Tpetra_MultiVector_def.hpp

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// @HEADER
// *****************************************************************************
//          Tpetra: Templated Linear Algebra Services Package
//
// Copyright 2008 NTESS and the Tpetra contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER
 
#ifndef TPETRA_MULTIVECTOR_DEF_HPP
#define TPETRA_MULTIVECTOR_DEF_HPP
 
 
#include "Tpetra_Core.hpp"
#include "Tpetra_Util.hpp"
#include "Tpetra_Vector.hpp"
#include "Tpetra_Details_allReduceView.hpp"
#include "Tpetra_Details_Behavior.hpp"
#include "Tpetra_Details_checkView.hpp"
#include "Tpetra_Details_fill.hpp"
#include "Tpetra_Details_gathervPrint.hpp"
#include "Tpetra_Details_isInterComm.hpp"
#include "Tpetra_Details_lclDot.hpp"
#include "Tpetra_Details_normImpl.hpp"
#include "Tpetra_Details_PackTraits.hpp"
#include "Tpetra_Details_Profiling.hpp"
#include "Tpetra_Details_reallocDualViewIfNeeded.hpp"
#include "Tpetra_Details_Random.hpp"
#ifdef HAVE_TPETRACORE_TEUCHOSNUMERICS
#include "Teuchos_SerialDenseMatrix.hpp"
#endif  // HAVE_TPETRACORE_TEUCHOSNUMERICS
#include "Tpetra_KokkosRefactor_Details_MultiVectorDistObjectKernels.hpp"
#include "KokkosCompat_View.hpp"
#include "KokkosBlas.hpp"
#include "KokkosKernels_Utils.hpp"
#include "Kokkos_Random.hpp"
#if KOKKOS_VERSION >= 40799
#include "KokkosKernels_ArithTraits.hpp"
#else
#include "Kokkos_ArithTraits.hpp"
#endif
#include <memory>
#include <sstream>
 
#ifdef HAVE_TPETRA_INST_FLOAT128
namespace Kokkos {
// FIXME (mfh 04 Sep 2015) Just a stub for now!
template <class Generator>
struct rand<Generator, __float128> {
  static KOKKOS_INLINE_FUNCTION __float128 max() {
    return static_cast<__float128>(1.0);
  }
  static KOKKOS_INLINE_FUNCTION __float128
  draw(Generator& gen) {
    // Half the smallest normalized double, is the scaling factor of
    // the lower-order term in the double-double representation.
    const __float128 scalingFactor =
        static_cast<__float128>(std::numeric_limits<double>::min()) /
        static_cast<__float128>(2.0);
    const __float128 higherOrderTerm = static_cast<__float128>(gen.drand());
    const __float128 lowerOrderTerm =
        static_cast<__float128>(gen.drand()) * scalingFactor;
    return higherOrderTerm + lowerOrderTerm;
  }
  static KOKKOS_INLINE_FUNCTION __float128
  draw(Generator& gen, const __float128& range) {
    // FIXME (mfh 05 Sep 2015) Not sure if this is right.
    const __float128 scalingFactor =
        static_cast<__float128>(std::numeric_limits<double>::min()) /
        static_cast<__float128>(2.0);
    const __float128 higherOrderTerm =
        static_cast<__float128>(gen.drand(range));
    const __float128 lowerOrderTerm =
        static_cast<__float128>(gen.drand(range)) * scalingFactor;
    return higherOrderTerm + lowerOrderTerm;
  }
  static KOKKOS_INLINE_FUNCTION __float128
  draw(Generator& gen, const __float128& start, const __float128& end) {
    // FIXME (mfh 05 Sep 2015) Not sure if this is right.
    const __float128 scalingFactor =
        static_cast<__float128>(std::numeric_limits<double>::min()) /
        static_cast<__float128>(2.0);
    const __float128 higherOrderTerm =
        static_cast<__float128>(gen.drand(start, end));
    const __float128 lowerOrderTerm =
        static_cast<__float128>(gen.drand(start, end)) * scalingFactor;
    return higherOrderTerm + lowerOrderTerm;
  }
};
}  // namespace Kokkos
#endif  // HAVE_TPETRA_INST_FLOAT128
 
namespace {  // (anonymous)
 
template <class ST, class LO, class GO, class NT>
typename Tpetra::MultiVector<ST, LO, GO, NT>::wrapped_dual_view_type
allocDualView(const size_t lclNumRows,
              const size_t numCols,
              const bool zeroOut      = true,
              const bool allowPadding = false) {
  using Kokkos::AllowPadding;
  using Kokkos::view_alloc;
  using Kokkos::WithoutInitializing;
  using ::Tpetra::Details::Behavior;
  typedef typename Tpetra::MultiVector<ST, LO, GO, NT>::dual_view_type dual_view_type;
  typedef typename Tpetra::MultiVector<ST, LO, GO, NT>::wrapped_dual_view_type wrapped_dual_view_type;
  typedef typename dual_view_type::t_dev dev_view_type;
 
  // This needs to be a string and not a char*, if given as an
  // argument to Kokkos::view_alloc.  This is because view_alloc
  // also allows a raw pointer as its first argument.  See
  // https://github.com/kokkos/kokkos/issues/434.
  const std::string label("MV::DualView");
  const bool debug = Behavior::debug();
 
  // NOTE (mfh 18 Feb 2015, 12 Apr 2015, 22 Sep 2016) Our separate
  // creation of the DualView's Views works around
  // Kokkos::DualView's current inability to accept an
  // AllocationProperties initial argument (as Kokkos::View does).
  // However, the work-around is harmless, since it does what the
  // (currently nonexistent) equivalent DualView constructor would
  // have done anyway.
 
  dev_view_type d_view;
  if (zeroOut) {
    if (allowPadding) {
      d_view = dev_view_type(view_alloc(label, AllowPadding),
                             lclNumRows, numCols);
    } else {
      d_view = dev_view_type(view_alloc(label),
                             lclNumRows, numCols);
    }
  } else {
    if (allowPadding) {
      d_view = dev_view_type(view_alloc(label,
                                        WithoutInitializing,
                                        AllowPadding),
                             lclNumRows, numCols);
    } else {
      d_view = dev_view_type(view_alloc(label, WithoutInitializing),
                             lclNumRows, numCols);
    }
    if (debug) {
      // Filling with NaN is a cheap and effective way to tell if
      // downstream code is trying to use a MultiVector's data
      // without them having been initialized.  ArithTraits lets us
      // call nan() even if the scalar type doesn't define it; it
      // just returns some undefined value in the latter case.  This
      // won't hurt anything because by setting zeroOut=false, users
      // already agreed that they don't care about the contents of
      // the MultiVector.
#if KOKKOS_VERSION >= 40799
      const ST nan = KokkosKernels::ArithTraits<ST>::nan();
#else
      const ST nan = Kokkos::ArithTraits<ST>::nan();
#endif
      KokkosBlas::fill(d_view, nan);
    }
  }
  if (debug) {
    TEUCHOS_TEST_FOR_EXCEPTION(static_cast<size_t>(d_view.extent(0)) != lclNumRows ||
                                   static_cast<size_t>(d_view.extent(1)) != numCols,
                               std::logic_error,
                               "allocDualView: d_view's dimensions actual dimensions do not match "
                               "requested dimensions.  d_view is "
                                   << d_view.extent(0) << " x " << d_view.extent(1) << "; requested " << lclNumRows << " x " << numCols
                                   << ".  Please report this bug to the Tpetra developers.");
  }
 
  return wrapped_dual_view_type(d_view);
}
 
// Convert 1-D Teuchos::ArrayView to an unmanaged 1-D host Kokkos::View.
//
// T: The type of the entries of the View.
// ExecSpace: The Kokkos execution space.
template <class T, class ExecSpace>
struct MakeUnmanagedView {
  // The 'false' part of the branch carefully ensures that this
  // won't attempt to use a host execution space that hasn't been
  // initialized.  For example, if Kokkos::OpenMP is disabled and
  // Kokkos::Threads is enabled, the latter is always the default
  // execution space of Kokkos::HostSpace, even when ExecSpace is
  // Kokkos::Serial.  That's why we go through the trouble of asking
  // Kokkos::DualView what _its_ space is.  That seems to work
  // around this default execution space issue.
  //
  typedef typename std::conditional<
      Kokkos::SpaceAccessibility<
          typename ExecSpace::memory_space,
          Kokkos::HostSpace>::accessible,
      typename ExecSpace::device_type,
      typename Kokkos::DualView<T*, ExecSpace>::host_mirror_space>::type host_exec_space;
  typedef Kokkos::LayoutLeft array_layout;
  typedef Kokkos::View<T*, array_layout, host_exec_space,
                       Kokkos::MemoryUnmanaged>
      view_type;
 
  static view_type getView(const Teuchos::ArrayView<T>& x_in) {
    const size_t numEnt = static_cast<size_t>(x_in.size());
    if (numEnt == 0) {
      return view_type();
    } else {
      return view_type(x_in.getRawPtr(), numEnt);
    }
  }
};
 
template <class WrappedDualViewType>
WrappedDualViewType
takeSubview(const WrappedDualViewType& X,
            const std::pair<size_t, size_t>& rowRng,
            const Kokkos::ALL_t& colRng)
 
{
  // The bug we saw below should be harder to trigger here.
  return WrappedDualViewType(X, rowRng, colRng);
}
 
template <class WrappedDualViewType>
WrappedDualViewType
takeSubview(const WrappedDualViewType& X,
            const Kokkos::ALL_t& rowRng,
            const std::pair<size_t, size_t>& colRng) {
  using DualViewType = typename WrappedDualViewType::DVT;
  // Look carefullly at the comment in the below version of this function.
  // The comment applies here as well.
  if (X.extent(0) == 0 && X.extent(1) != 0) {
    return WrappedDualViewType(DualViewType("MV::DualView", 0, colRng.second - colRng.first));
  } else {
    return WrappedDualViewType(X, rowRng, colRng);
  }
}
 
template <class WrappedDualViewType>
WrappedDualViewType
takeSubview(const WrappedDualViewType& X,
            const std::pair<size_t, size_t>& rowRng,
            const std::pair<size_t, size_t>& colRng) {
  using DualViewType = typename WrappedDualViewType::DVT;
  // If you take a subview of a view with zero rows Kokkos::subview()
  // always returns a DualView with the same data pointers.  This will break
  // pointer equality testing in between two subviews of the same 2D View if
  // it has zero row extent.  While the one (known) case where this was actually used
  // has been fixed, that sort of check could very easily be reintroduced in the future,
  // hence I've added this if check here.
  //
  // This is not a bug in Kokkos::subview(), just some very subtle behavior which
  // future developers should be wary of.
  if (X.extent(0) == 0 && X.extent(1) != 0) {
    return WrappedDualViewType(DualViewType("MV::DualView", 0, colRng.second - colRng.first));
  } else {
    return WrappedDualViewType(X, rowRng, colRng);
  }
}
 
template <class WrappedOrNotDualViewType>
size_t
getDualViewStride(const WrappedOrNotDualViewType& dv) {
  // FIXME (mfh 15 Mar 2019) DualView doesn't have a stride
  // method yet, but its Views do.
  // NOTE: dv.stride() returns a vector of length one
  // more than its rank
  size_t strides[WrappedOrNotDualViewType::t_dev::rank + 1];
  dv.stride(strides);
  const size_t LDA     = strides[1];
  const size_t numRows = dv.extent(0);
 
  if (LDA == 0) {
    return (numRows == 0) ? size_t(1) : numRows;
  } else {
    return LDA;
  }
}
 
template <class ViewType>
size_t
getViewStride(const ViewType& view) {
  const size_t LDA     = view.stride(1);
  const size_t numRows = view.extent(0);
 
  if (LDA == 0) {
    return (numRows == 0) ? size_t(1) : numRows;
  } else {
    return LDA;
  }
}
 
template <class impl_scalar_type, class buffer_device_type>
bool runKernelOnHost(
    Kokkos::DualView<impl_scalar_type*, buffer_device_type> imports) {
  if (!imports.need_sync_device()) {
    return false;  // most up-to-date on device
  } else {         // most up-to-date on host,
                   // but if large enough, worth running on device anyway
    size_t localLengthThreshold =
        Tpetra::Details::Behavior::multivectorKernelLocationThreshold();
    return imports.extent(0) <= localLengthThreshold;
  }
}
 
template <class SC, class LO, class GO, class NT>
bool runKernelOnHost(const ::Tpetra::MultiVector<SC, LO, GO, NT>& X) {
  if (!X.need_sync_device()) {
    return false;  // most up-to-date on device
  } else {         // most up-to-date on host
                   // but if large enough, worth running on device anyway
    size_t localLengthThreshold =
        Tpetra::Details::Behavior::multivectorKernelLocationThreshold();
    return X.getLocalLength() <= localLengthThreshold;
  }
}
 
template <class SC, class LO, class GO, class NT>
void multiVectorNormImpl(typename ::Tpetra::MultiVector<SC, LO, GO, NT>::mag_type norms[],
                         ::Tpetra::MultiVector<SC, LO, GO, NT>& X,
                         const ::Tpetra::Details::EWhichNorm whichNorm) {
  using namespace Tpetra;
  using ::Tpetra::Details::normImpl;
  using MV             = ::Tpetra::MultiVector<SC, LO, GO, NT>;
  using val_type       = typename MV::impl_scalar_type;
  using mag_type       = typename MV::mag_type;
  using dual_view_type = typename MV::dual_view_type;
 
  auto map                    = X.getMap();
  auto comm                   = map.is_null() ? nullptr : map->getComm().getRawPtr();
  auto whichVecs              = getMultiVectorWhichVectors(X);
  const bool isConstantStride = X.isConstantStride();
  const bool isDistributed    = X.isDistributed();
 
  const bool runOnHost = runKernelOnHost(X);
  if (runOnHost) {
    using view_type    = typename dual_view_type::t_host;
    using array_layout = typename view_type::array_layout;
    using device_type  = typename view_type::device_type;
 
    auto X_lcl = X.getLocalViewHost(Access::ReadOnly);
    normImpl<val_type, array_layout, device_type,
             mag_type>(norms, X_lcl, whichNorm, whichVecs,
                       isConstantStride, isDistributed, comm);
  } else {
    using view_type    = typename dual_view_type::t_dev;
    using array_layout = typename view_type::array_layout;
    using device_type  = typename view_type::device_type;
 
    auto X_lcl = X.getLocalViewDevice(Access::ReadOnly);
    normImpl<val_type, array_layout, device_type,
             mag_type>(norms, X_lcl, whichNorm, whichVecs,
                       isConstantStride, isDistributed, comm);
  }
}
}  // namespace
 
namespace Tpetra {
 
namespace Details {
template <typename DstView, typename SrcView>
struct AddAssignFunctor {
  // This functor would be better as a lambda, but CUDA cannot compile
  // lambdas in protected functions.  It compiles fine with the functor.
  AddAssignFunctor(DstView& tgt_, SrcView& src_)
    : tgt(tgt_)
    , src(src_) {}
 
  KOKKOS_INLINE_FUNCTION void
  operator()(const size_t k) const { tgt(k) += src(k); }
 
  DstView tgt;
  SrcView src;
};
}  // namespace Details
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
bool MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    vectorIndexOutOfRange(const size_t VectorIndex) const {
  return (VectorIndex < 1 && VectorIndex != 0) || VectorIndex >= getNumVectors();
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector()
  : base_type(Teuchos::rcp(new map_type())) {}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector(const Teuchos::RCP<const map_type>& map,
                const size_t numVecs,
                const bool zeroOut)
  : /* default is true */
  base_type(map) {
  ::Tpetra::Details::ProfilingRegion region("Tpetra::MV ctor (map,numVecs,zeroOut)");
 
  const size_t lclNumRows = this->getLocalLength();
  view_                   = allocDualView<Scalar, LocalOrdinal, GlobalOrdinal, Node>(lclNumRows, numVecs, zeroOut);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector(const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& source,
                const Teuchos::DataAccess copyOrView)
  : base_type(source)
  , view_(source.view_)
  , whichVectors_(source.whichVectors_) {
  typedef MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> MV;
  const char tfecfFuncName[] =
      "MultiVector(const MultiVector&, "
      "const Teuchos::DataAccess): ";
 
  ::Tpetra::Details::ProfilingRegion region("Tpetra::MV 2-arg \"copy\" ctor");
 
  if (copyOrView == Teuchos::Copy) {
    // Reuse the conveniently already existing function that creates
    // a deep copy.
    MV cpy              = createCopy(source);
    this->view_         = cpy.view_;
    this->whichVectors_ = cpy.whichVectors_;
  } else if (copyOrView == Teuchos::View) {
  } else {
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        true, std::invalid_argument,
        "Second argument 'copyOrView' has an "
        "invalid value "
            << copyOrView << ".  Valid values include "
                             "Teuchos::Copy = "
            << Teuchos::Copy << " and Teuchos::View = "
            << Teuchos::View << ".");
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector(const Teuchos::RCP<const map_type>& map,
                const dual_view_type& view)
  : base_type(map)
  , view_(wrapped_dual_view_type(view)) {
  const char tfecfFuncName[]   = "MultiVector(Map,DualView): ";
  const size_t lclNumRows_map  = map.is_null() ? size_t(0) : map->getLocalNumElements();
  const size_t lclNumRows_view = view.extent(0);
  const size_t LDA             = getDualViewStride(view_);
 
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(LDA < lclNumRows_map || lclNumRows_map != lclNumRows_view,
                                        std::invalid_argument,
                                        "Kokkos::DualView does not match Map. "
                                        "map->getLocalNumElements() = "
                                            << lclNumRows_map
                                            << ", view.extent(0) = " << lclNumRows_view
                                            << ", and getStride() = " << LDA << ".");
 
  using ::Tpetra::Details::Behavior;
  const bool debug = Behavior::debug();
  if (debug) {
    using ::Tpetra::Details::checkGlobalDualViewValidity;
    std::ostringstream gblErrStrm;
    const bool verbose = Behavior::verbose();
    const auto comm    = map.is_null() ? Teuchos::null : map->getComm();
    const bool gblValid =
        checkGlobalDualViewValidity(&gblErrStrm, view, verbose,
                                    comm.getRawPtr());
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(!gblValid, std::runtime_error, gblErrStrm.str());
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector(const Teuchos::RCP<const map_type>& map,
                const wrapped_dual_view_type& view)
  : base_type(map)
  , view_(view) {
  const char tfecfFuncName[]   = "MultiVector(Map,DualView): ";
  const size_t lclNumRows_map  = map.is_null() ? size_t(0) : map->getLocalNumElements();
  const size_t lclNumRows_view = view.extent(0);
  const size_t LDA             = getDualViewStride(view);
 
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(LDA < lclNumRows_map || lclNumRows_map != lclNumRows_view,
                                        std::invalid_argument,
                                        "Kokkos::DualView does not match Map. "
                                        "map->getLocalNumElements() = "
                                            << lclNumRows_map
                                            << ", view.extent(0) = " << lclNumRows_view
                                            << ", and getStride() = " << LDA << ".");
 
  using ::Tpetra::Details::Behavior;
  const bool debug = Behavior::debug();
  if (debug) {
    using ::Tpetra::Details::checkGlobalWrappedDualViewValidity;
    std::ostringstream gblErrStrm;
    const bool verbose = Behavior::verbose();
    const auto comm    = map.is_null() ? Teuchos::null : map->getComm();
    const bool gblValid =
        checkGlobalWrappedDualViewValidity(&gblErrStrm, view, verbose,
                                           comm.getRawPtr());
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(!gblValid, std::runtime_error, gblErrStrm.str());
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector(const Teuchos::RCP<const map_type>& map,
                const typename dual_view_type::t_dev& d_view)
  : base_type(map) {
  using Teuchos::ArrayRCP;
  using Teuchos::RCP;
  const char tfecfFuncName[] = "MultiVector(map,d_view): ";
 
  ::Tpetra::Details::ProfilingRegion region("Tpetra::MV ctor (map,d_view)");
 
  const size_t LDA        = getViewStride(d_view);
  const size_t lclNumRows = map->getLocalNumElements();
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(LDA < lclNumRows, std::invalid_argument,
                                        "Map does not match "
                                        "Kokkos::View.  map->getLocalNumElements() = "
                                            << lclNumRows
                                            << ", View's column stride = " << LDA
                                            << ", and View's extent(0) = " << d_view.extent(0) << ".");
 
  auto h_view    = Kokkos::create_mirror_view(d_view);
  auto dual_view = dual_view_type(d_view, h_view);
  view_          = wrapped_dual_view_type(dual_view);
 
  using ::Tpetra::Details::Behavior;
  const bool debug = Behavior::debug();
  if (debug) {
    using ::Tpetra::Details::checkGlobalWrappedDualViewValidity;
    std::ostringstream gblErrStrm;
    const bool verbose = Behavior::verbose();
    const auto comm    = map.is_null() ? Teuchos::null : map->getComm();
    const bool gblValid =
        checkGlobalWrappedDualViewValidity(&gblErrStrm, view_, verbose,
                                           comm.getRawPtr());
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(!gblValid, std::runtime_error, gblErrStrm.str());
  }
  // The user gave us a device view.  In order to respect its
  // initial contents, we mark the DualView as "modified on device."
  // That way, the next sync will synchronize it with the host view.
  dual_view.modify_device();
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector(const Teuchos::RCP<const map_type>& map,
                const dual_view_type& view,
                const dual_view_type& origView)
  : base_type(map)
  , view_(wrapped_dual_view_type(view, origView)) {
  const char tfecfFuncName[] = "MultiVector(map,view,origView): ";
 
  const size_t LDA        = getDualViewStride(origView);
  const size_t lclNumRows = this->getLocalLength();  // comes from the Map
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      LDA < lclNumRows, std::invalid_argument,
      "The input Kokkos::DualView's "
      "column stride LDA = "
          << LDA << " < getLocalLength() = " << lclNumRows
          << ".  This may also mean that the input origView's first dimension (number "
             "of rows = "
          << origView.extent(0) << ") does not not match the number "
                                   "of entries in the Map on the calling process.");
 
  using ::Tpetra::Details::Behavior;
  const bool debug = Behavior::debug();
  if (debug) {
    using ::Tpetra::Details::checkGlobalDualViewValidity;
    std::ostringstream gblErrStrm;
    const bool verbose = Behavior::verbose();
    const auto comm    = map.is_null() ? Teuchos::null : map->getComm();
    const bool gblValid_0 =
        checkGlobalDualViewValidity(&gblErrStrm, view, verbose,
                                    comm.getRawPtr());
    const bool gblValid_1 =
        checkGlobalDualViewValidity(&gblErrStrm, origView, verbose,
                                    comm.getRawPtr());
    const bool gblValid = gblValid_0 && gblValid_1;
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(!gblValid, std::runtime_error, gblErrStrm.str());
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector(const Teuchos::RCP<const map_type>& map,
                const dual_view_type& view,
                const Teuchos::ArrayView<const size_t>& whichVectors)
  : base_type(map)
  , view_(view)
  , whichVectors_(whichVectors.begin(), whichVectors.end()) {
  using Kokkos::ALL;
  using Kokkos::subview;
  const char tfecfFuncName[] = "MultiVector(map,view,whichVectors): ";
 
  using ::Tpetra::Details::Behavior;
  const bool debug = Behavior::debug();
  if (debug) {
    using ::Tpetra::Details::checkGlobalDualViewValidity;
    std::ostringstream gblErrStrm;
    const bool verbose = Behavior::verbose();
    const auto comm    = map.is_null() ? Teuchos::null : map->getComm();
    const bool gblValid =
        checkGlobalDualViewValidity(&gblErrStrm, view, verbose,
                                    comm.getRawPtr());
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(!gblValid, std::runtime_error, gblErrStrm.str());
  }
 
  const size_t lclNumRows = map.is_null() ? size_t(0) : map->getLocalNumElements();
  // Check dimensions of the input DualView.  We accept that Kokkos
  // might not allow construction of a 0 x m (Dual)View with m > 0,
  // so we only require the number of rows to match if the
  // (Dual)View has more than zero columns.  Likewise, we only
  // require the number of columns to match if the (Dual)View has
  // more than zero rows.
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      view.extent(1) != 0 && static_cast<size_t>(view.extent(0)) < lclNumRows,
      std::invalid_argument, "view.extent(0) = " << view.extent(0) << " < map->getLocalNumElements() = " << lclNumRows << ".");
  if (whichVectors.size() != 0) {
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        view.extent(1) != 0 && view.extent(1) == 0,
        std::invalid_argument,
        "view.extent(1) = 0, but whichVectors.size()"
        " = "
            << whichVectors.size() << " > 0.");
    size_t maxColInd = 0;
    typedef Teuchos::ArrayView<const size_t>::size_type size_type;
    for (size_type k = 0; k < whichVectors.size(); ++k) {
      TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
          whichVectors[k] == Teuchos::OrdinalTraits<size_t>::invalid(),
          std::invalid_argument, "whichVectors[" << k << "] = "
                                                         "Teuchos::OrdinalTraits<size_t>::invalid().");
      maxColInd = std::max(maxColInd, whichVectors[k]);
    }
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        view.extent(1) != 0 && static_cast<size_t>(view.extent(1)) <= maxColInd,
        std::invalid_argument, "view.extent(1) = " << view.extent(1) << " <= max(whichVectors) = " << maxColInd << ".");
  }
 
  // If extent(1) is 0, the stride might be 0.  BLAS doesn't like
  // zero strides, so modify in that case.
  const size_t LDA = getDualViewStride(view);
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(LDA < lclNumRows, std::invalid_argument,
                                        "LDA = " << LDA << " < this->getLocalLength() = " << lclNumRows << ".");
 
  if (whichVectors.size() == 1) {
    // If whichVectors has only one entry, we don't need to bother
    // with nonconstant stride.  Just shift the view over so it
    // points to the desired column.
    //
    // NOTE (mfh 10 May 2014) This is a special case where we set
    // origView_ just to view that one column, not all of the
    // original columns.  This ensures that the use of origView_ in
    // offsetView works correctly.
    //
    const std::pair<size_t, size_t> colRng(whichVectors[0],
                                           whichVectors[0] + 1);
    view_ = takeSubview(view_, ALL(), colRng);
    // whichVectors_.size() == 0 means "constant stride."
    whichVectors_.clear();
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector(const Teuchos::RCP<const map_type>& map,
                const wrapped_dual_view_type& view,
                const Teuchos::ArrayView<const size_t>& whichVectors)
  : base_type(map)
  , view_(view)
  , whichVectors_(whichVectors.begin(), whichVectors.end()) {
  using Kokkos::ALL;
  using Kokkos::subview;
  const char tfecfFuncName[] = "MultiVector(map,view,whichVectors): ";
 
  using ::Tpetra::Details::Behavior;
  const bool debug = Behavior::debug();
  if (debug) {
    using ::Tpetra::Details::checkGlobalWrappedDualViewValidity;
    std::ostringstream gblErrStrm;
    const bool verbose = Behavior::verbose();
    const auto comm    = map.is_null() ? Teuchos::null : map->getComm();
    const bool gblValid =
        checkGlobalWrappedDualViewValidity(&gblErrStrm, view, verbose,
                                           comm.getRawPtr());
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(!gblValid, std::runtime_error, gblErrStrm.str());
  }
 
  const size_t lclNumRows = map.is_null() ? size_t(0) : map->getLocalNumElements();
  // Check dimensions of the input DualView.  We accept that Kokkos
  // might not allow construction of a 0 x m (Dual)View with m > 0,
  // so we only require the number of rows to match if the
  // (Dual)View has more than zero columns.  Likewise, we only
  // require the number of columns to match if the (Dual)View has
  // more than zero rows.
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      view.extent(1) != 0 && static_cast<size_t>(view.extent(0)) < lclNumRows,
      std::invalid_argument, "view.extent(0) = " << view.extent(0) << " < map->getLocalNumElements() = " << lclNumRows << ".");
  if (whichVectors.size() != 0) {
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        view.extent(1) != 0 && view.extent(1) == 0,
        std::invalid_argument,
        "view.extent(1) = 0, but whichVectors.size()"
        " = "
            << whichVectors.size() << " > 0.");
    size_t maxColInd = 0;
    typedef Teuchos::ArrayView<const size_t>::size_type size_type;
    for (size_type k = 0; k < whichVectors.size(); ++k) {
      TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
          whichVectors[k] == Teuchos::OrdinalTraits<size_t>::invalid(),
          std::invalid_argument, "whichVectors[" << k << "] = "
                                                         "Teuchos::OrdinalTraits<size_t>::invalid().");
      maxColInd = std::max(maxColInd, whichVectors[k]);
    }
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        view.extent(1) != 0 && static_cast<size_t>(view.extent(1)) <= maxColInd,
        std::invalid_argument, "view.extent(1) = " << view.extent(1) << " <= max(whichVectors) = " << maxColInd << ".");
  }
 
  // If extent(1) is 0, the stride might be 0.  BLAS doesn't like
  // zero strides, so modify in that case.
  const size_t LDA = getDualViewStride(view);
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(LDA < lclNumRows, std::invalid_argument,
                                        "LDA = " << LDA << " < this->getLocalLength() = " << lclNumRows << ".");
 
  if (whichVectors.size() == 1) {
    // If whichVectors has only one entry, we don't need to bother
    // with nonconstant stride.  Just shift the view over so it
    // points to the desired column.
    //
    // NOTE (mfh 10 May 2014) This is a special case where we set
    // origView_ just to view that one column, not all of the
    // original columns.  This ensures that the use of origView_ in
    // offsetView works correctly.
    //
    const std::pair<size_t, size_t> colRng(whichVectors[0],
                                           whichVectors[0] + 1);
    view_ = takeSubview(view_, ALL(), colRng);
    // whichVectors_.size() == 0 means "constant stride."
    whichVectors_.clear();
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector(const Teuchos::RCP<const map_type>& map,
                const dual_view_type& view,
                const dual_view_type& origView,
                const Teuchos::ArrayView<const size_t>& whichVectors)
  : base_type(map)
  , view_(wrapped_dual_view_type(view, origView))
  , whichVectors_(whichVectors.begin(), whichVectors.end()) {
  using Kokkos::ALL;
  using Kokkos::subview;
  const char tfecfFuncName[] = "MultiVector(map,view,origView,whichVectors): ";
 
  using ::Tpetra::Details::Behavior;
  const bool debug = Behavior::debug();
  if (debug) {
    using ::Tpetra::Details::checkGlobalDualViewValidity;
    std::ostringstream gblErrStrm;
    const bool verbose = Behavior::verbose();
    const auto comm    = map.is_null() ? Teuchos::null : map->getComm();
    const bool gblValid_0 =
        checkGlobalDualViewValidity(&gblErrStrm, view, verbose,
                                    comm.getRawPtr());
    const bool gblValid_1 =
        checkGlobalDualViewValidity(&gblErrStrm, origView, verbose,
                                    comm.getRawPtr());
    const bool gblValid = gblValid_0 && gblValid_1;
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(!gblValid, std::runtime_error, gblErrStrm.str());
  }
 
  const size_t lclNumRows = this->getLocalLength();
  // Check dimensions of the input DualView.  We accept that Kokkos
  // might not allow construction of a 0 x m (Dual)View with m > 0,
  // so we only require the number of rows to match if the
  // (Dual)View has more than zero columns.  Likewise, we only
  // require the number of columns to match if the (Dual)View has
  // more than zero rows.
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      view.extent(1) != 0 && static_cast<size_t>(view.extent(0)) < lclNumRows,
      std::invalid_argument, "view.extent(0) = " << view.extent(0) << " < map->getLocalNumElements() = " << lclNumRows << ".");
  if (whichVectors.size() != 0) {
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        view.extent(1) != 0 && view.extent(1) == 0,
        std::invalid_argument,
        "view.extent(1) = 0, but whichVectors.size()"
        " = "
            << whichVectors.size() << " > 0.");
    size_t maxColInd = 0;
    typedef Teuchos::ArrayView<const size_t>::size_type size_type;
    for (size_type k = 0; k < whichVectors.size(); ++k) {
      TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
          whichVectors[k] == Teuchos::OrdinalTraits<size_t>::invalid(),
          std::invalid_argument, "whichVectors[" << k << "] = "
                                                         "Teuchos::OrdinalTraits<size_t>::invalid().");
      maxColInd = std::max(maxColInd, whichVectors[k]);
    }
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        view.extent(1) != 0 && static_cast<size_t>(view.extent(1)) <= maxColInd,
        std::invalid_argument, "view.extent(1) = " << view.extent(1) << " <= max(whichVectors) = " << maxColInd << ".");
  }
 
  // If extent(1) is 0, the stride might be 0.  BLAS doesn't like
  // zero strides, so modify in that case.
  const size_t LDA = getDualViewStride(origView);
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(LDA < lclNumRows, std::invalid_argument,
                                        "Map and DualView origView "
                                        "do not match.  LDA = "
                                            << LDA << " < this->getLocalLength() = " << lclNumRows << ".  origView.extent(0) = " << origView.extent(0)
                                            << ", origView.stride(1) = " << origView.view_device().stride(1) << ".");
 
  if (whichVectors.size() == 1) {
    // If whichVectors has only one entry, we don't need to bother
    // with nonconstant stride.  Just shift the view over so it
    // points to the desired column.
    //
    // NOTE (mfh 10 May 2014) This is a special case where we set
    // origView_ just to view that one column, not all of the
    // original columns.  This ensures that the use of origView_ in
    // offsetView works correctly.
    const std::pair<size_t, size_t> colRng(whichVectors[0],
                                           whichVectors[0] + 1);
    view_ = takeSubview(view_, ALL(), colRng);
    //      origView_ = takeSubview (origView_, ALL (), colRng);
    // whichVectors_.size() == 0 means "constant stride."
    whichVectors_.clear();
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector(const Teuchos::RCP<const map_type>& map,
                const Teuchos::ArrayView<const Scalar>& data,
                const size_t LDA,
                const size_t numVecs)
  : base_type(map) {
  typedef LocalOrdinal LO;
  typedef GlobalOrdinal GO;
  const char tfecfFuncName[] = "MultiVector(map,data,LDA,numVecs): ";
  ::Tpetra::Details::ProfilingRegion region("Tpetra::MV ctor (map,Teuchos::ArrayView,LDA,numVecs)");
 
  // Deep copy constructor, constant stride (NO whichVectors_).
  // There is no need for a deep copy constructor with nonconstant stride.
 
  const size_t lclNumRows =
      map.is_null() ? size_t(0) : map->getLocalNumElements();
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(LDA < lclNumRows, std::invalid_argument, "LDA = " << LDA << " < "
                                                                                                    "map->getLocalNumElements() = "
                                                                                          << lclNumRows << ".");
  if (numVecs != 0) {
    const size_t minNumEntries = LDA * (numVecs - 1) + lclNumRows;
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(static_cast<size_t>(data.size()) < minNumEntries,
                                          std::invalid_argument,
                                          "Input Teuchos::ArrayView does not have enough "
                                          "entries, given the input Map and number of vectors in the MultiVector."
                                          "  data.size() = "
                                              << data.size() << " < (LDA*(numVecs-1)) + "
                                                                "map->getLocalNumElements () = "
                                              << minNumEntries << ".");
  }
 
  this->view_ = allocDualView<Scalar, LO, GO, Node>(lclNumRows, numVecs);
  // Note: X_out will be completely overwritten
  auto X_out = this->getLocalViewDevice(Access::OverwriteAll);
 
  // Make an unmanaged host Kokkos::View of the input data.  First
  // create a View (X_in_orig) with the original stride.  Then,
  // create a subview (X_in) with the right number of columns.
  const impl_scalar_type* const X_in_raw =
      reinterpret_cast<const impl_scalar_type*>(data.getRawPtr());
  Kokkos::View<const impl_scalar_type**,
               Kokkos::LayoutLeft,
               Kokkos::HostSpace,
               Kokkos::MemoryUnmanaged>
      X_in_orig(X_in_raw, LDA, numVecs);
  const Kokkos::pair<size_t, size_t> rowRng(0, lclNumRows);
  auto X_in = Kokkos::subview(X_in_orig, rowRng, Kokkos::ALL());
 
  // If LDA != X_out's column stride, then we need to copy one
  // column at a time; Kokkos::deep_copy refuses to work in that
  // case.
  const size_t outStride =
      X_out.extent(1) == 0 ? size_t(1) : X_out.stride(1);
  if (LDA == outStride) {  // strides are the same; deep_copy once
    // This only works because MultiVector uses LayoutLeft.
    // We would need a custom copy functor otherwise.
    // DEEP_COPY REVIEW - HOST-TO-DEVICE
    Kokkos::deep_copy(execution_space(), X_out, X_in);
  } else {  // strides differ; copy one column at a time
    typedef decltype(Kokkos::subview(X_out, Kokkos::ALL(), 0))
        out_col_view_type;
    typedef decltype(Kokkos::subview(X_in, Kokkos::ALL(), 0))
        in_col_view_type;
    for (size_t j = 0; j < numVecs; ++j) {
      out_col_view_type X_out_j = Kokkos::subview(X_out, Kokkos::ALL(), j);
      in_col_view_type X_in_j   = Kokkos::subview(X_in, Kokkos::ALL(), j);
      // DEEP_COPY REVIEW - HOST-TO-DEVICE
      Kokkos::deep_copy(execution_space(), X_out_j, X_in_j);
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector(const Teuchos::RCP<const map_type>& map,
                const Teuchos::ArrayView<const Teuchos::ArrayView<const Scalar> >& ArrayOfPtrs,
                const size_t numVecs)
  : base_type(map) {
  typedef impl_scalar_type IST;
  typedef LocalOrdinal LO;
  typedef GlobalOrdinal GO;
  const char tfecfFuncName[] = "MultiVector(map,ArrayOfPtrs,numVecs): ";
  ::Tpetra::Details::ProfilingRegion region("Tpetra::MV ctor (map,Teuchos::ArrayView of ArrayView,numVecs)");
 
  const size_t lclNumRows =
      map.is_null() ? size_t(0) : map->getLocalNumElements();
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(numVecs < 1 || numVecs != static_cast<size_t>(ArrayOfPtrs.size()),
                                        std::runtime_error, "Either numVecs (= " << numVecs << ") < 1, or "
                                                                                               "ArrayOfPtrs.size() (= "
                                                                                 << ArrayOfPtrs.size() << ") != numVecs.");
  for (size_t j = 0; j < numVecs; ++j) {
    Teuchos::ArrayView<const Scalar> X_j_av = ArrayOfPtrs[j];
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        static_cast<size_t>(X_j_av.size()) < lclNumRows,
        std::invalid_argument, "ArrayOfPtrs[" << j << "].size() = " << X_j_av.size() << " < map->getLocalNumElements() = " << lclNumRows << ".");
  }
 
  view_      = allocDualView<Scalar, LO, GO, Node>(lclNumRows, numVecs);
  auto X_out = this->getLocalViewDevice(Access::ReadWrite);
 
  // Make sure that the type of a single input column has the same
  // array layout as each output column does, so we can deep_copy.
  using array_layout        = typename decltype(X_out)::array_layout;
  using input_col_view_type = typename Kokkos::View<const IST*,
                                                    array_layout,
                                                    Kokkos::HostSpace,
                                                    Kokkos::MemoryUnmanaged>;
 
  const std::pair<size_t, size_t> rowRng(0, lclNumRows);
  for (size_t j = 0; j < numVecs; ++j) {
    Teuchos::ArrayView<const IST> X_j_av =
        Teuchos::av_reinterpret_cast<const IST>(ArrayOfPtrs[j]);
    input_col_view_type X_j_in(X_j_av.getRawPtr(), lclNumRows);
    auto X_j_out = Kokkos::subview(X_out, rowRng, j);
    // DEEP_COPY REVIEW - HOST-TO-DEVICE
    Kokkos::deep_copy(execution_space(), X_j_out, X_j_in);
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
bool MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    isConstantStride() const {
  return whichVectors_.empty();
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
size_t
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getLocalLength() const {
  if (this->getMap().is_null()) {  // possible, due to replaceMap().
    return static_cast<size_t>(0);
  } else {
    return this->getMap()->getLocalNumElements();
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
global_size_t
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getGlobalLength() const {
  if (this->getMap().is_null()) {  // possible, due to replaceMap().
    return static_cast<size_t>(0);
  } else {
    return this->getMap()->getGlobalNumElements();
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
size_t
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getStride() const {
  return isConstantStride() ? getDualViewStride(view_) : size_t(0);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
bool MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    aliases(const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& other) const {
  // Don't actually get a view, just get pointers.
  auto thisData    = view_.getDualView().view_host().data();
  auto otherData   = other.view_.getDualView().view_host().data();
  size_t thisSpan  = view_.getDualView().view_host().span();
  size_t otherSpan = other.view_.getDualView().view_host().span();
  return (otherData <= thisData && thisData < otherData + otherSpan) || (thisData <= otherData && otherData < thisData + thisSpan);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
bool MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    checkSizes(const SrcDistObject& sourceObj) {
  // Check whether the source object is a MultiVector.  If not, then
  // we can't even compare sizes, so it's definitely not OK to
  // Import or Export from it.
  typedef MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> MV;
  const MV* src = dynamic_cast<const MV*>(&sourceObj);
  if (src == nullptr) {
    return false;
  } else {
    // The target of the Import or Export calls checkSizes() in
    // DistObject::doTransfer().  By that point, we've already
    // constructed an Import or Export object using the two
    // multivectors' Maps, which means that (hopefully) we've
    // already checked other attributes of the multivectors.  Thus,
    // all we need to do here is check the number of columns.
    return src->getNumVectors() == this->getNumVectors();
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
size_t
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    constantNumberOfPackets() const {
  return this->getNumVectors();
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    copyAndPermute(const SrcDistObject& sourceObj,
                   const size_t numSameIDs,
                   const Kokkos::DualView<const local_ordinal_type*, buffer_device_type>& permuteToLIDs,
                   const Kokkos::DualView<const local_ordinal_type*, buffer_device_type>& permuteFromLIDs,
                   const CombineMode CM,
                   const execution_space& space) {
  using Kokkos::Compat::create_const_view;
  using KokkosRefactor::Details::permute_array_multi_column;
  using KokkosRefactor::Details::permute_array_multi_column_variable_stride;
  using std::endl;
  using ::Tpetra::Details::Behavior;
  using ::Tpetra::Details::getDualViewCopyFromArrayView;
  using ::Tpetra::Details::ProfilingRegion;
  using MV = MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>;
 
  // We've already called checkSizes(), so this cast must succeed.
  MV& sourceMV = const_cast<MV&>(dynamic_cast<const MV&>(sourceObj));
 
  bool copyOnHost;
  if (importsAreAliased() && (this->constantNumberOfPackets() != 0) && Behavior::enableGranularTransfers()) {
    // imports are aliased to the target. We already posted Irecvs
    // into imports using a memory space that depends on GPU
    // awareness. Therefore we want to modify target in the same
    // memory space. See comments in DistObject::beginTransfer.
    copyOnHost = !Behavior::assumeMpiIsGPUAware();
  } else {
    // We are free to choose the better memory space for copyAndPermute.
    copyOnHost = runKernelOnHost(sourceMV);
  }
  const char longFuncNameHost[]   = "Tpetra::MultiVector::copyAndPermute[Host]";
  const char longFuncNameDevice[] = "Tpetra::MultiVector::copyAndPermute[Device]";
  const char tfecfFuncName[]      = "copyAndPermute: ";
  ProfilingRegion regionCAP(copyOnHost ? longFuncNameHost : longFuncNameDevice);
 
  const bool verbose = Behavior::verbose();
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    auto map         = this->getMap();
    auto comm        = map.is_null() ? Teuchos::null : map->getComm();
    const int myRank = comm.is_null() ? -1 : comm->getRank();
    std::ostringstream os;
    os << "Proc " << myRank << ": MV::copyAndPermute: ";
    prefix = std::unique_ptr<std::string>(new std::string(os.str()));
    os << "Start" << endl;
    std::cerr << os.str();
  }
 
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(permuteToLIDs.extent(0) != permuteFromLIDs.extent(0),
                                        std::logic_error, "permuteToLIDs.extent(0) = " << permuteToLIDs.extent(0) << " != permuteFromLIDs.extent(0) = " << permuteFromLIDs.extent(0) << ".");
  const size_t numCols = this->getNumVectors();
 
  // sourceMV doesn't belong to us, so we can't sync it.  Do the
  // copying where it's currently sync'd.
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(sourceMV.need_sync_device() && sourceMV.need_sync_host(),
                                        std::logic_error,
                                        "Input MultiVector needs sync to both host "
                                        "and device.");
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "copyOnHost=" << (copyOnHost ? "true" : "false") << endl;
    std::cerr << os.str();
  }
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Copy first " << numSameIDs << " elements" << endl;
    std::cerr << os.str();
  }
 
  // TODO (mfh 15 Sep 2013) When we replace
  // KokkosClassic::MultiVector with a Kokkos::View, there are two
  // ways to copy the data:
  //
  // 1. Get a (sub)view of each column and call deep_copy on that.
  // 2. Write a custom kernel to copy the data.
  //
  // The first is easier, but the second might be more performant in
  // case we decide to use layouts other than LayoutLeft.  It might
  // even make sense to hide whichVectors_ in an entirely new layout
  // for Kokkos Views.
 
  // Copy rows [0, numSameIDs-1] of the local multivectors.
  //
  // Note (ETP 2 Jul 2014)  We need to always copy one column at a
  // time, even when both multivectors are constant-stride, since
  // deep_copy between strided subviews with more than one column
  // doesn't currently work.
 
  // FIXME (mfh 04 Feb 2019) Need to optimize for the case where
  // both source and target are constant stride and have multiple
  // columns.
  if (numSameIDs > 0) {
    const std::pair<size_t, size_t> rows(0, numSameIDs);
    if (copyOnHost) {
      ProfilingRegion regionC("Tpetra::MultiVector::copy[Host]");
      auto tgt_h = this->getLocalViewHost(Access::ReadWrite);
      auto src_h = sourceMV.getLocalViewHost(Access::ReadOnly);
 
      for (size_t j = 0; j < numCols; ++j) {
        const size_t tgtCol = isConstantStride() ? j : whichVectors_[j];
        const size_t srcCol =
            sourceMV.isConstantStride() ? j : sourceMV.whichVectors_[j];
 
        auto tgt_j = Kokkos::subview(tgt_h, rows, tgtCol);
        auto src_j = Kokkos::subview(src_h, rows, srcCol);
        if (CM == ADD_ASSIGN) {
          // Sum src_j into tgt_j
          using range_t =
              Kokkos::RangePolicy<execution_space, size_t>;
          range_t rp(space, 0, numSameIDs);
          Tpetra::Details::AddAssignFunctor<decltype(tgt_j), decltype(src_j)>
              aaf(tgt_j, src_j);
          Kokkos::parallel_for(rp, aaf);
        } else {
          // Copy src_j into tgt_j
          // DEEP_COPY REVIEW - HOSTMIRROR-TO-HOSTMIRROR
          Kokkos::deep_copy(space, tgt_j, src_j);
          space.fence("Tpetra::MultiVector::copyAndPermute-1");
        }
      }
    } else {  // copy on device
      ProfilingRegion regionC("Tpetra::MultiVector::copy[Device]");
      auto tgt_d = this->getLocalViewDevice(Access::ReadWrite);
      auto src_d = sourceMV.getLocalViewDevice(Access::ReadOnly);
 
      for (size_t j = 0; j < numCols; ++j) {
        const size_t tgtCol = isConstantStride() ? j : whichVectors_[j];
        const size_t srcCol =
            sourceMV.isConstantStride() ? j : sourceMV.whichVectors_[j];
 
        auto tgt_j = Kokkos::subview(tgt_d, rows, tgtCol);
        auto src_j = Kokkos::subview(src_d, rows, srcCol);
        if (CM == ADD_ASSIGN) {
          // Sum src_j into tgt_j
          using range_t =
              Kokkos::RangePolicy<execution_space, size_t>;
          range_t rp(space, 0, numSameIDs);
          Tpetra::Details::AddAssignFunctor<decltype(tgt_j), decltype(src_j)>
              aaf(tgt_j, src_j);
          Kokkos::parallel_for(rp, aaf);
        } else {
          // Copy src_j into tgt_j
          // DEEP_COPY REVIEW - DEVICE-TO-DEVICE
          Kokkos::deep_copy(space, tgt_j, src_j);
          space.fence("Tpetra::MultiVector::copyAndPermute-2");
        }
      }
    }
  }
 
  // For the remaining GIDs, execute the permutations.  This may
  // involve noncontiguous access of both source and destination
  // vectors, depending on the LID lists.
  //
  // FIXME (mfh 20 June 2012) For an Export with duplicate GIDs on
  // the same process, this merges their values by replacement of
  // the last encountered GID, not by the specified merge rule
  // (such as ADD).
 
  // If there are no permutations, we are done
  if (permuteFromLIDs.extent(0) == 0 ||
      permuteToLIDs.extent(0) == 0) {
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "No permutations. Done!" << endl;
      std::cerr << os.str();
    }
    return;
  }
  ProfilingRegion regionP("Tpetra::MultiVector::permute");
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Permute" << endl;
    std::cerr << os.str();
  }
 
  // We could in theory optimize for the case where exactly one of
  // them is constant stride, but we don't currently do that.
  const bool nonConstStride =
      !this->isConstantStride() || !sourceMV.isConstantStride();
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "nonConstStride="
       << (nonConstStride ? "true" : "false") << endl;
    std::cerr << os.str();
  }
 
  // We only need the "which vectors" arrays if either the source or
  // target MV is not constant stride.  Since we only have one
  // kernel that must do double-duty, we have to create a "which
  // vectors" array for the MV that _is_ constant stride.
  Kokkos::DualView<const size_t*, device_type> srcWhichVecs;
  Kokkos::DualView<const size_t*, device_type> tgtWhichVecs;
  if (nonConstStride) {
    if (this->whichVectors_.size() == 0) {
      Kokkos::DualView<size_t*, device_type> tmpTgt("tgtWhichVecs", numCols);
      tmpTgt.modify_host();
      for (size_t j = 0; j < numCols; ++j) {
        tmpTgt.view_host()(j) = j;
      }
      if (!copyOnHost) {
        tmpTgt.sync_device();
      }
      tgtWhichVecs = tmpTgt;
    } else {
      Teuchos::ArrayView<const size_t> tgtWhichVecsT = this->whichVectors_();
      tgtWhichVecs =
          getDualViewCopyFromArrayView<size_t, device_type>(tgtWhichVecsT,
                                                            "tgtWhichVecs",
                                                            copyOnHost);
    }
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(static_cast<size_t>(tgtWhichVecs.extent(0)) !=
                                              this->getNumVectors(),
                                          std::logic_error, "tgtWhichVecs.extent(0) = " << tgtWhichVecs.extent(0) << " != this->getNumVectors() = " << this->getNumVectors() << ".");
 
    if (sourceMV.whichVectors_.size() == 0) {
      Kokkos::DualView<size_t*, device_type> tmpSrc("srcWhichVecs", numCols);
      tmpSrc.modify_host();
      for (size_t j = 0; j < numCols; ++j) {
        tmpSrc.view_host()(j) = j;
      }
      if (!copyOnHost) {
        tmpSrc.sync_device();
      }
      srcWhichVecs = tmpSrc;
    } else {
      Teuchos::ArrayView<const size_t> srcWhichVecsT =
          sourceMV.whichVectors_();
      srcWhichVecs =
          getDualViewCopyFromArrayView<size_t, device_type>(srcWhichVecsT,
                                                            "srcWhichVecs",
                                                            copyOnHost);
    }
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(static_cast<size_t>(srcWhichVecs.extent(0)) !=
                                              sourceMV.getNumVectors(),
                                          std::logic_error,
                                          "srcWhichVecs.extent(0) = " << srcWhichVecs.extent(0)
                                                                      << " != sourceMV.getNumVectors() = " << sourceMV.getNumVectors()
                                                                      << ".");
  }
 
  if (copyOnHost) {  // permute on host too
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Get permute LIDs on host" << std::endl;
      std::cerr << os.str();
    }
    auto tgt_h = this->getLocalViewHost(Access::ReadWrite);
    auto src_h = sourceMV.getLocalViewHost(Access::ReadOnly);
 
    TEUCHOS_ASSERT(!permuteToLIDs.need_sync_host());
    auto permuteToLIDs_h = create_const_view(permuteToLIDs.view_host());
    TEUCHOS_ASSERT(!permuteFromLIDs.need_sync_host());
    auto permuteFromLIDs_h =
        create_const_view(permuteFromLIDs.view_host());
 
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Permute on host" << endl;
      std::cerr << os.str();
    }
    if (nonConstStride) {
      // No need to sync first, because copyOnHost argument to
      // getDualViewCopyFromArrayView puts them in the right place.
      auto tgtWhichVecs_h =
          create_const_view(tgtWhichVecs.view_host());
      auto srcWhichVecs_h =
          create_const_view(srcWhichVecs.view_host());
      if (CM == ADD_ASSIGN) {
        using op_type = KokkosRefactor::Details::AddOp;
        permute_array_multi_column_variable_stride(tgt_h, src_h,
                                                   permuteToLIDs_h,
                                                   permuteFromLIDs_h,
                                                   tgtWhichVecs_h,
                                                   srcWhichVecs_h, numCols,
                                                   op_type());
      } else {
        using op_type = KokkosRefactor::Details::InsertOp;
        permute_array_multi_column_variable_stride(tgt_h, src_h,
                                                   permuteToLIDs_h,
                                                   permuteFromLIDs_h,
                                                   tgtWhichVecs_h,
                                                   srcWhichVecs_h, numCols,
                                                   op_type());
      }
    } else {
      if (CM == ADD_ASSIGN) {
        using op_type = KokkosRefactor::Details::AddOp;
        permute_array_multi_column(tgt_h, src_h, permuteToLIDs_h,
                                   permuteFromLIDs_h, numCols, op_type());
      } else {
        using op_type = KokkosRefactor::Details::InsertOp;
        permute_array_multi_column(tgt_h, src_h, permuteToLIDs_h,
                                   permuteFromLIDs_h, numCols, op_type());
      }
    }
  } else {  // permute on device
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Get permute LIDs on device" << endl;
      std::cerr << os.str();
    }
    auto tgt_d = this->getLocalViewDevice(Access::ReadWrite);
    auto src_d = sourceMV.getLocalViewDevice(Access::ReadOnly);
 
    TEUCHOS_ASSERT(!permuteToLIDs.need_sync_device());
    auto permuteToLIDs_d = create_const_view(permuteToLIDs.view_device());
    TEUCHOS_ASSERT(!permuteFromLIDs.need_sync_device());
    auto permuteFromLIDs_d =
        create_const_view(permuteFromLIDs.view_device());
 
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Permute on device" << endl;
      std::cerr << os.str();
    }
    if (nonConstStride) {
      // No need to sync first, because copyOnHost argument to
      // getDualViewCopyFromArrayView puts them in the right place.
      auto tgtWhichVecs_d = create_const_view(tgtWhichVecs.view_device());
      auto srcWhichVecs_d = create_const_view(srcWhichVecs.view_device());
      if (CM == ADD_ASSIGN) {
        using op_type = KokkosRefactor::Details::AddOp;
        permute_array_multi_column_variable_stride(space, tgt_d, src_d,
                                                   permuteToLIDs_d,
                                                   permuteFromLIDs_d,
                                                   tgtWhichVecs_d,
                                                   srcWhichVecs_d, numCols,
                                                   op_type());
      } else {
        using op_type = KokkosRefactor::Details::InsertOp;
        permute_array_multi_column_variable_stride(space, tgt_d, src_d,
                                                   permuteToLIDs_d,
                                                   permuteFromLIDs_d,
                                                   tgtWhichVecs_d,
                                                   srcWhichVecs_d, numCols,
                                                   op_type());
      }
    } else {
      if (CM == ADD_ASSIGN) {
        using op_type = KokkosRefactor::Details::AddOp;
        permute_array_multi_column(space, tgt_d, src_d, permuteToLIDs_d,
                                   permuteFromLIDs_d, numCols, op_type());
      } else {
        using op_type = KokkosRefactor::Details::InsertOp;
        permute_array_multi_column(space, tgt_d, src_d, permuteToLIDs_d,
                                   permuteFromLIDs_d, numCols, op_type());
      }
    }
  }
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done!" << endl;
    std::cerr << os.str();
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::copyAndPermute(
    const SrcDistObject& sourceObj, const size_t numSameIDs,
    const Kokkos::DualView<const local_ordinal_type*, buffer_device_type>& permuteToLIDs,
    const Kokkos::DualView<const local_ordinal_type*, buffer_device_type>& permuteFromLIDs,
    const CombineMode CM) {
  copyAndPermute(sourceObj, numSameIDs, permuteToLIDs, permuteFromLIDs, CM,
                 execution_space());
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    packAndPrepare(const SrcDistObject& sourceObj,
                   const Kokkos::DualView<const local_ordinal_type*, buffer_device_type>& exportLIDs,
                   Kokkos::DualView<impl_scalar_type*, buffer_device_type>& exports,
                   Kokkos::DualView<size_t*, buffer_device_type> /* numExportPacketsPerLID */,
                   size_t& constantNumPackets,
                   const execution_space& space) {
  using Kokkos::Compat::create_const_view;
  using Kokkos::Compat::getKokkosViewDeepCopy;
  using std::endl;
  using ::Tpetra::Details::Behavior;
  using ::Tpetra::Details::ProfilingRegion;
  using ::Tpetra::Details::reallocDualViewIfNeeded;
  using MV = MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>;
 
  // We've already called checkSizes(), so this cast must succeed.
  MV& sourceMV = const_cast<MV&>(dynamic_cast<const MV&>(sourceObj));
 
  const bool packOnHost           = runKernelOnHost(sourceMV);
  const char longFuncNameHost[]   = "Tpetra::MultiVector::packAndPrepare[Host]";
  const char longFuncNameDevice[] = "Tpetra::MultiVector::packAndPrepare[Device]";
  const char tfecfFuncName[]      = "packAndPrepare: ";
  ProfilingRegion regionPAP(packOnHost ? longFuncNameHost : longFuncNameDevice);
 
  // mfh 09 Sep 2016, 26 Sep 2017: The pack and unpack functions now
  // have the option to check indices.  We do so when Tpetra is in
  // debug mode.  It is in debug mode by default in a debug build,
  // but you may control this at run time, before launching the
  // executable, by setting the TPETRA_DEBUG environment variable to
  // "1" (or "TRUE").
  const bool debugCheckIndices = Behavior::debug();
  // mfh 03 Aug 2017, 27 Sep 2017: Set the TPETRA_VERBOSE
  // environment variable to "1" (or "TRUE") for copious debug
  // output to std::cerr on every MPI process.  This is unwise for
  // runs with large numbers of MPI processes.
  const bool printDebugOutput = Behavior::verbose();
 
  std::unique_ptr<std::string> prefix;
  if (printDebugOutput) {
    auto map         = this->getMap();
    auto comm        = map.is_null() ? Teuchos::null : map->getComm();
    const int myRank = comm.is_null() ? -1 : comm->getRank();
    std::ostringstream os;
    os << "Proc " << myRank << ": MV::packAndPrepare: ";
    prefix = std::unique_ptr<std::string>(new std::string(os.str()));
    os << "Start" << endl;
    std::cerr << os.str();
  }
 
  const size_t numCols = sourceMV.getNumVectors();
 
  // This spares us from needing to fill numExportPacketsPerLID.
  // Setting constantNumPackets to a nonzero value signals that
  // all packets have the same number of entries.
  constantNumPackets = numCols;
 
  // If we have no exports, there is nothing to do.  Make sure this
  // goes _after_ setting constantNumPackets correctly.
  if (exportLIDs.extent(0) == 0) {
    if (printDebugOutput) {
      std::ostringstream os;
      os << *prefix << "No exports on this proc, DONE" << std::endl;
      std::cerr << os.str();
    }
    return;
  }
 
  /* The layout in the export for MultiVectors is as follows:
     exports = { all of the data from row exportLIDs.front() ;
                 ....
                 all of the data from row exportLIDs.back() }
    This doesn't have the best locality, but is necessary because
    the data for a Packet (all data associated with an LID) is
    required to be contiguous. */
 
  // FIXME (mfh 15 Sep 2013) Would it make sense to rethink the
  // packing scheme in the above comment?  The data going to a
  // particular process must be contiguous, of course, but those
  // data could include entries from multiple LIDs.  DistObject just
  // needs to know how to index into that data.  Kokkos is good at
  // decoupling storage intent from data layout choice.
 
  const size_t numExportLIDs  = exportLIDs.extent(0);
  const size_t newExportsSize = numCols * numExportLIDs;
  if (printDebugOutput) {
    std::ostringstream os;
    os << *prefix << "realloc: "
       << "numExportLIDs: " << numExportLIDs
       << ", exports.extent(0): " << exports.extent(0)
       << ", newExportsSize: " << newExportsSize << std::endl;
    std::cerr << os.str();
  }
  reallocDualViewIfNeeded(exports, newExportsSize, "exports");
 
  // mfh 04 Feb 2019: sourceMV doesn't belong to us, so we can't
  // sync it.  Pack it where it's currently sync'd.
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(sourceMV.need_sync_device() && sourceMV.need_sync_host(),
                                        std::logic_error,
                                        "Input MultiVector needs sync to both host "
                                        "and device.");
  if (printDebugOutput) {
    std::ostringstream os;
    os << *prefix << "packOnHost=" << (packOnHost ? "true" : "false") << endl;
    std::cerr << os.str();
  }
 
  // Mark 'exports' here, since we might have resized it above.
  // Resizing currently requires calling the constructor, which
  // clears out the 'modified' flags.
  if (packOnHost) {
    // nde 06 Feb 2020: If 'exports' does not require resize
    // when reallocDualViewIfNeeded is called, the modified flags
    // are not cleared out. This can result in host and device views
    // being out-of-sync, resuling in an error in exports.modify_* calls.
    // Clearing the sync flags prevents this possible case.
    exports.clear_sync_state();
    exports.modify_host();
  } else {
    // nde 06 Feb 2020: If 'exports' does not require resize
    // when reallocDualViewIfNeeded is called, the modified flags
    // are not cleared out. This can result in host and device views
    // being out-of-sync, resuling in an error in exports.modify_* calls.
    // Clearing the sync flags prevents this possible case.
    exports.clear_sync_state();
    exports.modify_device();
  }
 
  if (numCols == 1) {  // special case for one column only
    // MultiVector always represents a single column with constant
    // stride, but it doesn't hurt to implement both cases anyway.
    //
    // ETP:  I'm not sure I agree with the above statement.  Can't a single-
    // column multivector be a subview of another multi-vector, in which case
    // sourceMV.whichVectors_[0] != 0 ?  I think we have to handle that case
    // separately.
    //
    // mfh 18 Jan 2016: In answer to ETP's comment above:
    // MultiVector treats single-column MultiVectors created using a
    // "nonconstant stride constructor" as a special case, and makes
    // them constant stride (by making whichVectors_ have length 0).
    if (sourceMV.isConstantStride()) {
      using KokkosRefactor::Details::pack_array_single_column;
      if (printDebugOutput) {
        std::ostringstream os;
        os << *prefix << "Pack numCols=1 const stride" << endl;
        std::cerr << os.str();
      }
      if (packOnHost) {
        auto src_host = sourceMV.getLocalViewHost(Access::ReadOnly);
        pack_array_single_column(exports.view_host(),
                                 src_host,
                                 exportLIDs.view_host(),
                                 0,
                                 debugCheckIndices);
      } else {  // pack on device
        auto src_dev = sourceMV.getLocalViewDevice(Access::ReadOnly);
        pack_array_single_column(exports.view_device(),
                                 src_dev,
                                 exportLIDs.view_device(),
                                 0,
                                 debugCheckIndices,
                                 space);
      }
    } else {
      using KokkosRefactor::Details::pack_array_single_column;
      if (printDebugOutput) {
        std::ostringstream os;
        os << *prefix << "Pack numCols=1 nonconst stride" << endl;
        std::cerr << os.str();
      }
      if (packOnHost) {
        auto src_host = sourceMV.getLocalViewHost(Access::ReadOnly);
        pack_array_single_column(exports.view_host(),
                                 src_host,
                                 exportLIDs.view_host(),
                                 sourceMV.whichVectors_[0],
                                 debugCheckIndices);
      } else {  // pack on device
        auto src_dev = sourceMV.getLocalViewDevice(Access::ReadOnly);
        pack_array_single_column(exports.view_device(),
                                 src_dev,
                                 exportLIDs.view_device(),
                                 sourceMV.whichVectors_[0],
                                 debugCheckIndices,
                                 space);
      }
    }
  } else {  // the source MultiVector has multiple columns
    if (sourceMV.isConstantStride()) {
      using KokkosRefactor::Details::pack_array_multi_column;
      if (printDebugOutput) {
        std::ostringstream os;
        os << *prefix << "Pack numCols=" << numCols << " const stride" << endl;
        std::cerr << os.str();
      }
      if (packOnHost) {
        auto src_host = sourceMV.getLocalViewHost(Access::ReadOnly);
        pack_array_multi_column(exports.view_host(),
                                src_host,
                                exportLIDs.view_host(),
                                numCols,
                                debugCheckIndices);
      } else {  // pack on device
        auto src_dev = sourceMV.getLocalViewDevice(Access::ReadOnly);
        pack_array_multi_column(exports.view_device(),
                                src_dev,
                                exportLIDs.view_device(),
                                numCols,
                                debugCheckIndices,
                                space);
      }
    } else {
      using KokkosRefactor::Details::pack_array_multi_column_variable_stride;
      if (printDebugOutput) {
        std::ostringstream os;
        os << *prefix << "Pack numCols=" << numCols << " nonconst stride"
           << endl;
        std::cerr << os.str();
      }
      // FIXME (mfh 04 Feb 2019) Creating a Kokkos::View for
      // whichVectors_ can be expensive, but pack and unpack for
      // nonconstant-stride MultiVectors is slower anyway.
      using IST                                  = impl_scalar_type;
      using DV                                   = Kokkos::DualView<IST*, device_type>;
      using HES                                  = typename DV::t_host::execution_space;
      using DES                                  = typename DV::t_dev::execution_space;
      Teuchos::ArrayView<const size_t> whichVecs = sourceMV.whichVectors_();
      if (packOnHost) {
        auto src_host = sourceMV.getLocalViewHost(Access::ReadOnly);
        pack_array_multi_column_variable_stride(exports.view_host(),
                                                src_host,
                                                exportLIDs.view_host(),
                                                getKokkosViewDeepCopy<HES>(whichVecs),
                                                numCols,
                                                debugCheckIndices);
      } else {  // pack on device
        auto src_dev = sourceMV.getLocalViewDevice(Access::ReadOnly);
        pack_array_multi_column_variable_stride(exports.view_device(),
                                                src_dev,
                                                exportLIDs.view_device(),
                                                getKokkosViewDeepCopy<DES>(whichVecs),
                                                numCols,
                                                debugCheckIndices, space);
      }
    }
  }
 
  if (printDebugOutput) {
    std::ostringstream os;
    os << *prefix << "Done!" << endl;
    std::cerr << os.str();
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    packAndPrepare(const SrcDistObject& sourceObj,
                   const Kokkos::DualView<const local_ordinal_type*, buffer_device_type>& exportLIDs,
                   Kokkos::DualView<impl_scalar_type*, buffer_device_type>& exports,
                   Kokkos::DualView<size_t*, buffer_device_type> numExportPacketsPerLID,
                   size_t& constantNumPackets) {
  packAndPrepare(sourceObj, exportLIDs, exports, numExportPacketsPerLID, constantNumPackets, execution_space());
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
template <class NO>
typename std::enable_if<std::is_same<typename Tpetra::Details::DefaultTypes::CommBufferMemorySpace<typename NO::execution_space>::type,
                                     typename NO::device_type::memory_space>::value,
                        bool>::type
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    reallocImportsIfNeededImpl(const size_t newSize,
                               const bool verbose,
                               const std::string* prefix,
                               const bool areRemoteLIDsContiguous,
                               const CombineMode CM) {
  // This implementation of reallocImportsIfNeeded is an
  // optimization that is specific to MultiVector. We check if the
  // imports_ view can be aliased to the end of the data view_. If
  // that is the case, we can skip the unpackAndCombine call.
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Realloc (if needed) imports_ from "
       << this->imports_.extent(0) << " to " << newSize << std::endl;
    std::cerr << os.str();
  }
 
  bool reallocated = false;
 
  using IST = impl_scalar_type;
  using DV  = Kokkos::DualView<IST*, Kokkos::LayoutLeft, buffer_device_type>;
 
  // Conditions for aliasing memory:
  // - When both sides of the dual view are in the same memory
  //   space, we do not need to worry about syncing things.
  // - When both memory spaces are different, we only alias if this
  //   does not incur additional sync'ing.
  // - The remote LIDs need to be contiguous, so that we do not need
  //   to reorder received information.
  // - CombineMode needs to be INSERT.
  // - The number of vectors needs to be 1, otherwise we need to
  //   reorder the received data.
  if ((std::is_same_v<typename dual_view_type::t_dev::device_type, typename dual_view_type::t_host::device_type> ||
       (Details::Behavior::assumeMpiIsGPUAware() && !this->need_sync_device()) ||
       (!Details::Behavior::assumeMpiIsGPUAware() && !this->need_sync_host())) &&
      areRemoteLIDsContiguous &&
      (CM == INSERT || CM == REPLACE) &&
      (getNumVectors() == 1) &&
      (newSize > 0)) {
    size_t offset = getLocalLength() - newSize;
    reallocated   = this->imports_.view_device().data() != view_.getDualView().view_device().data() + offset;
    if (reallocated) {
      typedef std::pair<size_t, size_t> range_type;
      this->imports_ = DV(view_.getDualView(),
                          range_type(offset, getLocalLength()),
                          0);
 
      if (verbose) {
        std::ostringstream os;
        os << *prefix << "Aliased imports_ to MV.view_" << std::endl;
        std::cerr << os.str();
      }
    }
    return reallocated;
  }
  {
    using ::Tpetra::Details::reallocDualViewIfNeeded;
    reallocated =
        reallocDualViewIfNeeded(this->unaliased_imports_, newSize, "imports");
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Finished realloc'ing unaliased_imports_" << std::endl;
      std::cerr << os.str();
    }
    this->imports_ = this->unaliased_imports_;
  }
  return reallocated;
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
template <class NO>
typename std::enable_if<!std::is_same<typename Tpetra::Details::DefaultTypes::CommBufferMemorySpace<typename NO::execution_space>::type,
                                      typename NO::device_type::memory_space>::value,
                        bool>::type
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    reallocImportsIfNeededImpl(const size_t newSize,
                               const bool verbose,
                               const std::string* prefix,
                               const bool areRemoteLIDsContiguous,
                               const CombineMode CM) {
  return DistObject<Scalar, LocalOrdinal, GlobalOrdinal, Node>::reallocImportsIfNeeded(newSize, verbose, prefix, areRemoteLIDsContiguous, CM);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
bool MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    reallocImportsIfNeeded(const size_t newSize,
                           const bool verbose,
                           const std::string* prefix,
                           const bool areRemoteLIDsContiguous,
                           const CombineMode CM) {
  return reallocImportsIfNeededImpl<Node>(newSize, verbose, prefix, areRemoteLIDsContiguous, CM);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
bool MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    importsAreAliased() {
  return (this->imports_.view_device().data() + this->imports_.view_device().extent(0) ==
          view_.getDualView().view_device().data() + view_.getDualView().view_device().extent(0));
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    unpackAndCombine(const Kokkos::DualView<const local_ordinal_type*, buffer_device_type>& importLIDs,
                     Kokkos::DualView<impl_scalar_type*, buffer_device_type> imports,
                     Kokkos::DualView<size_t*, buffer_device_type> /* numPacketsPerLID */,
                     const size_t constantNumPackets,
                     const CombineMode CM,
                     const execution_space& space) {
  using Kokkos::Compat::getKokkosViewDeepCopy;
  using KokkosRefactor::Details::unpack_array_multi_column;
  using KokkosRefactor::Details::unpack_array_multi_column_variable_stride;
  using std::endl;
  using ::Tpetra::Details::Behavior;
  using ::Tpetra::Details::ProfilingRegion;
 
  const bool unpackOnHost = runKernelOnHost(imports);
 
  const char longFuncNameHost[]   = "Tpetra::MultiVector::unpackAndCombine[Host]";
  const char longFuncNameDevice[] = "Tpetra::MultiVector::unpackAndCombine[Device]";
  const char* longFuncName        = unpackOnHost ? longFuncNameHost : longFuncNameDevice;
  const char tfecfFuncName[]      = "unpackAndCombine: ";
 
  // mfh 09 Sep 2016, 26 Sep 2017: The pack and unpack functions now
  // have the option to check indices.  We do so when Tpetra is in
  // debug mode.  It is in debug mode by default in a debug build,
  // but you may control this at run time, before launching the
  // executable, by setting the TPETRA_DEBUG environment variable to
  // "1" (or "TRUE").
  const bool debugCheckIndices = Behavior::debug();
 
  const bool printDebugOutput = Behavior::verbose();
  std::unique_ptr<std::string> prefix;
  if (printDebugOutput) {
    auto map         = this->getMap();
    auto comm        = map.is_null() ? Teuchos::null : map->getComm();
    const int myRank = comm.is_null() ? -1 : comm->getRank();
    std::ostringstream os;
    os << "Proc " << myRank << ": " << longFuncName << ": ";
    prefix = std::unique_ptr<std::string>(new std::string(os.str()));
    os << "Start" << endl;
    std::cerr << os.str();
  }
 
  // If we have no imports, there is nothing to do
  if (importLIDs.extent(0) == 0) {
    if (printDebugOutput) {
      std::ostringstream os;
      os << *prefix << "No imports. Done!" << endl;
      std::cerr << os.str();
    }
    return;
  }
 
  // Check, whether imports_ is a subview of the MV view.
  if (importsAreAliased()) {
    if (printDebugOutput) {
      std::ostringstream os;
      os << *prefix << "Skipping unpack, since imports_ is aliased to MV.view_. Done!" << endl;
      std::cerr << os.str();
    }
    return;
  }
 
  ProfilingRegion regionUAC(longFuncName);
 
  const size_t numVecs = getNumVectors();
  if (debugCheckIndices) {
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(static_cast<size_t>(imports.extent(0)) !=
                                              numVecs * importLIDs.extent(0),
                                          std::runtime_error,
                                          "imports.extent(0) = " << imports.extent(0)
                                                                 << " != getNumVectors() * importLIDs.extent(0) = " << numVecs
                                                                 << " * " << importLIDs.extent(0) << " = "
                                                                 << numVecs * importLIDs.extent(0) << ".");
 
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(constantNumPackets == static_cast<size_t>(0), std::runtime_error,
                                          "constantNumPackets input argument must be nonzero.");
 
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(static_cast<size_t>(numVecs) !=
                                              static_cast<size_t>(constantNumPackets),
                                          std::runtime_error, "constantNumPackets must equal numVecs.");
  }
 
  // mfh 12 Apr 2016, 04 Feb 2019: Decide where to unpack based on
  // the memory space in which the imports buffer was last modified and
  // the size of the imports buffer.
  // DistObject::doTransferNew decides where it was last modified (based on
  // whether communication buffers used were on host or device).
  if (unpackOnHost) {
    if (this->imports_.need_sync_host()) this->imports_.sync_host();
  } else {
    if (this->imports_.need_sync_device()) this->imports_.sync_device();
  }
 
  if (printDebugOutput) {
    std::ostringstream os;
    os << *prefix << "unpackOnHost=" << (unpackOnHost ? "true" : "false")
       << endl;
    std::cerr << os.str();
  }
 
  // We have to sync before modifying, because this method may read
  // as well as write (depending on the CombineMode).
  auto imports_d    = imports.view_device();
  auto imports_h    = imports.view_host();
  auto importLIDs_d = importLIDs.view_device();
  auto importLIDs_h = importLIDs.view_host();
 
  Kokkos::DualView<size_t*, device_type> whichVecs;
  if (!isConstantStride()) {
    Kokkos::View<const size_t*, Kokkos::HostSpace,
                 Kokkos::MemoryUnmanaged>
        whichVecsIn(whichVectors_.getRawPtr(),
                    numVecs);
    whichVecs = Kokkos::DualView<size_t*, device_type>("whichVecs", numVecs);
    if (unpackOnHost) {
      whichVecs.modify_host();
      // DEEP_COPY REVIEW - NOT TESTED FOR CUDA BUILD
      Kokkos::deep_copy(whichVecs.view_host(), whichVecsIn);
    } else {
      whichVecs.modify_device();
      // DEEP_COPY REVIEW - HOST-TO-DEVICE
      Kokkos::deep_copy(whichVecs.view_device(), whichVecsIn);
    }
  }
  auto whichVecs_d = whichVecs.view_device();
  auto whichVecs_h = whichVecs.view_host();
 
  /* The layout in the export for MultiVectors is as follows:
     imports = { all of the data from row exportLIDs.front() ;
                 ....
                 all of the data from row exportLIDs.back() }
    This doesn't have the best locality, but is necessary because
    the data for a Packet (all data associated with an LID) is
    required to be contiguous. */
 
  if (numVecs > 0 && importLIDs.extent(0) > 0) {
    using dev_exec_space  = typename dual_view_type::t_dev::execution_space;
    using host_exec_space = typename dual_view_type::t_host::execution_space;
 
    // This fixes GitHub Issue #4418.
    const bool use_atomic_updates = unpackOnHost ? host_exec_space().concurrency() != 1 : dev_exec_space().concurrency() != 1;
 
    if (printDebugOutput) {
      std::ostringstream os;
      os << *prefix << "Unpack: " << combineModeToString(CM) << endl;
      std::cerr << os.str();
    }
 
    // NOTE (mfh 10 Mar 2012, 24 Mar 2014) If you want to implement
    // custom combine modes, start editing here.
 
    if (CM == INSERT || CM == REPLACE) {
      using op_type = KokkosRefactor::Details::InsertOp;
      if (isConstantStride()) {
        if (unpackOnHost) {
          auto X_h = this->getLocalViewHost(Access::ReadWrite);
          unpack_array_multi_column(host_exec_space(),
                                    X_h, imports_h, importLIDs_h,
                                    op_type(), numVecs,
                                    use_atomic_updates,
                                    debugCheckIndices);
 
        } else {  // unpack on device
          auto X_d = this->getLocalViewDevice(Access::ReadWrite);
          unpack_array_multi_column(space,
                                    X_d, imports_d, importLIDs_d,
                                    op_type(), numVecs,
                                    use_atomic_updates,
                                    debugCheckIndices);
        }
      } else {  // not constant stride
        if (unpackOnHost) {
          auto X_h = this->getLocalViewHost(Access::ReadWrite);
          unpack_array_multi_column_variable_stride(host_exec_space(),
                                                    X_h, imports_h,
                                                    importLIDs_h,
                                                    whichVecs_h,
                                                    op_type(),
                                                    numVecs,
                                                    use_atomic_updates,
                                                    debugCheckIndices);
        } else {  // unpack on device
          auto X_d = this->getLocalViewDevice(Access::ReadWrite);
          unpack_array_multi_column_variable_stride(space,
                                                    X_d, imports_d,
                                                    importLIDs_d,
                                                    whichVecs_d,
                                                    op_type(),
                                                    numVecs,
                                                    use_atomic_updates,
                                                    debugCheckIndices);
        }
      }
    } else if (CM == ADD || CM == ADD_ASSIGN) {
      using op_type = KokkosRefactor::Details::AddOp;
      if (isConstantStride()) {
        if (unpackOnHost) {
          auto X_h = this->getLocalViewHost(Access::ReadWrite);
          unpack_array_multi_column(host_exec_space(),
                                    X_h, imports_h, importLIDs_h,
                                    op_type(), numVecs,
                                    use_atomic_updates,
                                    debugCheckIndices);
        } else {  // unpack on device
          auto X_d = this->getLocalViewDevice(Access::ReadWrite);
          unpack_array_multi_column(space,
                                    X_d, imports_d, importLIDs_d,
                                    op_type(), numVecs,
                                    use_atomic_updates,
                                    debugCheckIndices);
        }
      } else {  // not constant stride
        if (unpackOnHost) {
          auto X_h = this->getLocalViewHost(Access::ReadWrite);
          unpack_array_multi_column_variable_stride(host_exec_space(),
                                                    X_h, imports_h,
                                                    importLIDs_h,
                                                    whichVecs_h,
                                                    op_type(),
                                                    numVecs,
                                                    use_atomic_updates,
                                                    debugCheckIndices);
        } else {  // unpack on device
          auto X_d = this->getLocalViewDevice(Access::ReadWrite);
          unpack_array_multi_column_variable_stride(space,
                                                    X_d, imports_d,
                                                    importLIDs_d,
                                                    whichVecs_d,
                                                    op_type(),
                                                    numVecs,
                                                    use_atomic_updates,
                                                    debugCheckIndices);
        }
      }
    } else if (CM == ABSMAX) {
      using op_type = KokkosRefactor::Details::AbsMaxOp;
      if (isConstantStride()) {
        if (unpackOnHost) {
          auto X_h = this->getLocalViewHost(Access::ReadWrite);
          unpack_array_multi_column(host_exec_space(),
                                    X_h, imports_h, importLIDs_h,
                                    op_type(), numVecs,
                                    use_atomic_updates,
                                    debugCheckIndices);
        } else {  // unpack on device
          auto X_d = this->getLocalViewDevice(Access::ReadWrite);
          unpack_array_multi_column(space,
                                    X_d, imports_d, importLIDs_d,
                                    op_type(), numVecs,
                                    use_atomic_updates,
                                    debugCheckIndices);
        }
      } else {
        if (unpackOnHost) {
          auto X_h = this->getLocalViewHost(Access::ReadWrite);
          unpack_array_multi_column_variable_stride(host_exec_space(),
                                                    X_h, imports_h,
                                                    importLIDs_h,
                                                    whichVecs_h,
                                                    op_type(),
                                                    numVecs,
                                                    use_atomic_updates,
                                                    debugCheckIndices);
        } else {  // unpack on device
          auto X_d = this->getLocalViewDevice(Access::ReadWrite);
          unpack_array_multi_column_variable_stride(space,
                                                    X_d, imports_d,
                                                    importLIDs_d,
                                                    whichVecs_d,
                                                    op_type(),
                                                    numVecs,
                                                    use_atomic_updates,
                                                    debugCheckIndices);
        }
      }
    } else {
      TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(true, std::logic_error, "Invalid CombineMode");
    }
  } else {
    if (printDebugOutput) {
      std::ostringstream os;
      os << *prefix << "Nothing to unpack" << endl;
      std::cerr << os.str();
    }
  }
 
  if (printDebugOutput) {
    std::ostringstream os;
    os << *prefix << "Done!" << endl;
    std::cerr << os.str();
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    unpackAndCombine(const Kokkos::DualView<const local_ordinal_type*, buffer_device_type>& importLIDs,
                     Kokkos::DualView<impl_scalar_type*, buffer_device_type> imports,
                     Kokkos::DualView<size_t*, buffer_device_type> numPacketsPerLID,
                     const size_t constantNumPackets,
                     const CombineMode CM) {
  unpackAndCombine(importLIDs, imports, numPacketsPerLID, constantNumPackets, CM, execution_space());
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
size_t
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getNumVectors() const {
  if (isConstantStride()) {
    return static_cast<size_t>(view_.extent(1));
  } else {
    return static_cast<size_t>(whichVectors_.size());
  }
}
 
namespace {  // (anonymous)
 
template <class RV>
void gblDotImpl(const RV& dotsOut,
                const Teuchos::RCP<const Teuchos::Comm<int> >& comm,
                const bool distributed) {
  using Teuchos::REDUCE_MAX;
  using Teuchos::REDUCE_SUM;
  using Teuchos::reduceAll;
  typedef typename RV::non_const_value_type dot_type;
 
  const size_t numVecs = dotsOut.extent(0);
 
  // If the MultiVector is distributed over multiple processes, do
  // the distributed (interprocess) part of the dot product.  We
  // assume that the MPI implementation can read from and write to
  // device memory.
  //
  // replaceMap() may have removed some processes.  Those
  // processes have a null Map.  They must not participate in any
  // collective operations.  We ask first whether the Map is null,
  // because isDistributed() defers that question to the Map.  We
  // still compute and return local dots for processes not
  // participating in collective operations; those probably don't
  // make any sense, but it doesn't hurt to do them, since it's
  // illegal to call dot() on those processes anyway.
  if (distributed && !comm.is_null()) {
    // The calling process only participates in the collective if
    // both the Map and its Comm on that process are nonnull.
    const int nv               = static_cast<int>(numVecs);
    const bool commIsInterComm = ::Tpetra::Details::isInterComm(*comm);
 
    if (commIsInterComm) {
      // If comm is an intercomm, then we may not alias input and
      // output buffers, so we have to make a copy of the local
      // sum.
      typename RV::non_const_type lclDots(Kokkos::ViewAllocateWithoutInitializing("tmp"), numVecs);
      // DEEP_COPY REVIEW - NOT TESTED
      Kokkos::deep_copy(lclDots, dotsOut);
      const dot_type* const lclSum = lclDots.data();
      dot_type* const gblSum       = dotsOut.data();
      reduceAll<int, dot_type>(*comm, REDUCE_SUM, nv, lclSum, gblSum);
    } else {
      dot_type* const inout = dotsOut.data();
      reduceAll<int, dot_type>(*comm, REDUCE_SUM, nv, inout, inout);
    }
  }
}
}  // namespace
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    dot(const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& A,
        const Kokkos::View<dot_type*, Kokkos::HostSpace>& dots) const {
  using Kokkos::subview;
  using Teuchos::Comm;
  using Teuchos::null;
  using Teuchos::RCP;
  using ::Tpetra::Details::Behavior;
  // View of all the dot product results.
  typedef Kokkos::View<dot_type*, Kokkos::HostSpace> RV;
  typedef typename dual_view_type::t_dev_const XMV;
  const char tfecfFuncName[] = "Tpetra::MultiVector::dot: ";
 
  ::Tpetra::Details::ProfilingRegion region("Tpetra::MV::dot (Kokkos::View)");
 
  const size_t numVecs = this->getNumVectors();
  if (numVecs == 0) {
    return;  // nothing to do
  }
  const size_t lclNumRows = this->getLocalLength();
  const size_t numDots    = static_cast<size_t>(dots.extent(0));
  const bool debug        = Behavior::debug();
 
  if (debug) {
    const bool compat = this->getMap()->isCompatible(*(A.getMap()));
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(!compat, std::invalid_argument,
                                          "'*this' MultiVector is not "
                                          "compatible with the input MultiVector A.  We only test for this "
                                          "in debug mode.");
  }
 
  // FIXME (mfh 11 Jul 2014) These exception tests may not
  // necessarily be thrown on all processes consistently.  We should
  // instead pass along error state with the inner product.  We
  // could do this by setting an extra slot to
  // Kokkos::ArithTraits<dot_type>::one() on error.  The
  // final sum should be
  // Kokkos::ArithTraits<dot_type>::zero() if not error.
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      lclNumRows != A.getLocalLength(), std::runtime_error,
      "MultiVectors do not have the same local length.  "
      "this->getLocalLength() = "
          << lclNumRows << " != "
                           "A.getLocalLength() = "
          << A.getLocalLength() << ".");
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      numVecs != A.getNumVectors(), std::runtime_error,
      "MultiVectors must have the same number of columns (vectors).  "
      "this->getNumVectors() = "
          << numVecs << " != "
                        "A.getNumVectors() = "
          << A.getNumVectors() << ".");
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      numDots != numVecs, std::runtime_error,
      "The output array 'dots' must have the same number of entries as the "
      "number of columns (vectors) in *this and A.  dots.extent(0) = "
          << numDots << " != this->getNumVectors() = " << numVecs << ".");
 
  const std::pair<size_t, size_t> colRng(0, numVecs);
  RV dotsOut                 = subview(dots, colRng);
  RCP<const Comm<int> > comm = this->getMap().is_null() ? null : this->getMap()->getComm();
 
  auto thisView = this->getLocalViewDevice(Access::ReadOnly);
  auto A_view   = A.getLocalViewDevice(Access::ReadOnly);
 
  ::Tpetra::Details::lclDot<RV, XMV>(dotsOut, thisView, A_view, lclNumRows, numVecs,
                                     this->whichVectors_.getRawPtr(),
                                     A.whichVectors_.getRawPtr(),
                                     this->isConstantStride(), A.isConstantStride());
 
  // lbv 15 mar 2023: Kokkos Kernels provides non-blocking BLAS
  // functions unless they explicitely return a value to Host.
  // Here while the lclDot are on host, they are not a return
  // value, therefore they might be avaible to us immediately.
  // Adding a frnce here guarantees that we will have the lclDot
  // ahead of the MPI reduction.
  execution_space exec_space_instance = execution_space();
  exec_space_instance.fence("Tpetra::MultiVector::dot");
 
  gblDotImpl(dotsOut, comm, this->isDistributed());
}
 
namespace {  // (anonymous)
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
typename MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::dot_type
multiVectorSingleColumnDot(const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& x,
                           const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& y) {
  using ::Tpetra::Details::ProfilingRegion;
  using MV       = ::Tpetra::MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>;
  using dot_type = typename MV::dot_type;
  ProfilingRegion region("Tpetra::multiVectorSingleColumnDot");
 
  auto map = x.getMap();
  Teuchos::RCP<const Teuchos::Comm<int> > comm =
      map.is_null() ? Teuchos::null : map->getComm();
  if (comm.is_null()) {
#if KOKKOS_VERSION >= 40799
    return KokkosKernels::ArithTraits<dot_type>::zero();
#else
    return Kokkos::ArithTraits<dot_type>::zero();
#endif
  } else {
    using LO = LocalOrdinal;
    // The min just ensures that we don't overwrite memory that
    // doesn't belong to us, in the erroneous input case where x
    // and y have different numbers of rows.
    const LO lclNumRows = static_cast<LO>(std::min(x.getLocalLength(),
                                                   y.getLocalLength()));
    const Kokkos::pair<LO, LO> rowRng(0, lclNumRows);
#if KOKKOS_VERSION >= 40799
    dot_type lclDot = KokkosKernels::ArithTraits<dot_type>::zero();
#else
    dot_type lclDot = Kokkos::ArithTraits<dot_type>::zero();
#endif
#if KOKKOS_VERSION >= 40799
    dot_type gblDot = KokkosKernels::ArithTraits<dot_type>::zero();
#else
    dot_type gblDot = Kokkos::ArithTraits<dot_type>::zero();
#endif
 
    // All non-unary kernels are executed on the device as per Tpetra policy.  Sync to device if needed.
    // const_cast<MV&>(x).sync_device ();
    // const_cast<MV&>(y).sync_device ();
 
    auto x_2d = x.getLocalViewDevice(Access::ReadOnly);
    auto x_1d = Kokkos::subview(x_2d, rowRng, 0);
    auto y_2d = y.getLocalViewDevice(Access::ReadOnly);
    auto y_1d = Kokkos::subview(y_2d, rowRng, 0);
    lclDot    = KokkosBlas::dot(x_1d, y_1d);
 
    if (x.isDistributed()) {
      using Teuchos::outArg;
      using Teuchos::REDUCE_SUM;
      using Teuchos::reduceAll;
      reduceAll<int, dot_type>(*comm, REDUCE_SUM, lclDot, outArg(gblDot));
    } else {
      gblDot = lclDot;
    }
    return gblDot;
  }
}
}  // namespace
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    dot(const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& A,
        const Teuchos::ArrayView<dot_type>& dots) const {
  const char tfecfFuncName[] = "dot: ";
  ::Tpetra::Details::ProfilingRegion region("Tpetra::MV::dot (Teuchos::ArrayView)");
 
  const size_t numVecs    = this->getNumVectors();
  const size_t lclNumRows = this->getLocalLength();
  const size_t numDots    = static_cast<size_t>(dots.size());
 
  // FIXME (mfh 11 Jul 2014, 31 May 2017) These exception tests may
  // not necessarily be thrown on all processes consistently.  We
  // keep them for now, because MultiVector's unit tests insist on
  // them.  In the future, we should instead pass along error state
  // with the inner product.  We could do this by setting an extra
  // slot to Kokkos::ArithTraits<dot_type>::one() on error.
  // The final sum should be
  // Kokkos::ArithTraits<dot_type>::zero() if not error.
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(lclNumRows != A.getLocalLength(), std::runtime_error,
                                        "MultiVectors do not have the same local length.  "
                                        "this->getLocalLength() = "
                                            << lclNumRows << " != "
                                                             "A.getLocalLength() = "
                                            << A.getLocalLength() << ".");
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(numVecs != A.getNumVectors(), std::runtime_error,
                                        "MultiVectors must have the same number of columns (vectors).  "
                                        "this->getNumVectors() = "
                                            << numVecs << " != "
                                                          "A.getNumVectors() = "
                                            << A.getNumVectors() << ".");
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(numDots != numVecs, std::runtime_error,
                                        "The output array 'dots' must have the same number of entries as the "
                                        "number of columns (vectors) in *this and A.  dots.extent(0) = "
                                            << numDots << " != this->getNumVectors() = " << numVecs << ".");
 
  if (numVecs == 1 && this->isConstantStride() && A.isConstantStride()) {
    const dot_type gblDot = multiVectorSingleColumnDot(*this, A);
    dots[0]               = gblDot;
  } else {
    this->dot(A, Kokkos::View<dot_type*, Kokkos::HostSpace>(dots.getRawPtr(), numDots));
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    norm2(const Teuchos::ArrayView<mag_type>& norms) const {
  using MV = MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>;
  using ::Tpetra::Details::NORM_TWO;
  using ::Tpetra::Details::ProfilingRegion;
  ProfilingRegion region("Tpetra::MV::norm2 (host output)");
 
  // The function needs to be able to sync X.
  MV& X = const_cast<MV&>(*this);
  multiVectorNormImpl(norms.getRawPtr(), X, NORM_TWO);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    norm2(const Kokkos::View<mag_type*, Kokkos::HostSpace>& norms) const {
  Teuchos::ArrayView<mag_type> norms_av(norms.data(), norms.extent(0));
  this->norm2(norms_av);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    norm1(const Teuchos::ArrayView<mag_type>& norms) const {
  using MV = MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>;
  using ::Tpetra::Details::NORM_ONE;
  using ::Tpetra::Details::ProfilingRegion;
  ProfilingRegion region("Tpetra::MV::norm1 (host output)");
 
  // The function needs to be able to sync X.
  MV& X = const_cast<MV&>(*this);
  multiVectorNormImpl(norms.data(), X, NORM_ONE);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    norm1(const Kokkos::View<mag_type*, Kokkos::HostSpace>& norms) const {
  Teuchos::ArrayView<mag_type> norms_av(norms.data(), norms.extent(0));
  this->norm1(norms_av);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    normInf(const Teuchos::ArrayView<mag_type>& norms) const {
  using MV = MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>;
  using ::Tpetra::Details::NORM_INF;
  using ::Tpetra::Details::ProfilingRegion;
  ProfilingRegion region("Tpetra::MV::normInf (host output)");
 
  // The function needs to be able to sync X.
  MV& X = const_cast<MV&>(*this);
  multiVectorNormImpl(norms.getRawPtr(), X, NORM_INF);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    normInf(const Kokkos::View<mag_type*, Kokkos::HostSpace>& norms) const {
  Teuchos::ArrayView<mag_type> norms_av(norms.data(), norms.extent(0));
  this->normInf(norms_av);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    meanValue(const Teuchos::ArrayView<impl_scalar_type>& means) const {
  // KR FIXME Overload this method to take a View.
  using Kokkos::ALL;
  using Kokkos::subview;
  using Teuchos::Comm;
  using Teuchos::RCP;
  using Teuchos::REDUCE_SUM;
  using Teuchos::reduceAll;
#if KOKKOS_VERSION >= 40799
  typedef KokkosKernels::ArithTraits<impl_scalar_type> ATS;
#else
  typedef Kokkos::ArithTraits<impl_scalar_type> ATS;
#endif
 
  const size_t lclNumRows = this->getLocalLength();
  const size_t numVecs    = this->getNumVectors();
  const size_t numMeans   = static_cast<size_t>(means.size());
 
  TEUCHOS_TEST_FOR_EXCEPTION(
      numMeans != numVecs, std::runtime_error,
      "Tpetra::MultiVector::meanValue: means.size() = " << numMeans
                                                        << " != this->getNumVectors() = " << numVecs << ".");
 
  const std::pair<size_t, size_t> rowRng(0, lclNumRows);
  const std::pair<size_t, size_t> colRng(0, numVecs);
 
  // Make sure that the final output view has the same layout as the
  // temporary view's host_mirror_type.  Left or Right doesn't matter for
  // a 1-D array anyway; this is just to placate the compiler.
  typedef Kokkos::View<impl_scalar_type*, device_type> local_view_type;
  typedef Kokkos::View<impl_scalar_type*,
                       typename local_view_type::host_mirror_type::array_layout,
                       Kokkos::HostSpace,
                       Kokkos::MemoryTraits<Kokkos::Unmanaged> >
      host_local_view_type;
  host_local_view_type meansOut(means.getRawPtr(), numMeans);
 
  RCP<const Comm<int> > comm = this->getMap().is_null() ? Teuchos::null : this->getMap()->getComm();
 
  // If we need sync to device, then host has the most recent version.
  const bool useHostVersion = this->need_sync_device();
  if (useHostVersion) {
    // DualView was last modified on host, so run the local kernel there.
    auto X_lcl = subview(getLocalViewHost(Access::ReadOnly),
                         rowRng, Kokkos::ALL());
    // Compute the local sum of each column.
    Kokkos::View<impl_scalar_type*, Kokkos::HostSpace> lclSums("MV::meanValue tmp", numVecs);
    if (isConstantStride()) {
      KokkosBlas::sum(lclSums, X_lcl);
    } else {
      for (size_t j = 0; j < numVecs; ++j) {
        const size_t col = whichVectors_[j];
        KokkosBlas::sum(subview(lclSums, j), subview(X_lcl, ALL(), col));
      }
    }
 
    // If there are multiple MPI processes, the all-reduce reads
    // from lclSums, and writes to meansOut.  Otherwise, we just
    // copy lclSums into meansOut.
    if (!comm.is_null() && this->isDistributed()) {
      reduceAll(*comm, REDUCE_SUM, static_cast<int>(numVecs),
                lclSums.data(), meansOut.data());
    } else {
      // DEEP_COPY REVIEW - NOT TESTED
      Kokkos::deep_copy(meansOut, lclSums);
    }
  } else {
    // DualView was last modified on device, so run the local kernel there.
    auto X_lcl = subview(this->getLocalViewDevice(Access::ReadOnly),
                         rowRng, Kokkos::ALL());
 
    // Compute the local sum of each column.
    Kokkos::View<impl_scalar_type*, Kokkos::HostSpace> lclSums("MV::meanValue tmp", numVecs);
    if (isConstantStride()) {
      KokkosBlas::sum(lclSums, X_lcl);
    } else {
      for (size_t j = 0; j < numVecs; ++j) {
        const size_t col = whichVectors_[j];
        KokkosBlas::sum(subview(lclSums, j), subview(X_lcl, ALL(), col));
      }
    }
    // lbv 10 mar 2023: Kokkos Kernels provides non-blocking BLAS
    // functions unless they explicitly return a value to Host.
    // Here while the lclSums are on the host, they are not a return
    // value, therefore they might be available to us immediately.
    // Adding a fence here guarantees that we will have the lclSums
    // ahead of the MPI reduction.
    execution_space exec_space_instance = execution_space();
    exec_space_instance.fence("Tpetra::MultiVector::mean");
 
    // If there are multiple MPI processes, the all-reduce reads
    // from lclSums, and writes to meansOut.  (We assume that MPI
    // can read device memory.)  Otherwise, we just copy lclSums
    // into meansOut.
    if (!comm.is_null() && this->isDistributed()) {
      reduceAll(*comm, REDUCE_SUM, static_cast<int>(numVecs),
                lclSums.data(), meansOut.data());
    } else {
      // DEEP_COPY REVIEW - HOST-TO-HOST - NOT TESTED FOR MPI BUILD
      Kokkos::deep_copy(meansOut, lclSums);
    }
  }
 
  // mfh 12 Apr 2012: Don't take out the cast from the ordinal type
  // to the magnitude type, since operator/ (std::complex<T>, int)
  // isn't necessarily defined.
  const impl_scalar_type OneOverN =
      ATS::one() / static_cast<mag_type>(this->getGlobalLength());
  for (size_t k = 0; k < numMeans; ++k) {
    meansOut(k) = meansOut(k) * OneOverN;
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    randomize() {
  typedef impl_scalar_type IST;
#if KOKKOS_VERSION >= 40799
  typedef KokkosKernels::ArithTraits<IST> ATS;
#else
  typedef Kokkos::ArithTraits<IST> ATS;
#endif
  typedef Kokkos::Random_XorShift64_Pool<typename device_type::execution_space> pool_type;
  typedef typename pool_type::generator_type generator_type;
 
  const IST max = Kokkos::rand<generator_type, IST>::max();
  const IST min = ATS::is_signed ? IST(-max) : ATS::zero();
 
  this->randomize(static_cast<Scalar>(min), static_cast<Scalar>(max));
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    randomize(const Scalar& minVal, const Scalar& maxVal) {
  typedef impl_scalar_type IST;
  typedef Tpetra::Details::Static_Random_XorShift64_Pool<typename device_type::execution_space> tpetra_pool_type;
  typedef Kokkos::Random_XorShift64_Pool<typename device_type::execution_space> pool_type;
 
  // Seed the pool based on the system RNG and the MPI rank, if needed
  if (!tpetra_pool_type::isSet())
    tpetra_pool_type::resetPool(this->getMap()->getComm()->getRank());
 
  pool_type& rand_pool = tpetra_pool_type::getPool();
  const IST max        = static_cast<IST>(maxVal);
  const IST min        = static_cast<IST>(minVal);
 
  auto thisView = this->getLocalViewDevice(Access::OverwriteAll);
 
  if (isConstantStride()) {
    Kokkos::fill_random(thisView, rand_pool, min, max);
  } else {
    const size_t numVecs = getNumVectors();
    for (size_t k = 0; k < numVecs; ++k) {
      const size_t col = whichVectors_[k];
      auto X_k         = Kokkos::subview(thisView, Kokkos::ALL(), col);
      Kokkos::fill_random(X_k, rand_pool, min, max);
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    putScalar(const Scalar& alpha) {
  using ::Tpetra::Details::ProfilingRegion;
  using ::Tpetra::Details::Blas::fill;
  using DES = typename dual_view_type::t_dev::execution_space;
  using HES = typename dual_view_type::t_host::execution_space;
  using LO  = LocalOrdinal;
  ProfilingRegion region("Tpetra::MultiVector::putScalar");
 
  // We need this cast for cases like Scalar = std::complex<T> but
  // impl_scalar_type = Kokkos::complex<T>.
  const impl_scalar_type theAlpha = static_cast<impl_scalar_type>(alpha);
  const LO lclNumRows             = static_cast<LO>(this->getLocalLength());
  const LO numVecs                = static_cast<LO>(this->getNumVectors());
 
  // Modify the most recently updated version of the data.  This
  // avoids sync'ing, which could violate users' expectations.
  //
  // If we need sync to device, then host has the most recent version.
  const bool runOnHost = runKernelOnHost(*this);
  if (!runOnHost) {
    auto X = this->getLocalViewDevice(Access::OverwriteAll);
    if (this->isConstantStride()) {
      fill(DES(), X, theAlpha, lclNumRows, numVecs);
    } else {
      fill(DES(), X, theAlpha, lclNumRows, numVecs,
           this->whichVectors_.getRawPtr());
    }
  } else {  // last modified in host memory, so modify data there.
    auto X = this->getLocalViewHost(Access::OverwriteAll);
    if (this->isConstantStride()) {
      fill(HES(), X, theAlpha, lclNumRows, numVecs);
    } else {
      fill(HES(), X, theAlpha, lclNumRows, numVecs,
           this->whichVectors_.getRawPtr());
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    replaceMap(const Teuchos::RCP<const map_type>& newMap) {
  using Teuchos::ArrayRCP;
  using Teuchos::Comm;
  using Teuchos::RCP;
  using ST = Scalar;
  using LO = LocalOrdinal;
  using GO = GlobalOrdinal;
 
  // mfh 28 Mar 2013: This method doesn't forget whichVectors_, so
  // it might work if the MV is a column view of another MV.
  // However, things might go wrong when restoring the original
  // Map, so we don't allow this case for now.
  TEUCHOS_TEST_FOR_EXCEPTION(
      !this->isConstantStride(), std::logic_error,
      "Tpetra::MultiVector::replaceMap: This method does not currently work "
      "if the MultiVector is a column view of another MultiVector (that is, if "
      "isConstantStride() == false).");
 
  // Case 1: current Map and new Map are both nonnull on this process.
  // Case 2: current Map is nonnull, new Map is null.
  // Case 3: current Map is null, new Map is nonnull.
  // Case 4: both Maps are null: forbidden.
  //
  // Case 1 means that we don't have to do anything on this process,
  // other than assign the new Map.  (We always have to do that.)
  // It's an error for the user to supply a Map that requires
  // resizing in this case.
  //
  // Case 2 means that the calling process is in the current Map's
  // communicator, but will be excluded from the new Map's
  // communicator.  We don't have to do anything on the calling
  // process; just leave whatever data it may have alone.
  //
  // Case 3 means that the calling process is excluded from the
  // current Map's communicator, but will be included in the new
  // Map's communicator.  This means we need to (re)allocate the
  // local DualView if it does not have the right number of rows.
  // If the new number of rows is nonzero, we'll fill the newly
  // allocated local data with zeros, as befits a projection
  // operation.
  //
  // The typical use case for Case 3 is that the MultiVector was
  // first created with the Map with more processes, then that Map
  // was replaced with a Map with fewer processes, and finally the
  // original Map was restored on this call to replaceMap.
 
  if (this->getMap().is_null()) {  // current Map is null
    // If this->getMap() is null, that means that this MultiVector
    // has already had replaceMap happen to it.  In that case, just
    // reallocate the DualView with the right size.
 
    TEUCHOS_TEST_FOR_EXCEPTION(
        newMap.is_null(), std::invalid_argument,
        "Tpetra::MultiVector::replaceMap: both current and new Maps are null.  "
        "This probably means that the input Map is incorrect.");
 
    // Case 3: current Map is null, new Map is nonnull.
    // Reallocate the DualView with the right dimensions.
    const size_t newNumRows  = newMap->getLocalNumElements();
    const size_t origNumRows = view_.extent(0);
    const size_t numCols     = this->getNumVectors();
 
    if (origNumRows != newNumRows || view_.extent(1) != numCols) {
      view_ = allocDualView<ST, LO, GO, Node>(newNumRows, numCols);
    }
  } else if (newMap.is_null()) {  // Case 2: current Map is nonnull, new Map is null
    // I am an excluded process.  Reinitialize my data so that I
    // have 0 rows.  Keep the number of columns as before.
    const size_t newNumRows = static_cast<size_t>(0);
    const size_t numCols    = this->getNumVectors();
    view_                   = allocDualView<ST, LO, GO, Node>(newNumRows, numCols);
  }
 
  this->map_ = newMap;
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    scale(const Scalar& alpha) {
  using Kokkos::ALL;
  using IST = impl_scalar_type;
 
  const IST theAlpha = static_cast<IST>(alpha);
#if KOKKOS_VERSION >= 40799
  if (theAlpha == KokkosKernels::ArithTraits<IST>::one()) {
#else
  if (theAlpha == Kokkos::ArithTraits<IST>::one()) {
#endif
    return;  // do nothing
  }
  const size_t lclNumRows = getLocalLength();
  const size_t numVecs    = getNumVectors();
  const std::pair<size_t, size_t> rowRng(0, lclNumRows);
  const std::pair<size_t, size_t> colRng(0, numVecs);
 
  // We can't substitute putScalar(0.0) for scale(0.0), because the
  // former will overwrite NaNs present in the MultiVector.  The
  // semantics of this call require multiplying them by 0, which
  // IEEE 754 requires to be NaN.
 
  // If we need sync to device, then host has the most recent version.
  const bool useHostVersion = need_sync_device();
  if (useHostVersion) {
    auto Y_lcl = Kokkos::subview(getLocalViewHost(Access::ReadWrite), rowRng, ALL());
    if (isConstantStride()) {
      KokkosBlas::scal(Y_lcl, theAlpha, Y_lcl);
    } else {
      for (size_t k = 0; k < numVecs; ++k) {
        const size_t Y_col = whichVectors_[k];
        auto Y_k           = Kokkos::subview(Y_lcl, ALL(), Y_col);
        KokkosBlas::scal(Y_k, theAlpha, Y_k);
      }
    }
  } else {  // work on device
    auto Y_lcl = Kokkos::subview(getLocalViewDevice(Access::ReadWrite), rowRng, ALL());
    if (isConstantStride()) {
      KokkosBlas::scal(Y_lcl, theAlpha, Y_lcl);
    } else {
      for (size_t k = 0; k < numVecs; ++k) {
        const size_t Y_col = isConstantStride() ? k : whichVectors_[k];
        auto Y_k           = Kokkos::subview(Y_lcl, ALL(), Y_col);
        KokkosBlas::scal(Y_k, theAlpha, Y_k);
      }
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    scale(const Teuchos::ArrayView<const Scalar>& alphas) {
  const size_t numVecs   = this->getNumVectors();
  const size_t numAlphas = static_cast<size_t>(alphas.size());
  TEUCHOS_TEST_FOR_EXCEPTION(
      numAlphas != numVecs, std::invalid_argument,
      "Tpetra::MultiVector::"
      "scale: alphas.size() = "
          << numAlphas << " != this->getNumVectors() = "
          << numVecs << ".");
 
  // Use a DualView to copy the scaling constants onto the device.
  using k_alphas_type = Kokkos::DualView<impl_scalar_type*, device_type>;
  k_alphas_type k_alphas("alphas::tmp", numAlphas);
  k_alphas.modify_host();
  for (size_t i = 0; i < numAlphas; ++i) {
    k_alphas.view_host()(i) = static_cast<impl_scalar_type>(alphas[i]);
  }
  k_alphas.sync_device();
  // Invoke the scale() overload that takes a device View of coefficients.
  this->scale(k_alphas.view_device());
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    scale(const Kokkos::View<const impl_scalar_type*, device_type>& alphas) {
  using Kokkos::ALL;
  using Kokkos::subview;
 
  const size_t lclNumRows = this->getLocalLength();
  const size_t numVecs    = this->getNumVectors();
  TEUCHOS_TEST_FOR_EXCEPTION(
      static_cast<size_t>(alphas.extent(0)) != numVecs,
      std::invalid_argument,
      "Tpetra::MultiVector::scale(alphas): "
      "alphas.extent(0) = "
          << alphas.extent(0)
          << " != this->getNumVectors () = " << numVecs << ".");
  const std::pair<size_t, size_t> rowRng(0, lclNumRows);
  const std::pair<size_t, size_t> colRng(0, numVecs);
 
  // NOTE (mfh 08 Apr 2015) We prefer to let the compiler deduce the
  // type of the return value of subview.  This is because if we
  // switch the array layout from LayoutLeft to LayoutRight
  // (preferred for performance of block operations), the types
  // below won't be valid.  (A view of a column of a LayoutRight
  // multivector has LayoutStride, not LayoutLeft.)
 
  // If we need sync to device, then host has the most recent version.
  const bool useHostVersion = this->need_sync_device();
  if (useHostVersion) {
    // Work in host memory.  This means we need to create a host
    // mirror of the input View of coefficients.
    auto alphas_h = Kokkos::create_mirror_view(alphas);
    // DEEP_COPY REVIEW - NOT TESTED
    Kokkos::deep_copy(alphas_h, alphas);
 
    auto Y_lcl = subview(this->getLocalViewHost(Access::ReadWrite), rowRng, ALL());
    if (isConstantStride()) {
      KokkosBlas::scal(Y_lcl, alphas_h, Y_lcl);
    } else {
      for (size_t k = 0; k < numVecs; ++k) {
        const size_t Y_col = this->isConstantStride() ? k : this->whichVectors_[k];
        auto Y_k           = subview(Y_lcl, ALL(), Y_col);
        // We don't have to use the entire 1-D View here; we can use
        // the version that takes a scalar coefficient.
        KokkosBlas::scal(Y_k, alphas_h(k), Y_k);
      }
    }
  } else {  // Work in device memory, using the input View 'alphas' directly.
    auto Y_lcl = subview(this->getLocalViewDevice(Access::ReadWrite), rowRng, ALL());
    if (isConstantStride()) {
      KokkosBlas::scal(Y_lcl, alphas, Y_lcl);
    } else {
      // FIXME (mfh 15 Mar 2019) We need one coefficient at a time,
      // as values on host, so copy them to host.  Another approach
      // would be to fix scal() so that it takes a 0-D View as the
      // second argument.
      auto alphas_h = Kokkos::create_mirror_view(alphas);
      // DEEP_COPY REVIEW - NOT TESTED
      Kokkos::deep_copy(alphas_h, alphas);
 
      for (size_t k = 0; k < numVecs; ++k) {
        const size_t Y_col = this->isConstantStride() ? k : this->whichVectors_[k];
        auto Y_k           = subview(Y_lcl, ALL(), Y_col);
        KokkosBlas::scal(Y_k, alphas_h(k), Y_k);
      }
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    scale(const Scalar& alpha,
          const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& A) {
  using Kokkos::ALL;
  using Kokkos::subview;
  const char tfecfFuncName[] = "scale: ";
 
  const size_t lclNumRows = getLocalLength();
  const size_t numVecs    = getNumVectors();
 
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      lclNumRows != A.getLocalLength(), std::invalid_argument,
      "this->getLocalLength() = " << lclNumRows << " != A.getLocalLength() = "
                                  << A.getLocalLength() << ".");
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      numVecs != A.getNumVectors(), std::invalid_argument,
      "this->getNumVectors() = " << numVecs << " != A.getNumVectors() = "
                                 << A.getNumVectors() << ".");
 
  const impl_scalar_type theAlpha = static_cast<impl_scalar_type>(alpha);
  const std::pair<size_t, size_t> rowRng(0, lclNumRows);
  const std::pair<size_t, size_t> colRng(0, numVecs);
 
  auto Y_lcl_orig = this->getLocalViewDevice(Access::ReadWrite);
  auto X_lcl_orig = A.getLocalViewDevice(Access::ReadOnly);
  auto Y_lcl      = subview(Y_lcl_orig, rowRng, ALL());
  auto X_lcl      = subview(X_lcl_orig, rowRng, ALL());
 
  if (isConstantStride() && A.isConstantStride()) {
    KokkosBlas::scal(Y_lcl, theAlpha, X_lcl);
  } else {
    // Make sure that Kokkos only uses the local length for add.
    for (size_t k = 0; k < numVecs; ++k) {
      const size_t Y_col = this->isConstantStride() ? k : this->whichVectors_[k];
      const size_t X_col = A.isConstantStride() ? k : A.whichVectors_[k];
      auto Y_k           = subview(Y_lcl, ALL(), Y_col);
      auto X_k           = subview(X_lcl, ALL(), X_col);
 
      KokkosBlas::scal(Y_k, theAlpha, X_k);
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    reciprocal(const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& A) {
  const char tfecfFuncName[] = "reciprocal: ";
 
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      getLocalLength() != A.getLocalLength(), std::runtime_error,
      "MultiVectors do not have the same local length.  "
      "this->getLocalLength() = "
          << getLocalLength()
          << " != A.getLocalLength() = " << A.getLocalLength() << ".");
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      A.getNumVectors() != this->getNumVectors(), std::runtime_error,
      ": MultiVectors do not have the same number of columns (vectors).  "
      "this->getNumVectors() = "
          << getNumVectors()
          << " != A.getNumVectors() = " << A.getNumVectors() << ".");
 
  const size_t numVecs = getNumVectors();
 
  auto this_view_dev = this->getLocalViewDevice(Access::ReadWrite);
  auto A_view_dev    = A.getLocalViewDevice(Access::ReadOnly);
 
  if (isConstantStride() && A.isConstantStride()) {
    KokkosBlas::reciprocal(this_view_dev, A_view_dev);
  } else {
    using Kokkos::ALL;
    using Kokkos::subview;
    for (size_t k = 0; k < numVecs; ++k) {
      const size_t this_col = isConstantStride() ? k : whichVectors_[k];
      auto vector_k         = subview(this_view_dev, ALL(), this_col);
      const size_t A_col    = isConstantStride() ? k : A.whichVectors_[k];
      auto vector_Ak        = subview(A_view_dev, ALL(), A_col);
      KokkosBlas::reciprocal(vector_k, vector_Ak);
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    abs(const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& A) {
  const char tfecfFuncName[] = "abs";
 
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      getLocalLength() != A.getLocalLength(), std::runtime_error,
      ": MultiVectors do not have the same local length.  "
      "this->getLocalLength() = "
          << getLocalLength()
          << " != A.getLocalLength() = " << A.getLocalLength() << ".");
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      A.getNumVectors() != this->getNumVectors(), std::runtime_error,
      ": MultiVectors do not have the same number of columns (vectors).  "
      "this->getNumVectors() = "
          << getNumVectors()
          << " != A.getNumVectors() = " << A.getNumVectors() << ".");
  const size_t numVecs = getNumVectors();
 
  auto this_view_dev = this->getLocalViewDevice(Access::ReadWrite);
  auto A_view_dev    = A.getLocalViewDevice(Access::ReadOnly);
 
  if (isConstantStride() && A.isConstantStride()) {
    KokkosBlas::abs(this_view_dev, A_view_dev);
  } else {
    using Kokkos::ALL;
    using Kokkos::subview;
 
    for (size_t k = 0; k < numVecs; ++k) {
      const size_t this_col = isConstantStride() ? k : whichVectors_[k];
      auto vector_k         = subview(this_view_dev, ALL(), this_col);
      const size_t A_col    = isConstantStride() ? k : A.whichVectors_[k];
      auto vector_Ak        = subview(A_view_dev, ALL(), A_col);
      KokkosBlas::abs(vector_k, vector_Ak);
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    update(const Scalar& alpha,
           const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& A,
           const Scalar& beta) {
  const char tfecfFuncName[] = "update: ";
  using Kokkos::ALL;
  using Kokkos::subview;
 
  ::Tpetra::Details::ProfilingRegion region("Tpetra::MV::update(alpha,A,beta)");
 
  const size_t lclNumRows = getLocalLength();
  const size_t numVecs    = getNumVectors();
 
  if (::Tpetra::Details::Behavior::debug()) {
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        lclNumRows != A.getLocalLength(), std::invalid_argument,
        "this->getLocalLength() = " << lclNumRows << " != A.getLocalLength() = "
                                    << A.getLocalLength() << ".");
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        numVecs != A.getNumVectors(), std::invalid_argument,
        "this->getNumVectors() = " << numVecs << " != A.getNumVectors() = "
                                   << A.getNumVectors() << ".");
  }
 
  const impl_scalar_type theAlpha = static_cast<impl_scalar_type>(alpha);
  const impl_scalar_type theBeta  = static_cast<impl_scalar_type>(beta);
  const std::pair<size_t, size_t> rowRng(0, lclNumRows);
  const std::pair<size_t, size_t> colRng(0, numVecs);
 
  auto Y_lcl_orig = this->getLocalViewDevice(Access::ReadWrite);
  auto Y_lcl      = subview(Y_lcl_orig, rowRng, Kokkos::ALL());
  auto X_lcl_orig = A.getLocalViewDevice(Access::ReadOnly);
  auto X_lcl      = subview(X_lcl_orig, rowRng, Kokkos::ALL());
 
  // The device memory of *this is about to be modified
  if (isConstantStride() && A.isConstantStride()) {
    KokkosBlas::axpby(theAlpha, X_lcl, theBeta, Y_lcl);
  } else {
    // Make sure that Kokkos only uses the local length for add.
    for (size_t k = 0; k < numVecs; ++k) {
      const size_t Y_col = this->isConstantStride() ? k : this->whichVectors_[k];
      const size_t X_col = A.isConstantStride() ? k : A.whichVectors_[k];
      auto Y_k           = subview(Y_lcl, ALL(), Y_col);
      auto X_k           = subview(X_lcl, ALL(), X_col);
 
      KokkosBlas::axpby(theAlpha, X_k, theBeta, Y_k);
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    update(const Scalar& alpha,
           const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& A,
           const Scalar& beta,
           const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& B,
           const Scalar& gamma) {
  using Kokkos::ALL;
  using Kokkos::subview;
 
  const char tfecfFuncName[] = "update(alpha,A,beta,B,gamma): ";
 
  ::Tpetra::Details::ProfilingRegion region("Tpetra::MV::update(alpha,A,beta,B,gamma)");
 
  const size_t lclNumRows = this->getLocalLength();
  const size_t numVecs    = getNumVectors();
 
  if (::Tpetra::Details::Behavior::debug()) {
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        lclNumRows != A.getLocalLength(), std::invalid_argument,
        "The input MultiVector A has " << A.getLocalLength() << " local "
                                                                "row(s), but this MultiVector has "
                                       << lclNumRows << " local "
                                                        "row(s).");
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        lclNumRows != B.getLocalLength(), std::invalid_argument,
        "The input MultiVector B has " << B.getLocalLength() << " local "
                                                                "row(s), but this MultiVector has "
                                       << lclNumRows << " local "
                                                        "row(s).");
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        A.getNumVectors() != numVecs, std::invalid_argument,
        "The input MultiVector A has " << A.getNumVectors() << " column(s), "
                                                               "but this MultiVector has "
                                       << numVecs << " column(s).");
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
        B.getNumVectors() != numVecs, std::invalid_argument,
        "The input MultiVector B has " << B.getNumVectors() << " column(s), "
                                                               "but this MultiVector has "
                                       << numVecs << " column(s).");
  }
 
  const impl_scalar_type theAlpha = static_cast<impl_scalar_type>(alpha);
  const impl_scalar_type theBeta  = static_cast<impl_scalar_type>(beta);
  const impl_scalar_type theGamma = static_cast<impl_scalar_type>(gamma);
 
  const std::pair<size_t, size_t> rowRng(0, lclNumRows);
  const std::pair<size_t, size_t> colRng(0, numVecs);
 
  // Prefer 'auto' over specifying the type explicitly.  This avoids
  // issues with a subview possibly having a different type than the
  // original view.
  auto C_lcl = subview(this->getLocalViewDevice(Access::ReadWrite), rowRng, ALL());
  auto A_lcl = subview(A.getLocalViewDevice(Access::ReadOnly), rowRng, ALL());
  auto B_lcl = subview(B.getLocalViewDevice(Access::ReadOnly), rowRng, ALL());
 
  if (isConstantStride() && A.isConstantStride() && B.isConstantStride()) {
    KokkosBlas::update(theAlpha, A_lcl, theBeta, B_lcl, theGamma, C_lcl);
  } else {
    // Some input (or *this) is not constant stride,
    // so perform the update one column at a time.
    for (size_t k = 0; k < numVecs; ++k) {
      const size_t this_col = isConstantStride() ? k : whichVectors_[k];
      const size_t A_col    = A.isConstantStride() ? k : A.whichVectors_[k];
      const size_t B_col    = B.isConstantStride() ? k : B.whichVectors_[k];
      KokkosBlas::update(theAlpha, subview(A_lcl, rowRng, A_col),
                         theBeta, subview(B_lcl, rowRng, B_col),
                         theGamma, subview(C_lcl, rowRng, this_col));
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::ArrayRCP<const Scalar>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getData(size_t j) const {
  using Kokkos::ALL;
  using IST                  = impl_scalar_type;
  const char tfecfFuncName[] = "getData: ";
 
  // Any MultiVector method that called the (classic) Kokkos Node's
  // viewBuffer or viewBufferNonConst methods always implied a
  // device->host synchronization.  Thus, we synchronize here as
  // well.
 
  auto hostView    = getLocalViewHost(Access::ReadOnly);
  const size_t col = isConstantStride() ? j : whichVectors_[j];
  auto hostView_j  = Kokkos::subview(hostView, ALL(), col);
  Teuchos::ArrayRCP<const IST> dataAsArcp =
      Kokkos::Compat::persistingView(hostView_j, 0, getLocalLength());
 
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(static_cast<size_t>(hostView_j.extent(0)) <
                                            static_cast<size_t>(dataAsArcp.size()),
                                        std::logic_error,
                                        "hostView_j.extent(0) = " << hostView_j.extent(0)
                                                                  << " < dataAsArcp.size() = " << dataAsArcp.size() << ".  "
                                                                                                                       "Please report this bug to the Tpetra developers.");
 
  return Teuchos::arcp_reinterpret_cast<const Scalar>(dataAsArcp);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::ArrayRCP<Scalar>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getDataNonConst(size_t j) {
  using Kokkos::ALL;
  using Kokkos::subview;
  using IST                  = impl_scalar_type;
  const char tfecfFuncName[] = "getDataNonConst: ";
 
  auto hostView    = getLocalViewHost(Access::ReadWrite);
  const size_t col = isConstantStride() ? j : whichVectors_[j];
  auto hostView_j  = subview(hostView, ALL(), col);
  Teuchos::ArrayRCP<IST> dataAsArcp =
      Kokkos::Compat::persistingView(hostView_j, 0, getLocalLength());
 
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(static_cast<size_t>(hostView_j.extent(0)) <
                                            static_cast<size_t>(dataAsArcp.size()),
                                        std::logic_error,
                                        "hostView_j.extent(0) = " << hostView_j.extent(0)
                                                                  << " < dataAsArcp.size() = " << dataAsArcp.size() << ".  "
                                                                                                                       "Please report this bug to the Tpetra developers.");
 
  return Teuchos::arcp_reinterpret_cast<Scalar>(dataAsArcp);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    subCopy(const Teuchos::ArrayView<const size_t>& cols) const {
  using Teuchos::RCP;
  typedef MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> MV;
 
  // Check whether the index set in cols is contiguous.  If it is,
  // use the more efficient Range1D version of subCopy.
  bool contiguous          = true;
  const size_t numCopyVecs = static_cast<size_t>(cols.size());
  for (size_t j = 1; j < numCopyVecs; ++j) {
    if (cols[j] != cols[j - 1] + static_cast<size_t>(1)) {
      contiguous = false;
      break;
    }
  }
  if (contiguous && numCopyVecs > 0) {
    return this->subCopy(Teuchos::Range1D(cols[0], cols[numCopyVecs - 1]));
  } else {
    RCP<const MV> X_sub = this->subView(cols);
    RCP<MV> Y(new MV(this->getMap(), numCopyVecs, false));
    Y->assign(*X_sub);
    return Y;
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    subCopy(const Teuchos::Range1D& colRng) const {
  using Teuchos::RCP;
  typedef MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> MV;
 
  RCP<const MV> X_sub = this->subView(colRng);
  RCP<MV> Y(new MV(this->getMap(), static_cast<size_t>(colRng.size()), false));
  Y->assign(*X_sub);
  return Y;
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
size_t
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getOrigNumLocalRows() const {
  return view_.origExtent(0);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
size_t
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getOrigNumLocalCols() const {
  return view_.origExtent(1);
}
 
template <class Scalar, class LO, class GO, class Node>
MultiVector<Scalar, LO, GO, Node>::
    MultiVector(const MultiVector<Scalar, LO, GO, Node>& X,
                const Teuchos::RCP<const map_type>& subMap,
                const local_ordinal_type rowOffset)
  : base_type(subMap) {
  using Kokkos::ALL;
  using Kokkos::subview;
  using std::endl;
  using Teuchos::outArg;
  using Teuchos::RCP;
  using Teuchos::rcp;
  using Teuchos::REDUCE_MIN;
  using Teuchos::reduceAll;
  using MV            = MultiVector<Scalar, LO, GO, Node>;
  const char prefix[] = "Tpetra::MultiVector constructor (offsetView): ";
  const char suffix[] = "Please report this bug to the Tpetra developers.";
  int lclGood         = 1;
  int gblGood         = 1;
  std::unique_ptr<std::ostringstream> errStrm;
  const bool debug   = ::Tpetra::Details::Behavior::debug();
  const bool verbose = ::Tpetra::Details::Behavior::verbose();
 
  // Be careful to use the input Map's communicator, not X's.  The
  // idea is that, on return, *this is a subview of X, using the
  // input Map.
  const auto comm = subMap->getComm();
  TEUCHOS_ASSERT(!comm.is_null());
  const int myRank = comm->getRank();
 
  const LO lclNumRowsBefore = static_cast<LO>(X.getLocalLength());
  const LO numCols          = static_cast<LO>(X.getNumVectors());
  const LO newNumRows       = static_cast<LO>(subMap->getLocalNumElements());
  if (verbose) {
    std::ostringstream os;
    os << "Proc " << myRank << ": " << prefix
       << "X: {lclNumRows: " << lclNumRowsBefore
       << ", origLclNumRows: " << X.getOrigNumLocalRows()
       << ", numCols: " << numCols << "}, "
       << "subMap: {lclNumRows: " << newNumRows << "}" << endl;
    std::cerr << os.str();
  }
  // We ask for the _original_ number of rows in X, because X could
  // be a shorter (fewer rows) view of a longer MV.  (For example, X
  // could be a domain Map view of a column Map MV.)
  const bool tooManyElts =
      newNumRows + rowOffset > static_cast<LO>(X.getOrigNumLocalRows());
  if (tooManyElts) {
    errStrm = std::unique_ptr<std::ostringstream>(new std::ostringstream);
    *errStrm << "  Proc " << myRank << ": subMap->getLocalNumElements() (="
             << newNumRows << ") + rowOffset (=" << rowOffset
             << ") > X.getOrigNumLocalRows() (=" << X.getOrigNumLocalRows()
             << ")." << endl;
    lclGood = 0;
    TEUCHOS_TEST_FOR_EXCEPTION(!debug && tooManyElts, std::invalid_argument,
                               prefix << errStrm->str() << suffix);
  }
 
  if (debug) {
    reduceAll<int, int>(*comm, REDUCE_MIN, lclGood, outArg(gblGood));
    if (gblGood != 1) {
      std::ostringstream gblErrStrm;
      const std::string myErrStr =
          errStrm.get() != nullptr ? errStrm->str() : std::string("");
      ::Tpetra::Details::gathervPrint(gblErrStrm, myErrStr, *comm);
      TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, gblErrStrm.str());
    }
  }
 
  using range_type = std::pair<LO, LO>;
  const range_type origRowRng(rowOffset, static_cast<LO>(X.view_.origExtent(0)));
  const range_type rowRng(rowOffset, rowOffset + newNumRows);
 
  wrapped_dual_view_type newView = takeSubview(X.view_, rowRng, ALL());
 
  // NOTE (mfh 06 Jan 2015) Work-around to deal with Kokkos not
  // handling subviews of degenerate Views quite so well.  For some
  // reason, the ([0,0], [0,2]) subview of a 0 x 2 DualView is 0 x
  // 0.  We work around by creating a new empty DualView of the
  // desired (degenerate) dimensions.
  if (newView.extent(0) == 0 &&
      newView.extent(1) != X.view_.extent(1)) {
    newView =
        allocDualView<Scalar, LO, GO, Node>(0, X.getNumVectors());
  }
 
  MV subViewMV = X.isConstantStride() ? MV(subMap, newView) : MV(subMap, newView, X.whichVectors_());
 
  if (debug) {
    const LO lclNumRowsRet = static_cast<LO>(subViewMV.getLocalLength());
    const LO numColsRet    = static_cast<LO>(subViewMV.getNumVectors());
    if (newNumRows != lclNumRowsRet || numCols != numColsRet) {
      lclGood = 0;
      if (errStrm.get() == nullptr) {
        errStrm = std::unique_ptr<std::ostringstream>(new std::ostringstream);
      }
      *errStrm << "  Proc " << myRank << ": subMap.getLocalNumElements(): " << newNumRows << ", subViewMV.getLocalLength(): " << lclNumRowsRet << ", X.getNumVectors(): " << numCols << ", subViewMV.getNumVectors(): " << numColsRet << endl;
    }
    reduceAll<int, int>(*comm, REDUCE_MIN, lclGood, outArg(gblGood));
    if (gblGood != 1) {
      std::ostringstream gblErrStrm;
      if (myRank == 0) {
        gblErrStrm << prefix << "Returned MultiVector has the wrong local "
                                "dimensions on one or more processes:"
                   << endl;
      }
      const std::string myErrStr =
          errStrm.get() != nullptr ? errStrm->str() : std::string("");
      ::Tpetra::Details::gathervPrint(gblErrStrm, myErrStr, *comm);
      gblErrStrm << suffix << endl;
      TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, gblErrStrm.str());
    }
  }
 
  if (verbose) {
    std::ostringstream os;
    os << "Proc " << myRank << ": " << prefix << "Call op=" << endl;
    std::cerr << os.str();
  }
 
  *this = subViewMV;  // shallow copy
 
  if (verbose) {
    std::ostringstream os;
    os << "Proc " << myRank << ": " << prefix << "Done!" << endl;
    std::cerr << os.str();
  }
}
 
template <class Scalar, class LO, class GO, class Node>
MultiVector<Scalar, LO, GO, Node>::
    MultiVector(const MultiVector<Scalar, LO, GO, Node>& X,
                const map_type& subMap,
                const size_t rowOffset)
  : MultiVector(X, Teuchos::RCP<const map_type>(new map_type(subMap)),
                static_cast<local_ordinal_type>(rowOffset)) {}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    offsetView(const Teuchos::RCP<const map_type>& subMap,
               const size_t offset) const {
  typedef MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> MV;
  return Teuchos::rcp(new MV(*this, *subMap, offset));
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    offsetViewNonConst(const Teuchos::RCP<const map_type>& subMap,
                       const size_t offset) {
  typedef MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> MV;
  return Teuchos::rcp(new MV(*this, *subMap, offset));
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    subView(const Teuchos::ArrayView<const size_t>& cols) const {
  using Teuchos::Array;
  using Teuchos::rcp;
  typedef MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> MV;
 
  const size_t numViewCols = static_cast<size_t>(cols.size());
  TEUCHOS_TEST_FOR_EXCEPTION(
      numViewCols < 1, std::runtime_error,
      "Tpetra::MultiVector::subView"
      "(const Teuchos::ArrayView<const size_t>&): The input array cols must "
      "contain at least one entry, but cols.size() = "
          << cols.size()
          << " == 0.");
 
  // Check whether the index set in cols is contiguous.  If it is,
  // use the more efficient Range1D version of subView.
  bool contiguous = true;
  for (size_t j = 1; j < numViewCols; ++j) {
    if (cols[j] != cols[j - 1] + static_cast<size_t>(1)) {
      contiguous = false;
      break;
    }
  }
  if (contiguous) {
    if (numViewCols == 0) {
      // The output MV has no columns, so there is nothing to view.
      return rcp(new MV(this->getMap(), numViewCols));
    } else {
      // Use the more efficient contiguous-index-range version.
      return this->subView(Teuchos::Range1D(cols[0], cols[numViewCols - 1]));
    }
  }
 
  if (isConstantStride()) {
    return rcp(new MV(this->getMap(), view_, cols));
  } else {
    Array<size_t> newcols(cols.size());
    for (size_t j = 0; j < numViewCols; ++j) {
      newcols[j] = whichVectors_[cols[j]];
    }
    return rcp(new MV(this->getMap(), view_, newcols()));
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    subView(const Teuchos::Range1D& colRng) const {
  using Kokkos::ALL;
  using Kokkos::subview;
  using Teuchos::Array;
  using Teuchos::RCP;
  using Teuchos::rcp;
  using ::Tpetra::Details::Behavior;
  typedef MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> MV;
  const char tfecfFuncName[] = "subView(Range1D): ";
 
  const size_t lclNumRows = this->getLocalLength();
  const size_t numVecs    = this->getNumVectors();
  // TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
  //   colRng.size() == 0, std::runtime_error, prefix << "Range must include "
  //   "at least one vector.");
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      static_cast<size_t>(colRng.size()) > numVecs, std::runtime_error,
      "colRng.size() = " << colRng.size() << " > this->getNumVectors() = "
                         << numVecs << ".");
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      numVecs != 0 && colRng.size() != 0 &&
          (colRng.lbound() < static_cast<Teuchos::Ordinal>(0) ||
           static_cast<size_t>(colRng.ubound()) >= numVecs),
      std::invalid_argument, "Nonempty input range [" << colRng.lbound() << "," << colRng.ubound() << "] exceeds the valid range of column indices "
                                                                                                      "[0, "
                                                      << numVecs << "].");
 
  RCP<const MV> X_ret;  // the MultiVector subview to return
 
  // FIXME (mfh 14 Apr 2015) Apparently subview on DualView is still
  // broken for the case of views with zero rows.  I will brutally
  // enforce that the subview has the correct dimensions.  In
  // particular, in the case of zero rows, I will, if necessary,
  // create a new dual_view_type with zero rows and the correct
  // number of columns.  In a debug build, I will use an all-reduce
  // to ensure that it has the correct dimensions on all processes.
 
  const std::pair<size_t, size_t> rows(0, lclNumRows);
  if (colRng.size() == 0) {
    const std::pair<size_t, size_t> cols(0, 0);  // empty range
    wrapped_dual_view_type X_sub = takeSubview(this->view_, ALL(), cols);
    X_ret                        = rcp(new MV(this->getMap(), X_sub));
  } else {
    // Returned MultiVector is constant stride only if *this is.
    if (isConstantStride()) {
      const std::pair<size_t, size_t> cols(colRng.lbound(),
                                           colRng.ubound() + 1);
      wrapped_dual_view_type X_sub = takeSubview(this->view_, ALL(), cols);
      X_ret                        = rcp(new MV(this->getMap(), X_sub));
    } else {
      if (static_cast<size_t>(colRng.size()) == static_cast<size_t>(1)) {
        // We're only asking for one column, so the result does have
        // constant stride, even though this MultiVector does not.
        const std::pair<size_t, size_t> col(whichVectors_[0] + colRng.lbound(),
                                            whichVectors_[0] + colRng.ubound() + 1);
        wrapped_dual_view_type X_sub = takeSubview(view_, ALL(), col);
        X_ret                        = rcp(new MV(this->getMap(), X_sub));
      } else {
        Array<size_t> which(whichVectors_.begin() + colRng.lbound(),
                            whichVectors_.begin() + colRng.ubound() + 1);
        X_ret = rcp(new MV(this->getMap(), view_, which));
      }
    }
  }
 
  const bool debug = Behavior::debug();
  if (debug) {
    using Teuchos::Comm;
    using Teuchos::outArg;
    using Teuchos::REDUCE_MIN;
    using Teuchos::reduceAll;
 
    RCP<const Comm<int> > comm = this->getMap().is_null() ? Teuchos::null : this->getMap()->getComm();
    if (!comm.is_null()) {
      int lclSuccess = 1;
      int gblSuccess = 1;
 
      if (X_ret.is_null()) {
        lclSuccess = 0;
      }
      reduceAll<int, int>(*comm, REDUCE_MIN, lclSuccess, outArg(gblSuccess));
      TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(lclSuccess != 1, std::logic_error,
                                            "X_ret (the subview of this "
                                            "MultiVector; the return value of this method) is null on some MPI "
                                            "process in this MultiVector's communicator.  This should never "
                                            "happen.  Please report this bug to the Tpetra developers.");
      if (!X_ret.is_null() &&
          X_ret->getNumVectors() != static_cast<size_t>(colRng.size())) {
        lclSuccess = 0;
      }
      reduceAll<int, int>(*comm, REDUCE_MIN, lclSuccess,
                          outArg(gblSuccess));
      TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(lclSuccess != 1, std::logic_error,
                                            "X_ret->getNumVectors() != "
                                            "colRng.size(), on at least one MPI process in this MultiVector's "
                                            "communicator.  This should never happen.  "
                                            "Please report this bug to the Tpetra developers.");
    }
  }
  return X_ret;
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    subViewNonConst(const Teuchos::ArrayView<const size_t>& cols) {
  typedef MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> MV;
  return Teuchos::rcp_const_cast<MV>(this->subView(cols));
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    subViewNonConst(const Teuchos::Range1D& colRng) {
  typedef MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node> MV;
  return Teuchos::rcp_const_cast<MV>(this->subView(colRng));
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    MultiVector(const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& X,
                const size_t j)
  : base_type(X.getMap()) {
  using Kokkos::subview;
  typedef std::pair<size_t, size_t> range_type;
  const char tfecfFuncName[] = "MultiVector(const MultiVector&, const size_t): ";
 
  const size_t numCols = X.getNumVectors();
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(j >= numCols, std::invalid_argument, "Input index j (== " << j << ") exceeds valid column index range [0, " << numCols << " - 1].");
  const size_t jj = X.isConstantStride() ? static_cast<size_t>(j) : static_cast<size_t>(X.whichVectors_[j]);
  this->view_     = takeSubview(X.view_, Kokkos::ALL(), range_type(jj, jj + 1));
 
  // mfh 31 Jul 2017: It would be unwise to execute concurrent
  // Export or Import operations with different subviews of a
  // MultiVector.  Thus, it is safe to reuse communication buffers.
  // See #1560 discussion.
  //
  // We only need one column's worth of buffer for imports_ and
  // exports_.  Taking subviews now ensures that their lengths will
  // be exactly what we need, so we won't have to resize them later.
  {
    const size_t newSize = X.imports_.extent(0) / numCols;
    const size_t offset  = jj * newSize;
    auto device_view     = subview(X.imports_.view_device(),
                                   range_type(offset, offset + newSize));
    auto host_view       = subview(X.imports_.view_host(),
                                   range_type(offset, offset + newSize));
    this->imports_       = decltype(X.imports_)(device_view, host_view);
  }
  {
    const size_t newSize = X.exports_.extent(0) / numCols;
    const size_t offset  = jj * newSize;
    auto device_view     = subview(X.exports_.view_device(),
                                   range_type(offset, offset + newSize));
    auto host_view       = subview(X.exports_.view_host(),
                                   range_type(offset, offset + newSize));
    this->exports_       = decltype(X.exports_)(device_view, host_view);
  }
  // These two DualViews already either have the right number of
  // entries, or zero entries.  This means that we don't need to
  // resize them.
  this->numImportPacketsPerLID_ = X.numImportPacketsPerLID_;
  this->numExportPacketsPerLID_ = X.numExportPacketsPerLID_;
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<const Vector<Scalar, LocalOrdinal, GlobalOrdinal, Node> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getVector(const size_t j) const {
  typedef Vector<Scalar, LocalOrdinal, GlobalOrdinal, Node> V;
  return Teuchos::rcp(new V(*this, j));
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<Vector<Scalar, LocalOrdinal, GlobalOrdinal, Node> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getVectorNonConst(const size_t j) {
  typedef Vector<Scalar, LocalOrdinal, GlobalOrdinal, Node> V;
  return Teuchos::rcp(new V(*this, j));
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    get1dCopy(const Teuchos::ArrayView<Scalar>& A, const size_t LDA) const {
  using IST                  = impl_scalar_type;
  using input_view_type      = Kokkos::View<IST**, Kokkos::LayoutLeft,
                                       Kokkos::HostSpace,
                                       Kokkos::MemoryUnmanaged>;
  const char tfecfFuncName[] = "get1dCopy: ";
 
  const size_t numRows = this->getLocalLength();
  const size_t numCols = this->getNumVectors();
 
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(LDA < numRows, std::runtime_error,
                                        "LDA = " << LDA << " < numRows = " << numRows << ".");
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(numRows > size_t(0) && numCols > size_t(0) &&
                                            size_t(A.size()) < LDA * (numCols - 1) + numRows,
                                        std::runtime_error,
                                        "A.size() = " << A.size() << ", but its size must be at least "
                                                      << (LDA * (numCols - 1) + numRows) << " to hold all the entries.");
 
  const std::pair<size_t, size_t> rowRange(0, numRows);
  const std::pair<size_t, size_t> colRange(0, numCols);
 
  input_view_type A_view_orig(reinterpret_cast<IST*>(A.getRawPtr()),
                              LDA, numCols);
  auto A_view = Kokkos::subview(A_view_orig, rowRange, colRange);
 
  if (this->need_sync_host() && this->need_sync_device()) {
    throw std::runtime_error("Tpetra::MultiVector: A non-const view is alive outside and we cannot give a copy where host or device view can be modified outside");
  } else {
    const bool useHostView = view_.host_view_use_count() >= view_.device_view_use_count();
    if (this->isConstantStride()) {
      if (useHostView) {
        auto srcView_host = this->getLocalViewHost(Access::ReadOnly);
        // DEEP_COPY REVIEW - NOT TESTED
        Kokkos::deep_copy(A_view, srcView_host);
      } else {
        auto srcView_device = this->getLocalViewDevice(Access::ReadOnly);
        // DEEP_COPY REVIEW - NOT TESTED
        Kokkos::deep_copy(A_view, srcView_device);
      }
    } else {
      for (size_t j = 0; j < numCols; ++j) {
        const size_t srcCol = this->whichVectors_[j];
        auto dstColView     = Kokkos::subview(A_view, rowRange, j);
 
        if (useHostView) {
          auto srcView_host    = this->getLocalViewHost(Access::ReadOnly);
          auto srcColView_host = Kokkos::subview(srcView_host, rowRange, srcCol);
          // DEEP_COPY REVIEW - NOT TESTED
          Kokkos::deep_copy(dstColView, srcColView_host);
        } else {
          auto srcView_device    = this->getLocalViewDevice(Access::ReadOnly);
          auto srcColView_device = Kokkos::subview(srcView_device, rowRange, srcCol);
          // DEEP_COPY REVIEW - NOT TESTED
          Kokkos::deep_copy(dstColView, srcColView_device);
        }
      }
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    get2dCopy(const Teuchos::ArrayView<const Teuchos::ArrayView<Scalar> >& ArrayOfPtrs) const {
  typedef Vector<Scalar, LocalOrdinal, GlobalOrdinal, Node> V;
  const char tfecfFuncName[] = "get2dCopy: ";
  const size_t numRows       = this->getLocalLength();
  const size_t numCols       = this->getNumVectors();
 
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      static_cast<size_t>(ArrayOfPtrs.size()) != numCols,
      std::runtime_error,
      "Input array of pointers must contain as many "
      "entries (arrays) as the MultiVector has columns.  ArrayOfPtrs.size() = "
          << ArrayOfPtrs.size() << " != getNumVectors() = " << numCols << ".");
 
  if (numRows != 0 && numCols != 0) {
    // No side effects until we've validated the input.
    for (size_t j = 0; j < numCols; ++j) {
      const size_t dstLen = static_cast<size_t>(ArrayOfPtrs[j].size());
      TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
          dstLen < numRows, std::invalid_argument, "Array j = " << j << " of "
                                                                        "the input array of arrays is not long enough to fit all entries in "
                                                                        "that column of the MultiVector.  ArrayOfPtrs[j].size() = "
                                                                << dstLen << " < getLocalLength() = " << numRows << ".");
    }
 
    // We've validated the input, so it's safe to start copying.
    for (size_t j = 0; j < numCols; ++j) {
      Teuchos::RCP<const V> X_j = this->getVector(j);
      const size_t LDA          = static_cast<size_t>(ArrayOfPtrs[j].size());
      X_j->get1dCopy(ArrayOfPtrs[j], LDA);
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::ArrayRCP<const Scalar>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    get1dView() const {
  if (getLocalLength() == 0 || getNumVectors() == 0) {
    return Teuchos::null;
  } else {
    TEUCHOS_TEST_FOR_EXCEPTION(
        !isConstantStride(), std::runtime_error,
        "Tpetra::MultiVector::"
        "get1dView: This MultiVector does not have constant stride, so it is "
        "not possible to view its data as a single array.  You may check "
        "whether a MultiVector has constant stride by calling "
        "isConstantStride().");
    // Since get1dView() is and was always marked const, I have to
    // cast away const here in order not to break backwards
    // compatibility.
    auto X_lcl = getLocalViewHost(Access::ReadOnly);
    Teuchos::ArrayRCP<const impl_scalar_type> dataAsArcp =
        Kokkos::Compat::persistingView(X_lcl);
    return Teuchos::arcp_reinterpret_cast<const Scalar>(dataAsArcp);
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::ArrayRCP<Scalar>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    get1dViewNonConst() {
  if (this->getLocalLength() == 0 || this->getNumVectors() == 0) {
    return Teuchos::null;
  } else {
    TEUCHOS_TEST_FOR_EXCEPTION(!isConstantStride(), std::runtime_error,
                               "Tpetra::MultiVector::"
                               "get1dViewNonConst: This MultiVector does not have constant stride, "
                               "so it is not possible to view its data as a single array.  You may "
                               "check whether a MultiVector has constant stride by calling "
                               "isConstantStride().");
    auto X_lcl = getLocalViewHost(Access::ReadWrite);
    Teuchos::ArrayRCP<impl_scalar_type> dataAsArcp =
        Kokkos::Compat::persistingView(X_lcl);
    return Teuchos::arcp_reinterpret_cast<Scalar>(dataAsArcp);
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::ArrayRCP<Teuchos::ArrayRCP<Scalar> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    get2dViewNonConst() {
  auto X_lcl = getLocalViewHost(Access::ReadWrite);
 
  // Don't use the row range here on the outside, in order to avoid
  // a strided return type (in case Kokkos::subview is conservative
  // about that).  Instead, use the row range for the column views
  // in the loop.
  const size_t myNumRows = this->getLocalLength();
  const size_t numCols   = this->getNumVectors();
  const Kokkos::pair<size_t, size_t> rowRange(0, myNumRows);
 
  Teuchos::ArrayRCP<Teuchos::ArrayRCP<Scalar> > views(numCols);
  for (size_t j = 0; j < numCols; ++j) {
    const size_t col = this->isConstantStride() ? j : this->whichVectors_[j];
    auto X_lcl_j     = Kokkos::subview(X_lcl, rowRange, col);
    Teuchos::ArrayRCP<impl_scalar_type> X_lcl_j_arcp =
        Kokkos::Compat::persistingView(X_lcl_j);
    views[j] = Teuchos::arcp_reinterpret_cast<Scalar>(X_lcl_j_arcp);
  }
  return views;
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
typename MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::dual_view_type::t_host::const_type
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getLocalViewHost(Access::ReadOnlyStruct s) const {
  return view_.getHostView(s);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
typename MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::dual_view_type::t_host
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getLocalViewHost(Access::ReadWriteStruct s) {
  return view_.getHostView(s);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
typename MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::dual_view_type::t_host
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getLocalViewHost(Access::OverwriteAllStruct s) {
  return view_.getHostView(s);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
typename MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::dual_view_type::t_dev::const_type
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getLocalViewDevice(Access::ReadOnlyStruct s) const {
  return view_.getDeviceView(s);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
typename MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::dual_view_type::t_dev
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getLocalViewDevice(Access::ReadWriteStruct s) {
  return view_.getDeviceView(s);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
typename MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::dual_view_type::t_dev
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getLocalViewDevice(Access::OverwriteAllStruct s) {
  return view_.getDeviceView(s);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
typename MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::wrapped_dual_view_type
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getWrappedDualView() const {
  return view_;
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::ArrayRCP<Teuchos::ArrayRCP<const Scalar> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    get2dView() const {
  // Since get2dView() is and was always marked const, I have to
  // cast away const here in order not to break backwards
  // compatibility.
  auto X_lcl = getLocalViewHost(Access::ReadOnly);
 
  // Don't use the row range here on the outside, in order to avoid
  // a strided return type (in case Kokkos::subview is conservative
  // about that).  Instead, use the row range for the column views
  // in the loop.
  const size_t myNumRows = this->getLocalLength();
  const size_t numCols   = this->getNumVectors();
  const Kokkos::pair<size_t, size_t> rowRange(0, myNumRows);
 
  Teuchos::ArrayRCP<Teuchos::ArrayRCP<const Scalar> > views(numCols);
  for (size_t j = 0; j < numCols; ++j) {
    const size_t col = this->isConstantStride() ? j : this->whichVectors_[j];
    auto X_lcl_j     = Kokkos::subview(X_lcl, rowRange, col);
    Teuchos::ArrayRCP<const impl_scalar_type> X_lcl_j_arcp =
        Kokkos::Compat::persistingView(X_lcl_j);
    views[j] = Teuchos::arcp_reinterpret_cast<const Scalar>(X_lcl_j_arcp);
  }
  return views;
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    multiply(Teuchos::ETransp transA,
             Teuchos::ETransp transB,
             const Scalar& alpha,
             const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& A,
             const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& B,
             const Scalar& beta) {
  using std::endl;
  using Teuchos::CONJ_TRANS;
  using Teuchos::NO_TRANS;
  using Teuchos::RCP;
  using Teuchos::rcp;
  using Teuchos::rcpFromRef;
  using Teuchos::TRANS;
  using ::Tpetra::Details::ProfilingRegion;
#if KOKKOS_VERSION >= 40799
  using ATS = KokkosKernels::ArithTraits<impl_scalar_type>;
#else
  using ATS = Kokkos::ArithTraits<impl_scalar_type>;
#endif
  using LO                   = local_ordinal_type;
  using STS                  = Teuchos::ScalarTraits<Scalar>;
  using MV                   = MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>;
  const char tfecfFuncName[] = "multiply: ";
  ProfilingRegion region("Tpetra::MV::multiply");
 
  // This routine performs a variety of matrix-matrix multiply
  // operations, interpreting the MultiVector (this-aka C , A and B)
  // as 2D matrices.  Variations are due to the fact that A, B and C
  // can be locally replicated or globally distributed MultiVectors
  // and that we may or may not operate with the transpose of A and
  // B.  Possible cases are:
  //
  //     Operations                          # Cases  Notes
  //  1) C(local) = A^X(local) * B^X(local)  4        X=Trans or Not, no comm needed
  //  2) C(local) = A^T(distr) * B  (distr)  1        2-D dot product, replicate C
  //  3) C(distr) = A  (distr) * B^X(local)  2        2-D vector update, no comm needed
  //
  // The following operations are not meaningful for 1-D
  // distributions:
  //
  // u1) C(local) = A^T(distr) * B^T(distr)  1
  // u2) C(local) = A  (distr) * B^X(distr)  2
  // u3) C(distr) = A^X(local) * B^X(local)  4
  // u4) C(distr) = A^X(local) * B^X(distr)  4
  // u5) C(distr) = A^T(distr) * B^X(local)  2
  // u6) C(local) = A^X(distr) * B^X(local)  4
  // u7) C(distr) = A^X(distr) * B^X(local)  4
  // u8) C(local) = A^X(local) * B^X(distr)  4
  //
  // Total number of cases: 32 (= 2^5).
 
  impl_scalar_type beta_local = beta;  // local copy of beta; might be reassigned below
 
  const bool A_is_local = !A.isDistributed();
  const bool B_is_local = !B.isDistributed();
  const bool C_is_local = !this->isDistributed();
 
  // In debug mode, check compatibility of local dimensions.  We
  // only do this in debug mode, since it requires an all-reduce
  // to ensure correctness on all processses.  It's entirely
  // possible that only some processes may have incompatible local
  // dimensions.  Throwing an exception only on those processes
  // could cause this method to hang.
  const bool debug = ::Tpetra::Details::Behavior::debug();
  if (debug) {
    auto myMap = this->getMap();
    if (!myMap.is_null() && !myMap->getComm().is_null()) {
      using Teuchos::outArg;
      using Teuchos::REDUCE_MIN;
      using Teuchos::reduceAll;
 
      auto comm = myMap->getComm();
      const size_t A_nrows =
          (transA != NO_TRANS) ? A.getNumVectors() : A.getLocalLength();
      const size_t A_ncols =
          (transA != NO_TRANS) ? A.getLocalLength() : A.getNumVectors();
      const size_t B_nrows =
          (transB != NO_TRANS) ? B.getNumVectors() : B.getLocalLength();
      const size_t B_ncols =
          (transB != NO_TRANS) ? B.getLocalLength() : B.getNumVectors();
 
      const bool lclBad = this->getLocalLength() != A_nrows ||
                          this->getNumVectors() != B_ncols || A_ncols != B_nrows;
 
      const int myRank = comm->getRank();
      std::ostringstream errStrm;
      if (this->getLocalLength() != A_nrows) {
        errStrm << "Proc " << myRank << ": this->getLocalLength()="
                << this->getLocalLength() << " != A_nrows=" << A_nrows
                << "." << std::endl;
      }
      if (this->getNumVectors() != B_ncols) {
        errStrm << "Proc " << myRank << ": this->getNumVectors()="
                << this->getNumVectors() << " != B_ncols=" << B_ncols
                << "." << std::endl;
      }
      if (A_ncols != B_nrows) {
        errStrm << "Proc " << myRank << ": A_ncols="
                << A_ncols << " != B_nrows=" << B_nrows
                << "." << std::endl;
      }
 
      const int lclGood = lclBad ? 0 : 1;
      int gblGood       = 0;
      reduceAll<int, int>(*comm, REDUCE_MIN, lclGood, outArg(gblGood));
      if (gblGood != 1) {
        std::ostringstream os;
        ::Tpetra::Details::gathervPrint(os, errStrm.str(), *comm);
 
        TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(true, std::runtime_error,
                                              "Inconsistent local dimensions on at "
                                              "least one process in this object's communicator."
                                                  << std::endl
                                                  << "Operation: "
                                                  << "C(" << (C_is_local ? "local" : "distr") << ") = "
                                                  << alpha << "*A"
                                                  << (transA == Teuchos::TRANS ? "^T" : (transA == Teuchos::CONJ_TRANS ? "^H" : ""))
                                                  << "(" << (A_is_local ? "local" : "distr") << ") * "
                                                  << beta << "*B"
                                                  << (transA == Teuchos::TRANS ? "^T" : (transA == Teuchos::CONJ_TRANS ? "^H" : ""))
                                                  << "(" << (B_is_local ? "local" : "distr") << ")." << std::endl
                                                  << "Global dimensions: C(" << this->getGlobalLength() << ", "
                                                  << this->getNumVectors() << "), A(" << A.getGlobalLength()
                                                  << ", " << A.getNumVectors() << "), B(" << B.getGlobalLength()
                                                  << ", " << B.getNumVectors() << ")." << std::endl
                                                  << os.str());
      }
    }
  }
 
  // Case 1: C(local) = A^X(local) * B^X(local)
  const bool Case1 = C_is_local && A_is_local && B_is_local;
  // Case 2: C(local) = A^T(distr) * B  (distr)
  const bool Case2 = C_is_local && !A_is_local && !B_is_local &&
                     transA != NO_TRANS &&
                     transB == NO_TRANS;
  // Case 3: C(distr) = A  (distr) * B^X(local)
  const bool Case3 = !C_is_local && !A_is_local && B_is_local &&
                     transA == NO_TRANS;
 
  // Test that we are considering a meaningful case
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(!Case1 && !Case2 && !Case3, std::runtime_error,
                                        "Multiplication of op(A) and op(B) into *this is not a "
                                        "supported use case.");
 
  if (beta != STS::zero() && Case2) {
    // If Case2, then C is local and contributions must be summed
    // across all processes.  However, if beta != 0, then accumulate
    // beta*C into the sum.  When summing across all processes, we
    // only want to accumulate this once, so set beta == 0 on all
    // processes except Process 0.
    const int myRank = this->getMap()->getComm()->getRank();
    if (myRank != 0) {
      beta_local = ATS::zero();
    }
  }
 
  // We only know how to do matrix-matrix multiplies if all the
  // MultiVectors have constant stride.  If not, we have to make
  // temporary copies of those MultiVectors (including possibly
  // *this) that don't have constant stride.
  RCP<MV> C_tmp;
  if (!isConstantStride()) {
    C_tmp = rcp(new MV(*this, Teuchos::Copy));  // deep copy
  } else {
    C_tmp = rcp(this, false);
  }
 
  RCP<const MV> A_tmp;
  if (!A.isConstantStride()) {
    A_tmp = rcp(new MV(A, Teuchos::Copy));  // deep copy
  } else {
    A_tmp = rcpFromRef(A);
  }
 
  RCP<const MV> B_tmp;
  if (!B.isConstantStride()) {
    B_tmp = rcp(new MV(B, Teuchos::Copy));  // deep copy
  } else {
    B_tmp = rcpFromRef(B);
  }
 
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(!C_tmp->isConstantStride() || !B_tmp->isConstantStride() ||
                                            !A_tmp->isConstantStride(),
                                        std::logic_error,
                                        "Failed to make temporary constant-stride copies of MultiVectors.");
 
  {
    const LO A_lclNumRows = A_tmp->getLocalLength();
    const LO A_numVecs    = A_tmp->getNumVectors();
    auto A_lcl            = A_tmp->getLocalViewDevice(Access::ReadOnly);
    auto A_sub            = Kokkos::subview(A_lcl,
                                            std::make_pair(LO(0), A_lclNumRows),
                                            std::make_pair(LO(0), A_numVecs));
 
    const LO B_lclNumRows = B_tmp->getLocalLength();
    const LO B_numVecs    = B_tmp->getNumVectors();
    auto B_lcl            = B_tmp->getLocalViewDevice(Access::ReadOnly);
    auto B_sub            = Kokkos::subview(B_lcl,
                                            std::make_pair(LO(0), B_lclNumRows),
                                            std::make_pair(LO(0), B_numVecs));
 
    const LO C_lclNumRows = C_tmp->getLocalLength();
    const LO C_numVecs    = C_tmp->getNumVectors();
 
    auto C_lcl         = C_tmp->getLocalViewDevice(Access::ReadWrite);
    auto C_sub         = Kokkos::subview(C_lcl,
                                         std::make_pair(LO(0), C_lclNumRows),
                                         std::make_pair(LO(0), C_numVecs));
    const char ctransA = (transA == Teuchos::NO_TRANS ? 'N' : (transA == Teuchos::TRANS ? 'T' : 'C'));
    const char ctransB = (transB == Teuchos::NO_TRANS ? 'N' : (transB == Teuchos::TRANS ? 'T' : 'C'));
    const impl_scalar_type alpha_IST(alpha);
 
    ProfilingRegion regionGemm("Tpetra::MV::multiply-call-gemm");
 
    KokkosBlas::gemm(&ctransA, &ctransB, alpha_IST, A_sub, B_sub,
                     beta_local, C_sub);
  }
 
  if (!isConstantStride()) {
    ::Tpetra::deep_copy(*this, *C_tmp);  // Copy the result back into *this.
  }
 
  // Dispose of (possibly) extra copies of A and B.
  A_tmp = Teuchos::null;
  B_tmp = Teuchos::null;
 
  // If Case 2 then sum up *this and distribute it to all processes.
  if (Case2) {
    this->reduce();
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    elementWiseMultiply(Scalar scalarAB,
                        const Vector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& A,
                        const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& B,
                        Scalar scalarThis) {
  using Kokkos::ALL;
  using Kokkos::subview;
  const char tfecfFuncName[] = "elementWiseMultiply: ";
 
  const size_t lclNumRows = this->getLocalLength();
  const size_t numVecs    = this->getNumVectors();
 
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(lclNumRows != A.getLocalLength() || lclNumRows != B.getLocalLength(),
                                        std::runtime_error, "MultiVectors do not have the same local length.");
  TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(
      numVecs != B.getNumVectors(), std::runtime_error,
      "this->getNumVectors"
      "() = "
          << numVecs << " != B.getNumVectors() = " << B.getNumVectors()
          << ".");
 
  auto this_view = this->getLocalViewDevice(Access::ReadWrite);
  auto A_view    = A.getLocalViewDevice(Access::ReadOnly);
  auto B_view    = B.getLocalViewDevice(Access::ReadOnly);
 
  if (isConstantStride() && B.isConstantStride()) {
    // A is just a Vector; it only has one column, so it always has
    // constant stride.
    //
    // If both *this and B have constant stride, we can do an
    // element-wise multiply on all columns at once.
    KokkosBlas::mult(scalarThis,
                     this_view,
                     scalarAB,
                     subview(A_view, ALL(), 0),
                     B_view);
  } else {
    for (size_t j = 0; j < numVecs; ++j) {
      const size_t C_col = isConstantStride() ? j : whichVectors_[j];
      const size_t B_col = B.isConstantStride() ? j : B.whichVectors_[j];
      KokkosBlas::mult(scalarThis,
                       subview(this_view, ALL(), C_col),
                       scalarAB,
                       subview(A_view, ALL(), 0),
                       subview(B_view, ALL(), B_col));
    }
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    reduce() {
  using ::Tpetra::Details::allReduceView;
  using ::Tpetra::Details::ProfilingRegion;
  ProfilingRegion region("Tpetra::MV::reduce");
 
  const auto map = this->getMap();
  if (map.get() == nullptr) {
    return;
  }
  const auto comm = map->getComm();
  if (comm.get() == nullptr) {
    return;
  }
 
  // Avoid giving device buffers to MPI.  Even if MPI handles them
  // correctly, doing so may not perform well.
  const bool changed_on_device = this->need_sync_host();
  if (changed_on_device) {
    // NOTE (mfh 17 Mar 2019) If we ever get rid of UVM, then device
    // and host will be separate allocations.  In that case, it may
    // pay to do the all-reduce from device to host.
    Kokkos::fence("MultiVector::reduce");  // for UVM getLocalViewDevice is UVM which can be read as host by allReduceView, so we must not read until device is fenced
    auto X_lcl = this->getLocalViewDevice(Access::ReadWrite);
    allReduceView(X_lcl, X_lcl, *comm);
  } else {
    auto X_lcl = this->getLocalViewHost(Access::ReadWrite);
    allReduceView(X_lcl, X_lcl, *comm);
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    replaceLocalValue(const LocalOrdinal lclRow,
                      const size_t col,
                      const impl_scalar_type& ScalarValue) {
  if (::Tpetra::Details::Behavior::debug()) {
    const LocalOrdinal minLocalIndex = this->getMap()->getMinLocalIndex();
    const LocalOrdinal maxLocalIndex = this->getMap()->getMaxLocalIndex();
    TEUCHOS_TEST_FOR_EXCEPTION(
        lclRow < minLocalIndex || lclRow > maxLocalIndex,
        std::runtime_error,
        "Tpetra::MultiVector::replaceLocalValue: row index " << lclRow
                                                             << " is invalid.  The range of valid row indices on this process "
                                                             << this->getMap()->getComm()->getRank() << " is [" << minLocalIndex
                                                             << ", " << maxLocalIndex << "].");
    TEUCHOS_TEST_FOR_EXCEPTION(
        vectorIndexOutOfRange(col),
        std::runtime_error,
        "Tpetra::MultiVector::replaceLocalValue: vector index " << col
                                                                << " of the multivector is invalid.");
  }
 
  auto view            = this->getLocalViewHost(Access::ReadWrite);
  const size_t colInd  = isConstantStride() ? col : whichVectors_[col];
  view(lclRow, colInd) = ScalarValue;
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    sumIntoLocalValue(const LocalOrdinal lclRow,
                      const size_t col,
                      const impl_scalar_type& value,
                      const bool atomic) {
  if (::Tpetra::Details::Behavior::debug()) {
    const LocalOrdinal minLocalIndex = this->getMap()->getMinLocalIndex();
    const LocalOrdinal maxLocalIndex = this->getMap()->getMaxLocalIndex();
    TEUCHOS_TEST_FOR_EXCEPTION(
        lclRow < minLocalIndex || lclRow > maxLocalIndex,
        std::runtime_error,
        "Tpetra::MultiVector::sumIntoLocalValue: row index " << lclRow
                                                             << " is invalid.  The range of valid row indices on this process "
                                                             << this->getMap()->getComm()->getRank() << " is [" << minLocalIndex
                                                             << ", " << maxLocalIndex << "].");
    TEUCHOS_TEST_FOR_EXCEPTION(
        vectorIndexOutOfRange(col),
        std::runtime_error,
        "Tpetra::MultiVector::sumIntoLocalValue: vector index " << col
                                                                << " of the multivector is invalid.");
  }
 
  const size_t colInd = isConstantStride() ? col : whichVectors_[col];
 
  auto view = this->getLocalViewHost(Access::ReadWrite);
  if (atomic) {
    Kokkos::atomic_add(&(view(lclRow, colInd)), value);
  } else {
    view(lclRow, colInd) += value;
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    replaceGlobalValue(const GlobalOrdinal gblRow,
                       const size_t col,
                       const impl_scalar_type& ScalarValue) {
  // mfh 23 Nov 2015: Use map_ and not getMap(), because the latter
  // touches the RCP's reference count, which isn't thread safe.
  const LocalOrdinal lclRow = this->map_->getLocalElement(gblRow);
 
  if (::Tpetra::Details::Behavior::debug()) {
    const char tfecfFuncName[] = "replaceGlobalValue: ";
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(lclRow == Teuchos::OrdinalTraits<LocalOrdinal>::invalid(),
                                          std::runtime_error,
                                          "Global row index " << gblRow << " is not present on this process "
                                                              << this->getMap()->getComm()->getRank() << ".");
    TEUCHOS_TEST_FOR_EXCEPTION_CLASS_FUNC(this->vectorIndexOutOfRange(col), std::runtime_error,
                                          "Vector index " << col << " of the MultiVector is invalid.");
  }
 
  this->replaceLocalValue(lclRow, col, ScalarValue);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    sumIntoGlobalValue(const GlobalOrdinal globalRow,
                       const size_t col,
                       const impl_scalar_type& value,
                       const bool atomic) {
  // mfh 23 Nov 2015: Use map_ and not getMap(), because the latter
  // touches the RCP's reference count, which isn't thread safe.
  const LocalOrdinal lclRow = this->map_->getLocalElement(globalRow);
 
  if (::Tpetra::Details::Behavior::debug()) {
    TEUCHOS_TEST_FOR_EXCEPTION(
        lclRow == Teuchos::OrdinalTraits<LocalOrdinal>::invalid(),
        std::runtime_error,
        "Tpetra::MultiVector::sumIntoGlobalValue: Global row index " << globalRow
                                                                     << " is not present on this process "
                                                                     << this->getMap()->getComm()->getRank() << ".");
    TEUCHOS_TEST_FOR_EXCEPTION(
        vectorIndexOutOfRange(col),
        std::runtime_error,
        "Tpetra::MultiVector::sumIntoGlobalValue: Vector index " << col
                                                                 << " of the multivector is invalid.");
  }
 
  this->sumIntoLocalValue(lclRow, col, value, atomic);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
template <class T>
Teuchos::ArrayRCP<T>
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    getSubArrayRCP(Teuchos::ArrayRCP<T> arr,
                   size_t j) const {
  typedef Kokkos::DualView<impl_scalar_type*,
                           typename dual_view_type::array_layout,
                           execution_space>
      col_dual_view_type;
  const size_t col = isConstantStride() ? j : whichVectors_[j];
  col_dual_view_type X_col =
      Kokkos::subview(view_, Kokkos::ALL(), col);
  return Kokkos::Compat::persistingView(X_col.view_device());
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
bool MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    need_sync_host() const {
  return view_.need_sync_host();
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
bool MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    need_sync_device() const {
  return view_.need_sync_device();
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
std::string
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    descriptionImpl(const std::string& className) const {
  using Teuchos::TypeNameTraits;
 
  std::ostringstream out;
  out << "\"" << className << "\": {";
  out << "Template parameters: {Scalar: " << TypeNameTraits<Scalar>::name()
      << ", LocalOrdinal: " << TypeNameTraits<LocalOrdinal>::name()
      << ", GlobalOrdinal: " << TypeNameTraits<GlobalOrdinal>::name()
      << ", Node" << Node::name()
      << "}, ";
  if (this->getObjectLabel() != "") {
    out << "Label: \"" << this->getObjectLabel() << "\", ";
  }
  out << ", numRows: " << this->getGlobalLength();
  if (className != "Tpetra::Vector") {
    out << ", numCols: " << this->getNumVectors()
        << ", isConstantStride: " << this->isConstantStride();
  }
  if (this->isConstantStride()) {
    out << ", columnStride: " << this->getStride();
  }
  out << "}";
 
  return out.str();
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
std::string
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    description() const {
  return this->descriptionImpl("Tpetra::MultiVector");
}
 
namespace Details {
template <typename ViewType>
void print_vector(Teuchos::FancyOStream& out, const char* prefix, const ViewType& v) {
  using std::endl;
  static_assert(Kokkos::SpaceAccessibility<Kokkos::HostSpace, typename ViewType::memory_space>::accessible,
                "Tpetra::MultiVector::localDescribeToString: Details::print_vector should be given a host-accessible view.");
  static_assert(ViewType::rank == 2,
                "Tpetra::MultiVector::localDescribeToString: Details::print_vector should be given a rank-2 view.");
  // The square braces [] and their contents are in Matlab
  // format, so users may copy and paste directly into Matlab.
  out << "Values(" << prefix << "): " << std::endl
      << "[";
  const size_t numRows = v.extent(0);
  const size_t numCols = v.extent(1);
  if (numCols == 1) {
    for (size_t i = 0; i < numRows; ++i) {
      out << v(i, 0);
      if (i + 1 < numRows) {
        out << "; ";
      }
    }
  } else {
    for (size_t i = 0; i < numRows; ++i) {
      for (size_t j = 0; j < numCols; ++j) {
        out << v(i, j);
        if (j + 1 < numCols) {
          out << ", ";
        }
      }
      if (i + 1 < numRows) {
        out << "; ";
      }
    }
  }
  out << "]" << endl;
}
}  // namespace Details
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
std::string
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    localDescribeToString(const Teuchos::EVerbosityLevel vl) const {
  typedef LocalOrdinal LO;
  using std::endl;
 
  if (vl <= Teuchos::VERB_LOW) {
    return std::string();
  }
  auto map = this->getMap();
  if (map.is_null()) {
    return std::string();
  }
  auto outStringP            = Teuchos::rcp(new std::ostringstream());
  auto outp                  = Teuchos::getFancyOStream(outStringP);
  Teuchos::FancyOStream& out = *outp;
  auto comm                  = map->getComm();
  const int myRank           = comm->getRank();
  const int numProcs         = comm->getSize();
 
  out << "Process " << myRank << " of " << numProcs << ":" << endl;
  Teuchos::OSTab tab1(out);
 
  // VERB_MEDIUM and higher prints getLocalLength()
  const LO lclNumRows = static_cast<LO>(this->getLocalLength());
  out << "Local number of rows: " << lclNumRows << endl;
 
  if (vl > Teuchos::VERB_MEDIUM) {
    // VERB_HIGH and higher prints isConstantStride() and getStride().
    // The first is only relevant if the Vector has multiple columns.
    if (this->getNumVectors() != static_cast<size_t>(1)) {
      out << "isConstantStride: " << this->isConstantStride() << endl;
    }
    if (this->isConstantStride()) {
      out << "Column stride: " << this->getStride() << endl;
    }
 
    if (vl > Teuchos::VERB_HIGH && lclNumRows > 0) {
      // VERB_EXTREME prints values.  If we're not doing univied memory, we'll
      // so we can't use our regular accessor functins
 
      // NOTE: This is an occasion where we do *not* want the auto-sync stuff
      // to trigger (since this function is conceptually const).  Thus, we
      // get *copies* of the view's data instead.
      auto X_dev  = view_.getDeviceCopy();
      auto X_host = view_.getHostCopy();
 
      if (X_dev.data() == X_host.data()) {
        // One single allocation
        Details::print_vector(out, "unified", X_host);
      } else {
        Details::print_vector(out, "host", X_host);
        Details::print_vector(out, "dev", X_dev);
      }
    }
  }
  out.flush();  // make sure the ostringstream got everything
  return outStringP->str();
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    describeImpl(Teuchos::FancyOStream& out,
                 const std::string& className,
                 const Teuchos::EVerbosityLevel verbLevel) const {
  using std::endl;
  using Teuchos::TypeNameTraits;
  using Teuchos::VERB_DEFAULT;
  using Teuchos::VERB_LOW;
  using Teuchos::VERB_NONE;
  const Teuchos::EVerbosityLevel vl =
      (verbLevel == VERB_DEFAULT) ? VERB_LOW : verbLevel;
 
  if (vl == VERB_NONE) {
    return;  // don't print anything
  }
  // If this Vector's Comm is null, then the Vector does not
  // participate in collective operations with the other processes.
  // In that case, it is not even legal to call this method.  The
  // reasonable thing to do in that case is nothing.
  auto map = this->getMap();
  if (map.is_null()) {
    return;
  }
  auto comm = map->getComm();
  if (comm.is_null()) {
    return;
  }
 
  const int myRank = comm->getRank();
 
  // Only Process 0 should touch the output stream, but this method
  // in general may need to do communication.  Thus, we may need to
  // preserve the current tab level across multiple "if (myRank ==
  // 0) { ... }" inner scopes.  This is why we sometimes create
  // OSTab instances by pointer, instead of by value.  We only need
  // to create them by pointer if the tab level must persist through
  // multiple inner scopes.
  Teuchos::RCP<Teuchos::OSTab> tab0, tab1;
 
  // VERB_LOW and higher prints the equivalent of description().
  if (myRank == 0) {
    tab0 = Teuchos::rcp(new Teuchos::OSTab(out));
    out << "\"" << className << "\":" << endl;
    tab1 = Teuchos::rcp(new Teuchos::OSTab(out));
    {
      out << "Template parameters:" << endl;
      Teuchos::OSTab tab2(out);
      out << "Scalar: " << TypeNameTraits<Scalar>::name() << endl
          << "LocalOrdinal: " << TypeNameTraits<LocalOrdinal>::name() << endl
          << "GlobalOrdinal: " << TypeNameTraits<GlobalOrdinal>::name() << endl
          << "Node: " << Node::name() << endl;
    }
    if (this->getObjectLabel() != "") {
      out << "Label: \"" << this->getObjectLabel() << "\", ";
    }
    out << "Global number of rows: " << this->getGlobalLength() << endl;
    if (className != "Tpetra::Vector") {
      out << "Number of columns: " << this->getNumVectors() << endl;
    }
    // getStride() may differ on different processes, so it (and
    // isConstantStride()) properly belong to per-process data.
  }
 
  // This is collective over the Map's communicator.
  if (vl > VERB_LOW) {  // VERB_MEDIUM, VERB_HIGH, or VERB_EXTREME
    const std::string lclStr = this->localDescribeToString(vl);
    ::Tpetra::Details::gathervPrint(out, lclStr, *comm);
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    describe(Teuchos::FancyOStream& out,
             const Teuchos::EVerbosityLevel verbLevel) const {
  this->describeImpl(out, "Tpetra::MultiVector", verbLevel);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    removeEmptyProcessesInPlace(const Teuchos::RCP<const map_type>& newMap) {
  replaceMap(newMap);
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    assign(const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& src) {
  using ::Tpetra::Details::localDeepCopy;
  const char prefix[] = "Tpetra::MultiVector::assign: ";
 
  TEUCHOS_TEST_FOR_EXCEPTION(this->getGlobalLength() != src.getGlobalLength() ||
                                 this->getNumVectors() != src.getNumVectors(),
                             std::invalid_argument,
                             prefix << "Global dimensions of the two Tpetra::MultiVector "
                                       "objects do not match.  src has dimensions ["
                                    << src.getGlobalLength()
                                    << "," << src.getNumVectors() << "], and *this has dimensions ["
                                    << this->getGlobalLength() << "," << this->getNumVectors() << "].");
  // FIXME (mfh 28 Jul 2014) Don't throw; just set a local error flag.
  TEUCHOS_TEST_FOR_EXCEPTION(this->getLocalLength() != src.getLocalLength(), std::invalid_argument,
                             prefix << "The local row counts of the two Tpetra::MultiVector "
                                       "objects do not match.  src has "
                                    << src.getLocalLength() << " row(s) "
                                    << " and *this has " << this->getLocalLength() << " row(s).");
 
  // See #1510.  We're writing to *this, so we don't care about its
  // contents in either memory space, and we don't want
  // DualView::modify to complain about "concurrent modification" of
  // host and device Views.
 
  // KJ: this is problematic. assign funtion is used to construct a subvector
  //     if the sync flag is reset here, it lose all our control over getLocalView interface
  // this->clear_sync_state();
 
  // If need sync to device, then host has most recent version.
  const bool src_last_updated_on_host = src.need_sync_device();
 
  if (src_last_updated_on_host) {
    localDeepCopy(this->getLocalViewHost(Access::ReadWrite),
                  src.getLocalViewHost(Access::ReadOnly),
                  this->isConstantStride(),
                  src.isConstantStride(),
                  this->whichVectors_(),
                  src.whichVectors_());
  } else {
    localDeepCopy(this->getLocalViewDevice(Access::ReadWrite),
                  src.getLocalViewDevice(Access::ReadOnly),
                  this->isConstantStride(),
                  src.isConstantStride(),
                  this->whichVectors_(),
                  src.whichVectors_());
  }
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
template <class T>
Teuchos::RCP<MultiVector<T, LocalOrdinal, GlobalOrdinal, Node> >
MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    convert() const {
  using Teuchos::RCP;
 
  auto newMV = Teuchos::rcp(new MultiVector<T, LocalOrdinal, GlobalOrdinal, Node>(this->getMap(),
                                                                                  this->getNumVectors(),
                                                                                  /*zeroOut=*/false));
  Tpetra::deep_copy(*newMV, *this);
  return newMV;
}
 
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
bool MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
    isSameSize(const MultiVector<Scalar, LocalOrdinal, GlobalOrdinal, Node>& vec) const {
  using ::Tpetra::Details::PackTraits;
 
  const size_t l1 = this->getLocalLength();
  const size_t l2 = vec.getLocalLength();
  if ((l1 != l2) || (this->getNumVectors() != vec.getNumVectors())) {
    return false;
  }
 
  return true;
}
 
template <class ST, class LO, class GO, class NT>
void MultiVector<ST, LO, GO, NT>::
    swap(MultiVector<ST, LO, GO, NT>& mv) {
  std::swap(mv.map_, this->map_);
  std::swap(mv.view_, this->view_);
  std::swap(mv.whichVectors_, this->whichVectors_);
}
 
#ifdef HAVE_TPETRACORE_TEUCHOSNUMERICS
template <class ST, class LO, class GO, class NT>
void deep_copy(MultiVector<ST, LO, GO, NT>& dst,
               const Teuchos::SerialDenseMatrix<int, ST>& src) {
  using ::Tpetra::Details::localDeepCopy;
  using MV  = MultiVector<ST, LO, GO, NT>;
  using IST = typename MV::impl_scalar_type;
  using input_view_type =
      Kokkos::View<const IST**, Kokkos::LayoutLeft,
                   Kokkos::HostSpace, Kokkos::MemoryUnmanaged>;
  using pair_type = std::pair<LO, LO>;
 
  const LO numRows = static_cast<LO>(src.numRows());
  const LO numCols = static_cast<LO>(src.numCols());
 
  TEUCHOS_TEST_FOR_EXCEPTION(numRows != static_cast<LO>(dst.getLocalLength()) ||
                                 numCols != static_cast<LO>(dst.getNumVectors()),
                             std::invalid_argument, "Tpetra::deep_copy: On Process " << dst.getMap()->getComm()->getRank() << ", dst is " << dst.getLocalLength() << " x " << dst.getNumVectors() << ", but src is " << numRows << " x " << numCols << ".");
 
  const IST* src_raw = reinterpret_cast<const IST*>(src.values());
  input_view_type src_orig(src_raw, src.stride(), numCols);
  input_view_type src_view =
      Kokkos::subview(src_orig, pair_type(0, numRows), Kokkos::ALL());
 
  constexpr bool src_isConstantStride = true;
  Teuchos::ArrayView<const size_t> srcWhichVectors(nullptr, 0);
  localDeepCopy(dst.getLocalViewHost(Access::ReadWrite),
                src_view,
                dst.isConstantStride(),
                src_isConstantStride,
                getMultiVectorWhichVectors(dst),
                srcWhichVectors);
}
 
template <class ST, class LO, class GO, class NT>
void deep_copy(Teuchos::SerialDenseMatrix<int, ST>& dst,
               const MultiVector<ST, LO, GO, NT>& src) {
  using ::Tpetra::Details::localDeepCopy;
  using MV  = MultiVector<ST, LO, GO, NT>;
  using IST = typename MV::impl_scalar_type;
  using output_view_type =
      Kokkos::View<IST**, Kokkos::LayoutLeft,
                   Kokkos::HostSpace, Kokkos::MemoryUnmanaged>;
  using pair_type = std::pair<LO, LO>;
 
  const LO numRows = static_cast<LO>(dst.numRows());
  const LO numCols = static_cast<LO>(dst.numCols());
 
  TEUCHOS_TEST_FOR_EXCEPTION(numRows != static_cast<LO>(src.getLocalLength()) ||
                                 numCols != static_cast<LO>(src.getNumVectors()),
                             std::invalid_argument, "Tpetra::deep_copy: On Process " << src.getMap()->getComm()->getRank() << ", src is " << src.getLocalLength() << " x " << src.getNumVectors() << ", but dst is " << numRows << " x " << numCols << ".");
 
  IST* dst_raw = reinterpret_cast<IST*>(dst.values());
  output_view_type dst_orig(dst_raw, dst.stride(), numCols);
  auto dst_view =
      Kokkos::subview(dst_orig, pair_type(0, numRows), Kokkos::ALL());
 
  constexpr bool dst_isConstantStride = true;
  Teuchos::ArrayView<const size_t> dstWhichVectors(nullptr, 0);
 
  // Prefer the host version of src's data.
  localDeepCopy(dst_view,
                src.getLocalViewHost(Access::ReadOnly),
                dst_isConstantStride,
                src.isConstantStride(),
                dstWhichVectors,
                getMultiVectorWhichVectors(src));
}
#endif  // HAVE_TPETRACORE_TEUCHOSNUMERICS
 
template <class Scalar, class LO, class GO, class NT>
Teuchos::RCP<MultiVector<Scalar, LO, GO, NT> >
createMultiVector(const Teuchos::RCP<const Map<LO, GO, NT> >& map,
                  size_t numVectors) {
  typedef MultiVector<Scalar, LO, GO, NT> MV;
  return Teuchos::rcp(new MV(map, numVectors));
}
 
template <class ST, class LO, class GO, class NT>
MultiVector<ST, LO, GO, NT>
createCopy(const MultiVector<ST, LO, GO, NT>& src) {
  typedef MultiVector<ST, LO, GO, NT> MV;
  MV cpy(src.getMap(), src.getNumVectors(), false);
  cpy.assign(src);
  return cpy;
}
 
}  // namespace Tpetra
 
//
// Explicit instantiation macro
//
// Must be expanded from within the Tpetra namespace!
//
 
#ifdef HAVE_TPETRACORE_TEUCHOSNUMERICS
#define TPETRA_MULTIVECTOR_INSTANT(SCALAR, LO, GO, NODE)                                                                                             \
  template class MultiVector<SCALAR, LO, GO, NODE>;                                                                                                  \
  template MultiVector<SCALAR, LO, GO, NODE> createCopy(const MultiVector<SCALAR, LO, GO, NODE>& src);                                               \
  template Teuchos::RCP<MultiVector<SCALAR, LO, GO, NODE> > createMultiVector(const Teuchos::RCP<const Map<LO, GO, NODE> >& map, size_t numVectors); \
  template void deep_copy(MultiVector<SCALAR, LO, GO, NODE>& dst, const Teuchos::SerialDenseMatrix<int, SCALAR>& src);                               \
  template void deep_copy(Teuchos::SerialDenseMatrix<int, SCALAR>& dst, const MultiVector<SCALAR, LO, GO, NODE>& src);
 
#else
#define TPETRA_MULTIVECTOR_INSTANT(SCALAR, LO, GO, NODE) \
  template class MultiVector<SCALAR, LO, GO, NODE>;      \
  template MultiVector<SCALAR, LO, GO, NODE> createCopy(const MultiVector<SCALAR, LO, GO, NODE>& src);
 
#endif  // HAVE_TPETRACORE_TEUCHOSNUMERICS
 
#define TPETRA_MULTIVECTOR_CONVERT_INSTANT(SO, SI, LO, GO, NODE) \
                                                                 \
  template Teuchos::RCP<MultiVector<SO, LO, GO, NODE> >          \
  MultiVector<SI, LO, GO, NODE>::convert<SO>() const;
 
#endif  // TPETRA_MULTIVECTOR_DEF_HPP