| Current File : //usr/include/eigen3/Eigen/src/Core/products/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
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 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 Version>
struct product_triangular_matrix_matrix<Scalar,Index,Mode,LhsIsTriangular,
LhsStorageOrder,ConjugateLhs,
RhsStorageOrder,ConjugateRhs,RowMajor,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 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>
::run(cols, rows, depth, rhs, rhsStride, lhs, lhsStride, res, 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 Version>
struct product_triangular_matrix_matrix<Scalar,Index,Mode,true,
LhsStorageOrder,ConjugateLhs,
RhsStorageOrder,ConjugateRhs,ColMajor,Version>
{
typedef gebp_traits<Scalar,Scalar> Traits;
enum {
SmallPanelWidth = 2 * EIGEN_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 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 Version>
EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,true,
LhsStorageOrder,ConjugateLhs,
RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run(
Index _rows, Index _cols, Index _depth,
const Scalar* _lhs, Index lhsStride,
const Scalar* _rhs, Index rhsStride,
Scalar* _res, 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> ResMapper;
LhsMapper lhs(_lhs,lhsStride);
RhsMapper rhs(_rhs,rhsStride);
ResMapper res(_res, resStride);
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());
// To work around an "error: member reference base type 'Matrix<...>
// (Eigen::internal::constructor_without_unaligned_array_assert (*)())' is
// not a structure or union" compilation error in nvcc (tested V8.0.61),
// create a dummy internal::constructor_without_unaligned_array_assert
// object to pass to the Matrix constructor.
internal::constructor_without_unaligned_array_assert a;
Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer(a);
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, 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, 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 Version>
struct product_triangular_matrix_matrix<Scalar,Index,Mode,false,
LhsStorageOrder,ConjugateLhs,
RhsStorageOrder,ConjugateRhs,ColMajor,Version>
{
typedef gebp_traits<Scalar,Scalar> Traits;
enum {
SmallPanelWidth = EIGEN_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 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 Version>
EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,false,
LhsStorageOrder,ConjugateLhs,
RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run(
Index _rows, Index _cols, Index _depth,
const Scalar* _lhs, Index lhsStride,
const Scalar* _rhs, Index rhsStride,
Scalar* _res, 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> ResMapper;
LhsMapper lhs(_lhs,lhsStride);
RhsMapper rhs(_rhs,rhsStride);
ResMapper res(_res, resStride);
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());
internal::constructor_without_unaligned_array_assert a;
Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer(a);
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, 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 typename internal::remove_all<ActualLhsType>::type ActualLhsTypeCleaned;
typedef internal::blas_traits<Rhs> RhsBlasTraits;
typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;
typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(a_lhs);
typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(a_rhs);
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>
::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.outerStride(), // result info
actualAlpha, blocking
);
// Apply correction if the diagonal is unit and a scalar factor was nested:
if ((Mode&UnitDiag)==UnitDiag)
{
if (LhsIsTriangular && lhs_alpha!=LhsScalar(1))
{
Index diagSize = (std::min)(lhs.rows(),lhs.cols());
dst.topRows(diagSize) -= ((lhs_alpha-LhsScalar(1))*a_rhs).topRows(diagSize);
}
else if ((!LhsIsTriangular) && rhs_alpha!=RhsScalar(1))
{
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