TriangularMatrixMatrix.h
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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     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     Scalar alpha, level3_blocking<Scalar,Scalar>& blocking)
00100   {
00101     // strip zeros
00102     Index diagSize  = (std::min)(_rows,_depth);
00103     Index rows      = IsLower ? _rows : diagSize;
00104     Index depth     = IsLower ? diagSize : _depth;
00105     Index cols      = _cols;
00106     
00107     const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
00108     const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
00109 
00110     Index kc = blocking.kc();                   // cache block size along the K direction
00111     Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction
00112 
00113     std::size_t sizeA = kc*mc;
00114     std::size_t sizeB = kc*cols;
00115     std::size_t sizeW = kc*Traits::WorkSpaceFactor;
00116 
00117     ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
00118     ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
00119     ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
00120 
00121     Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer;
00122     triangularBuffer.setZero();
00123     if((Mode&ZeroDiag)==ZeroDiag)
00124       triangularBuffer.diagonal().setZero();
00125     else
00126       triangularBuffer.diagonal().setOnes();
00127 
00128     gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
00129     gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
00130     gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
00131 
00132     for(Index k2=IsLower ? depth : 0;
00133         IsLower ? k2>0 : k2<depth;
00134         IsLower ? k2-=kc : k2+=kc)
00135     {
00136       Index actual_kc = (std::min)(IsLower ? k2 : depth-k2, kc);
00137       Index actual_k2 = IsLower ? k2-actual_kc : k2;
00138 
00139       // align blocks with the end of the triangular part for trapezoidal lhs
00140       if((!IsLower)&&(k2<rows)&&(k2+actual_kc>rows))
00141       {
00142         actual_kc = rows-k2;
00143         k2 = k2+actual_kc-kc;
00144       }
00145 
00146       pack_rhs(blockB, &rhs(actual_k2,0), rhsStride, actual_kc, cols);
00147 
00148       // the selected lhs's panel has to be split in three different parts:
00149       //  1 - the part which is zero => skip it
00150       //  2 - the diagonal block => special kernel
00151       //  3 - the dense panel below (lower case) or above (upper case) the diagonal block => GEPP
00152 
00153       // the block diagonal, if any:
00154       if(IsLower || actual_k2<rows)
00155       {
00156         // for each small vertical panels of lhs
00157         for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)
00158         {
00159           Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
00160           Index lengthTarget = IsLower ? actual_kc-k1-actualPanelWidth : k1;
00161           Index startBlock   = actual_k2+k1;
00162           Index blockBOffset = k1;
00163 
00164           // => GEBP with the micro triangular block
00165           // The trick is to pack this micro block while filling the opposite triangular part with zeros.
00166           // To this end we do an extra triangular copy to a small temporary buffer
00167           for (Index k=0;k<actualPanelWidth;++k)
00168           {
00169             if (SetDiag)
00170               triangularBuffer.coeffRef(k,k) = lhs(startBlock+k,startBlock+k);
00171             for (Index i=IsLower ? k+1 : 0; IsLower ? i<actualPanelWidth : i<k; ++i)
00172               triangularBuffer.coeffRef(i,k) = lhs(startBlock+i,startBlock+k);
00173           }
00174           pack_lhs(blockA, triangularBuffer.data(), triangularBuffer.outerStride(), actualPanelWidth, actualPanelWidth);
00175 
00176           gebp_kernel(res+startBlock, resStride, blockA, blockB, actualPanelWidth, actualPanelWidth, cols, alpha,
00177                       actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
00178 
00179           // GEBP with remaining micro panel
00180           if (lengthTarget>0)
00181           {
00182             Index startTarget  = IsLower ? actual_k2+k1+actualPanelWidth : actual_k2;
00183 
00184             pack_lhs(blockA, &lhs(startTarget,startBlock), lhsStride, actualPanelWidth, lengthTarget);
00185 
00186             gebp_kernel(res+startTarget, resStride, blockA, blockB, lengthTarget, actualPanelWidth, cols, alpha,
00187                         actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
00188           }
00189         }
00190       }
00191       // the part below (lower case) or above (upper case) the diagonal => GEPP
00192       {
00193         Index start = IsLower ? k2 : 0;
00194         Index end   = IsLower ? rows : (std::min)(actual_k2,rows);
00195         for(Index i2=start; i2<end; i2+=mc)
00196         {
00197           const Index actual_mc = (std::min)(i2+mc,end)-i2;
00198           gemm_pack_lhs<Scalar, Index, Traits::mr,Traits::LhsProgress, LhsStorageOrder,false>()
00199             (blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
00200 
00201           gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1, -1, 0, 0, blockW);
00202         }
00203       }
00204     }
00205   }
00206 };
00207 
00208 // implements col-major += alpha * op(general) * op(triangular)
00209 template <typename Scalar, typename Index, int Mode,
00210           int LhsStorageOrder, bool ConjugateLhs,
00211           int RhsStorageOrder, bool ConjugateRhs, int Version>
00212 struct product_triangular_matrix_matrix<Scalar,Index,Mode,false,
00213                                            LhsStorageOrder,ConjugateLhs,
00214                                            RhsStorageOrder,ConjugateRhs,ColMajor,Version>
00215 {
00216   typedef gebp_traits<Scalar,Scalar> Traits;
00217   enum {
00218     SmallPanelWidth   = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
00219     IsLower = (Mode&Lower) == Lower,
00220     SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
00221   };
00222 
00223   static EIGEN_DONT_INLINE void run(
00224     Index _rows, Index _cols, Index _depth,
00225     const Scalar* _lhs, Index lhsStride,
00226     const Scalar* _rhs, Index rhsStride,
00227     Scalar* res,        Index resStride,
00228     Scalar alpha, level3_blocking<Scalar,Scalar>& blocking)
00229   {
00230     // strip zeros
00231     Index diagSize  = (std::min)(_cols,_depth);
00232     Index rows      = _rows;
00233     Index depth     = IsLower ? _depth : diagSize;
00234     Index cols      = IsLower ? diagSize : _cols;
00235     
00236     const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
00237     const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
00238 
00239     Index kc = blocking.kc();                   // cache block size along the K direction
00240     Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction
00241 
00242     std::size_t sizeA = kc*mc;
00243     std::size_t sizeB = kc*cols;
00244     std::size_t sizeW = kc*Traits::WorkSpaceFactor;
00245 
00246     ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
00247     ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
00248     ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
00249 
00250     Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer;
00251     triangularBuffer.setZero();
00252     if((Mode&ZeroDiag)==ZeroDiag)
00253       triangularBuffer.diagonal().setZero();
00254     else
00255       triangularBuffer.diagonal().setOnes();
00256 
00257     gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
00258     gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
00259     gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
00260     gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
00261 
00262     for(Index k2=IsLower ? 0 : depth;
00263         IsLower ? k2<depth  : k2>0;
00264         IsLower ? k2+=kc   : k2-=kc)
00265     {
00266       Index actual_kc = (std::min)(IsLower ? depth-k2 : k2, kc);
00267       Index actual_k2 = IsLower ? k2 : k2-actual_kc;
00268 
00269       // align blocks with the end of the triangular part for trapezoidal rhs
00270       if(IsLower && (k2<cols) && (actual_k2+actual_kc>cols))
00271       {
00272         actual_kc = cols-k2;
00273         k2 = actual_k2 + actual_kc - kc;
00274       }
00275 
00276       // remaining size
00277       Index rs = IsLower ? (std::min)(cols,actual_k2) : cols - k2;
00278       // size of the triangular part
00279       Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc;
00280 
00281       Scalar* geb = blockB+ts*ts;
00282 
00283       pack_rhs(geb, &rhs(actual_k2,IsLower ? 0 : k2), rhsStride, actual_kc, rs);
00284 
00285       // pack the triangular part of the rhs padding the unrolled blocks with zeros
00286       if(ts>0)
00287       {
00288         for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
00289         {
00290           Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
00291           Index actual_j2 = actual_k2 + j2;
00292           Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
00293           Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
00294           // general part
00295           pack_rhs_panel(blockB+j2*actual_kc,
00296                          &rhs(actual_k2+panelOffset, actual_j2), rhsStride,
00297                          panelLength, actualPanelWidth,
00298                          actual_kc, panelOffset);
00299 
00300           // append the triangular part via a temporary buffer
00301           for (Index j=0;j<actualPanelWidth;++j)
00302           {
00303             if (SetDiag)
00304               triangularBuffer.coeffRef(j,j) = rhs(actual_j2+j,actual_j2+j);
00305             for (Index k=IsLower ? j+1 : 0; IsLower ? k<actualPanelWidth : k<j; ++k)
00306               triangularBuffer.coeffRef(k,j) = rhs(actual_j2+k,actual_j2+j);
00307           }
00308 
00309           pack_rhs_panel(blockB+j2*actual_kc,
00310                          triangularBuffer.data(), triangularBuffer.outerStride(),
00311                          actualPanelWidth, actualPanelWidth,
00312                          actual_kc, j2);
00313         }
00314       }
00315 
00316       for (Index i2=0; i2<rows; i2+=mc)
00317       {
00318         const Index actual_mc = (std::min)(mc,rows-i2);
00319         pack_lhs(blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
00320 
00321         // triangular kernel
00322         if(ts>0)
00323         {
00324           for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
00325           {
00326             Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
00327             Index panelLength = IsLower ? actual_kc-j2 : j2+actualPanelWidth;
00328             Index blockOffset = IsLower ? j2 : 0;
00329 
00330             gebp_kernel(res+i2+(actual_k2+j2)*resStride, resStride,
00331                         blockA, blockB+j2*actual_kc,
00332                         actual_mc, panelLength, actualPanelWidth,
00333                         alpha,
00334                         actual_kc, actual_kc,  // strides
00335                         blockOffset, blockOffset,// offsets
00336                         blockW); // workspace
00337           }
00338         }
00339         gebp_kernel(res+i2+(IsLower ? 0 : k2)*resStride, resStride,
00340                     blockA, geb, actual_mc, actual_kc, rs,
00341                     alpha,
00342                     -1, -1, 0, 0, blockW);
00343       }
00344     }
00345   }
00346 };
00347 
00348 /***************************************************************************
00349 * Wrapper to product_triangular_matrix_matrix
00350 ***************************************************************************/
00351 
00352 template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
00353 struct traits<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false> >
00354   : traits<ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs> >
00355 {};
00356 
00357 } // end namespace internal
00358 
00359 template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
00360 struct TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>
00361   : public ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs >
00362 {
00363   EIGEN_PRODUCT_PUBLIC_INTERFACE(TriangularProduct)
00364 
00365   TriangularProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
00366 
00367   template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const
00368   {
00369     typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
00370     typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
00371 
00372     Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
00373                                * RhsBlasTraits::extractScalarFactor(m_rhs);
00374 
00375     typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
00376               Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,4> BlockingType;
00377 
00378     enum { IsLower = (Mode&Lower) == Lower };
00379     Index stripedRows  = ((!LhsIsTriangular) || (IsLower))  ? lhs.rows() : (std::min)(lhs.rows(),lhs.cols());
00380     Index stripedCols  = ((LhsIsTriangular)  || (!IsLower)) ? rhs.cols() : (std::min)(rhs.cols(),rhs.rows());
00381     Index stripedDepth = LhsIsTriangular ? ((!IsLower) ? lhs.cols() : (std::min)(lhs.cols(),lhs.rows()))
00382                                          : ((IsLower)  ? rhs.rows() : (std::min)(rhs.rows(),rhs.cols()));
00383 
00384     BlockingType blocking(stripedRows, stripedCols, stripedDepth);
00385 
00386     internal::product_triangular_matrix_matrix<Scalar, Index,
00387       Mode, LhsIsTriangular,
00388       (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
00389       (internal::traits<_ActualRhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
00390       (internal::traits<Dest          >::Flags&RowMajorBit) ? RowMajor : ColMajor>
00391       ::run(
00392         stripedRows, stripedCols, stripedDepth,   // sizes
00393         &lhs.coeffRef(0,0),    lhs.outerStride(), // lhs info
00394         &rhs.coeffRef(0,0),    rhs.outerStride(), // rhs info
00395         &dst.coeffRef(0,0), dst.outerStride(),    // result info
00396         actualAlpha, blocking
00397       );
00398   }
00399 };
00400 
00401 } // end namespace Eigen
00402 
00403 #endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H


win_eigen
Author(s): Daniel Stonier
autogenerated on Mon Oct 6 2014 12:26:45