TriangularMatrixMatrix.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
#ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_H
#define EIGEN_TRIANGULAR_MATRIX_MATRIX_H
 
// IWYU pragma: private
#include "../InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
// template<typename Scalar, int mr, int StorageOrder, bool Conjugate, int Mode>
// struct gemm_pack_lhs_triangular
// {
//   Matrix<Scalar,mr,mr,
//   void operator()(Scalar* blockA, const EIGEN_RESTRICT Scalar* lhs_, int lhsStride, int depth, int rows)
//   {
//     conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
//     const_blas_data_mapper<Scalar, StorageOrder> lhs(lhs_,lhsStride);
//     int count = 0;
//     const int peeled_mc = (rows/mr)*mr;
//     for(int i=0; i<peeled_mc; i+=mr)
//     {
//       for(int k=0; k<depth; k++)
//         for(int w=0; w<mr; w++)
//           blockA[count++] = cj(lhs(i+w, k));
//     }
//     for(int i=peeled_mc; i<rows; i++)
//     {
//       for(int k=0; k<depth; k++)
//         blockA[count++] = cj(lhs(i, k));
//     }
//   }
// };
 
/* Optimized triangular matrix * matrix (_TRMM++) product built on top of
 * the general matrix matrix product.
 */
template <typename Scalar, typename Index, int Mode, bool LhsIsTriangular, int LhsStorageOrder, bool ConjugateLhs,
          int RhsStorageOrder, bool ConjugateRhs, int ResStorageOrder, int ResInnerStride, int Version = Specialized>
struct product_triangular_matrix_matrix;
 
template <typename Scalar, typename Index, int Mode, bool LhsIsTriangular, int LhsStorageOrder, bool ConjugateLhs,
          int RhsStorageOrder, bool ConjugateRhs, int ResInnerStride, int Version>
struct product_triangular_matrix_matrix<Scalar, Index, Mode, LhsIsTriangular, LhsStorageOrder, ConjugateLhs,
                                        RhsStorageOrder, ConjugateRhs, RowMajor, ResInnerStride, Version> {
  static EIGEN_STRONG_INLINE void run(Index rows, Index cols, Index depth, const Scalar* lhs, Index lhsStride,
                                      const Scalar* rhs, Index rhsStride, Scalar* res, Index resIncr, Index resStride,
                                      const Scalar& alpha, level3_blocking<Scalar, Scalar>& blocking) {
    product_triangular_matrix_matrix<Scalar, Index, (Mode & (UnitDiag | ZeroDiag)) | ((Mode & Upper) ? Lower : Upper),
                                     (!LhsIsTriangular), RhsStorageOrder == RowMajor ? ColMajor : RowMajor,
                                     ConjugateRhs, LhsStorageOrder == RowMajor ? ColMajor : RowMajor, ConjugateLhs,
                                     ColMajor, ResInnerStride>::run(cols, rows, depth, rhs, rhsStride, lhs, lhsStride,
                                                                    res, resIncr, resStride, alpha, blocking);
  }
};
 
// implements col-major += alpha * op(triangular) * op(general)
template <typename Scalar, typename Index, int Mode, int LhsStorageOrder, bool ConjugateLhs, int RhsStorageOrder,
          bool ConjugateRhs, int ResInnerStride, int Version>
struct product_triangular_matrix_matrix<Scalar, Index, Mode, true, LhsStorageOrder, ConjugateLhs, RhsStorageOrder,
                                        ConjugateRhs, ColMajor, ResInnerStride, Version> {
  typedef gebp_traits<Scalar, Scalar> Traits;
  enum {
    SmallPanelWidth = 2 * plain_enum_max(Traits::mr, Traits::nr),
    IsLower = (Mode & Lower) == Lower,
    SetDiag = (Mode & (ZeroDiag | UnitDiag)) ? 0 : 1
  };
 
  static EIGEN_DONT_INLINE void run(Index _rows, Index _cols, Index _depth, const Scalar* lhs_, Index lhsStride,
                                    const Scalar* rhs_, Index rhsStride, Scalar* res, Index resIncr, Index resStride,
                                    const Scalar& alpha, level3_blocking<Scalar, Scalar>& blocking);
};
 
template <typename Scalar, typename Index, int Mode, int LhsStorageOrder, bool ConjugateLhs, int RhsStorageOrder,
          bool ConjugateRhs, int ResInnerStride, int Version>
EIGEN_DONT_INLINE void product_triangular_matrix_matrix<
    Scalar, Index, Mode, true, LhsStorageOrder, ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, ResInnerStride,
    Version>::run(Index _rows, Index _cols, Index _depth, const Scalar* lhs_, Index lhsStride, const Scalar* rhs_,
                  Index rhsStride, Scalar* res_, Index resIncr, Index resStride, const Scalar& alpha,
                  level3_blocking<Scalar, Scalar>& blocking) {
  // strip zeros
  Index diagSize = (std::min)(_rows, _depth);
  Index rows = IsLower ? _rows : diagSize;
  Index depth = IsLower ? diagSize : _depth;
  Index cols = _cols;
 
  typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;
  typedef const_blas_data_mapper<Scalar, Index, RhsStorageOrder> RhsMapper;
  typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor, Unaligned, ResInnerStride> ResMapper;
  LhsMapper lhs(lhs_, lhsStride);
  RhsMapper rhs(rhs_, rhsStride);
  ResMapper res(res_, resStride, resIncr);
 
  Index kc = blocking.kc();                    // cache block size along the K direction
  Index mc = (std::min)(rows, blocking.mc());  // cache block size along the M direction
  // The small panel size must not be larger than blocking size.
  // Usually this should never be the case because SmallPanelWidth^2 is very small
  // compared to L2 cache size, but let's be safe:
  Index panelWidth = (std::min)(Index(SmallPanelWidth), (std::min)(kc, mc));
 
  std::size_t sizeA = kc * mc;
  std::size_t sizeB = kc * cols;
 
  ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
  ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
 
  Matrix<Scalar, SmallPanelWidth, SmallPanelWidth, LhsStorageOrder> triangularBuffer;
  triangularBuffer.setZero();
  if ((Mode & ZeroDiag) == ZeroDiag)
    triangularBuffer.diagonal().setZero();
  else
    triangularBuffer.diagonal().setOnes();
 
  gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
  gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing,
                LhsStorageOrder>
      pack_lhs;
  gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;
 
  for (Index k2 = IsLower ? depth : 0; IsLower ? k2 > 0 : k2 < depth; IsLower ? k2 -= kc : k2 += kc) {
    Index actual_kc = (std::min)(IsLower ? k2 : depth - k2, kc);
    Index actual_k2 = IsLower ? k2 - actual_kc : k2;
 
    // align blocks with the end of the triangular part for trapezoidal lhs
    if ((!IsLower) && (k2 < rows) && (k2 + actual_kc > rows)) {
      actual_kc = rows - k2;
      k2 = k2 + actual_kc - kc;
    }
 
    pack_rhs(blockB, rhs.getSubMapper(actual_k2, 0), actual_kc, cols);
 
    // the selected lhs's panel has to be split in three different parts:
    //  1 - the part which is zero => skip it
    //  2 - the diagonal block => special kernel
    //  3 - the dense panel below (lower case) or above (upper case) the diagonal block => GEPP
 
    // the block diagonal, if any:
    if (IsLower || actual_k2 < rows) {
      // for each small vertical panels of lhs
      for (Index k1 = 0; k1 < actual_kc; k1 += panelWidth) {
        Index actualPanelWidth = std::min<Index>(actual_kc - k1, panelWidth);
        Index lengthTarget = IsLower ? actual_kc - k1 - actualPanelWidth : k1;
        Index startBlock = actual_k2 + k1;
        Index blockBOffset = k1;
 
        // => GEBP with the micro triangular block
        // The trick is to pack this micro block while filling the opposite triangular part with zeros.
        // To this end we do an extra triangular copy to a small temporary buffer
        for (Index k = 0; k < actualPanelWidth; ++k) {
          if (SetDiag) triangularBuffer.coeffRef(k, k) = lhs(startBlock + k, startBlock + k);
          for (Index i = IsLower ? k + 1 : 0; IsLower ? i < actualPanelWidth : i < k; ++i)
            triangularBuffer.coeffRef(i, k) = lhs(startBlock + i, startBlock + k);
        }
        pack_lhs(blockA, LhsMapper(triangularBuffer.data(), triangularBuffer.outerStride()), actualPanelWidth,
                 actualPanelWidth);
 
        gebp_kernel(res.getSubMapper(startBlock, 0), blockA, blockB, actualPanelWidth, actualPanelWidth, cols, alpha,
                    actualPanelWidth, actual_kc, 0, blockBOffset);
 
        // GEBP with remaining micro panel
        if (lengthTarget > 0) {
          Index startTarget = IsLower ? actual_k2 + k1 + actualPanelWidth : actual_k2;
 
          pack_lhs(blockA, lhs.getSubMapper(startTarget, startBlock), actualPanelWidth, lengthTarget);
 
          gebp_kernel(res.getSubMapper(startTarget, 0), blockA, blockB, lengthTarget, actualPanelWidth, cols, alpha,
                      actualPanelWidth, actual_kc, 0, blockBOffset);
        }
      }
    }
    // the part below (lower case) or above (upper case) the diagonal => GEPP
    {
      Index start = IsLower ? k2 : 0;
      Index end = IsLower ? rows : (std::min)(actual_k2, rows);
      for (Index i2 = start; i2 < end; i2 += mc) {
        const Index actual_mc = (std::min)(i2 + mc, end) - i2;
        gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing,
                      LhsStorageOrder, false>()(blockA, lhs.getSubMapper(i2, actual_k2), actual_kc, actual_mc);
 
        gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha, -1, -1, 0, 0);
      }
    }
  }
}
 
// implements col-major += alpha * op(general) * op(triangular)
template <typename Scalar, typename Index, int Mode, int LhsStorageOrder, bool ConjugateLhs, int RhsStorageOrder,
          bool ConjugateRhs, int ResInnerStride, int Version>
struct product_triangular_matrix_matrix<Scalar, Index, Mode, false, LhsStorageOrder, ConjugateLhs, RhsStorageOrder,
                                        ConjugateRhs, ColMajor, ResInnerStride, Version> {
  typedef gebp_traits<Scalar, Scalar> Traits;
  enum {
    SmallPanelWidth = plain_enum_max(Traits::mr, Traits::nr),
    IsLower = (Mode & Lower) == Lower,
    SetDiag = (Mode & (ZeroDiag | UnitDiag)) ? 0 : 1
  };
 
  static EIGEN_DONT_INLINE void run(Index _rows, Index _cols, Index _depth, const Scalar* lhs_, Index lhsStride,
                                    const Scalar* rhs_, Index rhsStride, Scalar* res, Index resIncr, Index resStride,
                                    const Scalar& alpha, level3_blocking<Scalar, Scalar>& blocking);
};
 
template <typename Scalar, typename Index, int Mode, int LhsStorageOrder, bool ConjugateLhs, int RhsStorageOrder,
          bool ConjugateRhs, int ResInnerStride, int Version>
EIGEN_DONT_INLINE void product_triangular_matrix_matrix<
    Scalar, Index, Mode, false, LhsStorageOrder, ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, ResInnerStride,
    Version>::run(Index _rows, Index _cols, Index _depth, const Scalar* lhs_, Index lhsStride, const Scalar* rhs_,
                  Index rhsStride, Scalar* res_, Index resIncr, Index resStride, const Scalar& alpha,
                  level3_blocking<Scalar, Scalar>& blocking) {
  const Index PacketBytes = packet_traits<Scalar>::size * sizeof(Scalar);
  // strip zeros
  Index diagSize = (std::min)(_cols, _depth);
  Index rows = _rows;
  Index depth = IsLower ? _depth : diagSize;
  Index cols = IsLower ? diagSize : _cols;
 
  typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;
  typedef const_blas_data_mapper<Scalar, Index, RhsStorageOrder> RhsMapper;
  typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor, Unaligned, ResInnerStride> ResMapper;
  LhsMapper lhs(lhs_, lhsStride);
  RhsMapper rhs(rhs_, rhsStride);
  ResMapper res(res_, resStride, resIncr);
 
  Index kc = blocking.kc();                    // cache block size along the K direction
  Index mc = (std::min)(rows, blocking.mc());  // cache block size along the M direction
 
  std::size_t sizeA = kc * mc;
  std::size_t sizeB = kc * cols + EIGEN_MAX_ALIGN_BYTES / sizeof(Scalar);
 
  ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
  ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
 
  Matrix<Scalar, SmallPanelWidth, SmallPanelWidth, RhsStorageOrder> triangularBuffer;
  triangularBuffer.setZero();
  if ((Mode & ZeroDiag) == ZeroDiag)
    triangularBuffer.diagonal().setZero();
  else
    triangularBuffer.diagonal().setOnes();
 
  gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
  gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing,
                LhsStorageOrder>
      pack_lhs;
  gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;
  gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr, RhsStorageOrder, false, true> pack_rhs_panel;
 
  for (Index k2 = IsLower ? 0 : depth; IsLower ? k2 < depth : k2 > 0; IsLower ? k2 += kc : k2 -= kc) {
    Index actual_kc = (std::min)(IsLower ? depth - k2 : k2, kc);
    Index actual_k2 = IsLower ? k2 : k2 - actual_kc;
 
    // align blocks with the end of the triangular part for trapezoidal rhs
    if (IsLower && (k2 < cols) && (actual_k2 + actual_kc > cols)) {
      actual_kc = cols - k2;
      k2 = actual_k2 + actual_kc - kc;
    }
 
    // remaining size
    Index rs = IsLower ? (std::min)(cols, actual_k2) : cols - k2;
    // size of the triangular part
    Index ts = (IsLower && actual_k2 >= cols) ? 0 : actual_kc;
 
    Scalar* geb = blockB + ts * ts;
    geb = geb + internal::first_aligned<PacketBytes>(geb, PacketBytes / sizeof(Scalar));
 
    pack_rhs(geb, rhs.getSubMapper(actual_k2, IsLower ? 0 : k2), actual_kc, rs);
 
    // pack the triangular part of the rhs padding the unrolled blocks with zeros
    if (ts > 0) {
      for (Index j2 = 0; j2 < actual_kc; j2 += SmallPanelWidth) {
        Index actualPanelWidth = std::min<Index>(actual_kc - j2, SmallPanelWidth);
        Index actual_j2 = actual_k2 + j2;
        Index panelOffset = IsLower ? j2 + actualPanelWidth : 0;
        Index panelLength = IsLower ? actual_kc - j2 - actualPanelWidth : j2;
        // general part
        pack_rhs_panel(blockB + j2 * actual_kc, rhs.getSubMapper(actual_k2 + panelOffset, actual_j2), panelLength,
                       actualPanelWidth, actual_kc, panelOffset);
 
        // append the triangular part via a temporary buffer
        for (Index j = 0; j < actualPanelWidth; ++j) {
          if (SetDiag) triangularBuffer.coeffRef(j, j) = rhs(actual_j2 + j, actual_j2 + j);
          for (Index k = IsLower ? j + 1 : 0; IsLower ? k < actualPanelWidth : k < j; ++k)
            triangularBuffer.coeffRef(k, j) = rhs(actual_j2 + k, actual_j2 + j);
        }
 
        pack_rhs_panel(blockB + j2 * actual_kc, RhsMapper(triangularBuffer.data(), triangularBuffer.outerStride()),
                       actualPanelWidth, actualPanelWidth, actual_kc, j2);
      }
    }
 
    for (Index i2 = 0; i2 < rows; i2 += mc) {
      const Index actual_mc = (std::min)(mc, rows - i2);
      pack_lhs(blockA, lhs.getSubMapper(i2, actual_k2), actual_kc, actual_mc);
 
      // triangular kernel
      if (ts > 0) {
        for (Index j2 = 0; j2 < actual_kc; j2 += SmallPanelWidth) {
          Index actualPanelWidth = std::min<Index>(actual_kc - j2, SmallPanelWidth);
          Index panelLength = IsLower ? actual_kc - j2 : j2 + actualPanelWidth;
          Index blockOffset = IsLower ? j2 : 0;
 
          gebp_kernel(res.getSubMapper(i2, actual_k2 + j2), blockA, blockB + j2 * actual_kc, actual_mc, panelLength,
                      actualPanelWidth, alpha, actual_kc, actual_kc,  // strides
                      blockOffset, blockOffset);                      // offsets
        }
      }
      gebp_kernel(res.getSubMapper(i2, IsLower ? 0 : k2), blockA, geb, actual_mc, actual_kc, rs, alpha, -1, -1, 0, 0);
    }
  }
}
 
/***************************************************************************
 * Wrapper to product_triangular_matrix_matrix
 ***************************************************************************/
 
}  // end namespace internal
 
namespace internal {
template <int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
struct triangular_product_impl<Mode, LhsIsTriangular, Lhs, false, Rhs, false> {
  template <typename Dest>
  static void run(Dest& dst, const Lhs& a_lhs, const Rhs& a_rhs, const typename Dest::Scalar& alpha) {
    typedef typename Lhs::Scalar LhsScalar;
    typedef typename Rhs::Scalar RhsScalar;
    typedef typename Dest::Scalar Scalar;
 
    typedef internal::blas_traits<Lhs> LhsBlasTraits;
    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
    typedef internal::remove_all_t<ActualLhsType> ActualLhsTypeCleaned;
    typedef internal::blas_traits<Rhs> RhsBlasTraits;
    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
    typedef internal::remove_all_t<ActualRhsType> ActualRhsTypeCleaned;
 
    internal::add_const_on_value_type_t<ActualLhsType> lhs = LhsBlasTraits::extract(a_lhs);
    internal::add_const_on_value_type_t<ActualRhsType> rhs = RhsBlasTraits::extract(a_rhs);
 
    // Empty product, return early.  Otherwise, we get `nullptr` use errors below when we try to access
    // coeffRef(0,0).
    if (lhs.size() == 0 || rhs.size() == 0) {
      return;
    }
 
    LhsScalar lhs_alpha = LhsBlasTraits::extractScalarFactor(a_lhs);
    RhsScalar rhs_alpha = RhsBlasTraits::extractScalarFactor(a_rhs);
    Scalar actualAlpha = alpha * lhs_alpha * rhs_alpha;
 
    typedef internal::gemm_blocking_space<(Dest::Flags & RowMajorBit) ? RowMajor : ColMajor, Scalar, Scalar,
                                          Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime,
                                          Lhs::MaxColsAtCompileTime, 4>
        BlockingType;
 
    enum { IsLower = (Mode & Lower) == Lower };
    Index stripedRows = ((!LhsIsTriangular) || (IsLower)) ? lhs.rows() : (std::min)(lhs.rows(), lhs.cols());
    Index stripedCols = ((LhsIsTriangular) || (!IsLower)) ? rhs.cols() : (std::min)(rhs.cols(), rhs.rows());
    Index stripedDepth = LhsIsTriangular ? ((!IsLower) ? lhs.cols() : (std::min)(lhs.cols(), lhs.rows()))
                                         : ((IsLower) ? rhs.rows() : (std::min)(rhs.rows(), rhs.cols()));
 
    BlockingType blocking(stripedRows, stripedCols, stripedDepth, 1, false);
 
    internal::product_triangular_matrix_matrix<
        Scalar, Index, Mode, LhsIsTriangular,
        (internal::traits<ActualLhsTypeCleaned>::Flags & RowMajorBit) ? RowMajor : ColMajor,
        LhsBlasTraits::NeedToConjugate,
        (internal::traits<ActualRhsTypeCleaned>::Flags & RowMajorBit) ? RowMajor : ColMajor,
        RhsBlasTraits::NeedToConjugate, (internal::traits<Dest>::Flags & RowMajorBit) ? RowMajor : ColMajor,
        Dest::InnerStrideAtCompileTime>::run(stripedRows, stripedCols, stripedDepth,                     // sizes
                                             &lhs.coeffRef(0, 0), lhs.outerStride(),                     // lhs info
                                             &rhs.coeffRef(0, 0), rhs.outerStride(),                     // rhs info
                                             &dst.coeffRef(0, 0), dst.innerStride(), dst.outerStride(),  // result info
                                             actualAlpha, blocking);
 
    // Apply correction if the diagonal is unit and a scalar factor was nested:
    if ((Mode & UnitDiag) == UnitDiag) {
      if (LhsIsTriangular && !numext::is_exactly_one(lhs_alpha)) {
        Index diagSize = (std::min)(lhs.rows(), lhs.cols());
        dst.topRows(diagSize) -= ((lhs_alpha - LhsScalar(1)) * a_rhs).topRows(diagSize);
      } else if ((!LhsIsTriangular) && !numext::is_exactly_one(rhs_alpha)) {
        Index diagSize = (std::min)(rhs.rows(), rhs.cols());
        dst.leftCols(diagSize) -= (rhs_alpha - RhsScalar(1)) * a_lhs.leftCols(diagSize);
      }
    }
  }
};
 
}  // end namespace internal
 
}  // end namespace Eigen
 
#endif  // EIGEN_TRIANGULAR_MATRIX_MATRIX_H