MueLu_LocalQR.hpp

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#ifndef MUELU_LOCALQR_HPP
#define MUELU_LOCALQR_HPP
 
#include <Kokkos_Core.hpp>
#include <KokkosKernels_ArithTraits.hpp>
#include "Xpetra_ConfigDefs.hpp"
 
#include "KokkosBlas1_set.hpp"
#include "KokkosBatched_ApplyQ_Decl.hpp"
#include "KokkosBatched_SetIdentity_Decl.hpp"
#include "KokkosBatched_SetIdentity_Impl.hpp"
#include "Kokkos_DualView.hpp"
#include "Kokkos_Pair.hpp"
#include "KokkosBatched_QR_Decl.hpp"
 
namespace MueLu::LocalQR {
 
template <class LocalOrdinal, class View>
class ReduceMaxFunctor {
 public:
  ReduceMaxFunctor(View view)
    : view_(view) {}
 
  KOKKOS_INLINE_FUNCTION
  void operator()(const LocalOrdinal& i, LocalOrdinal& vmax) const {
    if (vmax < view_(i))
      vmax = view_(i);
  }
 
  KOKKOS_INLINE_FUNCTION
  void join(LocalOrdinal& dst, const LocalOrdinal& src) const {
    if (dst < src) {
      dst = src;
    }
  }
 
  KOKKOS_INLINE_FUNCTION
  void init(LocalOrdinal& dst) const {
    dst = 0;
  }
 
 private:
  View view_;
};
 
// local QR decomposition
template <class LOType, class GOType, class SCType, class DeviceType, class NspType, class aggRowsType, class maxAggDofSizeType, class agg2RowMapLOType, class statusType, class rowsType, class rowsAuxType, class colsAuxType, class valsAuxType>
class LocalQRDecompFunctor {
 private:
  typedef LOType LO;
  typedef GOType GO;
  typedef SCType SC;
 
  typedef typename DeviceType::execution_space execution_space;
  typedef typename KokkosKernels::ArithTraits<SC>::val_type impl_SC;
  typedef KokkosKernels::ArithTraits<impl_SC> impl_ATS;
  typedef typename impl_ATS::magnitudeType Magnitude;
 
 public:
  typedef Kokkos::View<impl_SC**, typename execution_space::scratch_memory_space, Kokkos::MemoryUnmanaged> shared_matrix;
  typedef Kokkos::View<impl_SC*, typename execution_space::scratch_memory_space, Kokkos::MemoryUnmanaged> shared_vector;
 
 private:
  NspType fineNS;
  NspType coarseNS;
  aggRowsType aggRows;
  maxAggDofSizeType maxAggDofSize;  //< maximum number of dofs in aggregate (max size of aggregate * numDofsPerNode)
  agg2RowMapLOType agg2RowMapLO;
  statusType statusAtomic;
  rowsType rows;
  rowsAuxType rowsAux;
  colsAuxType colsAux;
  valsAuxType valsAux;
  bool doQRStep;
  int scratchLevel;
 
 public:
  LocalQRDecompFunctor(NspType fineNS_, NspType coarseNS_, aggRowsType aggRows_, maxAggDofSizeType maxAggDofSize_, agg2RowMapLOType agg2RowMapLO_, statusType statusAtomic_, rowsType rows_, rowsAuxType rowsAux_, colsAuxType colsAux_, valsAuxType valsAux_, bool doQRStep_, int scratchLevel_)
    : fineNS(fineNS_)
    , coarseNS(coarseNS_)
    , aggRows(aggRows_)
    , maxAggDofSize(maxAggDofSize_)
    , agg2RowMapLO(agg2RowMapLO_)
    , statusAtomic(statusAtomic_)
    , rows(rows_)
    , rowsAux(rowsAux_)
    , colsAux(colsAux_)
    , valsAux(valsAux_)
    , doQRStep(doQRStep_)
    , scratchLevel(scratchLevel_) {}
 
  KOKKOS_INLINE_FUNCTION
  void operator()(const typename Kokkos::TeamPolicy<execution_space>::member_type& thread, size_t& nnz) const {
    auto agg = thread.league_rank();
 
    const auto aggOffset = aggRows(agg);
    // size of aggregate: number of DOFs in aggregate
    const auto aggSize = aggRows(agg + 1) - aggOffset;
 
    const impl_SC one  = impl_ATS::one();
    const impl_SC zero = impl_ATS::zero();
 
    const int m = aggSize;
    const int n = fineNS.extent(1);
 
    // calculate row offset for coarse nullspace
    Xpetra::global_size_t offset = agg * n;
 
    if (doQRStep) {
      // A is m x n
      // Q is m x m
      // R is m x n
 
      // A (initially) gets overwritten with R in QR
      shared_matrix r(thread.team_scratch(scratchLevel), m, n);
      // Q
      shared_matrix q(thread.team_scratch(scratchLevel), m, m);
 
      // Extract the piece of the nullspace corresponding to the aggregate
      for (int j = 0; j < n; j++)
        for (int k = 0; k < m; k++)
          r(k, j) = fineNS(agg2RowMapLO(aggOffset + k), j);
 
      if (m >= n) {
        // tau has size n
        shared_vector tau(thread.team_scratch(scratchLevel), n);
 
        // work has size m
        shared_vector work(thread.team_scratch(scratchLevel), m);
 
        // Calculate QR. After this call R will be in the upper triangular part of r.
        // Q is in encoded in the strictly lower triangular part of r and tau. We will
        // need to explicitly form Q as a matrix below.
        KokkosBatched::SerialQR<KokkosBlas::Algo::QR::Unblocked>::invoke(r, tau, work);
 
        // Initialize Q to an identity matrix
        KokkosBatched::SerialSetIdentity::invoke(q);
 
        // Form Q as a matrix but multiplying against the identity
        KokkosBatched::SerialApplyQ<KokkosBatched::Side::Left, KokkosBlas::Trans::NoTranspose, KokkosBlas::Algo::ApplyQ::Unblocked>::invoke(r, tau, q, work);
 
        // Build coarse nullspace using the upper triangular part of R
        for (int j = 0; j < n; j++) {
          for (int k = 0; k < n; k++)
            coarseNS(offset + k, j) = (k <= j) ? r(k, j) : zero;
        }
 
      } else {
        // Special handling for m < n (i.e. single node aggregates in structural mechanics)
 
        // The local QR decomposition is not possible in the "overconstrained"
        // case (i.e. number of columns in qr > number of rowsAux), which
        // corresponds to #DOFs in Aggregate < n. For usual problems this
        // is only possible for single node aggregates in structural mechanics.
        // (Similar problems may arise in discontinuous Galerkin problems...)
        // We bypass the QR decomposition and use an identity block in the
        // tentative prolongator for the single node aggregate and transfer the
        // corresponding fine level null space information 1-to-1 to the coarse
        // level null space part.
 
        // NOTE: The resulting tentative prolongation operator has
        // (m*DofsPerNode-n) zero columns leading to a singular
        // coarse level operator A.  To deal with that one has the following
        // options:
        // - Use the "RepairMainDiagonal" flag in the RAPFactory (default:
        //   false) to add some identity block to the diagonal of the zero rowsAux
        //   in the coarse level operator A, such that standard level smoothers
        //   can be used again.
        // - Use special (projection-based) level smoothers, which can deal
        //   with singular matrices (very application specific)
        // - Adapt the code below to avoid zero columns. However, we do not
        //   support a variable number of DOFs per node in MueLu/Xpetra which
        //   makes the implementation really hard.
        //
        // FIXME: do we need to check for singularity here somehow? Zero
        // columns would be easy but linear dependency would require proper QR.
 
        // R = extended (by adding identity rowsAux) qr
        for (int j = 0; j < n; j++)
          for (int k = 0; k < n; k++)
            if (k < m)
              coarseNS(offset + k, j) = r(k, j);
            else
              coarseNS(offset + k, j) = (k == j ? one : zero);
 
        // Q = I (rectangular)
        for (int i = 0; i < m; i++)
          for (int j = 0; j < n; j++)
            q(i, j) = (j == i ? one : zero);
      }
 
      // Process each row in the local Q factor and fill helper arrays to assemble P
      for (int j = 0; j < m; j++) {
        LO localRow     = agg2RowMapLO(aggRows(agg) + j);
        size_t rowStart = rowsAux(localRow);
        size_t lnnz     = 0;
        for (int k = 0; k < n; k++) {
          // skip zeros
          if (q(j, k) != zero) {
            colsAux(rowStart + lnnz) = offset + k;
            valsAux(rowStart + lnnz) = q(j, k);
            lnnz++;
          }
        }
        rows(localRow + 1) = lnnz;
        nnz += lnnz;
      }
    } else {
      //      "no-QR" option     //
      // Local Q factor is just the fine nullspace support over the current aggregate.
      // Local R factor is the identity.
      // TODO I have not implemented any special handling for aggregates that are too
      // TODO small to locally support the nullspace, as is done in the standard QR
      // TODO case above.
 
      for (int j = 0; j < m; j++) {
        LO localRow     = agg2RowMapLO(aggRows(agg) + j);
        size_t rowStart = rowsAux(localRow);
        size_t lnnz     = 0;
        for (int k = 0; k < n; k++) {
          const impl_SC qr_jk = fineNS(localRow, k);
          // skip zeros
          if (qr_jk != zero) {
            colsAux(rowStart + lnnz) = offset + k;
            valsAux(rowStart + lnnz) = qr_jk;
            lnnz++;
          }
        }
        rows(localRow + 1) = lnnz;
        nnz += lnnz;
      }
 
      for (int j = 0; j < n; j++)
        coarseNS(offset + j, j) = one;
    }
  }
};
 
}  // namespace MueLu::LocalQR
 
#endif