GeneralMatrixMatrixTriangular.h

00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2009-2010 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_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
00011 #define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
00012 
00013 namespace Eigen { 
00014 
00015 template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
00016 struct selfadjoint_rank1_update;
00017 
00018 namespace internal {
00019 
00020 /**********************************************************************
00021 * This file implements a general A * B product while
00022 * evaluating only one triangular part of the product.
00023 * This is more general version of self adjoint product (C += A A^T)
00024 * as the level 3 SYRK Blas routine.
00025 **********************************************************************/
00026 
00027 // forward declarations (defined at the end of this file)
00028 template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
00029 struct tribb_kernel;
00030   
00031 /* Optimized matrix-matrix product evaluating only one triangular half */
00032 template <typename Index,
00033           typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
00034           typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
00035                               int ResStorageOrder, int  UpLo, int Version = Specialized>
00036 struct general_matrix_matrix_triangular_product;
00037 
00038 // as usual if the result is row major => we transpose the product
00039 template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
00040                           typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int  UpLo, int Version>
00041 struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version>
00042 {
00043   typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
00044   static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride,
00045                                       const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride, const ResScalar& alpha)
00046   {
00047     general_matrix_matrix_triangular_product<Index,
00048         RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
00049         LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
00050         ColMajor, UpLo==Lower?Upper:Lower>
00051       ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha);
00052   }
00053 };
00054 
00055 template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
00056                           typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int  UpLo, int Version>
00057 struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version>
00058 {
00059   typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
00060   static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride,
00061                                       const RhsScalar* _rhs, Index rhsStride, ResScalar* res, Index resStride, const ResScalar& alpha)
00062   {
00063     const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
00064     const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
00065 
00066     typedef gebp_traits<LhsScalar,RhsScalar> Traits;
00067 
00068     Index kc = depth; // cache block size along the K direction
00069     Index mc = size;  // cache block size along the M direction
00070     Index nc = size;  // cache block size along the N direction
00071     computeProductBlockingSizes<LhsScalar,RhsScalar>(kc, mc, nc);
00072     // !!! mc must be a multiple of nr:
00073     if(mc > Traits::nr)
00074       mc = (mc/Traits::nr)*Traits::nr;
00075 
00076     std::size_t sizeW = kc*Traits::WorkSpaceFactor;
00077     std::size_t sizeB = sizeW + kc*size;
00078     ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, kc*mc, 0);
00079     ei_declare_aligned_stack_constructed_variable(RhsScalar, allocatedBlockB, sizeB, 0);
00080     RhsScalar* blockB = allocatedBlockB + sizeW;
00081     
00082     gemm_pack_lhs<LhsScalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
00083     gemm_pack_rhs<RhsScalar, Index, Traits::nr, RhsStorageOrder> pack_rhs;
00084     gebp_kernel <LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
00085     tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb;
00086 
00087     for(Index k2=0; k2<depth; k2+=kc)
00088     {
00089       const Index actual_kc = (std::min)(k2+kc,depth)-k2;
00090 
00091       // note that the actual rhs is the transpose/adjoint of mat
00092       pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, size);
00093 
00094       for(Index i2=0; i2<size; i2+=mc)
00095       {
00096         const Index actual_mc = (std::min)(i2+mc,size)-i2;
00097 
00098         pack_lhs(blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc);
00099 
00100         // the selected actual_mc * size panel of res is split into three different part:
00101         //  1 - before the diagonal => processed with gebp or skipped
00102         //  2 - the actual_mc x actual_mc symmetric block => processed with a special kernel
00103         //  3 - after the diagonal => processed with gebp or skipped
00104         if (UpLo==Lower)
00105           gebp(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, (std::min)(size,i2), alpha,
00106                -1, -1, 0, 0, allocatedBlockB);
00107 
00108         sybb(res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha, allocatedBlockB);
00109 
00110         if (UpLo==Upper)
00111         {
00112           Index j2 = i2+actual_mc;
00113           gebp(res+resStride*j2+i2, resStride, blockA, blockB+actual_kc*j2, actual_mc, actual_kc, (std::max)(Index(0), size-j2), alpha,
00114                -1, -1, 0, 0, allocatedBlockB);
00115         }
00116       }
00117     }
00118   }
00119 };
00120 
00121 // Optimized packed Block * packed Block product kernel evaluating only one given triangular part
00122 // This kernel is built on top of the gebp kernel:
00123 // - the current destination block is processed per panel of actual_mc x BlockSize
00124 //   where BlockSize is set to the minimal value allowing gebp to be as fast as possible
00125 // - then, as usual, each panel is split into three parts along the diagonal,
00126 //   the sub blocks above and below the diagonal are processed as usual,
00127 //   while the triangular block overlapping the diagonal is evaluated into a
00128 //   small temporary buffer which is then accumulated into the result using a
00129 //   triangular traversal.
00130 template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
00131 struct tribb_kernel
00132 {
00133   typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits;
00134   typedef typename Traits::ResScalar ResScalar;
00135   
00136   enum {
00137     BlockSize  = EIGEN_PLAIN_ENUM_MAX(mr,nr)
00138   };
00139   void operator()(ResScalar* res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha, RhsScalar* workspace)
00140   {
00141     gebp_kernel<LhsScalar, RhsScalar, Index, mr, nr, ConjLhs, ConjRhs> gebp_kernel;
00142     Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer;
00143 
00144     // let's process the block per panel of actual_mc x BlockSize,
00145     // again, each is split into three parts, etc.
00146     for (Index j=0; j<size; j+=BlockSize)
00147     {
00148       Index actualBlockSize = std::min<Index>(BlockSize,size - j);
00149       const RhsScalar* actual_b = blockB+j*depth;
00150 
00151       if(UpLo==Upper)
00152         gebp_kernel(res+j*resStride, resStride, blockA, actual_b, j, depth, actualBlockSize, alpha,
00153                     -1, -1, 0, 0, workspace);
00154 
00155       // selfadjoint micro block
00156       {
00157         Index i = j;
00158         buffer.setZero();
00159         // 1 - apply the kernel on the temporary buffer
00160         gebp_kernel(buffer.data(), BlockSize, blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha,
00161                     -1, -1, 0, 0, workspace);
00162         // 2 - triangular accumulation
00163         for(Index j1=0; j1<actualBlockSize; ++j1)
00164         {
00165           ResScalar* r = res + (j+j1)*resStride + i;
00166           for(Index i1=UpLo==Lower ? j1 : 0;
00167               UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1)
00168             r[i1] += buffer(i1,j1);
00169         }
00170       }
00171 
00172       if(UpLo==Lower)
00173       {
00174         Index i = j+actualBlockSize;
00175         gebp_kernel(res+j*resStride+i, resStride, blockA+depth*i, actual_b, size-i, depth, actualBlockSize, alpha,
00176                     -1, -1, 0, 0, workspace);
00177       }
00178     }
00179   }
00180 };
00181 
00182 } // end namespace internal
00183 
00184 // high level API
00185 
00186 template<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct>
00187 struct general_product_to_triangular_selector;
00188 
00189 
00190 template<typename MatrixType, typename ProductType, int UpLo>
00191 struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true>
00192 {
00193   static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha)
00194   {
00195     typedef typename MatrixType::Scalar Scalar;
00196     typedef typename MatrixType::Index Index;
00197     
00198     typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
00199     typedef internal::blas_traits<Lhs> LhsBlasTraits;
00200     typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
00201     typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
00202     typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
00203     
00204     typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
00205     typedef internal::blas_traits<Rhs> RhsBlasTraits;
00206     typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
00207     typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
00208     typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
00209 
00210     Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
00211 
00212     enum {
00213       StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor,
00214       UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1,
00215       UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1
00216     };
00217     
00218     internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs;
00219     ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(),
00220       (UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data()));
00221     if(!UseLhsDirectly) Map<typename _ActualLhs::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs;
00222     
00223     internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs;
00224     ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(),
00225       (UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data()));
00226     if(!UseRhsDirectly) Map<typename _ActualRhs::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
00227     
00228     
00229     selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo,
00230                               LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,
00231                               RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex>
00232           ::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha);
00233   }
00234 };
00235 
00236 template<typename MatrixType, typename ProductType, int UpLo>
00237 struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false>
00238 {
00239   static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha)
00240   {
00241     typedef typename MatrixType::Index Index;
00242     
00243     typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
00244     typedef internal::blas_traits<Lhs> LhsBlasTraits;
00245     typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
00246     typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
00247     typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
00248     
00249     typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
00250     typedef internal::blas_traits<Rhs> RhsBlasTraits;
00251     typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
00252     typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
00253     typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
00254 
00255     typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
00256 
00257     internal::general_matrix_matrix_triangular_product<Index,
00258       typename Lhs::Scalar, _ActualLhs::Flags&RowMajorBit ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
00259       typename Rhs::Scalar, _ActualRhs::Flags&RowMajorBit ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
00260       MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor, UpLo>
00261       ::run(mat.cols(), actualLhs.cols(),
00262             &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &actualRhs.coeffRef(0,0), actualRhs.outerStride(),
00263             mat.data(), mat.outerStride(), actualAlpha);
00264   }
00265 };
00266 
00267 template<typename MatrixType, unsigned int UpLo>
00268 template<typename ProductDerived, typename _Lhs, typename _Rhs>
00269 TriangularView<MatrixType,UpLo>& TriangularView<MatrixType,UpLo>::assignProduct(const ProductBase<ProductDerived, _Lhs,_Rhs>& prod, const Scalar& alpha)
00270 {
00271   general_product_to_triangular_selector<MatrixType, ProductDerived, UpLo, (_Lhs::ColsAtCompileTime==1) || (_Rhs::RowsAtCompileTime==1)>::run(m_matrix.const_cast_derived(), prod.derived(), alpha);
00272   
00273   return *this;
00274 }
00275 
00276 } // end namespace Eigen
00277 
00278 #endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H