/src/Geometry_Eigen/Eigen/src/Core/products/TriangularMatrixMatrix.h
http://github.com/Akranar/daguerreo · C Header · 403 lines · 277 code · 51 blank · 75 comment · 27 complexity · 5727edaa2fbe4675f68639107b5bb574 MD5 · raw file
- // This file is part of Eigen, a lightweight C++ template library
- // for linear algebra.
- //
- // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
- //
- // Eigen is free software; you can redistribute it and/or
- // modify it under the terms of the GNU Lesser General Public
- // License as published by the Free Software Foundation; either
- // version 3 of the License, or (at your option) any later version.
- //
- // Alternatively, you can redistribute it and/or
- // modify it under the terms of the GNU General Public License as
- // published by the Free Software Foundation; either version 2 of
- // the License, or (at your option) any later version.
- //
- // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
- // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
- // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
- // GNU General Public License for more details.
- //
- // You should have received a copy of the GNU Lesser General Public
- // License and a copy of the GNU General Public License along with
- // Eigen. If not, see <http://www.gnu.org/licenses/>.
- #ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_H
- #define EIGEN_TRIANGULAR_MATRIX_MATRIX_H
- 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>
- struct product_triangular_matrix_matrix;
- template <typename Scalar, typename Index,
- int Mode, bool LhsIsTriangular,
- int LhsStorageOrder, bool ConjugateLhs,
- int RhsStorageOrder, bool ConjugateRhs>
- struct product_triangular_matrix_matrix<Scalar,Index,Mode,LhsIsTriangular,
- LhsStorageOrder,ConjugateLhs,
- RhsStorageOrder,ConjugateRhs,RowMajor>
- {
- 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,
- Scalar alpha)
- {
- 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);
- }
- };
- // implements col-major += alpha * op(triangular) * op(general)
- template <typename Scalar, typename Index, int Mode,
- int LhsStorageOrder, bool ConjugateLhs,
- int RhsStorageOrder, bool ConjugateRhs>
- struct product_triangular_matrix_matrix<Scalar,Index,Mode,true,
- LhsStorageOrder,ConjugateLhs,
- RhsStorageOrder,ConjugateRhs,ColMajor>
- {
-
- 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,
- Scalar alpha)
- {
- // strip zeros
- Index diagSize = (std::min)(_rows,_depth);
- Index rows = IsLower ? _rows : diagSize;
- Index depth = IsLower ? diagSize : _depth;
- Index cols = _cols;
-
- const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
- const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
- Index kc = depth; // cache block size along the K direction
- Index mc = rows; // cache block size along the M direction
- Index nc = cols; // cache block size along the N direction
- computeProductBlockingSizes<Scalar,Scalar,4>(kc, mc, nc);
- std::size_t sizeW = kc*Traits::WorkSpaceFactor;
- std::size_t sizeB = sizeW + kc*cols;
- ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
- ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
- Scalar* blockB = allocatedBlockB + sizeW;
- Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer;
- triangularBuffer.setZero();
- if((Mode&ZeroDiag)==ZeroDiag)
- triangularBuffer.diagonal().setZero();
- else
- triangularBuffer.diagonal().setOnes();
- gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
- gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
- gemm_pack_rhs<Scalar, Index, 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(actual_k2,0), rhsStride, 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+=SmallPanelWidth)
- {
- Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
- 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, triangularBuffer.data(), triangularBuffer.outerStride(), actualPanelWidth, actualPanelWidth);
- gebp_kernel(res+startBlock, resStride, 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(startTarget,startBlock), lhsStride, actualPanelWidth, lengthTarget);
- gebp_kernel(res+startTarget, resStride, 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, Traits::mr,Traits::LhsProgress, LhsStorageOrder,false>()
- (blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
- gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
- }
- }
- }
- }
- };
- // implements col-major += alpha * op(general) * op(triangular)
- template <typename Scalar, typename Index, int Mode,
- int LhsStorageOrder, bool ConjugateLhs,
- int RhsStorageOrder, bool ConjugateRhs>
- struct product_triangular_matrix_matrix<Scalar,Index,Mode,false,
- LhsStorageOrder,ConjugateLhs,
- RhsStorageOrder,ConjugateRhs,ColMajor>
- {
- 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,
- Scalar alpha)
- {
- // strip zeros
- Index diagSize = (std::min)(_cols,_depth);
- Index rows = _rows;
- Index depth = IsLower ? _depth : diagSize;
- Index cols = IsLower ? diagSize : _cols;
-
- const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
- const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
- Index kc = depth; // cache block size along the K direction
- Index mc = rows; // cache block size along the M direction
- Index nc = cols; // cache block size along the N direction
- computeProductBlockingSizes<Scalar,Scalar,4>(kc, mc, nc);
- std::size_t sizeW = kc*Traits::WorkSpaceFactor;
- std::size_t sizeB = sizeW + kc*cols;
- ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
- ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
- Scalar* blockB = allocatedBlockB + sizeW;
- Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer;
- triangularBuffer.setZero();
- if((Mode&ZeroDiag)==ZeroDiag)
- triangularBuffer.diagonal().setZero();
- else
- triangularBuffer.diagonal().setOnes();
- gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
- gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
- gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
- gemm_pack_rhs<Scalar, Index, 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;
- pack_rhs(geb, &rhs(actual_k2,IsLower ? 0 : k2), rhsStride, 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(actual_k2+panelOffset, actual_j2), rhsStride,
- 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,
- 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(i2, actual_k2), lhsStride, 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+i2+(actual_k2+j2)*resStride, resStride,
- blockA, blockB+j2*actual_kc,
- actual_mc, panelLength, actualPanelWidth,
- alpha,
- actual_kc, actual_kc, // strides
- blockOffset, blockOffset,// offsets
- allocatedBlockB); // workspace
- }
- }
- gebp_kernel(res+i2+(IsLower ? 0 : k2)*resStride, resStride,
- blockA, geb, actual_mc, actual_kc, rs,
- alpha,
- -1, -1, 0, 0, allocatedBlockB);
- }
- }
- }
- };
- /***************************************************************************
- * Wrapper to product_triangular_matrix_matrix
- ***************************************************************************/
- template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
- struct traits<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false> >
- : traits<ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs> >
- {};
- } // end namespace internal
- template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
- struct TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>
- : public ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs >
- {
- EIGEN_PRODUCT_PUBLIC_INTERFACE(TriangularProduct)
- TriangularProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
- template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const
- {
- const ActualLhsType lhs = LhsBlasTraits::extract(m_lhs);
- const ActualRhsType rhs = RhsBlasTraits::extract(m_rhs);
- Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
- * RhsBlasTraits::extractScalarFactor(m_rhs);
- internal::product_triangular_matrix_matrix<Scalar, Index,
- Mode, LhsIsTriangular,
- (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
- (internal::traits<_ActualRhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
- (internal::traits<Dest >::Flags&RowMajorBit) ? RowMajor : ColMajor>
- ::run(
- lhs.rows(), rhs.cols(), lhs.cols(),// LhsIsTriangular ? rhs.cols() : lhs.rows(), // 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 // alpha
- );
- }
- };
- #endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H