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      1 /*
      2  Copyright (c) 2011, Intel Corporation. All rights reserved.
      3 
      4  Redistribution and use in source and binary forms, with or without modification,
      5  are permitted provided that the following conditions are met:
      6 
      7  * Redistributions of source code must retain the above copyright notice, this
      8    list of conditions and the following disclaimer.
      9  * Redistributions in binary form must reproduce the above copyright notice,
     10    this list of conditions and the following disclaimer in the documentation
     11    and/or other materials provided with the distribution.
     12  * Neither the name of Intel Corporation nor the names of its contributors may
     13    be used to endorse or promote products derived from this software without
     14    specific prior written permission.
     15 
     16  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
     17  ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
     18  WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
     19  DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
     20  ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
     21  (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
     22  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
     23  ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
     24  (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
     25  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
     26 
     27  ********************************************************************************
     28  *   Content : Eigen bindings to Intel(R) MKL
     29  *   Triangular matrix * matrix product functionality based on ?TRMM.
     30  ********************************************************************************
     31 */
     32 
     33 #ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_MKL_H
     34 #define EIGEN_TRIANGULAR_MATRIX_MATRIX_MKL_H
     35 
     36 namespace Eigen {
     37 
     38 namespace internal {
     39 
     40 
     41 template <typename Scalar, typename Index,
     42           int Mode, bool LhsIsTriangular,
     43           int LhsStorageOrder, bool ConjugateLhs,
     44           int RhsStorageOrder, bool ConjugateRhs,
     45           int ResStorageOrder>
     46 struct product_triangular_matrix_matrix_trmm :
     47        product_triangular_matrix_matrix<Scalar,Index,Mode,
     48           LhsIsTriangular,LhsStorageOrder,ConjugateLhs,
     49           RhsStorageOrder, ConjugateRhs, ResStorageOrder, BuiltIn> {};
     50 
     51 
     52 // try to go to BLAS specialization
     53 #define EIGEN_MKL_TRMM_SPECIALIZE(Scalar, LhsIsTriangular) \
     54 template <typename Index, int Mode, \
     55           int LhsStorageOrder, bool ConjugateLhs, \
     56           int RhsStorageOrder, bool ConjugateRhs> \
     57 struct product_triangular_matrix_matrix<Scalar,Index, Mode, LhsIsTriangular, \
     58            LhsStorageOrder,ConjugateLhs, RhsStorageOrder,ConjugateRhs,ColMajor,Specialized> { \
     59   static inline void run(Index _rows, Index _cols, Index _depth, const Scalar* _lhs, Index lhsStride,\
     60     const Scalar* _rhs, Index rhsStride, Scalar* res, Index resStride, Scalar alpha) { \
     61       product_triangular_matrix_matrix_trmm<Scalar,Index,Mode, \
     62         LhsIsTriangular,LhsStorageOrder,ConjugateLhs, \
     63         RhsStorageOrder, ConjugateRhs, ColMajor>::run( \
     64         _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha); \
     65   } \
     66 };
     67 
     68 EIGEN_MKL_TRMM_SPECIALIZE(double, true)
     69 EIGEN_MKL_TRMM_SPECIALIZE(double, false)
     70 EIGEN_MKL_TRMM_SPECIALIZE(dcomplex, true)
     71 EIGEN_MKL_TRMM_SPECIALIZE(dcomplex, false)
     72 EIGEN_MKL_TRMM_SPECIALIZE(float, true)
     73 EIGEN_MKL_TRMM_SPECIALIZE(float, false)
     74 EIGEN_MKL_TRMM_SPECIALIZE(scomplex, true)
     75 EIGEN_MKL_TRMM_SPECIALIZE(scomplex, false)
     76 
     77 // implements col-major += alpha * op(triangular) * op(general)
     78 #define EIGEN_MKL_TRMM_L(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
     79 template <typename Index, int Mode, \
     80           int LhsStorageOrder, bool ConjugateLhs, \
     81           int RhsStorageOrder, bool ConjugateRhs> \
     82 struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \
     83          LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \
     84 { \
     85   enum { \
     86     IsLower = (Mode&Lower) == Lower, \
     87     SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
     88     IsUnitDiag  = (Mode&UnitDiag) ? 1 : 0, \
     89     IsZeroDiag  = (Mode&ZeroDiag) ? 1 : 0, \
     90     LowUp = IsLower ? Lower : Upper, \
     91     conjA = ((LhsStorageOrder==ColMajor) && ConjugateLhs) ? 1 : 0 \
     92   }; \
     93 \
     94   static EIGEN_DONT_INLINE void run( \
     95     Index _rows, Index _cols, Index _depth, \
     96     const EIGTYPE* _lhs, Index lhsStride, \
     97     const EIGTYPE* _rhs, Index rhsStride, \
     98     EIGTYPE* res,        Index resStride, \
     99     EIGTYPE alpha) \
    100   { \
    101    Index diagSize  = (std::min)(_rows,_depth); \
    102    Index rows      = IsLower ? _rows : diagSize; \
    103    Index depth     = IsLower ? diagSize : _depth; \
    104    Index cols      = _cols; \
    105 \
    106    typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \
    107    typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \
    108 \
    109 /* Non-square case - doesn't fit to MKL ?TRMM. Fall to default triangular product or call MKL ?GEMM*/ \
    110    if (rows != depth) { \
    111 \
    112      int nthr = mkl_domain_get_max_threads(MKL_BLAS); \
    113 \
    114      if (((nthr==1) && (((std::max)(rows,depth)-diagSize)/(double)diagSize < 0.5))) { \
    115      /* Most likely no benefit to call TRMM or GEMM from MKL*/ \
    116        product_triangular_matrix_matrix<EIGTYPE,Index,Mode,true, \
    117        LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, BuiltIn>::run( \
    118            _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha); \
    119      /*std::cout << "TRMM_L: A is not square! Go to Eigen TRMM implementation!\n";*/ \
    120      } else { \
    121      /* Make sense to call GEMM */ \
    122        Map<const MatrixLhs, 0, OuterStride<> > lhsMap(_lhs,rows,depth,OuterStride<>(lhsStride)); \
    123        MatrixLhs aa_tmp=lhsMap.template triangularView<Mode>(); \
    124        MKL_INT aStride = aa_tmp.outerStride(); \
    125        gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> blocking(_rows,_cols,_depth); \
    126        general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor>::run( \
    127        rows, cols, depth, aa_tmp.data(), aStride, _rhs, rhsStride, res, resStride, alpha, blocking, 0); \
    128 \
    129      /*std::cout << "TRMM_L: A is not square! Go to MKL GEMM implementation! " << nthr<<" \n";*/ \
    130      } \
    131      return; \
    132    } \
    133    char side = 'L', transa, uplo, diag = 'N'; \
    134    EIGTYPE *b; \
    135    const EIGTYPE *a; \
    136    MKL_INT m, n, lda, ldb; \
    137    MKLTYPE alpha_; \
    138 \
    139 /* Set alpha_*/ \
    140    assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
    141 \
    142 /* Set m, n */ \
    143    m = (MKL_INT)diagSize; \
    144    n = (MKL_INT)cols; \
    145 \
    146 /* Set trans */ \
    147    transa = (LhsStorageOrder==RowMajor) ? ((ConjugateLhs) ? 'C' : 'T') : 'N'; \
    148 \
    149 /* Set b, ldb */ \
    150    Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols,OuterStride<>(rhsStride)); \
    151    MatrixX##EIGPREFIX b_tmp; \
    152 \
    153    if (ConjugateRhs) b_tmp = rhs.conjugate(); else b_tmp = rhs; \
    154    b = b_tmp.data(); \
    155    ldb = b_tmp.outerStride(); \
    156 \
    157 /* Set uplo */ \
    158    uplo = IsLower ? 'L' : 'U'; \
    159    if (LhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
    160 /* Set a, lda */ \
    161    Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \
    162    MatrixLhs a_tmp; \
    163 \
    164    if ((conjA!=0) || (SetDiag==0)) { \
    165      if (conjA) a_tmp = lhs.conjugate(); else a_tmp = lhs; \
    166      if (IsZeroDiag) \
    167        a_tmp.diagonal().setZero(); \
    168      else if (IsUnitDiag) \
    169        a_tmp.diagonal().setOnes();\
    170      a = a_tmp.data(); \
    171      lda = a_tmp.outerStride(); \
    172    } else { \
    173      a = _lhs; \
    174      lda = lhsStride; \
    175    } \
    176    /*std::cout << "TRMM_L: A is square! Go to MKL TRMM implementation! \n";*/ \
    177 /* call ?trmm*/ \
    178    MKLPREFIX##trmm(&side, &uplo, &transa, &diag, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (MKLTYPE*)b, &ldb); \
    179 \
    180 /* Add op(a_triangular)*b into res*/ \
    181    Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \
    182    res_tmp=res_tmp+b_tmp; \
    183   } \
    184 };
    185 
    186 EIGEN_MKL_TRMM_L(double, double, d, d)
    187 EIGEN_MKL_TRMM_L(dcomplex, MKL_Complex16, cd, z)
    188 EIGEN_MKL_TRMM_L(float, float, f, s)
    189 EIGEN_MKL_TRMM_L(scomplex, MKL_Complex8, cf, c)
    190 
    191 // implements col-major += alpha * op(general) * op(triangular)
    192 #define EIGEN_MKL_TRMM_R(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
    193 template <typename Index, int Mode, \
    194           int LhsStorageOrder, bool ConjugateLhs, \
    195           int RhsStorageOrder, bool ConjugateRhs> \
    196 struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \
    197          LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \
    198 { \
    199   enum { \
    200     IsLower = (Mode&Lower) == Lower, \
    201     SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
    202     IsUnitDiag  = (Mode&UnitDiag) ? 1 : 0, \
    203     IsZeroDiag  = (Mode&ZeroDiag) ? 1 : 0, \
    204     LowUp = IsLower ? Lower : Upper, \
    205     conjA = ((RhsStorageOrder==ColMajor) && ConjugateRhs) ? 1 : 0 \
    206   }; \
    207 \
    208   static EIGEN_DONT_INLINE void run( \
    209     Index _rows, Index _cols, Index _depth, \
    210     const EIGTYPE* _lhs, Index lhsStride, \
    211     const EIGTYPE* _rhs, Index rhsStride, \
    212     EIGTYPE* res,        Index resStride, \
    213     EIGTYPE alpha) \
    214   { \
    215    Index diagSize  = (std::min)(_cols,_depth); \
    216    Index rows      = _rows; \
    217    Index depth     = IsLower ? _depth : diagSize; \
    218    Index cols      = IsLower ? diagSize : _cols; \
    219 \
    220    typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \
    221    typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \
    222 \
    223 /* Non-square case - doesn't fit to MKL ?TRMM. Fall to default triangular product or call MKL ?GEMM*/ \
    224    if (cols != depth) { \
    225 \
    226      int nthr = mkl_domain_get_max_threads(MKL_BLAS); \
    227 \
    228      if ((nthr==1) && (((std::max)(cols,depth)-diagSize)/(double)diagSize < 0.5)) { \
    229      /* Most likely no benefit to call TRMM or GEMM from MKL*/ \
    230        product_triangular_matrix_matrix<EIGTYPE,Index,Mode,false, \
    231        LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, BuiltIn>::run( \
    232            _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha); \
    233        /*std::cout << "TRMM_R: A is not square! Go to Eigen TRMM implementation!\n";*/ \
    234      } else { \
    235      /* Make sense to call GEMM */ \
    236        Map<const MatrixRhs, 0, OuterStride<> > rhsMap(_rhs,depth,cols, OuterStride<>(rhsStride)); \
    237        MatrixRhs aa_tmp=rhsMap.template triangularView<Mode>(); \
    238        MKL_INT aStride = aa_tmp.outerStride(); \
    239        gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> blocking(_rows,_cols,_depth); \
    240        general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor>::run( \
    241        rows, cols, depth, _lhs, lhsStride, aa_tmp.data(), aStride, res, resStride, alpha, blocking, 0); \
    242 \
    243      /*std::cout << "TRMM_R: A is not square! Go to MKL GEMM implementation! " << nthr<<" \n";*/ \
    244      } \
    245      return; \
    246    } \
    247    char side = 'R', transa, uplo, diag = 'N'; \
    248    EIGTYPE *b; \
    249    const EIGTYPE *a; \
    250    MKL_INT m, n, lda, ldb; \
    251    MKLTYPE alpha_; \
    252 \
    253 /* Set alpha_*/ \
    254    assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
    255 \
    256 /* Set m, n */ \
    257    m = (MKL_INT)rows; \
    258    n = (MKL_INT)diagSize; \
    259 \
    260 /* Set trans */ \
    261    transa = (RhsStorageOrder==RowMajor) ? ((ConjugateRhs) ? 'C' : 'T') : 'N'; \
    262 \
    263 /* Set b, ldb */ \
    264    Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \
    265    MatrixX##EIGPREFIX b_tmp; \
    266 \
    267    if (ConjugateLhs) b_tmp = lhs.conjugate(); else b_tmp = lhs; \
    268    b = b_tmp.data(); \
    269    ldb = b_tmp.outerStride(); \
    270 \
    271 /* Set uplo */ \
    272    uplo = IsLower ? 'L' : 'U'; \
    273    if (RhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
    274 /* Set a, lda */ \
    275    Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols, OuterStride<>(rhsStride)); \
    276    MatrixRhs a_tmp; \
    277 \
    278    if ((conjA!=0) || (SetDiag==0)) { \
    279      if (conjA) a_tmp = rhs.conjugate(); else a_tmp = rhs; \
    280      if (IsZeroDiag) \
    281        a_tmp.diagonal().setZero(); \
    282      else if (IsUnitDiag) \
    283        a_tmp.diagonal().setOnes();\
    284      a = a_tmp.data(); \
    285      lda = a_tmp.outerStride(); \
    286    } else { \
    287      a = _rhs; \
    288      lda = rhsStride; \
    289    } \
    290    /*std::cout << "TRMM_R: A is square! Go to MKL TRMM implementation! \n";*/ \
    291 /* call ?trmm*/ \
    292    MKLPREFIX##trmm(&side, &uplo, &transa, &diag, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (MKLTYPE*)b, &ldb); \
    293 \
    294 /* Add op(a_triangular)*b into res*/ \
    295    Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \
    296    res_tmp=res_tmp+b_tmp; \
    297   } \
    298 };
    299 
    300 EIGEN_MKL_TRMM_R(double, double, d, d)
    301 EIGEN_MKL_TRMM_R(dcomplex, MKL_Complex16, cd, z)
    302 EIGEN_MKL_TRMM_R(float, float, f, s)
    303 EIGEN_MKL_TRMM_R(scomplex, MKL_Complex8, cf, c)
    304 
    305 } // end namespace internal
    306 
    307 } // end namespace Eigen
    308 
    309 #endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_MKL_H
    310