TriangularMatrixMatrix.h

00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
00005 //
00006 // This Source Code Form is subject to the terms of the Mozilla
00007 // Public License v. 2.0. If a copy of the MPL was not distributed
00008 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00009 
00010 #ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_H
00011 #define EIGEN_TRIANGULAR_MATRIX_MATRIX_H
00012 
00013 namespace Eigen { 
00014 
00015 namespace internal {
00016 
00017 // template<typename Scalar, int mr, int StorageOrder, bool Conjugate, int Mode>
00018 // struct gemm_pack_lhs_triangular
00019 // {
00020 //   Matrix<Scalar,mr,mr,
00021 //   void operator()(Scalar* blockA, const EIGEN_RESTRICT Scalar* _lhs, int lhsStride, int depth, int rows)
00022 //   {
00023 //     conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
00024 //     const_blas_data_mapper<Scalar, StorageOrder> lhs(_lhs,lhsStride);
00025 //     int count = 0;
00026 //     const int peeled_mc = (rows/mr)*mr;
00027 //     for(int i=0; i<peeled_mc; i+=mr)
00028 //     {
00029 //       for(int k=0; k<depth; k++)
00030 //         for(int w=0; w<mr; w++)
00031 //           blockA[count++] = cj(lhs(i+w, k));
00032 //     }
00033 //     for(int i=peeled_mc; i<rows; i++)
00034 //     {
00035 //       for(int k=0; k<depth; k++)
00036 //         blockA[count++] = cj(lhs(i, k));
00037 //     }
00038 //   }
00039 // };
00040 
00041 /* Optimized triangular matrix * matrix (_TRMM++) product built on top of
00042  * the general matrix matrix product.
00043  */
00044 template <typename Scalar, typename Index,
00045           int Mode, bool LhsIsTriangular,
00046           int LhsStorageOrder, bool ConjugateLhs,
00047           int RhsStorageOrder, bool ConjugateRhs,
00048           int ResStorageOrder, int Version = Specialized>
00049 struct product_triangular_matrix_matrix;
00050 
00051 template <typename Scalar, typename Index,
00052           int Mode, bool LhsIsTriangular,
00053           int LhsStorageOrder, bool ConjugateLhs,
00054           int RhsStorageOrder, bool ConjugateRhs, int Version>
00055 struct product_triangular_matrix_matrix<Scalar,Index,Mode,LhsIsTriangular,
00056                                            LhsStorageOrder,ConjugateLhs,
00057                                            RhsStorageOrder,ConjugateRhs,RowMajor,Version>
00058 {
00059   static EIGEN_STRONG_INLINE void run(
00060     Index rows, Index cols, Index depth,
00061     const Scalar* lhs, Index lhsStride,
00062     const Scalar* rhs, Index rhsStride,
00063     Scalar* res,       Index resStride,
00064     const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
00065   {
00066     product_triangular_matrix_matrix<Scalar, Index,
00067       (Mode&(UnitDiag|ZeroDiag)) | ((Mode&Upper) ? Lower : Upper),
00068       (!LhsIsTriangular),
00069       RhsStorageOrder==RowMajor ? ColMajor : RowMajor,
00070       ConjugateRhs,
00071       LhsStorageOrder==RowMajor ? ColMajor : RowMajor,
00072       ConjugateLhs,
00073       ColMajor>
00074       ::run(cols, rows, depth, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha, blocking);
00075   }
00076 };
00077 
00078 // implements col-major += alpha * op(triangular) * op(general)
00079 template <typename Scalar, typename Index, int Mode,
00080           int LhsStorageOrder, bool ConjugateLhs,
00081           int RhsStorageOrder, bool ConjugateRhs, int Version>
00082 struct product_triangular_matrix_matrix<Scalar,Index,Mode,true,
00083                                            LhsStorageOrder,ConjugateLhs,
00084                                            RhsStorageOrder,ConjugateRhs,ColMajor,Version>
00085 {
00086   
00087   typedef gebp_traits<Scalar,Scalar> Traits;
00088   enum {
00089     SmallPanelWidth   = 2 * EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
00090     IsLower = (Mode&Lower) == Lower,
00091     SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
00092   };
00093 
00094   static EIGEN_DONT_INLINE void run(
00095     Index _rows, Index _cols, Index _depth,
00096     const Scalar* _lhs, Index lhsStride,
00097     const Scalar* _rhs, Index rhsStride,
00098     Scalar* res,        Index resStride,
00099     const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
00100 };
00101 
00102 template <typename Scalar, typename Index, int Mode,
00103           int LhsStorageOrder, bool ConjugateLhs,
00104           int RhsStorageOrder, bool ConjugateRhs, int Version>
00105 EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,true,
00106                                                         LhsStorageOrder,ConjugateLhs,
00107                                                         RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run(
00108     Index _rows, Index _cols, Index _depth,
00109     const Scalar* _lhs, Index lhsStride,
00110     const Scalar* _rhs, Index rhsStride,
00111     Scalar* res,        Index resStride,
00112     const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
00113   {
00114     // strip zeros
00115     Index diagSize  = (std::min)(_rows,_depth);
00116     Index rows      = IsLower ? _rows : diagSize;
00117     Index depth     = IsLower ? diagSize : _depth;
00118     Index cols      = _cols;
00119     
00120     const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
00121     const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
00122 
00123     Index kc = blocking.kc();                   // cache block size along the K direction
00124     Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction
00125 
00126     std::size_t sizeA = kc*mc;
00127     std::size_t sizeB = kc*cols;
00128     std::size_t sizeW = kc*Traits::WorkSpaceFactor;
00129 
00130     ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
00131     ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
00132     ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
00133 
00134     Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer;
00135     triangularBuffer.setZero();
00136     if((Mode&ZeroDiag)==ZeroDiag)
00137       triangularBuffer.diagonal().setZero();
00138     else
00139       triangularBuffer.diagonal().setOnes();
00140 
00141     gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
00142     gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
00143     gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
00144 
00145     for(Index k2=IsLower ? depth : 0;
00146         IsLower ? k2>0 : k2<depth;
00147         IsLower ? k2-=kc : k2+=kc)
00148     {
00149       Index actual_kc = (std::min)(IsLower ? k2 : depth-k2, kc);
00150       Index actual_k2 = IsLower ? k2-actual_kc : k2;
00151 
00152       // align blocks with the end of the triangular part for trapezoidal lhs
00153       if((!IsLower)&&(k2<rows)&&(k2+actual_kc>rows))
00154       {
00155         actual_kc = rows-k2;
00156         k2 = k2+actual_kc-kc;
00157       }
00158 
00159       pack_rhs(blockB, &rhs(actual_k2,0), rhsStride, actual_kc, cols);
00160 
00161       // the selected lhs's panel has to be split in three different parts:
00162       //  1 - the part which is zero => skip it
00163       //  2 - the diagonal block => special kernel
00164       //  3 - the dense panel below (lower case) or above (upper case) the diagonal block => GEPP
00165 
00166       // the block diagonal, if any:
00167       if(IsLower || actual_k2<rows)
00168       {
00169         // for each small vertical panels of lhs
00170         for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)
00171         {
00172           Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
00173           Index lengthTarget = IsLower ? actual_kc-k1-actualPanelWidth : k1;
00174           Index startBlock   = actual_k2+k1;
00175           Index blockBOffset = k1;
00176 
00177           // => GEBP with the micro triangular block
00178           // The trick is to pack this micro block while filling the opposite triangular part with zeros.
00179           // To this end we do an extra triangular copy to a small temporary buffer
00180           for (Index k=0;k<actualPanelWidth;++k)
00181           {
00182             if (SetDiag)
00183               triangularBuffer.coeffRef(k,k) = lhs(startBlock+k,startBlock+k);
00184             for (Index i=IsLower ? k+1 : 0; IsLower ? i<actualPanelWidth : i<k; ++i)
00185               triangularBuffer.coeffRef(i,k) = lhs(startBlock+i,startBlock+k);
00186           }
00187           pack_lhs(blockA, triangularBuffer.data(), triangularBuffer.outerStride(), actualPanelWidth, actualPanelWidth);
00188 
00189           gebp_kernel(res+startBlock, resStride, blockA, blockB, actualPanelWidth, actualPanelWidth, cols, alpha,
00190                       actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
00191 
00192           // GEBP with remaining micro panel
00193           if (lengthTarget>0)
00194           {
00195             Index startTarget  = IsLower ? actual_k2+k1+actualPanelWidth : actual_k2;
00196 
00197             pack_lhs(blockA, &lhs(startTarget,startBlock), lhsStride, actualPanelWidth, lengthTarget);
00198 
00199             gebp_kernel(res+startTarget, resStride, blockA, blockB, lengthTarget, actualPanelWidth, cols, alpha,
00200                         actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
00201           }
00202         }
00203       }
00204       // the part below (lower case) or above (upper case) the diagonal => GEPP
00205       {
00206         Index start = IsLower ? k2 : 0;
00207         Index end   = IsLower ? rows : (std::min)(actual_k2,rows);
00208         for(Index i2=start; i2<end; i2+=mc)
00209         {
00210           const Index actual_mc = (std::min)(i2+mc,end)-i2;
00211           gemm_pack_lhs<Scalar, Index, Traits::mr,Traits::LhsProgress, LhsStorageOrder,false>()
00212             (blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
00213 
00214           gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1, -1, 0, 0, blockW);
00215         }
00216       }
00217     }
00218   }
00219 
00220 // implements col-major += alpha * op(general) * op(triangular)
00221 template <typename Scalar, typename Index, int Mode,
00222           int LhsStorageOrder, bool ConjugateLhs,
00223           int RhsStorageOrder, bool ConjugateRhs, int Version>
00224 struct product_triangular_matrix_matrix<Scalar,Index,Mode,false,
00225                                         LhsStorageOrder,ConjugateLhs,
00226                                         RhsStorageOrder,ConjugateRhs,ColMajor,Version>
00227 {
00228   typedef gebp_traits<Scalar,Scalar> Traits;
00229   enum {
00230     SmallPanelWidth   = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
00231     IsLower = (Mode&Lower) == Lower,
00232     SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
00233   };
00234 
00235   static EIGEN_DONT_INLINE void run(
00236     Index _rows, Index _cols, Index _depth,
00237     const Scalar* _lhs, Index lhsStride,
00238     const Scalar* _rhs, Index rhsStride,
00239     Scalar* res,        Index resStride,
00240     const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
00241 };
00242 
00243 template <typename Scalar, typename Index, int Mode,
00244           int LhsStorageOrder, bool ConjugateLhs,
00245           int RhsStorageOrder, bool ConjugateRhs, int Version>
00246 EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,false,
00247                                                         LhsStorageOrder,ConjugateLhs,
00248                                                         RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run(
00249     Index _rows, Index _cols, Index _depth,
00250     const Scalar* _lhs, Index lhsStride,
00251     const Scalar* _rhs, Index rhsStride,
00252     Scalar* res,        Index resStride,
00253     const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
00254   {
00255     // strip zeros
00256     Index diagSize  = (std::min)(_cols,_depth);
00257     Index rows      = _rows;
00258     Index depth     = IsLower ? _depth : diagSize;
00259     Index cols      = IsLower ? diagSize : _cols;
00260     
00261     const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
00262     const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
00263 
00264     Index kc = blocking.kc();                   // cache block size along the K direction
00265     Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction
00266 
00267     std::size_t sizeA = kc*mc;
00268     std::size_t sizeB = kc*cols;
00269     std::size_t sizeW = kc*Traits::WorkSpaceFactor;
00270 
00271     ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
00272     ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
00273     ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
00274 
00275     Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer;
00276     triangularBuffer.setZero();
00277     if((Mode&ZeroDiag)==ZeroDiag)
00278       triangularBuffer.diagonal().setZero();
00279     else
00280       triangularBuffer.diagonal().setOnes();
00281 
00282     gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
00283     gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
00284     gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
00285     gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
00286 
00287     for(Index k2=IsLower ? 0 : depth;
00288         IsLower ? k2<depth  : k2>0;
00289         IsLower ? k2+=kc   : k2-=kc)
00290     {
00291       Index actual_kc = (std::min)(IsLower ? depth-k2 : k2, kc);
00292       Index actual_k2 = IsLower ? k2 : k2-actual_kc;
00293 
00294       // align blocks with the end of the triangular part for trapezoidal rhs
00295       if(IsLower && (k2<cols) && (actual_k2+actual_kc>cols))
00296       {
00297         actual_kc = cols-k2;
00298         k2 = actual_k2 + actual_kc - kc;
00299       }
00300 
00301       // remaining size
00302       Index rs = IsLower ? (std::min)(cols,actual_k2) : cols - k2;
00303       // size of the triangular part
00304       Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc;
00305 
00306       Scalar* geb = blockB+ts*ts;
00307 
00308       pack_rhs(geb, &rhs(actual_k2,IsLower ? 0 : k2), rhsStride, actual_kc, rs);
00309 
00310       // pack the triangular part of the rhs padding the unrolled blocks with zeros
00311       if(ts>0)
00312       {
00313         for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
00314         {
00315           Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
00316           Index actual_j2 = actual_k2 + j2;
00317           Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
00318           Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
00319           // general part
00320           pack_rhs_panel(blockB+j2*actual_kc,
00321                          &rhs(actual_k2+panelOffset, actual_j2), rhsStride,
00322                          panelLength, actualPanelWidth,
00323                          actual_kc, panelOffset);
00324 
00325           // append the triangular part via a temporary buffer
00326           for (Index j=0;j<actualPanelWidth;++j)
00327           {
00328             if (SetDiag)
00329               triangularBuffer.coeffRef(j,j) = rhs(actual_j2+j,actual_j2+j);
00330             for (Index k=IsLower ? j+1 : 0; IsLower ? k<actualPanelWidth : k<j; ++k)
00331               triangularBuffer.coeffRef(k,j) = rhs(actual_j2+k,actual_j2+j);
00332           }
00333 
00334           pack_rhs_panel(blockB+j2*actual_kc,
00335                          triangularBuffer.data(), triangularBuffer.outerStride(),
00336                          actualPanelWidth, actualPanelWidth,
00337                          actual_kc, j2);
00338         }
00339       }
00340 
00341       for (Index i2=0; i2<rows; i2+=mc)
00342       {
00343         const Index actual_mc = (std::min)(mc,rows-i2);
00344         pack_lhs(blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
00345 
00346         // triangular kernel
00347         if(ts>0)
00348         {
00349           for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
00350           {
00351             Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
00352             Index panelLength = IsLower ? actual_kc-j2 : j2+actualPanelWidth;
00353             Index blockOffset = IsLower ? j2 : 0;
00354 
00355             gebp_kernel(res+i2+(actual_k2+j2)*resStride, resStride,
00356                         blockA, blockB+j2*actual_kc,
00357                         actual_mc, panelLength, actualPanelWidth,
00358                         alpha,
00359                         actual_kc, actual_kc,  // strides
00360                         blockOffset, blockOffset,// offsets
00361                         blockW); // workspace
00362           }
00363         }
00364         gebp_kernel(res+i2+(IsLower ? 0 : k2)*resStride, resStride,
00365                     blockA, geb, actual_mc, actual_kc, rs,
00366                     alpha,
00367                     -1, -1, 0, 0, blockW);
00368       }
00369     }
00370   }
00371 
00372 /***************************************************************************
00373 * Wrapper to product_triangular_matrix_matrix
00374 ***************************************************************************/
00375 
00376 template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
00377 struct traits<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false> >
00378   : traits<ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs> >
00379 {};
00380 
00381 } // end namespace internal
00382 
00383 template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
00384 struct TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>
00385   : public ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs >
00386 {
00387   EIGEN_PRODUCT_PUBLIC_INTERFACE(TriangularProduct)
00388 
00389   TriangularProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
00390 
00391   template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
00392   {
00393     typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
00394     typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
00395 
00396     Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
00397                                * RhsBlasTraits::extractScalarFactor(m_rhs);
00398 
00399     typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
00400               Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,4> BlockingType;
00401 
00402     enum { IsLower = (Mode&Lower) == Lower };
00403     Index stripedRows  = ((!LhsIsTriangular) || (IsLower))  ? lhs.rows() : (std::min)(lhs.rows(),lhs.cols());
00404     Index stripedCols  = ((LhsIsTriangular)  || (!IsLower)) ? rhs.cols() : (std::min)(rhs.cols(),rhs.rows());
00405     Index stripedDepth = LhsIsTriangular ? ((!IsLower) ? lhs.cols() : (std::min)(lhs.cols(),lhs.rows()))
00406                                          : ((IsLower)  ? rhs.rows() : (std::min)(rhs.rows(),rhs.cols()));
00407 
00408     BlockingType blocking(stripedRows, stripedCols, stripedDepth);
00409 
00410     internal::product_triangular_matrix_matrix<Scalar, Index,
00411       Mode, LhsIsTriangular,
00412       (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
00413       (internal::traits<_ActualRhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
00414       (internal::traits<Dest          >::Flags&RowMajorBit) ? RowMajor : ColMajor>
00415       ::run(
00416         stripedRows, stripedCols, stripedDepth,   // sizes
00417         &lhs.coeffRef(0,0),    lhs.outerStride(), // lhs info
00418         &rhs.coeffRef(0,0),    rhs.outerStride(), // rhs info
00419         &dst.coeffRef(0,0), dst.outerStride(),    // result info
00420         actualAlpha, blocking
00421       );
00422   }
00423 };
00424 
00425 } // end namespace Eigen
00426 
00427 #endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H