TriangularMatrixMatrix_BLAS.h

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 ********************************************************************************
 *   Content : Eigen bindings to BLAS F77
 *   Triangular matrix * matrix product functionality based on ?TRMM.
 ********************************************************************************
*/

#ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H
#define EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H

namespace Eigen { 

namespace internal {


template <typename Scalar, typename Index,
          int Mode, bool LhsIsTriangular,
          int LhsStorageOrder, bool ConjugateLhs,
          int RhsStorageOrder, bool ConjugateRhs,
          int ResStorageOrder>
struct product_triangular_matrix_matrix_trmm :
       product_triangular_matrix_matrix<Scalar,Index,Mode,
          LhsIsTriangular,LhsStorageOrder,ConjugateLhs,
          RhsStorageOrder, ConjugateRhs, ResStorageOrder, 1, BuiltIn> {};


// try to go to BLAS specialization
#define EIGEN_BLAS_TRMM_SPECIALIZE(Scalar, LhsIsTriangular) \
template <typename Index, int Mode, \
          int LhsStorageOrder, bool ConjugateLhs, \
          int RhsStorageOrder, bool ConjugateRhs> \
struct product_triangular_matrix_matrix<Scalar,Index, Mode, LhsIsTriangular, \
           LhsStorageOrder,ConjugateLhs, RhsStorageOrder,ConjugateRhs,ColMajor,1,Specialized> { \
  static inline void run(Index _rows, Index _cols, Index _depth, const Scalar* _lhs, Index lhsStride,\
    const Scalar* _rhs, Index rhsStride, Scalar* res, Index resIncr, Index resStride, Scalar alpha, level3_blocking<Scalar,Scalar>& blocking) { \
      EIGEN_ONLY_USED_FOR_DEBUG(resIncr); \
      eigen_assert(resIncr == 1); \
      product_triangular_matrix_matrix_trmm<Scalar,Index,Mode, \
        LhsIsTriangular,LhsStorageOrder,ConjugateLhs, \
        RhsStorageOrder, ConjugateRhs, ColMajor>::run( \
          _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha, blocking); \
  } \
};

EIGEN_BLAS_TRMM_SPECIALIZE(double, true)
EIGEN_BLAS_TRMM_SPECIALIZE(double, false)
EIGEN_BLAS_TRMM_SPECIALIZE(dcomplex, true)
EIGEN_BLAS_TRMM_SPECIALIZE(dcomplex, false)
EIGEN_BLAS_TRMM_SPECIALIZE(float, true)
EIGEN_BLAS_TRMM_SPECIALIZE(float, false)
EIGEN_BLAS_TRMM_SPECIALIZE(scomplex, true)
EIGEN_BLAS_TRMM_SPECIALIZE(scomplex, false)

// implements col-major += alpha * op(triangular) * op(general)
#define EIGEN_BLAS_TRMM_L(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \
template <typename Index, int Mode, \
          int LhsStorageOrder, bool ConjugateLhs, \
          int RhsStorageOrder, bool ConjugateRhs> \
struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \
         LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \
{ \
  enum { \
    IsLower = (Mode&Lower) == Lower, \
    SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
    IsUnitDiag  = (Mode&UnitDiag) ? 1 : 0, \
    IsZeroDiag  = (Mode&ZeroDiag) ? 1 : 0, \
    LowUp = IsLower ? Lower : Upper, \
    conjA = ((LhsStorageOrder==ColMajor) && ConjugateLhs) ? 1 : 0 \
  }; \
\
  static void run( \
    Index _rows, Index _cols, Index _depth, \
    const EIGTYPE* _lhs, Index lhsStride, \
    const EIGTYPE* _rhs, Index rhsStride, \
    EIGTYPE* res,        Index resStride, \
    EIGTYPE alpha, level3_blocking<EIGTYPE,EIGTYPE>& blocking) \
  { \
   Index diagSize  = (std::min)(_rows,_depth); \
   Index rows      = IsLower ? _rows : diagSize; \
   Index depth     = IsLower ? diagSize : _depth; \
   Index cols      = _cols; \
\
   typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \
   typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \
\
/* Non-square case - doesn't fit to BLAS ?TRMM. Fall to default triangular product or call BLAS ?GEMM*/ \
   if (rows != depth) { \
\
     /* FIXME handle mkl_domain_get_max_threads */ \
     /*int nthr = mkl_domain_get_max_threads(EIGEN_BLAS_DOMAIN_BLAS);*/ int nthr = 1;\
\
     if (((nthr==1) && (((std::max)(rows,depth)-diagSize)/(double)diagSize < 0.5))) { \
     /* Most likely no benefit to call TRMM or GEMM from BLAS */ \
       product_triangular_matrix_matrix<EIGTYPE,Index,Mode,true, \
       LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, 1, BuiltIn>::run( \
           _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, 1, resStride, alpha, blocking); \
     /*std::cout << "TRMM_L: A is not square! Go to Eigen TRMM implementation!\n";*/ \
     } else { \
     /* Make sense to call GEMM */ \
       Map<const MatrixLhs, 0, OuterStride<> > lhsMap(_lhs,rows,depth,OuterStride<>(lhsStride)); \
       MatrixLhs aa_tmp=lhsMap.template triangularView<Mode>(); \
       BlasIndex aStride = convert_index<BlasIndex>(aa_tmp.outerStride()); \
       gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> gemm_blocking(_rows,_cols,_depth, 1, true); \
       general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor,1>::run( \
       rows, cols, depth, aa_tmp.data(), aStride, _rhs, rhsStride, res, 1, resStride, alpha, gemm_blocking, 0); \
\
     /*std::cout << "TRMM_L: A is not square! Go to BLAS GEMM implementation! " << nthr<<" \n";*/ \
     } \
     return; \
   } \
   char side = 'L', transa, uplo, diag = 'N'; \
   EIGTYPE *b; \
   const EIGTYPE *a; \
   BlasIndex m, n, lda, ldb; \
\
/* Set m, n */ \
   m = convert_index<BlasIndex>(diagSize); \
   n = convert_index<BlasIndex>(cols); \
\
/* Set trans */ \
   transa = (LhsStorageOrder==RowMajor) ? ((ConjugateLhs) ? 'C' : 'T') : 'N'; \
\
/* Set b, ldb */ \
   Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols,OuterStride<>(rhsStride)); \
   MatrixX##EIGPREFIX b_tmp; \
\
   if (ConjugateRhs) b_tmp = rhs.conjugate(); else b_tmp = rhs; \
   b = b_tmp.data(); \
   ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
\
/* Set uplo */ \
   uplo = IsLower ? 'L' : 'U'; \
   if (LhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
/* Set a, lda */ \
   Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \
   MatrixLhs a_tmp; \
\
   if ((conjA!=0) || (SetDiag==0)) { \
     if (conjA) a_tmp = lhs.conjugate(); else a_tmp = lhs; \
     if (IsZeroDiag) \
       a_tmp.diagonal().setZero(); \
     else if (IsUnitDiag) \
       a_tmp.diagonal().setOnes();\
     a = a_tmp.data(); \
     lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
   } else { \
     a = _lhs; \
     lda = convert_index<BlasIndex>(lhsStride); \
   } \
   /*std::cout << "TRMM_L: A is square! Go to BLAS TRMM implementation! \n";*/ \
/* call ?trmm*/ \
   BLASFUNC(&side, &uplo, &transa, &diag, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)b, &ldb); \
\
/* Add op(a_triangular)*b into res*/ \
   Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \
   res_tmp=res_tmp+b_tmp; \
  } \
};

#ifdef EIGEN_USE_MKL
EIGEN_BLAS_TRMM_L(double, double, d, dtrmm)
EIGEN_BLAS_TRMM_L(dcomplex, MKL_Complex16, cd, ztrmm)
EIGEN_BLAS_TRMM_L(float, float, f, strmm)
EIGEN_BLAS_TRMM_L(scomplex, MKL_Complex8, cf, ctrmm)
#else
EIGEN_BLAS_TRMM_L(double, double, d, dtrmm_)
EIGEN_BLAS_TRMM_L(dcomplex, double, cd, ztrmm_)
EIGEN_BLAS_TRMM_L(float, float, f, strmm_)
EIGEN_BLAS_TRMM_L(scomplex, float, cf, ctrmm_)
#endif

// implements col-major += alpha * op(general) * op(triangular)
#define EIGEN_BLAS_TRMM_R(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \
template <typename Index, int Mode, \
          int LhsStorageOrder, bool ConjugateLhs, \
          int RhsStorageOrder, bool ConjugateRhs> \
struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \
         LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \
{ \
  enum { \
    IsLower = (Mode&Lower) == Lower, \
    SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
    IsUnitDiag  = (Mode&UnitDiag) ? 1 : 0, \
    IsZeroDiag  = (Mode&ZeroDiag) ? 1 : 0, \
    LowUp = IsLower ? Lower : Upper, \
    conjA = ((RhsStorageOrder==ColMajor) && ConjugateRhs) ? 1 : 0 \
  }; \
\
  static void run( \
    Index _rows, Index _cols, Index _depth, \
    const EIGTYPE* _lhs, Index lhsStride, \
    const EIGTYPE* _rhs, Index rhsStride, \
    EIGTYPE* res,        Index resStride, \
    EIGTYPE alpha, level3_blocking<EIGTYPE,EIGTYPE>& blocking) \
  { \
   Index diagSize  = (std::min)(_cols,_depth); \
   Index rows      = _rows; \
   Index depth     = IsLower ? _depth : diagSize; \
   Index cols      = IsLower ? diagSize : _cols; \
\
   typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \
   typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \
\
/* Non-square case - doesn't fit to BLAS ?TRMM. Fall to default triangular product or call BLAS ?GEMM*/ \
   if (cols != depth) { \
\
     int nthr = 1 /*mkl_domain_get_max_threads(EIGEN_BLAS_DOMAIN_BLAS)*/; \
\
     if ((nthr==1) && (((std::max)(cols,depth)-diagSize)/(double)diagSize < 0.5)) { \
     /* Most likely no benefit to call TRMM or GEMM from BLAS*/ \
       product_triangular_matrix_matrix<EIGTYPE,Index,Mode,false, \
       LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, 1, BuiltIn>::run( \
           _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, 1, resStride, alpha, blocking); \
       /*std::cout << "TRMM_R: A is not square! Go to Eigen TRMM implementation!\n";*/ \
     } else { \
     /* Make sense to call GEMM */ \
       Map<const MatrixRhs, 0, OuterStride<> > rhsMap(_rhs,depth,cols, OuterStride<>(rhsStride)); \
       MatrixRhs aa_tmp=rhsMap.template triangularView<Mode>(); \
       BlasIndex aStride = convert_index<BlasIndex>(aa_tmp.outerStride()); \
       gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> gemm_blocking(_rows,_cols,_depth, 1, true); \
       general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor,1>::run( \
       rows, cols, depth, _lhs, lhsStride, aa_tmp.data(), aStride, res, 1, resStride, alpha, gemm_blocking, 0); \
\
     /*std::cout << "TRMM_R: A is not square! Go to BLAS GEMM implementation! " << nthr<<" \n";*/ \
     } \
     return; \
   } \
   char side = 'R', transa, uplo, diag = 'N'; \
   EIGTYPE *b; \
   const EIGTYPE *a; \
   BlasIndex m, n, lda, ldb; \
\
/* Set m, n */ \
   m = convert_index<BlasIndex>(rows); \
   n = convert_index<BlasIndex>(diagSize); \
\
/* Set trans */ \
   transa = (RhsStorageOrder==RowMajor) ? ((ConjugateRhs) ? 'C' : 'T') : 'N'; \
\
/* Set b, ldb */ \
   Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \
   MatrixX##EIGPREFIX b_tmp; \
\
   if (ConjugateLhs) b_tmp = lhs.conjugate(); else b_tmp = lhs; \
   b = b_tmp.data(); \
   ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \
\
/* Set uplo */ \
   uplo = IsLower ? 'L' : 'U'; \
   if (RhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
/* Set a, lda */ \
   Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols, OuterStride<>(rhsStride)); \
   MatrixRhs a_tmp; \
\
   if ((conjA!=0) || (SetDiag==0)) { \
     if (conjA) a_tmp = rhs.conjugate(); else a_tmp = rhs; \
     if (IsZeroDiag) \
       a_tmp.diagonal().setZero(); \
     else if (IsUnitDiag) \
       a_tmp.diagonal().setOnes();\
     a = a_tmp.data(); \
     lda = convert_index<BlasIndex>(a_tmp.outerStride()); \
   } else { \
     a = _rhs; \
     lda = convert_index<BlasIndex>(rhsStride); \
   } \
   /*std::cout << "TRMM_R: A is square! Go to BLAS TRMM implementation! \n";*/ \
/* call ?trmm*/ \
   BLASFUNC(&side, &uplo, &transa, &diag, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)b, &ldb); \
\
/* Add op(a_triangular)*b into res*/ \
   Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \
   res_tmp=res_tmp+b_tmp; \
  } \
};

#ifdef EIGEN_USE_MKL
EIGEN_BLAS_TRMM_R(double, double, d, dtrmm)
EIGEN_BLAS_TRMM_R(dcomplex, MKL_Complex16, cd, ztrmm)
EIGEN_BLAS_TRMM_R(float, float, f, strmm)
EIGEN_BLAS_TRMM_R(scomplex, MKL_Complex8, cf, ctrmm)
#else
EIGEN_BLAS_TRMM_R(double, double, d, dtrmm_)
EIGEN_BLAS_TRMM_R(dcomplex, double, cd, ztrmm_)
EIGEN_BLAS_TRMM_R(float, float, f, strmm_)
EIGEN_BLAS_TRMM_R(scomplex, float, cf, ctrmm_)
#endif
} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H