TriangularSolverMatrix.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_SOLVER_MATRIX_H
00011 #define EIGEN_TRIANGULAR_SOLVER_MATRIX_H
00012 
00013 namespace Eigen { 
00014 
00015 namespace internal {
00016 
00017 // if the rhs is row major, let's transpose the product
00018 template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder>
00019 struct triangular_solve_matrix<Scalar,Index,Side,Mode,Conjugate,TriStorageOrder,RowMajor>
00020 {
00021   static void run(
00022     Index size, Index cols,
00023     const Scalar*  tri, Index triStride,
00024     Scalar* _other, Index otherStride,
00025     level3_blocking<Scalar,Scalar>& blocking)
00026   {
00027     triangular_solve_matrix<
00028       Scalar, Index, Side==OnTheLeft?OnTheRight:OnTheLeft,
00029       (Mode&UnitDiag) | ((Mode&Upper) ? Lower : Upper),
00030       NumTraits<Scalar>::IsComplex && Conjugate,
00031       TriStorageOrder==RowMajor ? ColMajor : RowMajor, ColMajor>
00032       ::run(size, cols, tri, triStride, _other, otherStride, blocking);
00033   }
00034 };
00035 
00036 /* Optimized triangular solver with multiple right hand side and the triangular matrix on the left
00037  */
00038 template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
00039 struct triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor>
00040 {
00041   static EIGEN_DONT_INLINE void run(
00042     Index size, Index otherSize,
00043     const Scalar* _tri, Index triStride,
00044     Scalar* _other, Index otherStride,
00045     level3_blocking<Scalar,Scalar>& blocking);
00046 };
00047 template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
00048 EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor>::run(
00049     Index size, Index otherSize,
00050     const Scalar* _tri, Index triStride,
00051     Scalar* _other, Index otherStride,
00052     level3_blocking<Scalar,Scalar>& blocking)
00053   {
00054     Index cols = otherSize;
00055     const_blas_data_mapper<Scalar, Index, TriStorageOrder> tri(_tri,triStride);
00056     blas_data_mapper<Scalar, Index, ColMajor> other(_other,otherStride);
00057 
00058     typedef gebp_traits<Scalar,Scalar> Traits;
00059     enum {
00060       SmallPanelWidth   = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
00061       IsLower = (Mode&Lower) == Lower
00062     };
00063 
00064     Index kc = blocking.kc();                   // cache block size along the K direction
00065     Index mc = (std::min)(size,blocking.mc());  // cache block size along the M direction
00066 
00067     std::size_t sizeA = kc*mc;
00068     std::size_t sizeB = kc*cols;
00069     std::size_t sizeW = kc*Traits::WorkSpaceFactor;
00070 
00071     ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
00072     ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
00073     ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
00074 
00075     conj_if<Conjugate> conj;
00076     gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, Conjugate, false> gebp_kernel;
00077     gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, TriStorageOrder> pack_lhs;
00078     gemm_pack_rhs<Scalar, Index, Traits::nr, ColMajor, false, true> pack_rhs;
00079 
00080     // the goal here is to subdivise the Rhs panels such that we keep some cache
00081     // coherence when accessing the rhs elements
00082     std::ptrdiff_t l1, l2;
00083     manage_caching_sizes(GetAction, &l1, &l2);
00084     Index subcols = cols>0 ? l2/(4 * sizeof(Scalar) * otherStride) : 0;
00085     subcols = std::max<Index>((subcols/Traits::nr)*Traits::nr, Traits::nr);
00086 
00087     for(Index k2=IsLower ? 0 : size;
00088         IsLower ? k2<size : k2>0;
00089         IsLower ? k2+=kc : k2-=kc)
00090     {
00091       const Index actual_kc = (std::min)(IsLower ? size-k2 : k2, kc);
00092 
00093       // We have selected and packed a big horizontal panel R1 of rhs. Let B be the packed copy of this panel,
00094       // and R2 the remaining part of rhs. The corresponding vertical panel of lhs is split into
00095       // A11 (the triangular part) and A21 the remaining rectangular part.
00096       // Then the high level algorithm is:
00097       //  - B = R1                    => general block copy (done during the next step)
00098       //  - R1 = A11^-1 B             => tricky part
00099       //  - update B from the new R1  => actually this has to be performed continuously during the above step
00100       //  - R2 -= A21 * B             => GEPP
00101 
00102       // The tricky part: compute R1 = A11^-1 B while updating B from R1
00103       // The idea is to split A11 into multiple small vertical panels.
00104       // Each panel can be split into a small triangular part T1k which is processed without optimization,
00105       // and the remaining small part T2k which is processed using gebp with appropriate block strides
00106       for(Index j2=0; j2<cols; j2+=subcols)
00107       {
00108         Index actual_cols = (std::min)(cols-j2,subcols);
00109         // for each small vertical panels [T1k^T, T2k^T]^T of lhs
00110         for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)
00111         {
00112           Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
00113           // tr solve
00114           for (Index k=0; k<actualPanelWidth; ++k)
00115           {
00116             // TODO write a small kernel handling this (can be shared with trsv)
00117             Index i  = IsLower ? k2+k1+k : k2-k1-k-1;
00118             Index rs = actualPanelWidth - k - 1; // remaining size
00119             Index s  = TriStorageOrder==RowMajor ? (IsLower ? k2+k1 : i+1)
00120                                                  :  IsLower ? i+1 : i-rs;
00121 
00122             Scalar a = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(tri(i,i));
00123             for (Index j=j2; j<j2+actual_cols; ++j)
00124             {
00125               if (TriStorageOrder==RowMajor)
00126               {
00127                 Scalar b(0);
00128                 const Scalar* l = &tri(i,s);
00129                 Scalar* r = &other(s,j);
00130                 for (Index i3=0; i3<k; ++i3)
00131                   b += conj(l[i3]) * r[i3];
00132 
00133                 other(i,j) = (other(i,j) - b)*a;
00134               }
00135               else
00136               {
00137                 Scalar b = (other(i,j) *= a);
00138                 Scalar* r = &other(s,j);
00139                 const Scalar* l = &tri(s,i);
00140                 for (Index i3=0;i3<rs;++i3)
00141                   r[i3] -= b * conj(l[i3]);
00142               }
00143             }
00144           }
00145 
00146           Index lengthTarget = actual_kc-k1-actualPanelWidth;
00147           Index startBlock   = IsLower ? k2+k1 : k2-k1-actualPanelWidth;
00148           Index blockBOffset = IsLower ? k1 : lengthTarget;
00149 
00150           // update the respective rows of B from other
00151           pack_rhs(blockB+actual_kc*j2, &other(startBlock,j2), otherStride, actualPanelWidth, actual_cols, actual_kc, blockBOffset);
00152 
00153           // GEBP
00154           if (lengthTarget>0)
00155           {
00156             Index startTarget  = IsLower ? k2+k1+actualPanelWidth : k2-actual_kc;
00157 
00158             pack_lhs(blockA, &tri(startTarget,startBlock), triStride, actualPanelWidth, lengthTarget);
00159 
00160             gebp_kernel(&other(startTarget,j2), otherStride, blockA, blockB+actual_kc*j2, lengthTarget, actualPanelWidth, actual_cols, Scalar(-1),
00161                         actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
00162           }
00163         }
00164       }
00165       
00166       // R2 -= A21 * B => GEPP
00167       {
00168         Index start = IsLower ? k2+kc : 0;
00169         Index end   = IsLower ? size : k2-kc;
00170         for(Index i2=start; i2<end; i2+=mc)
00171         {
00172           const Index actual_mc = (std::min)(mc,end-i2);
00173           if (actual_mc>0)
00174           {
00175             pack_lhs(blockA, &tri(i2, IsLower ? k2 : k2-kc), triStride, actual_kc, actual_mc);
00176 
00177             gebp_kernel(_other+i2, otherStride, blockA, blockB, actual_mc, actual_kc, cols, Scalar(-1), -1, -1, 0, 0, blockW);
00178           }
00179         }
00180       }
00181     }
00182   }
00183 
00184 /* Optimized triangular solver with multiple left hand sides and the trinagular matrix on the right
00185  */
00186 template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
00187 struct triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor>
00188 {
00189   static EIGEN_DONT_INLINE void run(
00190     Index size, Index otherSize,
00191     const Scalar* _tri, Index triStride,
00192     Scalar* _other, Index otherStride,
00193     level3_blocking<Scalar,Scalar>& blocking);
00194 };
00195 template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
00196 EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor>::run(
00197     Index size, Index otherSize,
00198     const Scalar* _tri, Index triStride,
00199     Scalar* _other, Index otherStride,
00200     level3_blocking<Scalar,Scalar>& blocking)
00201   {
00202     Index rows = otherSize;
00203     const_blas_data_mapper<Scalar, Index, TriStorageOrder> rhs(_tri,triStride);
00204     blas_data_mapper<Scalar, Index, ColMajor> lhs(_other,otherStride);
00205 
00206     typedef gebp_traits<Scalar,Scalar> Traits;
00207     enum {
00208       RhsStorageOrder   = TriStorageOrder,
00209       SmallPanelWidth   = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
00210       IsLower = (Mode&Lower) == Lower
00211     };
00212 
00213     Index kc = blocking.kc();                   // cache block size along the K direction
00214     Index mc = (std::min)(rows,blocking.mc());  // cache block size along the M direction
00215 
00216     std::size_t sizeA = kc*mc;
00217     std::size_t sizeB = kc*size;
00218     std::size_t sizeW = kc*Traits::WorkSpaceFactor;
00219 
00220     ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
00221     ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
00222     ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
00223 
00224     conj_if<Conjugate> conj;
00225     gebp_kernel<Scalar,Scalar, Index, Traits::mr, Traits::nr, false, Conjugate> gebp_kernel;
00226     gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
00227     gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
00228     gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, ColMajor, false, true> pack_lhs_panel;
00229 
00230     for(Index k2=IsLower ? size : 0;
00231         IsLower ? k2>0 : k2<size;
00232         IsLower ? k2-=kc : k2+=kc)
00233     {
00234       const Index actual_kc = (std::min)(IsLower ? k2 : size-k2, kc);
00235       Index actual_k2 = IsLower ? k2-actual_kc : k2 ;
00236 
00237       Index startPanel = IsLower ? 0 : k2+actual_kc;
00238       Index rs = IsLower ? actual_k2 : size - actual_k2 - actual_kc;
00239       Scalar* geb = blockB+actual_kc*actual_kc;
00240 
00241       if (rs>0) pack_rhs(geb, &rhs(actual_k2,startPanel), triStride, actual_kc, rs);
00242 
00243       // triangular packing (we only pack the panels off the diagonal,
00244       // neglecting the blocks overlapping the diagonal
00245       {
00246         for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
00247         {
00248           Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
00249           Index actual_j2 = actual_k2 + j2;
00250           Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
00251           Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
00252 
00253           if (panelLength>0)
00254           pack_rhs_panel(blockB+j2*actual_kc,
00255                          &rhs(actual_k2+panelOffset, actual_j2), triStride,
00256                          panelLength, actualPanelWidth,
00257                          actual_kc, panelOffset);
00258         }
00259       }
00260 
00261       for(Index i2=0; i2<rows; i2+=mc)
00262       {
00263         const Index actual_mc = (std::min)(mc,rows-i2);
00264 
00265         // triangular solver kernel
00266         {
00267           // for each small block of the diagonal (=> vertical panels of rhs)
00268           for (Index j2 = IsLower
00269                       ? (actual_kc - ((actual_kc%SmallPanelWidth) ? Index(actual_kc%SmallPanelWidth)
00270                                                                   : Index(SmallPanelWidth)))
00271                       : 0;
00272                IsLower ? j2>=0 : j2<actual_kc;
00273                IsLower ? j2-=SmallPanelWidth : j2+=SmallPanelWidth)
00274           {
00275             Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
00276             Index absolute_j2 = actual_k2 + j2;
00277             Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
00278             Index panelLength = IsLower ? actual_kc - j2 - actualPanelWidth : j2;
00279 
00280             // GEBP
00281             if(panelLength>0)
00282             {
00283               gebp_kernel(&lhs(i2,absolute_j2), otherStride,
00284                           blockA, blockB+j2*actual_kc,
00285                           actual_mc, panelLength, actualPanelWidth,
00286                           Scalar(-1),
00287                           actual_kc, actual_kc, // strides
00288                           panelOffset, panelOffset, // offsets
00289                           blockW);  // workspace
00290             }
00291 
00292             // unblocked triangular solve
00293             for (Index k=0; k<actualPanelWidth; ++k)
00294             {
00295               Index j = IsLower ? absolute_j2+actualPanelWidth-k-1 : absolute_j2+k;
00296 
00297               Scalar* r = &lhs(i2,j);
00298               for (Index k3=0; k3<k; ++k3)
00299               {
00300                 Scalar b = conj(rhs(IsLower ? j+1+k3 : absolute_j2+k3,j));
00301                 Scalar* a = &lhs(i2,IsLower ? j+1+k3 : absolute_j2+k3);
00302                 for (Index i=0; i<actual_mc; ++i)
00303                   r[i] -= a[i] * b;
00304               }
00305               if((Mode & UnitDiag)==0)
00306               {
00307                 Scalar b = conj(rhs(j,j));
00308                 for (Index i=0; i<actual_mc; ++i)
00309                   r[i] /= b;
00310               }
00311             }
00312 
00313             // pack the just computed part of lhs to A
00314             pack_lhs_panel(blockA, _other+absolute_j2*otherStride+i2, otherStride,
00315                            actualPanelWidth, actual_mc,
00316                            actual_kc, j2);
00317           }
00318         }
00319 
00320         if (rs>0)
00321           gebp_kernel(_other+i2+startPanel*otherStride, otherStride, blockA, geb,
00322                       actual_mc, actual_kc, rs, Scalar(-1),
00323                       -1, -1, 0, 0, blockW);
00324       }
00325     }
00326   }
00327 
00328 } // end namespace internal
00329 
00330 } // end namespace Eigen
00331 
00332 #endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_H