kokkos::ALL(), Kokkos::ALL(), v);
  auto X1 = Kokkos::subview(X_internal_vector_values, r0, Kokkos::ALL(), Kokkos::ALL(), v);
  auto X2 = X1;

  local_ordinal_type i = i0, r = r0;

  if (nrows > 1) {
    // solve Lx = x
    if (skip_first_pass) {
      i += (nrows - 2) * 3;
      r += (nrows - 2);
      A.assign_data(&D_internal_vector_values(i + 2, 0, 0, v));
      X2.assign_data(&X_internal_vector_values(++r, 0, 0, v));
      A.assign_data(&D_internal_vector_values(i + 3, 0, 0, v));
      KB::Trsm<member_type,
               KB::Side::Left, KB::Uplo::Lower, KB::Trans::NoTranspose, KB::Diag::Unit,
               default_mode_type, default_algo_type>::invoke(member, one, A, X2);
      X1.assign_data(X2.data());
      i += 3;
    } else {
      KB::Trsm<member_type,
               KB::Side::Left, KB::Uplo::Lower, KB::Trans::NoTranspose, KB::Diag::Unit,
               default_mode_type, default_algo_type>::invoke(member, one, A, X1);
      for (local_ordinal_type tr = 1; tr < nrows; ++tr, i += 3) {
        A.assign_data(&D_internal_vector_values(i + 2, 0, 0, v));
        X2.assign_data(&X_internal_vector_values(++r, 0, 0, v));
        member.team_barrier();
        KB::Gemm<member_type,
                 KB::Trans::NoTranspose, KB::Trans::NoTranspose,
                 default_mode_type, default_algo_type>::invoke(member, -one, A, X1, one, X2);
        A.assign_data(&D_internal_vector_values(i + 3, 0, 0, v));
        KB::Trsm<member_type,
                 KB::Side::Left, KB::Uplo::Lower, KB::Trans::NoTranspose, KB::Diag::Unit,
                 default_mode_type, default_algo_type>::invoke(member, one, A, X2);
        X1.assign_data(X2.data());
      }
    }

    // solve Ux = x
    KB::Trsm<member_type,
             KB::Side::Left, KB::Uplo::Upper, KB::Trans::NoTranspose, KB::Diag::NonUnit,
             default_mode_type, default_algo_type>::invoke(member, one, A, X1);
    for (local_ordinal_type tr = nrows; tr > 1; --tr) {
      i -= 3;
      A.assign_data(&D_internal_vector_values(i + 1, 0, 0, v));
      X2.assign_data(&X_internal_vector_values(--r, 0, 0, v));
      member.team_barrier();
      KB::Gemm<member_type,
               KB::Trans::NoTranspose, KB::Trans::NoTranspose,
               default_mode_type, default_algo_type>::invoke(member, -one, A, X1, one, X2);

      A.assign_data(&D_internal_vector_values(i, 0, 0, v));
      KB::Trsm<member_type,
               KB::Side::Left, KB::Uplo::Upper, KB::Trans::NoTranspose, KB::Diag::NonUnit,
               default_mode_type, default_algo_type>::invoke(member, one, A, X2);
      X1.assign_data(X2.data());
    }
  } else {
    // matrix is already inverted
    auto W = Kokkos::subview(WW, Kokkos::ALL(), Kokkos::ALL(), v);
    KB::Copy<member_type, KB::Trans::NoTranspose, default_mode_type>::invoke(member, X1, W);
    member.team_barrier();
    KB::Gemm<member_type,
             KB::Trans::NoTranspose, KB::Trans::NoTranspose,
             default_mode_type, default_algo_type>::invoke(member, one, A, W, zero, X1);
  }
}

template <typename impl_type, typename WWViewType, typename XViewType>
KOKKOS_INLINE_FUNCTION void
solveSingleVectorNew(const typename Kokkos::TeamPolicy<typename impl_type::execution_space>::member_type &member,
                     const typename impl_type::local_ordinal_type &blocksize,
                     const typename impl_type::local_ordinal_type &i0,
                     const typename impl_type::local_ordinal_type &r0,
                     const typename impl_type::local_ordinal_type &nrows,
                     const typename impl_type::local_ordinal_type &v,
                     const ConstUnmanaged<typename impl_type::internal_vector_type_4d_view> D_internal_vector_values,
                     const XViewType &X_internal_vector_values,  // Unmanaged<typename impl_type::internal_vector_type_4d_view>
                     const WWViewType &WW) {
  using execution_space = typename impl_type::execution_space;
  // using team_policy_type = Kokkos::TeamPolicy<execution_space>;
  // using member_type = typename team_policy_type::member_type;
  using local_ordinal_type = typename impl_type::local_ordinal_type;

  typedef SolveTridiagsDefaultModeAndAlgo<typename execution_space::memory_space> default_mode_and_algo_type;

  typedef typename default_mode_and_algo_type::mode_type default_mode_type;
  typedef typename default_mode_and_algo_type::single_vector_algo_type default_algo_type;

  using btdm_magnitude_type = typename impl_type::btdm_magnitude_type;

  // base pointers
  auto A = D_internal_vector_values.data();
  auto X = X_internal_vector_values.data();

  // constant
#if KOKKOS_VERSION >= 40799
  const auto one = KokkosKernels::ArithTraits<btdm_magnitude_type>::one();
#else
  const auto one  = Kokkos::ArithTraits<btdm_magnitude_type>::one();
#endif
#if KOKKOS_VERSION >= 40799
  const auto zero = KokkosKernels::ArithTraits<btdm_magnitude_type>::zero();
#else
  const auto zero = Kokkos::ArithTraits<btdm_magnitude_type>::zero();
#endif
  // const local_ordinal_type num_vectors = X_scalar_values.extent(2);

  // const local_ordinal_type blocksize = D_scalar_values.extent(1);
  const local_ordinal_type astep = D_internal_vector_values.stride(0);
  const local_ordinal_type as0   = D_internal_vector_values.stride(1);  // blocksize*vector_length;
  const local_ordinal_type as1   = D_internal_vector_values.stride(2);  // vector_length;
  const local_ordinal_type xstep = X_internal_vector_values.stride(0);
  const local_ordinal_type xs0   = X_internal_vector_values.stride(1);  // vector_length;

  // move to starting point
  A += i0 * astep + v;
  X += r0 * xstep + v;

  // for (local_ordinal_type col=0;col<num_vectors;++col)
  if (nrows > 1) {
    // solve Lx = x
    KOKKOSBATCHED_TRSV_LOWER_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                          member,
                                                          KB::Diag::Unit,
                                                          blocksize, blocksize,
                                                          one,
                                                          A, as0, as1,
                                                          X, xs0);

    for (local_ordinal_type tr = 1; tr < nrows; ++tr) {
      member.team_barrier();
      KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                      member,
                                                      blocksize, blocksize,
                                                      -one,
                                                      A + 2 * astep, as0, as1,
                                                      X, xs0,
                                                      one,
                                                      X + 1 * xstep, xs0);
      KOKKOSBATCHED_TRSV_LOWER_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                            member,
                                                            KB::Diag::Unit,
                                                            blocksize, blocksize,
                                                            one,
                                                            A + 3 * astep, as0, as1,
                                                            X + 1 * xstep, xs0);

      A += 3 * astep;
      X += 1 * xstep;
    }

    // solve Ux = x
    KOKKOSBATCHED_TRSV_UPPER_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                          member,
                                                          KB::Diag::NonUnit,
                                                          blocksize, blocksize,
                                                          one,
                                                          A, as0, as1,
                                                          X, xs0);

    for (local_ordinal_type tr = nrows; tr > 1; --tr) {
      A -= 3 * astep;
      member.team_barrier();
      KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                      member,
                                                      blocksize, blocksize,
                                                      -one,
                                                      A + 1 * astep, as0, as1,
                                                      X, xs0,
                                                      one,
                                                      X - 1 * xstep, xs0);
      KOKKOSBATCHED_TRSV_UPPER_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                            member,
                                                            KB::Diag::NonUnit,
                                                            blocksize, blocksize,
                                                            one,
                                                            A, as0, as1,
                                                            X - 1 * xstep, xs0);
      X -= 1 * xstep;
    }
    // for multiple rhs
    // X += xs1;
  } else {
    const local_ordinal_type ws0 = WW.stride(0);
    auto W                       = WW.data() + v;
    KOKKOSBATCHED_COPY_VECTOR_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type,
                                                           member, blocksize, X, xs0, W, ws0);
    member.team_barrier();
    KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                    member,
                                                    blocksize, blocksize,
                                                    one,
                                                    A, as0, as1,
                                                    W, xs0,
                                                    zero,
                                                    X, xs0);
  }
}

template <typename local_ordinal_type, typename ViewType>
void writeBTDValuesToFile(const local_ordinal_type &n_parts, const ViewType &scalar_values_device, std::string fileName) {
#ifdef IFPACK2_BLOCKTRIDICONTAINER_WRITE_MM
  auto scalar_values = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), scalar_values_device);
  std::ofstream myfile;
  myfile.open(fileName);

  const local_ordinal_type n_parts_per_pack  = n_parts < (local_ordinal_type)scalar_values.extent(3) ? n_parts : scalar_values.extent(3);
  local_ordinal_type nnz                     = scalar_values.extent(0) * scalar_values.extent(1) * scalar_values.extent(2) * n_parts_per_pack;
  const local_ordinal_type n_blocks          = scalar_values.extent(0) * n_parts_per_pack;
  const local_ordinal_type n_blocks_per_part = n_blocks / n_parts;

  const local_ordinal_type block_size = scalar_values.extent(1);

  const local_ordinal_type n_rows_per_part = (n_blocks_per_part + 2) / 3 * block_size;
  const local_ordinal_type n_rows          = n_rows_per_part * n_parts;

  const local_ordinal_type n_packs = ceil(float(n_parts) / n_parts_per_pack);

  myfile << "%%MatrixMarket matrix coordinate real general" << std::endl;
  myfile << "%%nnz = " << nnz;
  myfile << " block size = " << block_size;
  myfile << " number of blocks = " << n_blocks;
  myfile << " number of parts = " << n_parts;
  myfile << " number of blocks per part = " << n_blocks_per_part;
  myfile << " number of rows = " << n_rows;
  myfile << " number of cols = " << n_rows;
  myfile << " number of packs = " << n_packs << std::endl;

  myfile << n_rows << " " << n_rows << " " << nnz << std::setprecision(9) << std::endl;

  local_ordinal_type current_part_idx, current_block_idx, current_row_offset, current_col_offset, current_row, current_col;
  for (local_ordinal_type i_pack = 0; i_pack < n_packs; ++i_pack) {
    for (local_ordinal_type i_part_in_pack = 0; i_part_in_pack < n_parts_per_pack; ++i_part_in_pack) {
      current_part_idx = i_part_in_pack + i_pack * n_parts_per_pack;
      for (local_ordinal_type i_block_in_part = 0; i_block_in_part < n_blocks_per_part; ++i_block_in_part) {
        current_block_idx = i_block_in_part + i_pack * n_blocks_per_part;
        if (current_block_idx >= (local_ordinal_type)scalar_values.extent(0))
          continue;
        if (i_block_in_part % 3 == 0) {
          current_row_offset = i_block_in_part / 3 * block_size;
          current_col_offset = i_block_in_part / 3 * block_size;
        } else if (i_block_in_part % 3 == 1) {
          current_row_offset = (i_block_in_part - 1) / 3 * block_size;
          current_col_offset = ((i_block_in_part - 1) / 3 + 1) * block_size;
        } else if (i_block_in_part % 3 == 2) {
          current_row_offset = ((i_block_in_part - 2) / 3 + 1) * block_size;
          current_col_offset = (i_block_in_part - 2) / 3 * block_size;
        }
        current_row_offset += current_part_idx * n_rows_per_part;
        current_col_offset += current_part_idx * n_rows_per_part;
        for (local_ordinal_type i_in_block = 0; i_in_block < block_size; ++i_in_block) {
          for (local_ordinal_type j_in_block = 0; j_in_block < block_size; ++j_in_block) {
            current_row = current_row_offset + i_in_block + 1;
            current_col = current_col_offset + j_in_block + 1;
            myfile << current_row << " " << current_col << " " << scalar_values(current_block_idx, i_in_block, j_in_block, i_part_in_pack) << std::endl;
          }
        }
      }
    }
  }

  myfile.close();
#endif
}

template <typename local_ordinal_type, typename ViewType>
void write4DMultiVectorValuesToFile(const local_ordinal_type &n_parts, const ViewType &scalar_values_device, std::string fileName) {
#ifdef IFPACK2_BLOCKTRIDICONTAINER_WRITE_MM
  auto scalar_values = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), scalar_values_device);
  std::ofstream myfile;
  myfile.open(fileName);

  const local_ordinal_type n_parts_per_pack  = n_parts < scalar_values.extent(3) ? n_parts : scalar_values.extent(3);
  const local_ordinal_type n_blocks          = scalar_values.extent(0) * n_parts_per_pack;
  const local_ordinal_type n_blocks_per_part = n_blocks / n_parts;

  const local_ordinal_type block_size = scalar_values.extent(1);
  const local_ordinal_type n_cols     = scalar_values.extent(2);

  const local_ordinal_type n_rows_per_part = n_blocks_per_part * block_size;
  const local_ordinal_type n_rows          = n_rows_per_part * n_parts;

  const local_ordinal_type n_packs = ceil(float(n_parts) / n_parts_per_pack);

  myfile << "%%MatrixMarket matrix array real general" << std::endl;
  myfile << "%%block size = " << block_size;
  myfile << " number of blocks = " << n_blocks;
  myfile << " number of parts = " << n_parts;
  myfile << " number of blocks per part = " << n_blocks_per_part;
  myfile << " number of rows = " << n_rows;
  myfile << " number of cols = " << n_cols;
  myfile << " number of packs = " << n_packs << std::endl;

  myfile << n_rows << " " << n_cols << std::setprecision(9) << std::endl;

  local_ordinal_type current_part_idx, current_block_idx, current_row_offset;
  (void)current_row_offset;
  (void)current_part_idx;
  for (local_ordinal_type j_in_block = 0; j_in_block < n_cols; ++j_in_block) {
    for (local_ordinal_type i_pack = 0; i_pack < n_packs; ++i_pack) {
      for (local_ordinal_type i_part_in_pack = 0; i_part_in_pack < n_parts_per_pack; ++i_part_in_pack) {
        current_part_idx = i_part_in_pack + i_pack * n_parts_per_pack;
        for (local_ordinal_type i_block_in_part = 0; i_block_in_part < n_blocks_per_part; ++i_block_in_part) {
          current_block_idx = i_block_in_part + i_pack * n_blocks_per_part;

          if (current_block_idx >= (local_ordinal_type)scalar_values.extent(0))
            continue;
          for (local_ordinal_type i_in_block = 0; i_in_block < block_size; ++i_in_block) {
            myfile << scalar_values(current_block_idx, i_in_block, j_in_block, i_part_in_pack) << std::endl;
          }
        }
      }
    }
  }
  myfile.close();
#endif
}

template <typename local_ordinal_type, typename ViewType>
void write5DMultiVectorValuesToFile(const local_ordinal_type &n_parts, const ViewType &scalar_values_device, std::string fileName) {
#ifdef IFPACK2_BLOCKTRIDICONTAINER_WRITE_MM
  auto scalar_values = Kokkos::create_mirror_view_and_copy(Kokkos::HostSpace(), scalar_values_device);
  std::ofstream myfile;
  myfile.open(fileName);

  const local_ordinal_type n_parts_per_pack  = n_parts < scalar_values.extent(4) ? n_parts : scalar_values.extent(4);
  const local_ordinal_type n_blocks          = scalar_values.extent(1) * n_parts_per_pack;
  const local_ordinal_type n_blocks_per_part = n_blocks / n_parts;

  const local_ordinal_type block_size    = scalar_values.extent(2);
  const local_ordinal_type n_blocks_cols = scalar_values.extent(0);
  const local_ordinal_type n_cols        = n_blocks_cols * block_size;

  const local_ordinal_type n_rows_per_part = n_blocks_per_part * block_size;
  const local_ordinal_type n_rows          = n_rows_per_part * n_parts;

  const local_ordinal_type n_packs = ceil(float(n_parts) / n_parts_per_pack);

  myfile << "%%MatrixMarket matrix array real general" << std::endl;
  myfile << "%%block size = " << block_size;
  myfile << " number of blocks = " << n_blocks;
  myfile << " number of parts = " << n_parts;
  myfile << " number of blocks per part = " << n_blocks_per_part;
  myfile << " number of rows = " << n_rows;
  myfile << " number of cols = " << n_cols;
  myfile << " number of packs = " << n_packs << std::endl;

  myfile << n_rows << " " << n_cols << std::setprecision(9) << std::endl;

  local_ordinal_type current_part_idx, current_block_idx, current_row_offset;
  (void)current_row_offset;
  (void)current_part_idx;
  for (local_ordinal_type i_block_col = 0; i_block_col < n_blocks_cols; ++i_block_col) {
    for (local_ordinal_type j_in_block = 0; j_in_block < block_size; ++j_in_block) {
      for (local_ordinal_type i_pack = 0; i_pack < n_packs; ++i_pack) {
        for (local_ordinal_type i_part_in_pack = 0; i_part_in_pack < n_parts_per_pack; ++i_part_in_pack) {
          current_part_idx = i_part_in_pack + i_pack * n_parts_per_pack;
          for (local_ordinal_type i_block_in_part = 0; i_block_in_part < n_blocks_per_part; ++i_block_in_part) {
            current_block_idx = i_block_in_part + i_pack * n_blocks_per_part;

            if (current_block_idx >= (local_ordinal_type)scalar_values.extent(1))
              continue;
            for (local_ordinal_type i_in_block = 0; i_in_block < block_size; ++i_in_block) {
              myfile << scalar_values(i_block_col, current_block_idx, i_in_block, j_in_block, i_part_in_pack) << std::endl;
            }
          }
        }
      }
    }
  }
  myfile.close();
#endif
}

template <typename local_ordinal_type, typename member_type, typename ViewType1, typename ViewType2>
KOKKOS_INLINE_FUNCTION void
copy3DView(const member_type &member, const ViewType1 &view1, const ViewType2 &view2) {
  /*
        // Kokkos::Experimental::local_deep_copy
        auto teamVectorRange =
            Kokkos::TeamVectorMDRange<Kokkos::Rank<3>, member_type>(
                member, view1.extent(0), view1.extent(1), view1.extent(2));

        Kokkos::parallel_for
          (teamVectorRange,
        [&](const local_ordinal_type &i, const local_ordinal_type &j, const local_ordinal_type &k) {
          view1(i,j,k) = view2(i,j,k);
        });
  */
  Kokkos::Experimental::local_deep_copy(member, view1, view2);
}
template <typename MatrixType, int ScratchLevel>
struct ExtractAndFactorizeTridiags {
 public:
  using impl_type = BlockHelperDetails::ImplType<MatrixType>;
  // a functor cannot have both device_type and execution_space; specialization error in kokkos
  using execution_space = typename impl_type::execution_space;
  using memory_space    = typename impl_type::memory_space;
  using local_ordinal_type = typename impl_type::local_ordinal_type;
  using size_type          = typename impl_type::size_type;
  using impl_scalar_type   = typename impl_type::impl_scalar_type;
  using magnitude_type     = typename impl_type::magnitude_type;
  using row_matrix_type = typename impl_type::tpetra_row_matrix_type;
  using crs_graph_type  = typename impl_type::tpetra_crs_graph_type;
  using local_ordinal_type_1d_view      = typename impl_type::local_ordinal_type_1d_view;
  using local_ordinal_type_2d_view      = typename impl_type::local_ordinal_type_2d_view;
  using size_type_1d_view               = typename impl_type::size_type_1d_view;
  using size_type_2d_view               = typename impl_type::size_type_2d_view;
  using impl_scalar_type_1d_view_tpetra = typename impl_type::impl_scalar_type_1d_view_tpetra;
  using btdm_scalar_type                     = typename impl_type::btdm_scalar_type;
  using btdm_magnitude_type                  = typename impl_type::btdm_magnitude_type;
  using vector_type_3d_view                  = typename impl_type::vector_type_3d_view;
  using vector_type_4d_view                  = typename impl_type::vector_type_4d_view;
  using internal_vector_type_4d_view         = typename impl_type::internal_vector_type_4d_view;
  using internal_vector_type_5d_view         = typename impl_type::internal_vector_type_5d_view;
  using btdm_scalar_type_2d_view             = typename impl_type::btdm_scalar_type_2d_view;
  using btdm_scalar_type_3d_view             = typename impl_type::btdm_scalar_type_3d_view;
  using btdm_scalar_type_4d_view             = typename impl_type::btdm_scalar_type_4d_view;
  using btdm_scalar_type_5d_view             = typename impl_type::btdm_scalar_type_5d_view;
  using internal_vector_scratch_type_3d_view = Scratch<typename impl_type::internal_vector_type_3d_view>;
  using btdm_scalar_scratch_type_3d_view     = Scratch<typename impl_type::btdm_scalar_type_3d_view>;
  using tpetra_block_access_view_type        = typename impl_type::tpetra_block_access_view_type;  // block crs (layout right)
  using local_crs_graph_type                 = typename impl_type::local_crs_graph_type;
  using colinds_view                         = typename local_crs_graph_type::entries_type;

  using internal_vector_type                  = typename impl_type::internal_vector_type;
  static constexpr int vector_length          = impl_type::vector_length;
  static constexpr int internal_vector_length = impl_type::internal_vector_length;
  static_assert(vector_length >= internal_vector_length, "Ifpack2 BlockTriDi Numeric: vector_length must be at least as large as internal_vector_length");
  static_assert(vector_length % internal_vector_length == 0, "Ifpack2 BlockTriDi Numeric: vector_length must be divisible by internal_vector_length");
  // half_vector_length is used for block Jacobi factorization.
  // Shared memory requirement is twice as large (per vector lane) as for general tridi factorization, so
  // reducing vector length (if possible) keeps the shared requirement constant. This avoids the performance
  // cliff of switching from level 0 to level 1 scratch.
  static constexpr int half_vector_length = impl_type::half_vector_length;

  using team_policy_type = Kokkos::TeamPolicy<execution_space>;
  using member_type      = typename team_policy_type::member_type;

 private:
  // part interface
  const ConstUnmanaged<local_ordinal_type_1d_view> partptr, lclrow, packptr, packindices_sub, packptr_sub;
  const ConstUnmanaged<local_ordinal_type_2d_view> partptr_sub, part2packrowidx0_sub, packindices_schur;
  const local_ordinal_type max_partsz;
  // block crs matrix (it could be Kokkos::UVMSpace::size_type, which is int)
  using size_type_1d_view_tpetra = Kokkos::View<size_t *, typename impl_type::node_device_type>;
  ConstUnmanaged<size_type_1d_view_tpetra> A_block_rowptr;
  ConstUnmanaged<size_type_1d_view_tpetra> A_point_rowptr;
  ConstUnmanaged<impl_scalar_type_1d_view_tpetra> A_values;
  // block tridiags
  const ConstUnmanaged<size_type_2d_view> pack_td_ptr, flat_td_ptr, pack_td_ptr_schur;
  const ConstUnmanaged<local_ordinal_type_1d_view> A_colindsub;
  const Unmanaged<internal_vector_type_4d_view> internal_vector_values, internal_vector_values_schur;
  const Unmanaged<internal_vector_type_5d_view> e_internal_vector_values;
  const Unmanaged<btdm_scalar_type_4d_view> scalar_values, scalar_values_schur;
  const Unmanaged<btdm_scalar_type_5d_view> e_scalar_values;
  const Unmanaged<btdm_scalar_type_3d_view> d_inv;
  const Unmanaged<size_type_1d_view> diag_offsets;
  // shared information
  const local_ordinal_type blocksize, blocksize_square;
  // diagonal safety
  const magnitude_type tiny;
  const local_ordinal_type vector_loop_size;

  bool hasBlockCrsMatrix;

 public:
  ExtractAndFactorizeTridiags(const BlockTridiags<MatrixType> &btdm_,
                              const BlockHelperDetails::PartInterface<MatrixType> &interf_,
                              const Teuchos::RCP<const row_matrix_type> &A_,
                              const Teuchos::RCP<const crs_graph_type> &G_,
                              const magnitude_type &tiny_)
    :  // interface
    partptr(interf_.partptr)
    , lclrow(interf_.lclrow)
    , packptr(interf_.packptr)
    , packindices_sub(interf_.packindices_sub)
    , packptr_sub(interf_.packptr_sub)
    , partptr_sub(interf_.partptr_sub)
    , part2packrowidx0_sub(interf_.part2packrowidx0_sub)
    , packindices_schur(interf_.packindices_schur)
    , max_partsz(interf_.max_partsz)
    ,
    // block tridiags
    pack_td_ptr(btdm_.pack_td_ptr)
    , flat_td_ptr(btdm_.flat_td_ptr)
    , pack_td_ptr_schur(btdm_.pack_td_ptr_schur)
    , A_colindsub(btdm_.A_colindsub)
    , internal_vector_values((internal_vector_type *)btdm_.values.data(),
                             btdm_.values.extent(0),
                             btdm_.values.extent(1),
                             btdm_.values.extent(2),
                             vector_length / internal_vector_length)
    , internal_vector_values_schur((internal_vector_type *)btdm_.values_schur.data(),
                                   btdm_.values_schur.extent(0),
                                   btdm_.values_schur.extent(1),
                                   btdm_.values_schur.extent(2),
                                   vector_length / internal_vector_length)
    , e_internal_vector_values((internal_vector_type *)btdm_.e_values.data(),
                               btdm_.e_values.extent(0),
                               btdm_.e_values.extent(1),
                               btdm_.e_values.extent(2),
                               btdm_.e_values.extent(3),
                               vector_length / internal_vector_length)
    , scalar_values((btdm_scalar_type *)btdm_.values.data(),
                    btdm_.values.extent(0),
                    btdm_.values.extent(1),
                    btdm_.values.extent(2),
                    vector_length)
    , scalar_values_schur((btdm_scalar_type *)btdm_.values_schur.data(),
                          btdm_.values_schur.extent(0),
                          btdm_.values_schur.extent(1),
                          btdm_.values_schur.extent(2),
                          vector_length)
    , e_scalar_values((btdm_scalar_type *)btdm_.e_values.data(),
                      btdm_.e_values.extent(0),
                      btdm_.e_values.extent(1),
                      btdm_.e_values.extent(2),
                      btdm_.e_values.extent(3),
                      vector_length)
    , d_inv(btdm_.d_inv)
    , diag_offsets(btdm_.diag_offsets)
    , blocksize(btdm_.values.extent(1))
    , blocksize_square(blocksize * blocksize)
    ,
    // diagonal weight to avoid zero pivots
    tiny(tiny_)
    , vector_loop_size(vector_length / internal_vector_length) {
    using crs_matrix_type       = typename impl_type::tpetra_crs_matrix_type;
    using block_crs_matrix_type = typename impl_type::tpetra_block_crs_matrix_type;

    auto A_crs  = Teuchos::rcp_dynamic_cast<const crs_matrix_type>(A_);
    auto A_bcrs = Teuchos::rcp_dynamic_cast<const block_crs_matrix_type>(A_);

    hasBlockCrsMatrix = !A_bcrs.is_null();

    A_block_rowptr = G_->getLocalGraphDevice().row_map;
    if (hasBlockCrsMatrix) {
      A_values = const_cast<block_crs_matrix_type *>(A_bcrs.get())->getValuesDeviceNonConst();
    } else {
      A_point_rowptr = A_crs->getCrsGraph()->getLocalGraphDevice().row_map;
      A_values       = A_crs->getLocalValuesDevice(Tpetra::Access::ReadOnly);
    }
  }

 private:
  KOKKOS_INLINE_FUNCTION
  void
  extract(local_ordinal_type partidx,
          local_ordinal_type local_subpartidx,
          local_ordinal_type npacks) const {
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
    printf("extract partidx = %d, local_subpartidx = %d, npacks = %d;\n", partidx, local_subpartidx, npacks);
#endif
    using tlb                               = BlockHelperDetails::TpetraLittleBlock<Tpetra::Impl::BlockCrsMatrixLittleBlockArrayLayout>;
    const size_type kps                     = pack_td_ptr(partidx, local_subpartidx);
    local_ordinal_type kfs[vector_length]   = {};
    local_ordinal_type ri0[vector_length]   = {};
    local_ordinal_type nrows[vector_length] = {};

    for (local_ordinal_type vi = 0; vi < npacks; ++vi, ++partidx) {
      kfs[vi]   = flat_td_ptr(partidx, local_subpartidx);
      ri0[vi]   = partptr_sub(pack_td_ptr.extent(0) * local_subpartidx + partidx, 0);
      nrows[vi] = partptr_sub(pack_td_ptr.extent(0) * local_subpartidx + partidx, 1) - ri0[vi];
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
      printf("kfs[%d] = %d;\n", vi, kfs[vi]);
      printf("ri0[%d] = %d;\n", vi, ri0[vi]);
      printf("nrows[%d] = %d;\n", vi, nrows[vi]);
#endif
    }
    local_ordinal_type tr_min = 0;
    local_ordinal_type tr_max = nrows[0];
    if (local_subpartidx % 2 == 1) {
      tr_min -= 1;
      tr_max += 1;
    }
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
    printf("tr_min = %d and tr_max = %d;\n", tr_min, tr_max);
#endif
    for (local_ordinal_type tr = tr_min, j = 0; tr < tr_max; ++tr) {
      for (local_ordinal_type e = 0; e < 3; ++e) {
        if (hasBlockCrsMatrix) {
          const impl_scalar_type *block[vector_length] = {};
          for (local_ordinal_type vi = 0; vi < npacks; ++vi) {
            const size_type Aj = A_block_rowptr(lclrow(ri0[vi] + tr)) + A_colindsub(kfs[vi] + j);

            block[vi] = &A_values(Aj * blocksize_square);
          }
          const size_type pi = kps + j;
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
          printf("Extract pi = %ld, ri0 + tr = %d, kfs + j = %d\n", pi, ri0[0] + tr, kfs[0] + j);
#endif
          ++j;
          for (local_ordinal_type ii = 0; ii < blocksize; ++ii) {
            for (local_ordinal_type jj = 0; jj < blocksize; ++jj) {
              const auto idx = tlb::getFlatIndex(ii, jj, blocksize);
              auto &v        = internal_vector_values(pi, ii, jj, 0);
              for (local_ordinal_type vi = 0; vi < npacks; ++vi) {
                v[vi] = static_cast<btdm_scalar_type>(block[vi][idx]);
              }
            }
          }
        } else {
          const size_type pi = kps + j;

          for (local_ordinal_type vi = 0; vi < npacks; ++vi) {
            const size_type Aj_c = A_colindsub(kfs[vi] + j);

            for (local_ordinal_type ii = 0; ii < blocksize; ++ii) {
              auto point_row_offset = A_point_rowptr(lclrow(ri0[vi] + tr) * blocksize + ii);

              for (local_ordinal_type jj = 0; jj < blocksize; ++jj) {
                scalar_values(pi, ii, jj, vi) = A_values(point_row_offset + Aj_c * blocksize + jj);
              }
            }
          }
          ++j;
        }
        if (nrows[0] == 1) break;
        if (local_subpartidx % 2 == 0) {
          if (e == 1 && (tr == 0 || tr + 1 == nrows[0])) break;
          for (local_ordinal_type vi = 1; vi < npacks; ++vi) {
            if ((e == 0 && nrows[vi] == 1) || (e == 1 && tr + 1 == nrows[vi])) {
              npacks = vi;
              break;
            }
          }
        } else {
          if (e == 0 && (tr == -1 || tr == nrows[0])) break;
          for (local_ordinal_type vi = 1; vi < npacks; ++vi) {
            if ((e == 0 && nrows[vi] == 1) || (e == 0 && tr == nrows[vi])) {
              npacks = vi;
              break;
            }
          }
        }
      }
    }
  }

  KOKKOS_INLINE_FUNCTION
  void
  extract(const member_type &member,
          const local_ordinal_type &partidxbeg,
          local_ordinal_type local_subpartidx,
          const local_ordinal_type &npacks,
          const local_ordinal_type &vbeg) const {
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
    printf("extract partidxbeg = %d, local_subpartidx = %d, npacks = %d, vbeg = %d;\n", partidxbeg, local_subpartidx, npacks, vbeg);
#endif
    using tlb                                             = BlockHelperDetails::TpetraLittleBlock<Tpetra::Impl::BlockCrsMatrixLittleBlockArrayLayout>;
    local_ordinal_type kfs_vals[internal_vector_length]   = {};
    local_ordinal_type ri0_vals[internal_vector_length]   = {};
    local_ordinal_type nrows_vals[internal_vector_length] = {};

    const size_type kps = pack_td_ptr(partidxbeg, local_subpartidx);
    for (local_ordinal_type v = vbeg, vi = 0; v < npacks && vi < internal_vector_length; ++v, ++vi) {
      kfs_vals[vi]   = flat_td_ptr(partidxbeg + vi, local_subpartidx);
      ri0_vals[vi]   = partptr_sub(pack_td_ptr.extent(0) * local_subpartidx + partidxbeg + vi, 0);
      nrows_vals[vi] = partptr_sub(pack_td_ptr.extent(0) * local_subpartidx + partidxbeg + vi, 1) - ri0_vals[vi];
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
      printf("kfs_vals[%d] = %d;\n", vi, kfs_vals[vi]);
      printf("ri0_vals[%d] = %d;\n", vi, ri0_vals[vi]);
      printf("nrows_vals[%d] = %d;\n", vi, nrows_vals[vi]);
#endif
    }

    local_ordinal_type j_vals[internal_vector_length] = {};

    local_ordinal_type tr_min = 0;
    local_ordinal_type tr_max = nrows_vals[0];
    if (local_subpartidx % 2 == 1) {
      tr_min -= 1;
      tr_max += 1;
    }
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
    printf("tr_min = %d and tr_max = %d;\n", tr_min, tr_max);
#endif
    for (local_ordinal_type tr = tr_min; tr < tr_max; ++tr) {
      for (local_ordinal_type v = vbeg, vi = 0; v < npacks && vi < internal_vector_length; ++v, ++vi) {
        const local_ordinal_type nrows = (local_subpartidx % 2 == 0 ? nrows_vals[vi] : nrows_vals[vi]);
        if ((local_subpartidx % 2 == 0 && tr < nrows) || (local_subpartidx % 2 == 1 && tr < nrows + 1)) {
          auto &j                      = j_vals[vi];
          const local_ordinal_type kfs = kfs_vals[vi];
          const local_ordinal_type ri0 = ri0_vals[vi];
          local_ordinal_type lbeg, lend;
          if (local_subpartidx % 2 == 0) {
            lbeg = (tr == tr_min ? 1 : 0);
            lend = (tr == nrows - 1 ? 2 : 3);
          } else {
            lbeg = 0;
            lend = 3;
            if (tr == tr_min) {
              lbeg = 1;
              lend = 2;
            } else if (tr == nrows) {
              lbeg = 0;
              lend = 1;
            }
          }
          if (hasBlockCrsMatrix) {
            for (local_ordinal_type l = lbeg; l < lend; ++l, ++j) {
              const size_type Aj            = A_block_rowptr(lclrow(ri0 + tr)) + A_colindsub(kfs + j);
              const impl_scalar_type *block = &A_values(Aj * blocksize_square);
              const size_type pi            = kps + j;
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
              printf("Extract pi = %ld, ri0 + tr = %d, kfs + j = %d, tr = %d, lbeg = %d, lend = %d, l = %d\n", pi, ri0 + tr, kfs + j, tr, lbeg, lend, l);
#endif
              Kokkos::parallel_for(Kokkos::TeamThreadRange(member, blocksize),
                                   [&](const local_ordinal_type &ii) {
                                     for (local_ordinal_type jj = 0; jj < blocksize; ++jj) {
                                       scalar_values(pi, ii, jj, v) = static_cast<btdm_scalar_type>(block[tlb::getFlatIndex(ii, jj, blocksize)]);
                                     }
                                   });
            }
          } else {
            for (local_ordinal_type l = lbeg; l < lend; ++l, ++j) {
              const size_type Aj_c = A_colindsub(kfs + j);
              const size_type pi   = kps + j;
              Kokkos::parallel_for(Kokkos::TeamThreadRange(member, blocksize),
                                   [&](const local_ordinal_type &ii) {
                                     auto point_row_offset = A_point_rowptr(lclrow(ri0 + tr) * blocksize + ii);
                                     for (local_ordinal_type jj = 0; jj < blocksize; ++jj) {
                                       scalar_values(pi, ii, jj, v) = A_values(point_row_offset + Aj_c * blocksize + jj);
                                     }
                                   });
            }
          }
        }
      }
    }
  }

  template <typename AAViewType,
            typename WWViewType>
  KOKKOS_INLINE_FUNCTION void
  factorize_subline(const member_type &member,
                    const local_ordinal_type &i0,
                    const local_ordinal_type &nrows,
                    const local_ordinal_type &v,
                    const AAViewType &AA,
                    const WWViewType &WW) const {
    typedef ExtractAndFactorizeTridiagsDefaultModeAndAlgo<typename execution_space::memory_space> default_mode_and_algo_type;

    typedef typename default_mode_and_algo_type::mode_type default_mode_type;
    typedef typename default_mode_and_algo_type::algo_type default_algo_type;

    // constant
#if KOKKOS_VERSION >= 40799
    const auto one = KokkosKernels::ArithTraits<btdm_magnitude_type>::one();
#else
    const auto one = Kokkos::ArithTraits<btdm_magnitude_type>::one();
#endif

#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
    printf("i0 = %d, nrows = %d, v = %d, AA.extent(0) = %ld;\n", i0, nrows, v, AA.extent(0));
#endif

    // subview pattern
    auto A = Kokkos::subview(AA, i0, Kokkos::ALL(), Kokkos::ALL(), v);
    KB::LU<member_type,
           default_mode_type, KB::Algo::LU::Unblocked>::invoke(member, A, tiny);

    if (nrows > 1) {
      auto B               = A;
      auto C               = A;
      local_ordinal_type i = i0;
      for (local_ordinal_type tr = 1; tr < nrows; ++tr, i += 3) {
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
        printf("tr = %d, i = %d;\n", tr, i);
#endif
        B.assign_data(&AA(i + 1, 0, 0, v));
        KB::Trsm<member_type,
                 KB::Side::Left, KB::Uplo::Lower, KB::Trans::NoTranspose, KB::Diag::Unit,
                 default_mode_type, default_algo_type>::invoke(member, one, A, B);
        C.assign_data(&AA(i + 2, 0, 0, v));
        KB::Trsm<member_type,
                 KB::Side::Right, KB::Uplo::Upper, KB::Trans::NoTranspose, KB::Diag::NonUnit,
                 default_mode_type, default_algo_type>::invoke(member, one, A, C);
        A.assign_data(&AA(i + 3, 0, 0, v));

        member.team_barrier();
        KB::Gemm<member_type,
                 KB::Trans::NoTranspose, KB::Trans::NoTranspose,
                 default_mode_type, default_algo_type>::invoke(member, -one, C, B, one, A);
        KB::LU<member_type,
               default_mode_type, KB::Algo::LU::Unblocked>::invoke(member, A, tiny);
      }
    } else {
      // for block jacobi invert a matrix here
      auto W = Kokkos::subview(WW, Kokkos::ALL(), Kokkos::ALL(), v);
      KB::Copy<member_type, KB::Trans::NoTranspose, default_mode_type>::invoke(member, A, W);
      KB::SetIdentity<member_type, default_mode_type>::invoke(member, A);
      member.team_barrier();
      KB::Trsm<member_type,
               KB::Side::Left, KB::Uplo::Lower, KB::Trans::NoTranspose, KB::Diag::Unit,
               default_mode_type, default_algo_type>::invoke(member, one, W, A);
      KB::Trsm<member_type,
               KB::Side::Left, KB::Uplo::Upper, KB::Trans::NoTranspose, KB::Diag::NonUnit,
               default_mode_type, default_algo_type>::invoke(member, one, W, A);
    }
  }

 public:
  struct ExtractAndFactorizeSubLineTag {};
  struct ExtractAndFactorizeFusedJacobiTag {};
  struct ExtractBCDTag {};
  struct ComputeETag {};
  struct ComputeSchurTag {};
  struct FactorizeSchurTag {};

  KOKKOS_INLINE_FUNCTION
  void
  operator()(const ExtractAndFactorizeSubLineTag &, const member_type &member) const {
    // btdm is packed and sorted from largest one
    const local_ordinal_type packidx = packindices_sub(member.league_rank());

    const local_ordinal_type subpartidx       = packptr_sub(packidx);
    const local_ordinal_type n_parts          = part2packrowidx0_sub.extent(0);
    const local_ordinal_type local_subpartidx = subpartidx / n_parts;
    const local_ordinal_type partidx          = subpartidx % n_parts;

    const local_ordinal_type npacks = packptr_sub(packidx + 1) - subpartidx;
    const local_ordinal_type i0     = pack_td_ptr(partidx, local_subpartidx);
    const local_ordinal_type nrows  = partptr_sub(subpartidx, 1) - partptr_sub(subpartidx, 0);

    internal_vector_scratch_type_3d_view
        WW(member.team_scratch(ScratchLevel), blocksize, blocksize, vector_loop_size);

#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
    printf("rank = %d, i0 = %d, npacks = %d, nrows = %d, packidx = %d, subpartidx = %d, partidx = %d, local_subpartidx = %d;\n", member.league_rank(), i0, npacks, nrows, packidx, subpartidx, partidx, local_subpartidx);
    printf("vector_loop_size = %d\n", vector_loop_size);
#endif

    if (vector_loop_size == 1) {
      extract(partidx, local_subpartidx, npacks);
      factorize_subline(member, i0, nrows, 0, internal_vector_values, WW);
    } else {
      Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size),
                           [&](const local_ordinal_type &v) {
                             const local_ordinal_type vbeg = v * internal_vector_length;
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
                             printf("i0 = %d, npacks = %d, vbeg = %d;\n", i0, npacks, vbeg);
#endif
                             if (vbeg < npacks)
                               extract(member, partidx + vbeg, local_subpartidx, npacks, vbeg);
                             // this is not safe if vector loop size is different from vector size of
                             // the team policy. we always make sure this when constructing the team policy
                             member.team_barrier();
                             factorize_subline(member, i0, nrows, v, internal_vector_values, WW);
                           });
    }
  }

  KOKKOS_INLINE_FUNCTION
  void
  operator()(const ExtractAndFactorizeFusedJacobiTag &, const member_type &member) const {
    using default_mode_and_algo_type = ExtractAndFactorizeTridiagsDefaultModeAndAlgo<typename execution_space::memory_space>;
    using default_mode_type          = typename default_mode_and_algo_type::mode_type;
    using default_algo_type          = typename default_mode_and_algo_type::algo_type;
    // When fused block Jacobi can be used, the mapping between local rows and parts is trivial (i <-> i)
    // We can simply pull the diagonal entry from A into d_inv
    btdm_scalar_scratch_type_3d_view WW1(member.team_scratch(ScratchLevel), half_vector_length, blocksize, blocksize);
    btdm_scalar_scratch_type_3d_view WW2(member.team_scratch(ScratchLevel), half_vector_length, blocksize, blocksize);
#if KOKKOS_VERSION >= 40799
    const auto one = KokkosKernels::ArithTraits<btdm_magnitude_type>::one();
#else
    const auto one = Kokkos::ArithTraits<btdm_magnitude_type>::one();
#endif
    const local_ordinal_type nrows = lclrow.extent(0);
    Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, half_vector_length),
                         [&](const local_ordinal_type &v) {
                           local_ordinal_type row = member.league_rank() * half_vector_length + v;
                           // diagEntry has index of diagonal within row
                           auto W1 = Kokkos::subview(WW1, v, Kokkos::ALL(), Kokkos::ALL());
                           auto W2 = Kokkos::subview(WW2, v, Kokkos::ALL(), Kokkos::ALL());
                           if (row < nrows) {
                             // View the diagonal block of A in row as 2D row-major
                             const impl_scalar_type *A_diag = A_values.data() + diag_offsets(row);
                             // Copy the diag into scratch slice W1
                             // (copying elements directly is better than KokkosBatched copy)
                             Kokkos::parallel_for(Kokkos::TeamThreadRange(member, blocksize * blocksize),
                                                  [&](int i) {
                                                    W1.data()[i] = A_diag[i];
                                                  });
                             // and set W2 to identity in preparation to invert with 2 x Trsm
                             KB::SetIdentity<member_type, default_mode_type>::invoke(member, W2);
                           } else {
                             // if this vector lane has no block to invert, then set W1 to identity
                             // so that LU still has a matrix to work on. LU uses team barriers so
                             // having some lanes run it and some not will deadlock.
                             KB::SetIdentity<member_type, default_mode_type>::invoke(member, W1);
                           }
                           member.team_barrier();
                           // LU factorize in-place
                           KB::LU<member_type, default_mode_type, KB::Algo::LU::Unblocked>::invoke(member, W1, tiny);
                           member.team_barrier();
                           KB::Trsm<member_type,
                                    KB::Side::Left, KB::Uplo::Lower, KB::Trans::NoTranspose, KB::Diag::Unit,
                                    default_mode_type, default_algo_type>::invoke(member, one, W1, W2);
                           KB::Trsm<member_type,
                                    KB::Side::Left, KB::Uplo::Upper, KB::Trans::NoTranspose, KB::Diag::NonUnit,
                                    default_mode_type, default_algo_type>::invoke(member, one, W1, W2);
                           member.team_barrier();
                           if (row < nrows) {
                             Kokkos::parallel_for(Kokkos::TeamThreadRange(member, blocksize * blocksize),
                                                  [&](int i) {
                                                    auto d_inv_block = &d_inv(row, 0, 0);
                                                    d_inv_block[i]   = W2.data()[i];
                                                  });
                           }
                         });
  }

  KOKKOS_INLINE_FUNCTION
  void
  operator()(const ExtractBCDTag &, const member_type &member) const {
    // btdm is packed and sorted from largest one
    const local_ordinal_type packindices_schur_i = member.league_rank() % packindices_schur.extent(0);
    const local_ordinal_type packindices_schur_j = member.league_rank() / packindices_schur.extent(0);
    const local_ordinal_type packidx             = packindices_schur(packindices_schur_i, packindices_schur_j);

    const local_ordinal_type subpartidx       = packptr_sub(packidx);
    const local_ordinal_type n_parts          = part2packrowidx0_sub.extent(0);
    const local_ordinal_type local_subpartidx = subpartidx / n_parts;
    const local_ordinal_type partidx          = subpartidx % n_parts;

    const local_ordinal_type npacks = packptr_sub(packidx + 1) - subpartidx;
    // const local_ordinal_type i0 = pack_td_ptr(partidx,local_subpartidx);
    // const local_ordinal_type nrows = partptr_sub(subpartidx,1) - partptr_sub(subpartidx,0);

    if (vector_loop_size == 1) {
      extract(partidx, local_subpartidx, npacks);
    } else {
      Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size),
                           [&](const local_ordinal_type &v) {
                             const local_ordinal_type vbeg = v * internal_vector_length;
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
                             const local_ordinal_type i0 = pack_td_ptr(partidx, local_subpartidx);
                             printf("i0 = %d, npacks = %d, vbeg = %d;\n", i0, npacks, vbeg);
#endif
                             if (vbeg < npacks)
                               extract(member, partidx + vbeg, local_subpartidx, npacks, vbeg);
                           });
    }

    member.team_barrier();

    const size_type kps1 = pack_td_ptr(partidx, local_subpartidx);
    const size_type kps2 = pack_td_ptr(partidx, local_subpartidx + 1) - 1;

    const local_ordinal_type r1 = part2packrowidx0_sub(partidx, local_subpartidx) - 1;
    const local_ordinal_type r2 = part2packrowidx0_sub(partidx, local_subpartidx) + 2;

#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
    printf("Copy for Schur complement part id = %d from kps1 = %ld to r1 = %d and from kps2 = %ld to r2 = %d partidx = %d local_subpartidx = %d;\n", packidx, kps1, r1, kps2, r2, partidx, local_subpartidx);
#endif

    // Need to copy D to e_internal_vector_values.
    copy3DView<local_ordinal_type>(member, Kokkos::subview(e_internal_vector_values, 0, r1, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()),
                                   Kokkos::subview(internal_vector_values, kps1, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()));

    copy3DView<local_ordinal_type>(member, Kokkos::subview(e_internal_vector_values, 1, r2, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()),
                                   Kokkos::subview(internal_vector_values, kps2, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()));
  }

  KOKKOS_INLINE_FUNCTION
  void
  operator()(const ComputeETag &, const member_type &member) const {
    // btdm is packed and sorted from largest one
    const local_ordinal_type packidx = packindices_sub(member.league_rank());

    const local_ordinal_type subpartidx       = packptr_sub(packidx);
    const local_ordinal_type n_parts          = part2packrowidx0_sub.extent(0);
    const local_ordinal_type local_subpartidx = subpartidx / n_parts;
    const local_ordinal_type partidx          = subpartidx % n_parts;

    const local_ordinal_type npacks      = packptr_sub(packidx + 1) - subpartidx;
    const local_ordinal_type i0          = pack_td_ptr(partidx, local_subpartidx);
    const local_ordinal_type r0          = part2packrowidx0_sub(partidx, local_subpartidx);
    const local_ordinal_type nrows       = partptr_sub(subpartidx, 1) - partptr_sub(subpartidx, 0);
    const local_ordinal_type num_vectors = blocksize;

    (void)npacks;

    internal_vector_scratch_type_3d_view
        WW(member.team_scratch(ScratchLevel), blocksize, num_vectors, vector_loop_size);
    if (local_subpartidx == 0) {
      Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
        solveMultiVector<impl_type, internal_vector_scratch_type_3d_view>(member, blocksize, i0, r0, nrows, v, internal_vector_values, Kokkos::subview(e_internal_vector_values, 0, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()), WW, true);
      });
    } else if (local_subpartidx == (local_ordinal_type)part2packrowidx0_sub.extent(1) - 2) {
      Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
        solveMultiVector<impl_type, internal_vector_scratch_type_3d_view>(member, blocksize, i0, r0, nrows, v, internal_vector_values, Kokkos::subview(e_internal_vector_values, 1, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()), WW);
      });
    } else {
      Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
        solveMultiVector<impl_type, internal_vector_scratch_type_3d_view>(member, blocksize, i0, r0, nrows, v, internal_vector_values, Kokkos::subview(e_internal_vector_values, 0, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()), WW, true);
        solveMultiVector<impl_type, internal_vector_scratch_type_3d_view>(member, blocksize, i0, r0, nrows, v, internal_vector_values, Kokkos::subview(e_internal_vector_values, 1, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()), WW);
      });
    }
  }

  KOKKOS_INLINE_FUNCTION
  void
  operator()(const ComputeSchurTag &, const member_type &member) const {
    // btdm is packed and sorted from largest one
    const local_ordinal_type packindices_schur_i = member.league_rank() % packindices_schur.extent(0);
    const local_ordinal_type packindices_schur_j = member.league_rank() / packindices_schur.extent(0);
    const local_ordinal_type packidx             = packindices_schur(packindices_schur_i, packindices_schur_j);

    const local_ordinal_type subpartidx       = packptr_sub(packidx);
    const local_ordinal_type n_parts          = part2packrowidx0_sub.extent(0);
    const local_ordinal_type local_subpartidx = subpartidx / n_parts;
    const local_ordinal_type partidx          = subpartidx % n_parts;

    // const local_ordinal_type npacks = packptr_sub(packidx+1) - subpartidx;
    const local_ordinal_type i0 = pack_td_ptr(partidx, local_subpartidx);
    // const local_ordinal_type r0 = part2packrowidx0_sub(partidx,local_subpartidx);
    // const local_ordinal_type nrows = partptr_sub(subpartidx,1) - partptr_sub(subpartidx,0);

    // Compute S = D - C E

    const local_ordinal_type local_subpartidx_schur = (local_subpartidx - 1) / 2;
    const local_ordinal_type i0_schur               = local_subpartidx_schur == 0 ? pack_td_ptr_schur(partidx, local_subpartidx_schur) : pack_td_ptr_schur(partidx, local_subpartidx_schur) + 1;
    const local_ordinal_type i0_offset              = local_subpartidx_schur == 0 ? i0 + 2 : i0 + 2;

    for (local_ordinal_type i = 0; i < 4; ++i) {  // pack_td_ptr_schur(partidx,local_subpartidx_schur+1)-i0_schur
      copy3DView<local_ordinal_type>(member, Kokkos::subview(internal_vector_values_schur, i0_schur + i, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()),
                                     Kokkos::subview(internal_vector_values, i0_offset + i, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()));
    }

    member.team_barrier();

#if KOKKOS_VERSION >= 40799
    const auto one = KokkosKernels::ArithTraits<btdm_magnitude_type>::one();
#else
    const auto one = Kokkos::ArithTraits<btdm_magnitude_type>::one();
#endif

    const size_type c_kps1 = pack_td_ptr(partidx, local_subpartidx) + 1;
    const size_type c_kps2 = pack_td_ptr(partidx, local_subpartidx + 1) - 2;

    const local_ordinal_type e_r1 = part2packrowidx0_sub(partidx, local_subpartidx) - 1;
    const local_ordinal_type e_r2 = part2packrowidx0_sub(partidx, local_subpartidx) + 2;

    typedef ExtractAndFactorizeTridiagsDefaultModeAndAlgo<typename execution_space::memory_space> default_mode_and_algo_type;

    typedef typename default_mode_and_algo_type::mode_type default_mode_type;
    typedef typename default_mode_and_algo_type::algo_type default_algo_type;

    Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
      for (size_type i = 0; i < pack_td_ptr_schur(partidx, local_subpartidx_schur + 1) - pack_td_ptr_schur(partidx, local_subpartidx_schur); ++i) {
        local_ordinal_type e_r, e_c, c_kps;

        if (local_subpartidx_schur == 0) {
          if (i == 0) {
            e_r   = e_r1;
            e_c   = 0;
            c_kps = c_kps1;
          } else if (i == 3) {
            e_r   = e_r2;
            e_c   = 1;
            c_kps = c_kps2;
          } else if (i == 4) {
            e_r   = e_r2;
            e_c   = 0;
            c_kps = c_kps2;
          } else {
            continue;
          }
        } else {
          if (i == 0) {
            e_r   = e_r1;
            e_c   = 1;
            c_kps = c_kps1;
          } else if (i == 1) {
            e_r   = e_r1;
            e_c   = 0;
            c_kps = c_kps1;
          } else if (i == 4) {
            e_r   = e_r2;
            e_c   = 1;
            c_kps = c_kps2;
          } else if (i == 5) {
            e_r   = e_r2;
            e_c   = 0;
            c_kps = c_kps2;
          } else {
            continue;
          }
        }

        auto S = Kokkos::subview(internal_vector_values_schur, pack_td_ptr_schur(partidx, local_subpartidx_schur) + i, Kokkos::ALL(), Kokkos::ALL(), v);
        auto C = Kokkos::subview(internal_vector_values, c_kps, Kokkos::ALL(), Kokkos::ALL(), v);
        auto E = Kokkos::subview(e_internal_vector_values, e_c, e_r, Kokkos::ALL(), Kokkos::ALL(), v);
        KB::Gemm<member_type,
                 KB::Trans::NoTranspose, KB::Trans::NoTranspose,
                 default_mode_type, default_algo_type>::invoke(member, -one, C, E, one, S);
      }
    });
  }

  KOKKOS_INLINE_FUNCTION
  void
  operator()(const FactorizeSchurTag &, const member_type &member) const {
    const local_ordinal_type packidx = packindices_schur(member.league_rank(), 0);

    const local_ordinal_type subpartidx = packptr_sub(packidx);

    const local_ordinal_type n_parts = part2packrowidx0_sub.extent(0);
    const local_ordinal_type partidx = subpartidx % n_parts;

    const local_ordinal_type i0    = pack_td_ptr_schur(partidx, 0);
    const local_ordinal_type nrows = 2 * (pack_td_ptr_schur.extent(1) - 1);

    internal_vector_scratch_type_3d_view
        WW(member.team_scratch(ScratchLevel), blocksize, blocksize, vector_loop_size);

#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
    printf("FactorizeSchurTag rank = %d, i0 = %d, nrows = %d, vector_loop_size = %d;\n", member.league_rank(), i0, nrows, vector_loop_size);
#endif

    if (vector_loop_size == 1) {
      factorize_subline(member, i0, nrows, 0, internal_vector_values_schur, WW);
    } else {
      Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size),
                           [&](const local_ordinal_type &v) {
                             factorize_subline(member, i0, nrows, v, internal_vector_values_schur, WW);
                           });
    }
  }

  void run() {
    IFPACK2_BLOCKTRIDICONTAINER_PROFILER_REGION_BEGIN;
    const local_ordinal_type team_size =
        ExtractAndFactorizeTridiagsDefaultModeAndAlgo<typename execution_space::memory_space>::
            recommended_team_size(blocksize, vector_length, internal_vector_length);
    const local_ordinal_type per_team_scratch = internal_vector_scratch_type_3d_view::
        shmem_size(blocksize, blocksize, vector_loop_size);

    {
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
      printf("Start ExtractAndFactorizeSubLineTag\n");
#endif
      IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::NumericPhase::ExtractAndFactorizeSubLineTag", ExtractAndFactorizeSubLineTag0);
      Kokkos::TeamPolicy<execution_space, ExtractAndFactorizeSubLineTag>
          policy(packindices_sub.extent(0), team_size, vector_loop_size);

      const local_ordinal_type n_parts = part2packrowidx0_sub.extent(0);
      writeBTDValuesToFile(n_parts, scalar_values, "before.mm");

      policy.set_scratch_size(ScratchLevel, Kokkos::PerTeam(per_team_scratch));
      Kokkos::parallel_for("ExtractAndFactorize::TeamPolicy::run<ExtractAndFactorizeSubLineTag>",
                           policy, *this);
      execution_space().fence();

      writeBTDValuesToFile(n_parts, scalar_values, "after.mm");
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
      printf("End ExtractAndFactorizeSubLineTag\n");
#endif
    }

    if (packindices_schur.extent(1) > 0) {
      {
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
        printf("Start ExtractBCDTag\n");
#endif
#if KOKKOS_VERSION >= 40799
        Kokkos::deep_copy(e_scalar_values, KokkosKernels::ArithTraits<btdm_magnitude_type>::zero());
#else
        Kokkos::deep_copy(e_scalar_values, Kokkos::ArithTraits<btdm_magnitude_type>::zero());
#endif
#if KOKKOS_VERSION >= 40799
        Kokkos::deep_copy(scalar_values_schur, KokkosKernels::ArithTraits<btdm_magnitude_type>::zero());
#else
        Kokkos::deep_copy(scalar_values_schur, Kokkos::ArithTraits<btdm_magnitude_type>::zero());
#endif

        write5DMultiVectorValuesToFile(part2packrowidx0_sub.extent(0), e_scalar_values, "e_scalar_values_before_extract.mm");

        {
          IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::NumericPhase::ExtractBCDTag", ExtractBCDTag0);
          Kokkos::TeamPolicy<execution_space, ExtractBCDTag>
              policy(packindices_schur.extent(0) * packindices_schur.extent(1), team_size, vector_loop_size);

          policy.set_scratch_size(ScratchLevel, Kokkos::PerTeam(per_team_scratch));
          Kokkos::parallel_for("ExtractAndFactorize::TeamPolicy::run<ExtractBCDTag>",
                               policy, *this);
          execution_space().fence();
        }

#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
        printf("End ExtractBCDTag\n");
#endif
        writeBTDValuesToFile(part2packrowidx0_sub.extent(0), scalar_values, "after_extraction_of_BCD.mm");
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
        printf("Start ComputeETag\n");
#endif
        write5DMultiVectorValuesToFile(part2packrowidx0_sub.extent(0), e_scalar_values, "e_scalar_values_after_extract.mm");
        {
          IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::NumericPhase::ComputeETag", ComputeETag0);
          Kokkos::TeamPolicy<execution_space, ComputeETag>
              policy(packindices_sub.extent(0), team_size, vector_loop_size);

          policy.set_scratch_size(ScratchLevel, Kokkos::PerTeam(per_team_scratch));
          Kokkos::parallel_for("ExtractAndFactorize::TeamPolicy::run<ComputeETag>",
                               policy, *this);
          execution_space().fence();
        }
        write5DMultiVectorValuesToFile(part2packrowidx0_sub.extent(0), e_scalar_values, "e_scalar_values_after_compute.mm");

#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
        printf("End ComputeETag\n");
#endif
      }

      {
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
        printf("Start ComputeSchurTag\n");
#endif
        IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::NumericPhase::ComputeSchurTag", ComputeSchurTag0);
        writeBTDValuesToFile(part2packrowidx0_sub.extent(0), scalar_values_schur, "before_schur.mm");
        Kokkos::TeamPolicy<execution_space, ComputeSchurTag>
            policy(packindices_schur.extent(0) * packindices_schur.extent(1), team_size, vector_loop_size);

        Kokkos::parallel_for("ExtractAndFactorize::TeamPolicy::run<ComputeSchurTag>",
                             policy, *this);
        writeBTDValuesToFile(part2packrowidx0_sub.extent(0), scalar_values_schur, "after_schur.mm");
        execution_space().fence();
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
        printf("End ComputeSchurTag\n");
#endif
      }

      {
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
        printf("Start FactorizeSchurTag\n");
#endif
        IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::NumericPhase::FactorizeSchurTag", FactorizeSchurTag0);
        Kokkos::TeamPolicy<execution_space, FactorizeSchurTag>
            policy(packindices_schur.extent(0), team_size, vector_loop_size);
        policy.set_scratch_size(ScratchLevel, Kokkos::PerTeam(per_team_scratch));
        Kokkos::parallel_for("ExtractAndFactorize::TeamPolicy::run<FactorizeSchurTag>",
                             policy, *this);
        execution_space().fence();
        writeBTDValuesToFile(part2packrowidx0_sub.extent(0), scalar_values_schur, "after_factor_schur.mm");
#ifdef IFPACK2_BLOCKTRIDICONTAINER_USE_PRINTF
        printf("End FactorizeSchurTag\n");
#endif
      }
    }

    IFPACK2_BLOCKTRIDICONTAINER_PROFILER_REGION_END;
  }

  void run_fused_jacobi() {
    IFPACK2_BLOCKTRIDICONTAINER_PROFILER_REGION_BEGIN;
    const local_ordinal_type team_size =
        ExtractAndFactorizeTridiagsDefaultModeAndAlgo<typename execution_space::memory_space>::
            recommended_team_size(blocksize, half_vector_length, 1);
    const local_ordinal_type per_team_scratch =
        btdm_scalar_scratch_type_3d_view::shmem_size(blocksize, blocksize, 2 * half_vector_length);
    {
      IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::NumericPhase::ExtractAndFactorizeFusedJacobi", ExtractAndFactorizeFusedJacobiTag);
      Kokkos::TeamPolicy<execution_space, ExtractAndFactorizeFusedJacobiTag>
          policy((lclrow.extent(0) + half_vector_length - 1) / half_vector_length, team_size, half_vector_length);

      policy.set_scratch_size(ScratchLevel, Kokkos::PerTeam(per_team_scratch));
      Kokkos::parallel_for("ExtractAndFactorize::TeamPolicy::run<ExtractAndFactorizeFusedJacobiTag>",
                           policy, *this);
    }
    IFPACK2_BLOCKTRIDICONTAINER_PROFILER_REGION_END;
  }
};

template <typename MatrixType>
void performNumericPhase(const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_row_matrix_type> &A,
                         const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_crs_graph_type> &G,
                         const BlockHelperDetails::PartInterface<MatrixType> &interf,
                         BlockTridiags<MatrixType> &btdm,
                         const typename BlockHelperDetails::ImplType<MatrixType>::magnitude_type tiny,
                         bool use_fused_jacobi) {
  using impl_type                            = BlockHelperDetails::ImplType<MatrixType>;
  using execution_space                      = typename impl_type::execution_space;
  using team_policy_type                     = Kokkos::TeamPolicy<execution_space>;
  using internal_vector_scratch_type_3d_view = Scratch<typename impl_type::internal_vector_type_3d_view>;
  using btdm_scalar_scratch_type_3d_view     = Scratch<typename impl_type::btdm_scalar_type_3d_view>;

  IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::NumericPhase", NumericPhase);

  int blocksize = btdm.values.extent(1);
  // Both Kokkos policy vector length and SIMD type vector length are hardcoded in KokkosBatched.
  // For large block sizes, have to fall back to level 1 scratch.
  int scratch_required;
  if (!use_fused_jacobi) {
    // General path scratch requirement
    scratch_required = internal_vector_scratch_type_3d_view::shmem_size(blocksize, blocksize, impl_type::vector_length / impl_type::internal_vector_length);
  } else {
    // Block Jacobi scratch requirement: measured in scalars, and uses twice as much (in bytes) per vector lane as the general path.
    scratch_required = btdm_scalar_scratch_type_3d_view::shmem_size(blocksize, blocksize, 2 * impl_type::half_vector_length);
  }

  int max_scratch = team_policy_type::scratch_size_max(0);

  if (scratch_required < max_scratch) {
    // Can use level 0 scratch
    ExtractAndFactorizeTridiags<MatrixType, 0> function(btdm, interf, A, G, tiny);
    if (!use_fused_jacobi)
      function.run();
    else
      function.run_fused_jacobi();
  } else {
    // Not enough level 0 scratch, so fall back to level 1
    ExtractAndFactorizeTridiags<MatrixType, 1> function(btdm, interf, A, G, tiny);
    if (!use_fused_jacobi)
      function.run();
    else
      function.run_fused_jacobi();
  }
  IFPACK2_BLOCKHELPER_TIMER_FENCE(typename BlockHelperDetails::ImplType<MatrixType>::execution_space)
}

template <typename MatrixType>
struct MultiVectorConverter {
 public:
  using impl_type       = BlockHelperDetails::ImplType<MatrixType>;
  using execution_space = typename impl_type::execution_space;
  using memory_space    = typename impl_type::memory_space;

  using local_ordinal_type                    = typename impl_type::local_ordinal_type;
  using impl_scalar_type                      = typename impl_type::impl_scalar_type;
  using btdm_scalar_type                      = typename impl_type::btdm_scalar_type;
  using tpetra_multivector_type               = typename impl_type::tpetra_multivector_type;
  using local_ordinal_type_1d_view            = typename impl_type::local_ordinal_type_1d_view;
  using vector_type_3d_view                   = typename impl_type::vector_type_3d_view;
  using impl_scalar_type_2d_view_tpetra       = typename impl_type::impl_scalar_type_2d_view_tpetra;
  using const_impl_scalar_type_2d_view_tpetra = typename impl_scalar_type_2d_view_tpetra::const_type;
  static constexpr int vector_length          = impl_type::vector_length;

  using member_type = typename Kokkos::TeamPolicy<execution_space>::member_type;

 private:
  // part interface
  const ConstUnmanaged<local_ordinal_type_1d_view> partptr;
  const ConstUnmanaged<local_ordinal_type_1d_view> packptr;
  const ConstUnmanaged<local_ordinal_type_1d_view> part2packrowidx0;
  const ConstUnmanaged<local_ordinal_type_1d_view> part2rowidx0;
  const ConstUnmanaged<local_ordinal_type_1d_view> lclrow;
  const local_ordinal_type blocksize;
  const local_ordinal_type num_vectors;

  // packed multivector output (or input)
  vector_type_3d_view packed_multivector;
  const_impl_scalar_type_2d_view_tpetra scalar_multivector;

  template <typename TagType>
  KOKKOS_INLINE_FUNCTION void copy_multivectors(const local_ordinal_type &j,
                                                const local_ordinal_type &vi,
                                                const local_ordinal_type &pri,
                                                const local_ordinal_type &ri0) const {
    for (local_ordinal_type col = 0; col < num_vectors; ++col)
      for (local_ordinal_type i = 0; i < blocksize; ++i)
        packed_multivector(pri, i, col)[vi] = static_cast<btdm_scalar_type>(scalar_multivector(blocksize * lclrow(ri0 + j) + i, col));
  }

 public:
  MultiVectorConverter(const BlockHelperDetails::PartInterface<MatrixType> &interf,
                       const vector_type_3d_view &pmv)
    : partptr(interf.partptr)
    , packptr(interf.packptr)
    , part2packrowidx0(interf.part2packrowidx0)
    , part2rowidx0(interf.part2rowidx0)
    , lclrow(interf.lclrow)
    , blocksize(pmv.extent(1))
    , num_vectors(pmv.extent(2))
    , packed_multivector(pmv) {}

  // TODO:: modify this routine similar to the team level functions
  KOKKOS_INLINE_FUNCTION
  void
  operator()(const local_ordinal_type &packidx) const {
    local_ordinal_type partidx    = packptr(packidx);
    local_ordinal_type npacks     = packptr(packidx + 1) - partidx;
    const local_ordinal_type pri0 = part2packrowidx0(partidx);

    local_ordinal_type ri0[vector_length]   = {};
    local_ordinal_type nrows[vector_length] = {};
    for (local_ordinal_type v = 0; v < npacks; ++v, ++partidx) {
      ri0[v]   = part2rowidx0(partidx);
      nrows[v] = part2rowidx0(partidx + 1) - ri0[v];
    }
    for (local_ordinal_type j = 0; j < nrows[0]; ++j) {
      local_ordinal_type cnt = 1;
      for (; cnt < npacks && j != nrows[cnt]; ++cnt)
        ;
      npacks                       = cnt;
      const local_ordinal_type pri = pri0 + j;
      for (local_ordinal_type col = 0; col < num_vectors; ++col)
        for (local_ordinal_type i = 0; i < blocksize; ++i)
          for (local_ordinal_type v = 0; v < npacks; ++v)
            packed_multivector(pri, i, col)[v] = static_cast<btdm_scalar_type>(scalar_multivector(blocksize * lclrow(ri0[v] + j) + i, col));
    }
  }

  KOKKOS_INLINE_FUNCTION
  void
  operator()(const member_type &member) const {
    const local_ordinal_type packidx       = member.league_rank();
    const local_ordinal_type partidx_begin = packptr(packidx);
    const local_ordinal_type npacks        = packptr(packidx + 1) - partidx_begin;
    const local_ordinal_type pri0          = part2packrowidx0(partidx_begin);
    Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, npacks), [&](const local_ordinal_type &v) {
      const local_ordinal_type partidx = partidx_begin + v;
      const local_ordinal_type ri0     = part2rowidx0(partidx);
      const local_ordinal_type nrows   = part2rowidx0(partidx + 1) - ri0;

      if (nrows == 1) {
        const local_ordinal_type pri = pri0;
        for (local_ordinal_type col = 0; col < num_vectors; ++col) {
          Kokkos::parallel_for(Kokkos::TeamThreadRange(member, blocksize), [&](const local_ordinal_type &i) {
            packed_multivector(pri, i, col)[v] = static_cast<btdm_scalar_type>(scalar_multivector(blocksize * lclrow(ri0) + i, col));
          });
        }
      } else {
        Kokkos::parallel_for(Kokkos::TeamThreadRange(member, nrows), [&](const local_ordinal_type &j) {
          const local_ordinal_type pri = pri0 + j;
          for (local_ordinal_type col = 0; col < num_vectors; ++col)
            for (local_ordinal_type i = 0; i < blocksize; ++i)
              packed_multivector(pri, i, col)[v] = static_cast<btdm_scalar_type>(scalar_multivector(blocksize * lclrow(ri0 + j) + i, col));
        });
      }
    });
  }

  void run(const const_impl_scalar_type_2d_view_tpetra &scalar_multivector_) {
    IFPACK2_BLOCKTRIDICONTAINER_PROFILER_REGION_BEGIN;
    IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::MultiVectorConverter", MultiVectorConverter0);

    scalar_multivector = scalar_multivector_;
    if constexpr (BlockHelperDetails::is_device<execution_space>::value) {
      const local_ordinal_type vl = vector_length;
      const Kokkos::TeamPolicy<execution_space> policy(packptr.extent(0) - 1, Kokkos::AUTO(), vl);
      Kokkos::parallel_for("MultiVectorConverter::TeamPolicy", policy, *this);
    } else {
      const Kokkos::RangePolicy<execution_space> policy(0, packptr.extent(0) - 1);
      Kokkos::parallel_for("MultiVectorConverter::RangePolicy", policy, *this);
    }
    IFPACK2_BLOCKTRIDICONTAINER_PROFILER_REGION_END;
    IFPACK2_BLOCKHELPER_TIMER_FENCE(execution_space)
  }
};


template <>
struct SolveTridiagsDefaultModeAndAlgo<Kokkos::HostSpace> {
  typedef KB::Mode::Serial mode_type;
  typedef KB::Algo::Level2::Unblocked single_vector_algo_type;
#if defined(__KOKKOSBATCHED_INTEL_MKL_COMPACT_BATCHED__)
  typedef KB::Algo::Level3::CompactMKL multi_vector_algo_type;
#else
  typedef KB::Algo::Level3::Blocked multi_vector_algo_type;
#endif
  static int recommended_team_size(const int /* blksize */,
                                   const int /* vector_length */,
                                   const int /* internal_vector_length */) {
    return 1;
  }
};

#if defined(KOKKOS_ENABLE_CUDA)
static inline int SolveTridiagsRecommendedCudaTeamSize(const int blksize,
                                                       const int vector_length,
                                                       const int internal_vector_length) {
  const int vector_size = vector_length / internal_vector_length;
  int total_team_size(0);
  if (blksize <= 5)
    total_team_size = 32;
  else if (blksize <= 9)
    total_team_size = 32;  // 64
  else if (blksize <= 12)
    total_team_size = 96;
  else if (blksize <= 16)
    total_team_size = 128;
  else if (blksize <= 20)
    total_team_size = 160;
  else
    total_team_size = 160;
  return total_team_size / vector_size;
}

template <>
struct SolveTridiagsDefaultModeAndAlgo<Kokkos::CudaSpace> {
  typedef KB::Mode::Team mode_type;
  typedef KB::Algo::Level2::Unblocked single_vector_algo_type;
  typedef KB::Algo::Level3::Unblocked multi_vector_algo_type;
  static int recommended_team_size(const int blksize,
                                   const int vector_length,
                                   const int internal_vector_length) {
    return SolveTridiagsRecommendedCudaTeamSize(blksize, vector_length, internal_vector_length);
  }
};
template <>
struct SolveTridiagsDefaultModeAndAlgo<Kokkos::CudaUVMSpace> {
  typedef KB::Mode::Team mode_type;
  typedef KB::Algo::Level2::Unblocked single_vector_algo_type;
  typedef KB::Algo::Level3::Unblocked multi_vector_algo_type;
  static int recommended_team_size(const int blksize,
                                   const int vector_length,
                                   const int internal_vector_length) {
    return SolveTridiagsRecommendedCudaTeamSize(blksize, vector_length, internal_vector_length);
  }
};
#endif

#if defined(KOKKOS_ENABLE_HIP)
static inline int SolveTridiagsRecommendedHIPTeamSize(const int blksize,
                                                      const int vector_length,
                                                      const int internal_vector_length) {
  const int vector_size = vector_length / internal_vector_length;
  int total_team_size(0);
  if (blksize <= 5)
    total_team_size = 32;
  else if (blksize <= 9)
    total_team_size = 32;  // 64
  else if (blksize <= 12)
    total_team_size = 96;
  else if (blksize <= 16)
    total_team_size = 128;
  else if (blksize <= 20)
    total_team_size = 160;
  else
    total_team_size = 160;
  return total_team_size / vector_size;
}

template <>
struct SolveTridiagsDefaultModeAndAlgo<Kokkos::HIPSpace> {
  typedef KB::Mode::Team mode_type;
  typedef KB::Algo::Level2::Unblocked single_vector_algo_type;
  typedef KB::Algo::Level3::Unblocked multi_vector_algo_type;
  static int recommended_team_size(const int blksize,
                                   const int vector_length,
                                   const int internal_vector_length) {
    return SolveTridiagsRecommendedHIPTeamSize(blksize, vector_length, internal_vector_length);
  }
};
template <>
struct SolveTridiagsDefaultModeAndAlgo<Kokkos::HIPHostPinnedSpace> {
  typedef KB::Mode::Team mode_type;
  typedef KB::Algo::Level2::Unblocked single_vector_algo_type;
  typedef KB::Algo::Level3::Unblocked multi_vector_algo_type;
  static int recommended_team_size(const int blksize,
                                   const int vector_length,
                                   const int internal_vector_length) {
    return SolveTridiagsRecommendedHIPTeamSize(blksize, vector_length, internal_vector_length);
  }
};
#endif

#if defined(KOKKOS_ENABLE_SYCL)
static inline int SolveTridiagsRecommendedSYCLTeamSize(const int blksize,
                                                       const int vector_length,
                                                       const int internal_vector_length) {
  const int vector_size = vector_length / internal_vector_length;
  int total_team_size(0);
  if (blksize <= 5)
    total_team_size = 32;
  else if (blksize <= 9)
    total_team_size = 32;  // 64
  else if (blksize <= 12)
    total_team_size = 96;
  else if (blksize <= 16)
    total_team_size = 128;
  else if (blksize <= 20)
    total_team_size = 160;
  else
    total_team_size = 160;
  return total_team_size / vector_size;
}

template <>
struct SolveTridiagsDefaultModeAndAlgo<Kokkos::Experimental::SYCLSharedUSMSpace> {
  typedef KB::Mode::Team mode_type;
  typedef KB::Algo::Level2::Unblocked single_vector_algo_type;
  typedef KB::Algo::Level3::Unblocked multi_vector_algo_type;
  static int recommended_team_size(const int blksize,
                                   const int vector_length,
                                   const int internal_vector_length) {
    return SolveTridiagsRecommendedSYCLTeamSize(blksize, vector_length, internal_vector_length);
  }
};
template <>
struct SolveTridiagsDefaultModeAndAlgo<Kokkos::Experimental::SYCLDeviceUSMSpace> {
  typedef KB::Mode::Team mode_type;
  typedef KB::Algo::Level2::Unblocked single_vector_algo_type;
  typedef KB::Algo::Level3::Unblocked multi_vector_algo_type;
  static int recommended_team_size(const int blksize,
                                   const int vector_length,
                                   const int internal_vector_length) {
    return SolveTridiagsRecommendedSYCLTeamSize(blksize, vector_length, internal_vector_length);
  }
};
#endif

template <typename MatrixType>
struct SolveTridiags {
 public:
  using impl_type       = BlockHelperDetails::ImplType<MatrixType>;
  using execution_space = typename impl_type::execution_space;

  using local_ordinal_type  = typename impl_type::local_ordinal_type;
  using size_type           = typename impl_type::size_type;
  using impl_scalar_type    = typename impl_type::impl_scalar_type;
  using magnitude_type      = typename impl_type::magnitude_type;
  using btdm_scalar_type    = typename impl_type::btdm_scalar_type;
  using btdm_magnitude_type = typename impl_type::btdm_magnitude_type;
  using local_ordinal_type_1d_view = typename impl_type::local_ordinal_type_1d_view;
  using local_ordinal_type_2d_view = typename impl_type::local_ordinal_type_2d_view;
  using size_type_2d_view          = typename impl_type::size_type_2d_view;
  using vector_type_3d_view          = typename impl_type::vector_type_3d_view;
  using internal_vector_type_4d_view = typename impl_type::internal_vector_type_4d_view;
  using internal_vector_type_5d_view = typename impl_type::internal_vector_type_5d_view;
  using btdm_scalar_type_4d_view     = typename impl_type::btdm_scalar_type_4d_view;

  using internal_vector_scratch_type_3d_view = Scratch<typename impl_type::internal_vector_type_3d_view>;

  using internal_vector_type                  = typename impl_type::internal_vector_type;
  static constexpr int vector_length          = impl_type::vector_length;
  static constexpr int internal_vector_length = impl_type::internal_vector_length;

  using impl_scalar_type_1d_view        = typename impl_type::impl_scalar_type_1d_view;
  using impl_scalar_type_2d_view_tpetra = typename impl_type::impl_scalar_type_2d_view_tpetra;

  using team_policy_type = Kokkos::TeamPolicy<execution_space>;
  using member_type      = typename team_policy_type::member_type;

 private:
  // part interface
  local_ordinal_type n_subparts_per_part;
  const ConstUnmanaged<local_ordinal_type_1d_view> partptr;
  const ConstUnmanaged<local_ordinal_type_1d_view> packptr;
  const ConstUnmanaged<local_ordinal_type_1d_view> packindices_sub;
  const ConstUnmanaged<local_ordinal_type_2d_view> packindices_schur;
  const ConstUnmanaged<local_ordinal_type_1d_view> part2packrowidx0;
  const ConstUnmanaged<local_ordinal_type_2d_view> part2packrowidx0_sub;
  const ConstUnmanaged<local_ordinal_type_1d_view> lclrow;
  const ConstUnmanaged<local_ordinal_type_1d_view> packptr_sub;

  const ConstUnmanaged<local_ordinal_type_2d_view> partptr_sub;
  const ConstUnmanaged<size_type_2d_view> pack_td_ptr_schur;

  // block tridiags
  const ConstUnmanaged<size_type_2d_view> pack_td_ptr;

  // block tridiags values
  const ConstUnmanaged<internal_vector_type_4d_view> D_internal_vector_values;
  const Unmanaged<internal_vector_type_4d_view> X_internal_vector_values;
  const Unmanaged<btdm_scalar_type_4d_view> X_internal_scalar_values;

  internal_vector_type_4d_view X_internal_vector_values_schur;

  const ConstUnmanaged<internal_vector_type_4d_view> D_internal_vector_values_schur;
  const ConstUnmanaged<internal_vector_type_5d_view> e_internal_vector_values;

  const local_ordinal_type vector_loop_size;

  // copy to multivectors : damping factor and Y_scalar_multivector
  Unmanaged<impl_scalar_type_2d_view_tpetra> Y_scalar_multivector;
#if defined(__CUDA_ARCH__) || defined(__HIP_DEVICE_COMPILE__) || defined(__SYCL_DEVICE_ONLY__)
  AtomicUnmanaged<impl_scalar_type_1d_view> Z_scalar_vector;
#else
  /* */ Unmanaged<impl_scalar_type_1d_view> Z_scalar_vector;
#endif
  const impl_scalar_type df;
  const bool compute_diff;

 public:
  SolveTridiags(const BlockHelperDetails::PartInterface<MatrixType> &interf,
                const BlockTridiags<MatrixType> &btdm,
                const vector_type_3d_view &pmv,
                const impl_scalar_type damping_factor,
                const bool is_norm_manager_active)
    :  // interface
    n_subparts_per_part(interf.n_subparts_per_part)
    , partptr(interf.partptr)
    , packptr(interf.packptr)
    , packindices_sub(interf.packindices_sub)
    , packindices_schur(interf.packindices_schur)
    , part2packrowidx0(interf.part2packrowidx0)
    , part2packrowidx0_sub(interf.part2packrowidx0_sub)
    , lclrow(interf.lclrow)
    , packptr_sub(interf.packptr_sub)
    , partptr_sub(interf.partptr_sub)
    , pack_td_ptr_schur(btdm.pack_td_ptr_schur)
    ,
    // block tridiags and  multivector
    pack_td_ptr(btdm.pack_td_ptr)
    , D_internal_vector_values((internal_vector_type *)btdm.values.data(),
                               btdm.values.extent(0),
                               btdm.values.extent(1),
                               btdm.values.extent(2),
                               vector_length / internal_vector_length)
    , X_internal_vector_values((internal_vector_type *)pmv.data(),
                               pmv.extent(0),
                               pmv.extent(1),
                               pmv.extent(2),
                               vector_length / internal_vector_length)
    , X_internal_scalar_values((btdm_scalar_type *)pmv.data(),
                               pmv.extent(0),
                               pmv.extent(1),
                               pmv.extent(2),
                               vector_length)
    , X_internal_vector_values_schur(do_not_initialize_tag("X_internal_vector_values_schur"),
                                     2 * (n_subparts_per_part - 1) * part2packrowidx0_sub.extent(0),
                                     pmv.extent(1),
                                     pmv.extent(2),
                                     vector_length / internal_vector_length)
    , D_internal_vector_values_schur((internal_vector_type *)btdm.values_schur.data(),
                                     btdm.values_schur.extent(0),
                                     btdm.values_schur.extent(1),
                                     btdm.values_schur.extent(2),
                                     vector_length / internal_vector_length)
    , e_internal_vector_values((internal_vector_type *)btdm.e_values.data(),
                               btdm.e_values.extent(0),
                               btdm.e_values.extent(1),
                               btdm.e_values.extent(2),
                               btdm.e_values.extent(3),
                               vector_length / internal_vector_length)
    , vector_loop_size(vector_length / internal_vector_length)
    , Y_scalar_multivector()
    , Z_scalar_vector()
    , df(damping_factor)
    , compute_diff(is_norm_manager_active) {}

 public:
  KOKKOS_INLINE_FUNCTION
  void
  copyToFlatMultiVector(const member_type &member,
                        const local_ordinal_type partidxbeg,  // partidx for v = 0
                        const local_ordinal_type npacks,
                        const local_ordinal_type pri0,
                        const local_ordinal_type v,  // index with a loop of vector_loop_size
                        const local_ordinal_type blocksize,
                        const local_ordinal_type num_vectors) const {
    const local_ordinal_type vbeg = v * internal_vector_length;
    if (vbeg < npacks) {
      local_ordinal_type ri0_vals[internal_vector_length]   = {};
      local_ordinal_type nrows_vals[internal_vector_length] = {};
      for (local_ordinal_type vv = vbeg, vi = 0; vv < npacks && vi < internal_vector_length; ++vv, ++vi) {
        const local_ordinal_type partidx = partidxbeg + vv;
        ri0_vals[vi]                     = partptr(partidx);
        nrows_vals[vi]                   = partptr(partidx + 1) - ri0_vals[vi];
      }

      impl_scalar_type z_partial_sum(0);
      if (nrows_vals[0] == 1) {
        const local_ordinal_type j = 0, pri = pri0;
        {
          for (local_ordinal_type vv = vbeg, vi = 0; vv < npacks && vi < internal_vector_length; ++vv, ++vi) {
            const local_ordinal_type ri0   = ri0_vals[vi];
            const local_ordinal_type nrows = nrows_vals[vi];
            if (j < nrows) {
              Kokkos::parallel_for(Kokkos::TeamThreadRange(member, blocksize),
                                   [&](const local_ordinal_type &i) {
                                     const local_ordinal_type row = blocksize * lclrow(ri0 + j) + i;
                                     for (local_ordinal_type col = 0; col < num_vectors; ++col) {
                                       impl_scalar_type &y       = Y_scalar_multivector(row, col);
                                       const impl_scalar_type yd = X_internal_vector_values(pri, i, col, v)[vi] - y;
                                       y += df * yd;

                                       {  // if (compute_diff) {
#if KOKKOS_VERSION >= 40799
                                         const auto yd_abs = KokkosKernels::ArithTraits<impl_scalar_type>::abs(yd);
#else
                        const auto yd_abs = Kokkos::ArithTraits<impl_scalar_type>::abs(yd);
#endif
                                         z_partial_sum += yd_abs * yd_abs;
                                       }
                                     }
                                   });
            }
          }
        }
      } else {
        Kokkos::parallel_for(Kokkos::TeamThreadRange(member, nrows_vals[0]),
                             [&](const local_ordinal_type &j) {
                               const local_ordinal_type pri = pri0 + j;
                               for (local_ordinal_type vv = vbeg, vi = 0; vv < npacks && vi < internal_vector_length; ++vv, ++vi) {
                                 const local_ordinal_type ri0   = ri0_vals[vi];
                                 const local_ordinal_type nrows = nrows_vals[vi];
                                 if (j < nrows) {
                                   for (local_ordinal_type col = 0; col < num_vectors; ++col) {
                                     for (local_ordinal_type i = 0; i < blocksize; ++i) {
                                       const local_ordinal_type row = blocksize * lclrow(ri0 + j) + i;
                                       impl_scalar_type &y          = Y_scalar_multivector(row, col);
                                       const impl_scalar_type yd    = X_internal_vector_values(pri, i, col, v)[vi] - y;
                                       y += df * yd;

                                       {  // if (compute_diff) {
#if KOKKOS_VERSION >= 40799
                                         const auto yd_abs = KokkosKernels::ArithTraits<impl_scalar_type>::abs(yd);
#else
                        const auto yd_abs = Kokkos::ArithTraits<impl_scalar_type>::abs(yd);
#endif
                                         z_partial_sum += yd_abs * yd_abs;
                                       }
                                     }
                                   }
                                 }
                               }
                             });
      }
      // if (compute_diff)
      Z_scalar_vector(member.league_rank()) += z_partial_sum;
    }
  }

  template <typename WWViewType>
  KOKKOS_INLINE_FUNCTION void
  solveSingleVector(const member_type &member,
                    const local_ordinal_type &blocksize,
                    const local_ordinal_type &i0,
                    const local_ordinal_type &r0,
                    const local_ordinal_type &nrows,
                    const local_ordinal_type &v,
                    const WWViewType &WW) const {
    typedef SolveTridiagsDefaultModeAndAlgo<typename execution_space::memory_space> default_mode_and_algo_type;

    typedef typename default_mode_and_algo_type::mode_type default_mode_type;
    typedef typename default_mode_and_algo_type::single_vector_algo_type default_algo_type;

    // base pointers
    auto A = D_internal_vector_values.data();
    auto X = X_internal_vector_values.data();

    // constant
#if KOKKOS_VERSION >= 40799
    const auto one = KokkosKernels::ArithTraits<btdm_magnitude_type>::one();
#else
    const auto one  = Kokkos::ArithTraits<btdm_magnitude_type>::one();
#endif
#if KOKKOS_VERSION >= 40799
    const auto zero = KokkosKernels::ArithTraits<btdm_magnitude_type>::zero();
#else
    const auto zero = Kokkos::ArithTraits<btdm_magnitude_type>::zero();
#endif
    // const local_ordinal_type num_vectors = X_scalar_values.extent(2);

    // const local_ordinal_type blocksize = D_scalar_values.extent(1);
    const local_ordinal_type astep = D_internal_vector_values.stride(0);
    const local_ordinal_type as0   = D_internal_vector_values.stride(1);  // blocksize*vector_length;
    const local_ordinal_type as1   = D_internal_vector_values.stride(2);  // vector_length;
    const local_ordinal_type xstep = X_internal_vector_values.stride(0);
    const local_ordinal_type xs0   = X_internal_vector_values.stride(1);  // vector_length;

    // move to starting point
    A += i0 * astep + v;
    X += r0 * xstep + v;

    // for (local_ordinal_type col=0;col<num_vectors;++col)
    if (nrows > 1) {
      // solve Lx = x
      KOKKOSBATCHED_TRSV_LOWER_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                            member,
                                                            KB::Diag::Unit,
                                                            blocksize, blocksize,
                                                            one,
                                                            A, as0, as1,
                                                            X, xs0);

      for (local_ordinal_type tr = 1; tr < nrows; ++tr) {
        member.team_barrier();
        KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                        member,
                                                        blocksize, blocksize,
                                                        -one,
                                                        A + 2 * astep, as0, as1,
                                                        X, xs0,
                                                        one,
                                                        X + 1 * xstep, xs0);
        KOKKOSBATCHED_TRSV_LOWER_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                              member,
                                                              KB::Diag::Unit,
                                                              blocksize, blocksize,
                                                              one,
                                                              A + 3 * astep, as0, as1,
                                                              X + 1 * xstep, xs0);

        A += 3 * astep;
        X += 1 * xstep;
      }

      // solve Ux = x
      KOKKOSBATCHED_TRSV_UPPER_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                            member,
                                                            KB::Diag::NonUnit,
                                                            blocksize, blocksize,
                                                            one,
                                                            A, as0, as1,
                                                            X, xs0);

      for (local_ordinal_type tr = nrows; tr > 1; --tr) {
        A -= 3 * astep;
        member.team_barrier();
        KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                        member,
                                                        blocksize, blocksize,
                                                        -one,
                                                        A + 1 * astep, as0, as1,
                                                        X, xs0,
                                                        one,
                                                        X - 1 * xstep, xs0);
        KOKKOSBATCHED_TRSV_UPPER_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                              member,
                                                              KB::Diag::NonUnit,
                                                              blocksize, blocksize,
                                                              one,
                                                              A, as0, as1,
                                                              X - 1 * xstep, xs0);
        X -= 1 * xstep;
      }
      // for multiple rhs
      // X += xs1;
    } else {
      const local_ordinal_type ws0 = WW.stride(0);
      auto W                       = WW.data() + v;
      KOKKOSBATCHED_COPY_VECTOR_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type,
                                                             member, blocksize, X, xs0, W, ws0);
      member.team_barrier();
      KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                      member,
                                                      blocksize, blocksize,
                                                      one,
                                                      A, as0, as1,
                                                      W, xs0,
                                                      zero,
                                                      X, xs0);
    }
  }

  template <typename WWViewType>
  KOKKOS_INLINE_FUNCTION void
  solveMultiVector(const member_type &member,
                   const local_ordinal_type & /* blocksize */,
                   const local_ordinal_type &i0,
                   const local_ordinal_type &r0,
                   const local_ordinal_type &nrows,
                   const local_ordinal_type &v,
                   const WWViewType &WW) const {
    typedef SolveTridiagsDefaultModeAndAlgo<typename execution_space::memory_space> default_mode_and_algo_type;

    typedef typename default_mode_and_algo_type::mode_type default_mode_type;
    typedef typename default_mode_and_algo_type::multi_vector_algo_type default_algo_type;

    // constant
#if KOKKOS_VERSION >= 40799
    const auto one = KokkosKernels::ArithTraits<btdm_magnitude_type>::one();
#else
    const auto one  = Kokkos::ArithTraits<btdm_magnitude_type>::one();
#endif
#if KOKKOS_VERSION >= 40799
    const auto zero = KokkosKernels::ArithTraits<btdm_magnitude_type>::zero();
#else
    const auto zero = Kokkos::ArithTraits<btdm_magnitude_type>::zero();
#endif

    // subview pattern
    auto A  = Kokkos::subview(D_internal_vector_values, i0, Kokkos::ALL(), Kokkos::ALL(), v);
    auto X1 = Kokkos::subview(X_internal_vector_values, r0, Kokkos::ALL(), Kokkos::ALL(), v);
    auto X2 = X1;

    local_ordinal_type i = i0, r = r0;

    if (nrows > 1) {
      // solve Lx = x
      KB::Trsm<member_type,
               KB::Side::Left, KB::Uplo::Lower, KB::Trans::NoTranspose, KB::Diag::Unit,
               default_mode_type, default_algo_type>::invoke(member, one, A, X1);
      for (local_ordinal_type tr = 1; tr < nrows; ++tr, i += 3) {
        A.assign_data(&D_internal_vector_values(i + 2, 0, 0, v));
        X2.assign_data(&X_internal_vector_values(++r, 0, 0, v));
        member.team_barrier();
        KB::Gemm<member_type,
                 KB::Trans::NoTranspose, KB::Trans::NoTranspose,
                 default_mode_type, default_algo_type>::invoke(member, -one, A, X1, one, X2);
        A.assign_data(&D_internal_vector_values(i + 3, 0, 0, v));
        KB::Trsm<member_type,
                 KB::Side::Left, KB::Uplo::Lower, KB::Trans::NoTranspose, KB::Diag::Unit,
                 default_mode_type, default_algo_type>::invoke(member, one, A, X2);
        X1.assign_data(X2.data());
      }

      // solve Ux = x
      KB::Trsm<member_type,
               KB::Side::Left, KB::Uplo::Upper, KB::Trans::NoTranspose, KB::Diag::NonUnit,
               default_mode_type, default_algo_type>::invoke(member, one, A, X1);
      for (local_ordinal_type tr = nrows; tr > 1; --tr) {
        i -= 3;
        A.assign_data(&D_internal_vector_values(i + 1, 0, 0, v));
        X2.assign_data(&X_internal_vector_values(--r, 0, 0, v));
        member.team_barrier();
        KB::Gemm<member_type,
                 KB::Trans::NoTranspose, KB::Trans::NoTranspose,
                 default_mode_type, default_algo_type>::invoke(member, -one, A, X1, one, X2);

        A.assign_data(&D_internal_vector_values(i, 0, 0, v));
        KB::Trsm<member_type,
                 KB::Side::Left, KB::Uplo::Upper, KB::Trans::NoTranspose, KB::Diag::NonUnit,
                 default_mode_type, default_algo_type>::invoke(member, one, A, X2);
        X1.assign_data(X2.data());
      }
    } else {
      // matrix is already inverted
      auto W = Kokkos::subview(WW, Kokkos::ALL(), Kokkos::ALL(), v);
      KB::Copy<member_type, KB::Trans::NoTranspose, default_mode_type>::invoke(member, X1, W);
      member.team_barrier();
      KB::Gemm<member_type,
               KB::Trans::NoTranspose, KB::Trans::NoTranspose,
               default_mode_type, default_algo_type>::invoke(member, one, A, W, zero, X1);
    }
  }

  template <int B>
  struct SingleVectorTag {};
  template <int B>
  struct MultiVectorTag {};

  template <int B>
  struct SingleVectorSubLineTag {};
  template <int B>
  struct MultiVectorSubLineTag {};
  template <int B>
  struct SingleVectorApplyCTag {};
  template <int B>
  struct MultiVectorApplyCTag {};
  template <int B>
  struct SingleVectorSchurTag {};
  template <int B>
  struct MultiVectorSchurTag {};
  template <int B>
  struct SingleVectorApplyETag {};
  template <int B>
  struct MultiVectorApplyETag {};
  template <int B>
  struct SingleVectorCopyToFlatTag {};
  template <int B>
  struct SingleZeroingTag {};

  template <int B>
  KOKKOS_INLINE_FUNCTION void
  operator()(const SingleVectorTag<B> &, const member_type &member) const {
    const local_ordinal_type packidx     = member.league_rank();
    const local_ordinal_type partidx     = packptr(packidx);
    const local_ordinal_type npacks      = packptr(packidx + 1) - partidx;
    const local_ordinal_type pri0        = part2packrowidx0(partidx);
    const local_ordinal_type i0          = pack_td_ptr(partidx, 0);
    const local_ordinal_type r0          = part2packrowidx0(partidx);
    const local_ordinal_type nrows       = partptr(partidx + 1) - partptr(partidx);
    const local_ordinal_type blocksize   = (B == 0 ? D_internal_vector_values.extent(1) : B);
    const local_ordinal_type num_vectors = 1;
    internal_vector_scratch_type_3d_view
        WW(member.team_scratch(0), blocksize, 1, vector_loop_size);
    Kokkos::single(Kokkos::PerTeam(member), [&]() {
      Z_scalar_vector(member.league_rank()) = impl_scalar_type(0);
    });
    Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
      solveSingleVector(member, blocksize, i0, r0, nrows, v, WW);
      copyToFlatMultiVector(member, partidx, npacks, pri0, v, blocksize, num_vectors);
    });
  }

  template <int B>
  KOKKOS_INLINE_FUNCTION void
  operator()(const MultiVectorTag<B> &, const member_type &member) const {
    const local_ordinal_type packidx     = member.league_rank();
    const local_ordinal_type partidx     = packptr(packidx);
    const local_ordinal_type npacks      = packptr(packidx + 1) - partidx;
    const local_ordinal_type pri0        = part2packrowidx0(partidx);
    const local_ordinal_type i0          = pack_td_ptr(partidx, 0);
    const local_ordinal_type r0          = part2packrowidx0(partidx);
    const local_ordinal_type nrows       = partptr(partidx + 1) - partptr(partidx);
    const local_ordinal_type blocksize   = (B == 0 ? D_internal_vector_values.extent(1) : B);
    const local_ordinal_type num_vectors = X_internal_vector_values.extent(2);

    internal_vector_scratch_type_3d_view
        WW(member.team_scratch(0), blocksize, num_vectors, vector_loop_size);
    Kokkos::single(Kokkos::PerTeam(member), [&]() {
      Z_scalar_vector(member.league_rank()) = impl_scalar_type(0);
    });
    Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
      solveMultiVector(member, blocksize, i0, r0, nrows, v, WW);
      copyToFlatMultiVector(member, partidx, npacks, pri0, v, blocksize, num_vectors);
    });
  }

  template <int B>
  KOKKOS_INLINE_FUNCTION void
  operator()(const SingleVectorSubLineTag<B> &, const member_type &member) const {
    // btdm is packed and sorted from largest one
    const local_ordinal_type packidx = packindices_sub(member.league_rank());

    const local_ordinal_type subpartidx       = packptr_sub(packidx);
    const local_ordinal_type n_parts          = part2packrowidx0_sub.extent(0);
    const local_ordinal_type local_subpartidx = subpartidx / n_parts;
    const local_ordinal_type partidx          = subpartidx % n_parts;

    const local_ordinal_type npacks    = packptr_sub(packidx + 1) - subpartidx;
    const local_ordinal_type i0        = pack_td_ptr(partidx, local_subpartidx);
    const local_ordinal_type r0        = part2packrowidx0_sub(partidx, local_subpartidx);
    const local_ordinal_type nrows     = partptr_sub(subpartidx, 1) - partptr_sub(subpartidx, 0);
    const local_ordinal_type blocksize = e_internal_vector_values.extent(2);

    //(void) i0;
    //(void) nrows;
    (void)npacks;

    internal_vector_scratch_type_3d_view
        WW(member.team_scratch(0), blocksize, 1, vector_loop_size);

    Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
      solveSingleVectorNew<impl_type, internal_vector_scratch_type_3d_view>(member, blocksize, i0, r0, nrows, v, D_internal_vector_values, X_internal_vector_values, WW);
    });
  }

  template <int B>
  KOKKOS_INLINE_FUNCTION void
  operator()(const SingleVectorApplyCTag<B> &, const member_type &member) const {
    // btdm is packed and sorted from largest one
    // const local_ordinal_type packidx = packindices_schur(member.league_rank());
    const local_ordinal_type packidx = packindices_sub(member.league_rank());

    const local_ordinal_type subpartidx       = packptr_sub(packidx);
    const local_ordinal_type n_parts          = part2packrowidx0_sub.extent(0);
    const local_ordinal_type local_subpartidx = subpartidx / n_parts;
    const local_ordinal_type partidx          = subpartidx % n_parts;
    const local_ordinal_type blocksize        = e_internal_vector_values.extent(2);

    // const local_ordinal_type npacks = packptr_sub(packidx+1) - subpartidx;
    const local_ordinal_type i0    = pack_td_ptr(partidx, local_subpartidx);
    const local_ordinal_type r0    = part2packrowidx0_sub(partidx, local_subpartidx);
    const local_ordinal_type nrows = partptr_sub(subpartidx, 1) - partptr_sub(subpartidx, 0);

    internal_vector_scratch_type_3d_view
        WW(member.team_scratch(0), blocksize, blocksize, vector_loop_size);

    // Compute v_2 = v_2 - C v_1

    const local_ordinal_type local_subpartidx_schur = (local_subpartidx - 1) / 2;
    const local_ordinal_type i0_schur               = local_subpartidx_schur == 0 ? pack_td_ptr_schur(partidx, local_subpartidx_schur) : pack_td_ptr_schur(partidx, local_subpartidx_schur) + 1;
    const local_ordinal_type i0_offset              = local_subpartidx_schur == 0 ? i0 + 2 : i0 + 2;

    (void)i0_schur;
    (void)i0_offset;

#if KOKKOS_VERSION >= 40799
    const auto one = KokkosKernels::ArithTraits<btdm_magnitude_type>::one();
#else
    const auto one  = Kokkos::ArithTraits<btdm_magnitude_type>::one();
#endif

    const size_type c_kps2 = local_subpartidx > 0 ? pack_td_ptr(partidx, local_subpartidx) - 2 : 0;
    const size_type c_kps1 = pack_td_ptr(partidx, local_subpartidx + 1) + 1;

    typedef SolveTridiagsDefaultModeAndAlgo<typename execution_space::memory_space> default_mode_and_algo_type;

    typedef typename default_mode_and_algo_type::mode_type default_mode_type;
    typedef typename default_mode_and_algo_type::single_vector_algo_type default_algo_type;

    if (local_subpartidx == 0) {
      Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
        auto v_1 = Kokkos::subview(X_internal_vector_values, r0 + nrows - 1, Kokkos::ALL(), 0, v);
        auto v_2 = Kokkos::subview(X_internal_vector_values, r0 + nrows, Kokkos::ALL(), 0, v);
        auto C   = Kokkos::subview(D_internal_vector_values, c_kps1, Kokkos::ALL(), Kokkos::ALL(), v);

        KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                        member,
                                                        blocksize, blocksize,
                                                        -one,
                                                        C.data(), C.stride(0), C.stride(1),
                                                        v_1.data(), v_1.stride(0),
                                                        one,
                                                        v_2.data(), v_2.stride(0));
      });
    } else if (local_subpartidx == (local_ordinal_type)part2packrowidx0_sub.extent(1) - 2) {
      Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
        auto v_1 = Kokkos::subview(X_internal_vector_values, r0, Kokkos::ALL(), 0, v);
        auto v_2 = Kokkos::subview(X_internal_vector_values, r0 - 1, Kokkos::ALL(), 0, v);
        auto C   = Kokkos::subview(D_internal_vector_values, c_kps2, Kokkos::ALL(), Kokkos::ALL(), v);

        KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                        member,
                                                        blocksize, blocksize,
                                                        -one,
                                                        C.data(), C.stride(0), C.stride(1),
                                                        v_1.data(), v_1.stride(0),
                                                        one,
                                                        v_2.data(), v_2.stride(0));
      });
    } else {
      Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
        {
          auto v_1 = Kokkos::subview(X_internal_vector_values, r0 + nrows - 1, Kokkos::ALL(), 0, v);
          auto v_2 = Kokkos::subview(X_internal_vector_values, r0 + nrows, Kokkos::ALL(), 0, v);
          auto C   = Kokkos::subview(D_internal_vector_values, c_kps1, Kokkos::ALL(), Kokkos::ALL(), v);

          KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                          member,
                                                          blocksize, blocksize,
                                                          -one,
                                                          C.data(), C.stride(0), C.stride(1),
                                                          v_1.data(), v_1.stride(0),
                                                          one,
                                                          v_2.data(), v_2.stride(0));
        }
        {
          auto v_1 = Kokkos::subview(X_internal_vector_values, r0, Kokkos::ALL(), 0, v);
          auto v_2 = Kokkos::subview(X_internal_vector_values, r0 - 1, Kokkos::ALL(), 0, v);
          auto C   = Kokkos::subview(D_internal_vector_values, c_kps2, Kokkos::ALL(), Kokkos::ALL(), v);

          KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                          member,
                                                          blocksize, blocksize,
                                                          -one,
                                                          C.data(), C.stride(0), C.stride(1),
                                                          v_1.data(), v_1.stride(0),
                                                          one,
                                                          v_2.data(), v_2.stride(0));
        }
      });
    }
  }

  template <int B>
  KOKKOS_INLINE_FUNCTION void
  operator()(const SingleVectorSchurTag<B> &, const member_type &member) const {
    const local_ordinal_type packidx = packindices_sub(member.league_rank());

    const local_ordinal_type partidx = packptr_sub(packidx);

    const local_ordinal_type blocksize = e_internal_vector_values.extent(2);

    const local_ordinal_type i0_schur = pack_td_ptr_schur(partidx, 0);
    const local_ordinal_type nrows    = 2 * (n_subparts_per_part - 1);

    const local_ordinal_type r0_schur = nrows * member.league_rank();

    internal_vector_scratch_type_3d_view
        WW(member.team_scratch(0), blocksize, blocksize, vector_loop_size);

    for (local_ordinal_type schur_sub_part = 0; schur_sub_part < n_subparts_per_part - 1; ++schur_sub_part) {
      const local_ordinal_type r0 = part2packrowidx0_sub(partidx, 2 * schur_sub_part + 1);
      for (local_ordinal_type i = 0; i < 2; ++i) {
        copy3DView<local_ordinal_type>(member,
                                       Kokkos::subview(X_internal_vector_values_schur, r0_schur + 2 * schur_sub_part + i, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()),
                                       Kokkos::subview(X_internal_vector_values, r0 + i, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()));
      }
    }

    Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
      solveSingleVectorNew<impl_type, internal_vector_scratch_type_3d_view>(member, blocksize, i0_schur, r0_schur, nrows, v, D_internal_vector_values_schur, X_internal_vector_values_schur, WW);
    });

    for (local_ordinal_type schur_sub_part = 0; schur_sub_part < n_subparts_per_part - 1; ++schur_sub_part) {
      const local_ordinal_type r0 = part2packrowidx0_sub(partidx, 2 * schur_sub_part + 1);
      for (local_ordinal_type i = 0; i < 2; ++i) {
        copy3DView<local_ordinal_type>(member,
                                       Kokkos::subview(X_internal_vector_values, r0 + i, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()),
                                       Kokkos::subview(X_internal_vector_values_schur, r0_schur + 2 * schur_sub_part + i, Kokkos::ALL(), Kokkos::ALL(), Kokkos::ALL()));
      }
    }
  }

  template <int B>
  KOKKOS_INLINE_FUNCTION void
  operator()(const SingleVectorApplyETag<B> &, const member_type &member) const {
    const local_ordinal_type packidx = packindices_sub(member.league_rank());

    const local_ordinal_type subpartidx       = packptr_sub(packidx);
    const local_ordinal_type n_parts          = part2packrowidx0_sub.extent(0);
    const local_ordinal_type local_subpartidx = subpartidx / n_parts;
    const local_ordinal_type partidx          = subpartidx % n_parts;
    const local_ordinal_type blocksize        = e_internal_vector_values.extent(2);

    const local_ordinal_type r0    = part2packrowidx0_sub(partidx, local_subpartidx);
    const local_ordinal_type nrows = partptr_sub(subpartidx, 1) - partptr_sub(subpartidx, 0);

    internal_vector_scratch_type_3d_view
        WW(member.team_scratch(0), blocksize, blocksize, vector_loop_size);

    // Compute v_2 = v_2 - C v_1

#if KOKKOS_VERSION >= 40799
    const auto one = KokkosKernels::ArithTraits<btdm_magnitude_type>::one();
#else
    const auto one  = Kokkos::ArithTraits<btdm_magnitude_type>::one();
#endif

    typedef SolveTridiagsDefaultModeAndAlgo<typename execution_space::memory_space> default_mode_and_algo_type;

    typedef typename default_mode_and_algo_type::mode_type default_mode_type;
    typedef typename default_mode_and_algo_type::single_vector_algo_type default_algo_type;

    if (local_subpartidx == 0) {
      Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
        auto v_2 = Kokkos::subview(X_internal_vector_values, r0 + nrows, Kokkos::ALL(), 0, v);

        for (local_ordinal_type row = 0; row < nrows; ++row) {
          auto v_1 = Kokkos::subview(X_internal_vector_values, r0 + row, Kokkos::ALL(), 0, v);
          auto E   = Kokkos::subview(e_internal_vector_values, 0, r0 + row, Kokkos::ALL(), Kokkos::ALL(), v);

          KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                          member,
                                                          blocksize, blocksize,
                                                          -one,
                                                          E.data(), E.stride(0), E.stride(1),
                                                          v_2.data(), v_2.stride(0),
                                                          one,
                                                          v_1.data(), v_1.stride(0));
        }
      });
    } else if (local_subpartidx == (local_ordinal_type)part2packrowidx0_sub.extent(1) - 2) {
      Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
        auto v_2 = Kokkos::subview(X_internal_vector_values, r0 - 1, Kokkos::ALL(), 0, v);

        for (local_ordinal_type row = 0; row < nrows; ++row) {
          auto v_1 = Kokkos::subview(X_internal_vector_values, r0 + row, Kokkos::ALL(), 0, v);
          auto E   = Kokkos::subview(e_internal_vector_values, 1, r0 + row, Kokkos::ALL(), Kokkos::ALL(), v);

          KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                          member,
                                                          blocksize, blocksize,
                                                          -one,
                                                          E.data(), E.stride(0), E.stride(1),
                                                          v_2.data(), v_2.stride(0),
                                                          one,
                                                          v_1.data(), v_1.stride(0));
        }
      });
    } else {
      Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
        {
          auto v_2 = Kokkos::subview(X_internal_vector_values, r0 + nrows, Kokkos::ALL(), 0, v);

          for (local_ordinal_type row = 0; row < nrows; ++row) {
            auto v_1 = Kokkos::subview(X_internal_vector_values, r0 + row, Kokkos::ALL(), 0, v);
            auto E   = Kokkos::subview(e_internal_vector_values, 0, r0 + row, Kokkos::ALL(), Kokkos::ALL(), v);

            KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                            member,
                                                            blocksize, blocksize,
                                                            -one,
                                                            E.data(), E.stride(0), E.stride(1),
                                                            v_2.data(), v_2.stride(0),
                                                            one,
                                                            v_1.data(), v_1.stride(0));
          }
        }
        {
          auto v_2 = Kokkos::subview(X_internal_vector_values, r0 - 1, Kokkos::ALL(), 0, v);

          for (local_ordinal_type row = 0; row < nrows; ++row) {
            auto v_1 = Kokkos::subview(X_internal_vector_values, r0 + row, Kokkos::ALL(), 0, v);
            auto E   = Kokkos::subview(e_internal_vector_values, 1, r0 + row, Kokkos::ALL(), Kokkos::ALL(), v);

            KOKKOSBATCHED_GEMV_NO_TRANSPOSE_INTERNAL_INVOKE(default_mode_type, default_algo_type,
                                                            member,
                                                            blocksize, blocksize,
                                                            -one,
                                                            E.data(), E.stride(0), E.stride(1),
                                                            v_2.data(), v_2.stride(0),
                                                            one,
                                                            v_1.data(), v_1.stride(0));
          }
        }
      });
    }
  }

  template <int B>
  KOKKOS_INLINE_FUNCTION void
  operator()(const SingleVectorCopyToFlatTag<B> &, const member_type &member) const {
    const local_ordinal_type packidx     = member.league_rank();
    const local_ordinal_type partidx     = packptr(packidx);
    const local_ordinal_type npacks      = packptr(packidx + 1) - partidx;
    const local_ordinal_type pri0        = part2packrowidx0(partidx);
    const local_ordinal_type blocksize   = (B == 0 ? D_internal_vector_values.extent(1) : B);
    const local_ordinal_type num_vectors = 1;

    Kokkos::parallel_for(Kokkos::ThreadVectorRange(member, vector_loop_size), [&](const int &v) {
      copyToFlatMultiVector(member, partidx, npacks, pri0, v, blocksize, num_vectors);
    });
  }

  template <int B>
  KOKKOS_INLINE_FUNCTION void
  operator()(const SingleZeroingTag<B> &, const member_type &member) const {
    Kokkos::single(Kokkos::PerTeam(member), [&]() {
      Z_scalar_vector(member.league_rank()) = impl_scalar_type(0);
    });
  }

  void run(const impl_scalar_type_2d_view_tpetra &Y,
           const impl_scalar_type_1d_view &Z) {
    IFPACK2_BLOCKTRIDICONTAINER_PROFILER_REGION_BEGIN;
    IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::SolveTridiags", SolveTridiags);

    this->Y_scalar_multivector = Y;
    this->Z_scalar_vector      = Z;

    const local_ordinal_type num_vectors = X_internal_vector_values.extent(2);
    const local_ordinal_type blocksize   = D_internal_vector_values.extent(1);

    const local_ordinal_type team_size =
        SolveTridiagsDefaultModeAndAlgo<typename execution_space::memory_space>::
            recommended_team_size(blocksize, vector_length, internal_vector_length);
    const int per_team_scratch = internal_vector_scratch_type_3d_view ::shmem_size(blocksize, num_vectors, vector_loop_size);

#if defined(KOKKOS_ENABLE_DEPRECATED_CODE)
#define BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(B)                                            \
  if (num_vectors == 1) {                                                                       \
    const Kokkos::TeamPolicy<execution_space, SingleVectorTag<B>>                               \
        policy(packptr.extent(0) - 1, team_size, vector_loop_size);                             \
    Kokkos::parallel_for("SolveTridiags::TeamPolicy::run<SingleVector>",                        \
                         policy.set_scratch_size(0, Kokkos::PerTeam(per_team_scratch)), *this); \
  } else {                                                                                      \
    const Kokkos::TeamPolicy<execution_space, MultiVectorTag<B>>                                \
        policy(packptr.extent(0) - 1, team_size, vector_loop_size);                             \
    Kokkos::parallel_for("SolveTridiags::TeamPolicy::run<MultiVector>",                         \
                         policy.set_scratch_size(0, Kokkos::PerTeam(per_team_scratch)), *this); \
  }                                                                                             \
  break
#else
#define BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(B)                                                                                                  \
  if (num_vectors == 1) {                                                                                                                             \
    if (packindices_schur.extent(1) <= 0) {                                                                                                           \
      Kokkos::TeamPolicy<execution_space, SingleVectorTag<B>>                                                                                         \
          policy(packptr.extent(0) - 1, team_size, vector_loop_size);                                                                                 \
      policy.set_scratch_size(0, Kokkos::PerTeam(per_team_scratch));                                                                                  \
      Kokkos::parallel_for("SolveTridiags::TeamPolicy::run<SingleVector>",                                                                            \
                           policy, *this);                                                                                                            \
    } else {                                                                                                                                          \
      {                                                                                                                                               \
        Kokkos::TeamPolicy<execution_space, SingleZeroingTag<B>>                                                                                      \
            policy(packptr.extent(0) - 1, team_size, vector_loop_size);                                                                               \
        Kokkos::parallel_for("SolveTridiags::TeamPolicy::run<SingleZeroingTag>",                                                                      \
                             policy, *this);                                                                                                          \
      }                                                                                                                                               \
      {                                                                                                                                               \
        IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::ApplyInverseJacobi::SingleVectorSubLineTag", SingleVectorSubLineTag0);                                 \
        write4DMultiVectorValuesToFile(part2packrowidx0_sub.extent(0), X_internal_scalar_values, "x_scalar_values_before_SingleVectorSubLineTag.mm"); \
        Kokkos::TeamPolicy<execution_space, SingleVectorSubLineTag<B>>                                                                                \
            policy(packindices_sub.extent(0), team_size, vector_loop_size);                                                                           \
        policy.set_scratch_size(0, Kokkos::PerTeam(per_team_scratch));                                                                                \
        Kokkos::parallel_for("SolveTridiags::TeamPolicy::run<SingleVector>",                                                                          \
                             policy, *this);                                                                                                          \
        write4DMultiVectorValuesToFile(part2packrowidx0_sub.extent(0), X_internal_scalar_values, "x_scalar_values_after_SingleVectorSubLineTag.mm");  \
        IFPACK2_BLOCKHELPER_TIMER_FENCE(execution_space)                                                                                              \
      }                                                                                                                                               \
      {                                                                                                                                               \
        IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::ApplyInverseJacobi::SingleVectorApplyCTag", SingleVectorApplyCTag0);                                   \
        write4DMultiVectorValuesToFile(part2packrowidx0_sub.extent(0), X_internal_scalar_values, "x_scalar_values_before_SingleVectorApplyCTag.mm");  \
        Kokkos::TeamPolicy<execution_space, SingleVectorApplyCTag<B>>                                                                                 \
            policy(packindices_sub.extent(0), team_size, vector_loop_size);                                                                           \
        policy.set_scratch_size(0, Kokkos::PerTeam(per_team_scratch));                                                                                \
        Kokkos::parallel_for("SolveTridiags::TeamPolicy::run<SingleVector>",                                                                          \
                             policy, *this);                                                                                                          \
        write4DMultiVectorValuesToFile(part2packrowidx0_sub.extent(0), X_internal_scalar_values, "x_scalar_values_after_SingleVectorApplyCTag.mm");   \
        IFPACK2_BLOCKHELPER_TIMER_FENCE(execution_space)                                                                                              \
      }                                                                                                                                               \
      {                                                                                                                                               \
        IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::ApplyInverseJacobi::SingleVectorSchurTag", SingleVectorSchurTag0);                                     \
        write4DMultiVectorValuesToFile(part2packrowidx0_sub.extent(0), X_internal_scalar_values, "x_scalar_values_before_SingleVectorSchurTag.mm");   \
        Kokkos::TeamPolicy<execution_space, SingleVectorSchurTag<B>>                                                                                  \
            policy(packindices_schur.extent(0), team_size, vector_loop_size);                                                                         \
        policy.set_scratch_size(0, Kokkos::PerTeam(per_team_scratch));                                                                                \
        Kokkos::parallel_for("SolveTridiags::TeamPolicy::run<SingleVector>",                                                                          \
                             policy, *this);                                                                                                          \
        write4DMultiVectorValuesToFile(part2packrowidx0_sub.extent(0), X_internal_scalar_values, "x_scalar_values_after_SingleVectorSchurTag.mm");    \
        IFPACK2_BLOCKHELPER_TIMER_FENCE(execution_space)                                                                                              \
      }                                                                                                                                               \
      {                                                                                                                                               \
        IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::ApplyInverseJacobi::SingleVectorApplyETag", SingleVectorApplyETag0);                                   \
        write4DMultiVectorValuesToFile(part2packrowidx0_sub.extent(0), X_internal_scalar_values, "x_scalar_values_before_SingleVectorApplyETag.mm");  \
        Kokkos::TeamPolicy<execution_space, SingleVectorApplyETag<B>>                                                                                 \
            policy(packindices_sub.extent(0), team_size, vector_loop_size);                                                                           \
        policy.set_scratch_size(0, Kokkos::PerTeam(per_team_scratch));                                                                                \
        Kokkos::parallel_for("SolveTridiags::TeamPolicy::run<SingleVector>",                                                                          \
                             policy, *this);                                                                                                          \
        write4DMultiVectorValuesToFile(part2packrowidx0_sub.extent(0), X_internal_scalar_values, "x_scalar_values_after_SingleVectorApplyETag.mm");   \
        IFPACK2_BLOCKHELPER_TIMER_FENCE(execution_space)                                                                                              \
      }                                                                                                                                               \
      {                                                                                                                                               \
        Kokkos::TeamPolicy<execution_space, SingleVectorCopyToFlatTag<B>>                                                                             \
            policy(packptr.extent(0) - 1, team_size, vector_loop_size);                                                                               \
        Kokkos::parallel_for("SolveTridiags::TeamPolicy::run<SingleVectorCopyToFlatTag>",                                                             \
                             policy, *this);                                                                                                          \
      }                                                                                                                                               \
    }                                                                                                                                                 \
  } else {                                                                                                                                            \
    Kokkos::TeamPolicy<execution_space, MultiVectorTag<B>>                                                                                            \
        policy(packptr.extent(0) - 1, team_size, vector_loop_size);                                                                                   \
    policy.set_scratch_size(0, Kokkos::PerTeam(per_team_scratch));                                                                                    \
    Kokkos::parallel_for("SolveTridiags::TeamPolicy::run<MultiVector>",                                                                               \
                         policy, *this);                                                                                                              \
  }                                                                                                                                                   \
  break
#endif
    switch (blocksize) {
      case 3: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(3);
      case 5: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(5);
      case 6: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(6);
      case 7: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(7);
      case 10: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(10);
      case 11: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(11);
      case 12: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(12);
      case 13: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(13);
      case 16: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(16);
      case 17: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(17);
      case 18: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(18);
      case 19: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(19);
      default: BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS(0);
    }
#undef BLOCKTRIDICONTAINER_DETAILS_SOLVETRIDIAGS

    IFPACK2_BLOCKTRIDICONTAINER_PROFILER_REGION_END;
    IFPACK2_BLOCKHELPER_TIMER_FENCE(execution_space)
  }
};

template <typename MatrixType>
int applyInverseJacobi(  // importer
    const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_row_matrix_type> &A,
    const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_crs_graph_type> &G,
    const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_import_type> &tpetra_importer,
    const Teuchos::RCP<AsyncableImport<MatrixType>> &async_importer,
    const bool overlap_communication_and_computation,
    // tpetra interface
    const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_multivector_type &X,   // tpetra interface
    /* */ typename BlockHelperDetails::ImplType<MatrixType>::tpetra_multivector_type &Y,   // tpetra interface
    /* */ typename BlockHelperDetails::ImplType<MatrixType>::tpetra_multivector_type &Z,   // temporary tpetra interface (seq_method)
    /* */ typename BlockHelperDetails::ImplType<MatrixType>::impl_scalar_type_1d_view &W,  // temporary tpetra interface (diff)
    // local object interface
    const BlockHelperDetails::PartInterface<MatrixType> &interf,                         // mesh interface
    const BlockTridiags<MatrixType> &btdm,                                               // packed block tridiagonal matrices
    const BlockHelperDetails::AmD<MatrixType> &amd,                                      // R = A - D
    /* */ typename BlockHelperDetails::ImplType<MatrixType>::vector_type_1d_view &work,  // workspace for packed multivector of right hand side
    /* */ BlockHelperDetails::NormManager<MatrixType> &norm_manager,
    // preconditioner parameters
    const typename BlockHelperDetails::ImplType<MatrixType>::impl_scalar_type &damping_factor,
    /* */ bool is_y_zero,
    const int max_num_sweeps,
    const typename BlockHelperDetails::ImplType<MatrixType>::magnitude_type tol,
    const int check_tol_every) {
  IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::ApplyInverseJacobi", ApplyInverseJacobi);

  using impl_type                  = BlockHelperDetails::ImplType<MatrixType>;
  using node_memory_space          = typename impl_type::node_memory_space;
  using local_ordinal_type         = typename impl_type::local_ordinal_type;
  using size_type                  = typename impl_type::size_type;
  using impl_scalar_type           = typename impl_type::impl_scalar_type;
  using magnitude_type             = typename impl_type::magnitude_type;
  using local_ordinal_type_1d_view = typename impl_type::local_ordinal_type_1d_view;
  using vector_type_1d_view        = typename impl_type::vector_type_1d_view;
  using vector_type_3d_view        = typename impl_type::vector_type_3d_view;
  using tpetra_multivector_type    = typename impl_type::tpetra_multivector_type;

  using impl_scalar_type_1d_view = typename impl_type::impl_scalar_type_1d_view;

  // either tpetra importer or async importer must be active
  TEUCHOS_TEST_FOR_EXCEPT_MSG(!tpetra_importer.is_null() && !async_importer.is_null(),
                              "Neither Tpetra importer nor Async importer is null.");
  // max number of sweeps should be positive number
  TEUCHOS_TEST_FOR_EXCEPT_MSG(max_num_sweeps <= 0,
                              "Maximum number of sweeps must be >= 1.");

  // const parameters
  const bool is_seq_method_requested  = !tpetra_importer.is_null();
  const bool is_async_importer_active = !async_importer.is_null();
#if KOKKOS_VERSION >= 40799
  const bool is_norm_manager_active = tol > KokkosKernels::ArithTraits<magnitude_type>::zero();
#else
  const bool is_norm_manager_active = tol > Kokkos::ArithTraits<magnitude_type>::zero();
#endif
  const magnitude_type tolerance         = tol * tol;
  const local_ordinal_type blocksize     = btdm.values.extent(1);
  const local_ordinal_type num_vectors   = Y.getNumVectors();
  const local_ordinal_type num_blockrows = interf.part2packrowidx0_back;

  const impl_scalar_type zero(0.0);

  TEUCHOS_TEST_FOR_EXCEPT_MSG(is_norm_manager_active && is_seq_method_requested,
                              "The seq method for applyInverseJacobi, "
                                  << "which in any case is for developer use only, "
                                  << "does not support norm-based termination.");
  const bool device_accessible_from_host = Kokkos::SpaceAccessibility<
      Kokkos::DefaultHostExecutionSpace, node_memory_space>::accessible;
  TEUCHOS_TEST_FOR_EXCEPTION(is_seq_method_requested && !device_accessible_from_host,
                             std::invalid_argument,
                             "The seq method for applyInverseJacobi, "
                                 << "which in any case is for developer use only, "
                                 << "only supports memory spaces accessible from host.");

  // if workspace is needed more, resize it
  const size_type work_span_required = num_blockrows * num_vectors * blocksize;
  if (work.span() < work_span_required)
    work = vector_type_1d_view("vector workspace 1d view", work_span_required);

  // construct W
  const local_ordinal_type W_size = interf.packptr.extent(0) - 1;
  if (local_ordinal_type(W.extent(0)) < W_size)
    W = impl_scalar_type_1d_view("W", W_size);

  typename impl_type::impl_scalar_type_2d_view_tpetra remote_multivector;
  {
    if (is_seq_method_requested) {
      if (Z.getNumVectors() != Y.getNumVectors())
        Z = tpetra_multivector_type(tpetra_importer->getTargetMap(), num_vectors, false);
    } else {
      if (is_async_importer_active) {
        // create comm data buffer and keep it here
        async_importer->createDataBuffer(num_vectors);
        remote_multivector = async_importer->getRemoteMultiVectorLocalView();
      }
    }
  }

  // wrap the workspace with 3d view
  vector_type_3d_view pmv(work.data(), num_blockrows, blocksize, num_vectors);
  const auto XX = X.getLocalViewDevice(Tpetra::Access::ReadOnly);
  const auto YY = Y.getLocalViewDevice(Tpetra::Access::ReadWrite);
  const auto ZZ = Z.getLocalViewDevice(Tpetra::Access::ReadWrite);
  if (is_y_zero) Kokkos::deep_copy(YY, zero);

  MultiVectorConverter<MatrixType> multivector_converter(interf, pmv);
  SolveTridiags<MatrixType> solve_tridiags(interf, btdm, pmv,
                                           damping_factor, is_norm_manager_active);

  const local_ordinal_type_1d_view dummy_local_ordinal_type_1d_view;

  auto A_crs  = Teuchos::rcp_dynamic_cast<const typename impl_type::tpetra_crs_matrix_type>(A);
  auto A_bcrs = Teuchos::rcp_dynamic_cast<const typename impl_type::tpetra_block_crs_matrix_type>(A);

  bool hasBlockCrsMatrix = !A_bcrs.is_null();

  // This is OK here to use the graph of the A_crs matrix and a block size of 1
  const auto g = hasBlockCrsMatrix ? A_bcrs->getCrsGraph() : *(A_crs->getCrsGraph());  // tpetra crs graph object

  BlockHelperDetails::ComputeResidualVector<MatrixType>
      compute_residual_vector(amd, G->getLocalGraphDevice(), g.getLocalGraphDevice(), blocksize, interf,
                              is_async_importer_active ? async_importer->dm2cm : dummy_local_ordinal_type_1d_view,
                              hasBlockCrsMatrix);

  // norm manager workspace resize
  if (is_norm_manager_active)
    norm_manager.setCheckFrequency(check_tol_every);

  // iterate
  int sweep = 0;
  for (; sweep < max_num_sweeps; ++sweep) {
    {
      if (is_y_zero) {
        // pmv := x(lclrow)
        multivector_converter.run(XX);
      } else {
        if (is_seq_method_requested) {
          // SEQ METHOD IS TESTING ONLY

          // y := x - R y
          Z.doImport(Y, *tpetra_importer, Tpetra::REPLACE);
          compute_residual_vector.run(YY, XX, ZZ);

          // pmv := y(lclrow).
          multivector_converter.run(YY);
        } else {
          // fused y := x - R y and pmv := y(lclrow);
          // real use case does not use overlap comp and comm
          if (overlap_communication_and_computation || !is_async_importer_active) {
            if (is_async_importer_active) async_importer->asyncSendRecv(YY);
            // OverlapTag, compute_owned = true
            compute_residual_vector.run(pmv, XX, YY, remote_multivector, true);
            if (is_norm_manager_active && norm_manager.checkDone(sweep, tolerance)) {
              if (is_async_importer_active) async_importer->cancel();
              break;
            }
            if (is_async_importer_active) {
              async_importer->syncRecv();
              // OverlapTag, compute_owned = false
              compute_residual_vector.run(pmv, XX, YY, remote_multivector, false);
            }
          } else {
            if (is_async_importer_active)
              async_importer->syncExchange(YY);
            if (is_norm_manager_active && norm_manager.checkDone(sweep, tolerance)) break;
            // AsyncTag
            compute_residual_vector.run(pmv, XX, YY, remote_multivector);
          }
        }
      }
    }

    // pmv := inv(D) pmv.
    {
      solve_tridiags.run(YY, W);
    }
    {
      if (is_norm_manager_active) {
        // y(lclrow) = (b - a) y(lclrow) + a pmv, with b = 1 always.
        BlockHelperDetails::reduceVector<MatrixType>(W, norm_manager.getBuffer());
        if (sweep + 1 == max_num_sweeps) {
          norm_manager.ireduce(sweep, true);
          norm_manager.checkDone(sweep + 1, tolerance, true);
        } else {
          norm_manager.ireduce(sweep);
        }
      }
    }
    is_y_zero = false;
  }

  // sqrt the norms for the caller's use.
  if (is_norm_manager_active) norm_manager.finalize();

  return sweep;
}

// Implementation of fused block Jacobi for a specific block size,
// or (if B == 0) for a general block size.
template <typename MatrixType, int B>
int applyFusedBlockJacobi_Impl(
    const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_import_type> &tpetra_importer,
    const Teuchos::RCP<AsyncableImport<MatrixType>> &async_importer,
    const bool overlap_communication_and_computation,
    // tpetra interface
    const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_multivector_type &X,   // tpetra interface
    /* */ typename BlockHelperDetails::ImplType<MatrixType>::tpetra_multivector_type &Y,   // tpetra interface
    /* */ typename BlockHelperDetails::ImplType<MatrixType>::impl_scalar_type_1d_view &W,  // temporary tpetra interface (diff)
    // local object interface
    const BlockHelperDetails::PartInterface<MatrixType> &interf,                              // mesh interface
    const BlockTridiags<MatrixType> &btdm,                                                    // packed block tridiagonal matrices
    const BlockHelperDetails::AmD<MatrixType> &amd,                                           // R = A - D
    /* */ typename BlockHelperDetails::ImplType<MatrixType>::impl_scalar_type_1d_view &work,  // workspace
    /* */ BlockHelperDetails::NormManager<MatrixType> &norm_manager,
    // preconditioner parameters
    const typename BlockHelperDetails::ImplType<MatrixType>::impl_scalar_type &damping_factor,
    /* */ bool is_y_zero,
    const int max_num_sweeps,
    const typename BlockHelperDetails::ImplType<MatrixType>::magnitude_type tol,
    const int check_tol_every) {
  using impl_type                       = BlockHelperDetails::ImplType<MatrixType>;
  using local_ordinal_type              = typename impl_type::local_ordinal_type;
  using size_type                       = typename impl_type::size_type;
  using magnitude_type                  = typename impl_type::magnitude_type;
  using impl_scalar_type_1d_view        = typename impl_type::impl_scalar_type_1d_view;
  using impl_scalar_type_2d_view_tpetra = typename impl_type::impl_scalar_type_2d_view_tpetra;

  // the tpetra importer and async importer can't both be active
  TEUCHOS_TEST_FOR_EXCEPT_MSG(!tpetra_importer.is_null() && !async_importer.is_null(),
                              "Neither Tpetra importer nor Async importer is null.");
  // max number of sweeps should be positive number
  TEUCHOS_TEST_FOR_EXCEPT_MSG(max_num_sweeps <= 0,
                              "Maximum number of sweeps must be >= 1.");

  // const parameters
  const bool is_async_importer_active = !async_importer.is_null();
#if KOKKOS_VERSION >= 40799
  const bool is_norm_manager_active = tol > KokkosKernels::ArithTraits<magnitude_type>::zero();
#else
  const bool is_norm_manager_active = tol > Kokkos::ArithTraits<magnitude_type>::zero();
#endif
  const magnitude_type tolerance         = tol * tol;
  const local_ordinal_type blocksize     = btdm.d_inv.extent(1);
  const local_ordinal_type num_vectors   = Y.getNumVectors();
  const local_ordinal_type num_blockrows = interf.nparts;

  typename impl_type::impl_scalar_type_2d_view_tpetra remote_multivector;
  {
    if (is_async_importer_active) {
      // create comm data buffer and keep it here
      async_importer->createDataBuffer(num_vectors);
      remote_multivector = async_importer->getRemoteMultiVectorLocalView();
    }
  }

  const auto XX = X.getLocalViewDevice(Tpetra::Access::ReadOnly);
  const auto YY = Y.getLocalViewDevice(Tpetra::Access::ReadWrite);

  const bool two_pass_residual =
      overlap_communication_and_computation && is_async_importer_active;

  // Calculate the required work size and reallocate it if not already big enough.
  // Check that our assumptions about YY dimension are correct.
  TEUCHOS_TEST_FOR_EXCEPT_MSG(
      size_t(num_blockrows) * blocksize * num_vectors != YY.extent(0) * YY.extent(1),
      "Local LHS vector (YY) has total size " << YY.extent(0) << "x" << YY.extent(1) << " = " << YY.extent(0) * YY.extent(1) << ",\n"
                                              << "but expected " << num_blockrows << "x" << blocksize << "x" << num_vectors << " = " << size_t(num_blockrows) * blocksize * num_vectors << '\n');
  size_type work_required = size_type(num_blockrows) * blocksize * num_vectors;
  if (work.extent(0) < work_required) {
    work = impl_scalar_type_1d_view(do_not_initialize_tag("flat workspace 1d view"), work_required);
  }

  Unmanaged<impl_scalar_type_2d_view_tpetra> y_doublebuf(work.data(), num_blockrows * blocksize, num_vectors);

  // construct W
  if (W.extent(0) != size_t(num_blockrows))
    W = impl_scalar_type_1d_view(do_not_initialize_tag("W"), num_blockrows);

  // Create the required functors upfront (this is inexpensive - all shallow copies)
  BlockHelperDetails::ComputeResidualAndSolve_SolveOnly<MatrixType, B>
      functor_solve_only(amd, btdm.d_inv, W, blocksize, damping_factor);
  BlockHelperDetails::ComputeResidualAndSolve_1Pass<MatrixType, B>
      functor_1pass(amd, btdm.d_inv, W, blocksize, damping_factor);
  BlockHelperDetails::ComputeResidualAndSolve_2Pass<MatrixType, B>
      functor_2pass(amd, btdm.d_inv, W, blocksize, damping_factor);

  // norm manager workspace resize
  if (is_norm_manager_active)
    norm_manager.setCheckFrequency(check_tol_every);

  // For double-buffering.
  //   yy_buffers[current_y] has the current iterate of y.
  //   yy_buffers[1-current_y] has the next iterate of y.
  Unmanaged<impl_scalar_type_2d_view_tpetra> y_buffers[2] = {YY, y_doublebuf};
  int current_y                                           = 0;

  // iterate
  int sweep = 0;
  for (; sweep < max_num_sweeps; ++sweep) {
    if (is_y_zero) {
      // If y is initially zero, then we are just computing y := damping_factor * Dinv * x
      functor_solve_only.run(XX, y_buffers[1 - current_y]);
    } else {
      // real use case does not use overlap comp and comm
      if (overlap_communication_and_computation || !is_async_importer_active) {
        if (is_async_importer_active) async_importer->asyncSendRecv(y_buffers[current_y]);
        if (two_pass_residual) {
          // Pass 1 computes owned residual and stores into new y buffer,
          // but doesn't apply Dinv or produce a norm yet
          functor_2pass.run_pass1(XX, y_buffers[current_y], y_buffers[1 - current_y]);
        } else {
          // This case happens if running with single rank.
          // There are no remote columns, so residual and solve can happen in one step.
          functor_1pass.run(XX, y_buffers[current_y], remote_multivector, y_buffers[1 - current_y]);
        }
        if (is_norm_manager_active && norm_manager.checkDone(sweep, tolerance)) {
          if (is_async_importer_active) async_importer->cancel();
          break;
        }
        if (is_async_importer_active) {
          async_importer->syncRecv();
          // Stage 2 finishes computing the residual, then applies Dinv and computes norm.
          functor_2pass.run_pass2(y_buffers[current_y], remote_multivector, y_buffers[1 - current_y]);
        }
      } else {
        if (is_async_importer_active)
          async_importer->syncExchange(y_buffers[current_y]);
        if (is_norm_manager_active && norm_manager.checkDone(sweep, tolerance)) break;
        // Full residual, Dinv apply, and norm in one kernel
        functor_1pass.run(XX, y_buffers[current_y], remote_multivector, y_buffers[1 - current_y]);
      }
    }

    // Compute global norm.
    if (is_norm_manager_active) {
      BlockHelperDetails::reduceVector<MatrixType>(W, norm_manager.getBuffer());
      if (sweep + 1 == max_num_sweeps) {
        norm_manager.ireduce(sweep, true);
        norm_manager.checkDone(sweep + 1, tolerance, true);
      } else {
        norm_manager.ireduce(sweep);
      }
    }
    is_y_zero = false;
    // flip y buffers for next iteration, or termination if we reached max_num_sweeps.
    current_y = 1 - current_y;
  }
  if (current_y == 1) {
    // We finished iterating with y in the double buffer, so copy it to the user's vector.
    Kokkos::deep_copy(YY, y_doublebuf);
  }

  // sqrt the norms for the caller's use.
  if (is_norm_manager_active) norm_manager.finalize();
  return sweep;
}

template <typename MatrixType>
int applyFusedBlockJacobi(
    const Teuchos::RCP<const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_import_type> &tpetra_importer,
    const Teuchos::RCP<AsyncableImport<MatrixType>> &async_importer,
    const bool overlap_communication_and_computation,
    // tpetra interface
    const typename BlockHelperDetails::ImplType<MatrixType>::tpetra_multivector_type &X,   // tpetra interface
    /* */ typename BlockHelperDetails::ImplType<MatrixType>::tpetra_multivector_type &Y,   // tpetra interface
    /* */ typename BlockHelperDetails::ImplType<MatrixType>::impl_scalar_type_1d_view &W,  // temporary tpetra interface (diff)
    // local object interface
    const BlockHelperDetails::PartInterface<MatrixType> &interf,                              // mesh interface
    const BlockTridiags<MatrixType> &btdm,                                                    // packed block tridiagonal matrices
    const BlockHelperDetails::AmD<MatrixType> &amd,                                           // R = A - D
    /* */ typename BlockHelperDetails::ImplType<MatrixType>::impl_scalar_type_1d_view &work,  // workspace
    /* */ BlockHelperDetails::NormManager<MatrixType> &norm_manager,
    // preconditioner parameters
    const typename BlockHelperDetails::ImplType<MatrixType>::impl_scalar_type &damping_factor,
    /* */ bool is_y_zero,
    const int max_num_sweeps,
    const typename BlockHelperDetails::ImplType<MatrixType>::magnitude_type tol,
    const int check_tol_every) {
  IFPACK2_BLOCKHELPER_TIMER("BlockTriDi::ApplyFusedBlockJacobi", ApplyFusedBlockJacobi);
  int blocksize = btdm.d_inv.extent(1);
  int sweep     = 0;
#define BLOCKTRIDICONTAINER_APPLY_FUSED_JACOBI(B)                               \
  {                                                                             \
    sweep = applyFusedBlockJacobi_Impl<MatrixType, B>(                          \
        tpetra_importer, async_importer, overlap_communication_and_computation, \
        X, Y, W, interf, btdm, amd, work,                                       \
        norm_manager, damping_factor, is_y_zero,                                \
        max_num_sweeps, tol, check_tol_every);                                  \
  }                                                                             \
  break
  switch (blocksize) {
    case 3: BLOCKTRIDICONTAINER_APPLY_FUSED_JACOBI(3);
    case 5: BLOCKTRIDICONTAINER_APPLY_FUSED_JACOBI(5);
    case 7: BLOCKTRIDICONTAINER_APPLY_FUSED_JACOBI(7);
    case 9: BLOCKTRIDICONTAINER_APPLY_FUSED_JACOBI(9);
    case 10: BLOCKTRIDICONTAINER_APPLY_FUSED_JACOBI(10);
    case 11: BLOCKTRIDICONTAINER_APPLY_FUSED_JACOBI(11);
    case 16: BLOCKTRIDICONTAINER_APPLY_FUSED_JACOBI(16);
    case 17: BLOCKTRIDICONTAINER_APPLY_FUSED_JACOBI(17);
    case 18: BLOCKTRIDICONTAINER_APPLY_FUSED_JACOBI(18);
    default: BLOCKTRIDICONTAINER_APPLY_FUSED_JACOBI(0);
  }
#undef BLOCKTRIDICONTAINER_APPLY_FUSED_JACOBI

  return sweep;
}

template <typename MatrixType>
struct ImplObject {
  using impl_type           = BlockHelperDetails::ImplType<MatrixType>;
  using part_interface_type = BlockHelperDetails::PartInterface<MatrixType>;
  using block_tridiags_type = BlockTridiags<MatrixType>;
  using amd_type            = BlockHelperDetails::AmD<MatrixType>;
  using norm_manager_type   = BlockHelperDetails::NormManager<MatrixType>;
  using async_import_type   = AsyncableImport<MatrixType>;

  // distructed objects
  Teuchos::RCP<const typename impl_type::tpetra_row_matrix_type> A;
  Teuchos::RCP<const typename impl_type::tpetra_crs_graph_type> blockGraph;
  Teuchos::RCP<const typename impl_type::tpetra_import_type> tpetra_importer;
  Teuchos::RCP<async_import_type> async_importer;
  bool overlap_communication_and_computation;

  // copy of Y (mutable to penentrate const)
  mutable typename impl_type::tpetra_multivector_type Z;
  mutable typename impl_type::impl_scalar_type_1d_view W;

  // local objects
  part_interface_type part_interface;
  block_tridiags_type block_tridiags;  // D
  amd_type a_minus_d;                  // R = A - D

  // whether to use fused block Jacobi path
  bool use_fused_jacobi;

  // vector workspace is used for general block tridi case
  mutable typename impl_type::vector_type_1d_view work;  // right hand side workspace (1D view of vector)
  // scalar workspace is used for fused block jacobi case
  mutable typename impl_type::impl_scalar_type_1d_view work_flat;  // right hand side workspace (1D view of scalar)
  mutable norm_manager_type norm_manager;
};

}  // namespace BlockTriDiContainerDetails

}  // namespace Ifpack2

#endif