text: /*
   Copyright (c) 2011, Intel Corporation. All rights reserved.
  
   Redistribution and use in source and binary forms, with or without modification,
   are permitted provided that the following conditions are met:
  
   * Redistributions of source code must retain the above copyright notice, this
     list of conditions and the following disclaimer.
   * Redistributions in binary form must reproduce the above copyright notice,
     this list of conditions and the following disclaimer in the documentation
     and/or other materials provided with the distribution.
   * Neither the name of Intel Corporation nor the names of its contributors may
     be used to endorse or promote products derived from this software without
     specific prior written permission.
  
   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
   ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
   WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
   DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
   ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
   (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
   LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
   ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
   (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  
   ********************************************************************************
   *   Content : Eigen bindings to Intel(R) MKL
   *   Triangular matrix-vector product functionality based on ?TRMV.
   ********************************************************************************
  */
  
  #ifndef EIGEN_TRIANGULAR_MATRIX_VECTOR_MKL_H
  #define EIGEN_TRIANGULAR_MATRIX_VECTOR_MKL_H
  
  namespace Eigen { 
  
  namespace internal {
  
  /**********************************************************************
  * This file implements triangular matrix-vector multiplication using BLAS
  **********************************************************************/
  
  // trmv/hemv specialization
  
  template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int StorageOrder>
  struct triangular_matrix_vector_product_trmv :
    triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,StorageOrder,BuiltIn> {};
  
  #define EIGEN_MKL_TRMV_SPECIALIZE(Scalar) \
  template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
  struct triangular_matrix_vector_product<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,ColMajor,Specialized> { \
   static EIGEN_DONT_INLINE void run(Index _rows, Index _cols, const Scalar* _lhs, Index lhsStride, \
                                       const Scalar* _rhs, Index rhsIncr, Scalar* _res, Index resIncr, Scalar alpha) { \
        triangular_matrix_vector_product_trmv<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,ColMajor>::run( \
          _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \
    } \
  }; \
  template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
  struct triangular_matrix_vector_product<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,RowMajor,Specialized> { \
   static EIGEN_DONT_INLINE void run(Index _rows, Index _cols, const Scalar* _lhs, Index lhsStride, \
                                       const Scalar* _rhs, Index rhsIncr, Scalar* _res, Index resIncr, Scalar alpha) { \
        triangular_matrix_vector_product_trmv<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,RowMajor>::run( \
          _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \
    } \
  };
  
  EIGEN_MKL_TRMV_SPECIALIZE(double)
  EIGEN_MKL_TRMV_SPECIALIZE(float)
  EIGEN_MKL_TRMV_SPECIALIZE(dcomplex)
  EIGEN_MKL_TRMV_SPECIALIZE(scomplex)
  
  // implements col-major: res += alpha * op(triangular) * vector
  #define EIGEN_MKL_TRMV_CM(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
  template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
  struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,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 \
    }; \
   static EIGEN_DONT_INLINE void run(Index _rows, Index _cols, const EIGTYPE* _lhs, Index lhsStride, \
                               const EIGTYPE* _rhs, Index rhsIncr, EIGTYPE* _res, Index resIncr, EIGTYPE alpha, level3_blocking<EIGTYPE,EIGTYPE>& blocking) \
   { \
     if (ConjLhs || IsZeroDiag) { \
       triangular_matrix_vector_product<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,ColMajor,BuiltIn>::run( \
         _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha, blocking); \
       return; \
     }\
     Index size = (std::min)(_rows,_cols); \
     Index rows = IsLower ? _rows : size; \
     Index cols = IsLower ? size : _cols; \
  \
     typedef VectorX##EIGPREFIX VectorRhs; \
     EIGTYPE *x, *y;\
  \
  /* Set x*/ \
     Map<const VectorRhs, 0, InnerStride<> > rhs(_rhs,cols,InnerStride<>(rhsIncr)); \
     VectorRhs x_tmp; \
     if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
     x = x_tmp.data(); \
  \
  /* Square part handling */\
  \
     char trans, uplo, diag; \
     MKL_INT m, n, lda, incx, incy; \
     EIGTYPE const *a; \
     MKLTYPE alpha_, beta_; \
     assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
     assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(beta_, EIGTYPE(1)); \
  \
  /* Set m, n */ \
     n = (MKL_INT)size; \
     lda = lhsStride; \
     incx = 1; \
     incy = resIncr; \
  \
  /* Set uplo, trans and diag*/ \
     trans = 'N'; \
     uplo = IsLower ? 'L' : 'U'; \
     diag = IsUnitDiag ? 'U' : 'N'; \
  \
  /* call ?TRMV*/ \
     MKLPREFIX##trmv(&uplo, &trans, &diag, &n, (const MKLTYPE*)_lhs, &lda, (MKLTYPE*)x, &incx); \
  \
  /* Add op(a_tr)rhs into res*/ \
     MKLPREFIX##axpy(&n, &alpha_,(const MKLTYPE*)x, &incx, (MKLTYPE*)_res, &incy); \
  /* Non-square case - doesn't fit to MKL ?TRMV. Fall to default triangular product*/ \
     if (size<(std::max)(rows,cols)) { \
       typedef Matrix<EIGTYPE, Dynamic, Dynamic> MatrixLhs; \
       if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
       x = x_tmp.data(); \
       if (size<rows) { \
         y = _res + size*resIncr; \
         a = _lhs + size; \
         m = rows-size; \
         n = size; \
       } \
       else { \
         x += size; \
         y = _res; \
         a = _lhs + size*lda; \
         m = size; \
         n = cols-size; \
       } \
       MKLPREFIX##gemv(&trans, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)x, &incx, &beta_, (MKLTYPE*)y, &incy); \
     } \
    } \
  };
  
  EIGEN_MKL_TRMV_CM(double, double, d, d)
  EIGEN_MKL_TRMV_CM(dcomplex, MKL_Complex16, cd, z)
  EIGEN_MKL_TRMV_CM(float, float, f, s)
  EIGEN_MKL_TRMV_CM(scomplex, MKL_Complex8, cf, c)
  
  // implements row-major: res += alpha * op(triangular) * vector
  #define EIGEN_MKL_TRMV_RM(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
  template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \
  struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,RowMajor> { \
    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 \
    }; \
   static EIGEN_DONT_INLINE void run(Index _rows, Index _cols, const EIGTYPE* _lhs, Index lhsStride, \
                               const EIGTYPE* _rhs, Index rhsIncr, EIGTYPE* _res, Index resIncr, EIGTYPE alpha, level3_blocking<EIGTYPE,EIGTYPE>& blocking) \
   { \
     if (IsZeroDiag) { \
       triangular_matrix_vector_product<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,RowMajor,BuiltIn>::run( \
         _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha, blocking); \
       return; \
     }\
     Index size = (std::min)(_rows,_cols); \
     Index rows = IsLower ? _rows : size; \
     Index cols = IsLower ? size : _cols; \
  \
     typedef VectorX##EIGPREFIX VectorRhs; \
     EIGTYPE *x, *y;\
  \
  /* Set x*/ \
     Map<const VectorRhs, 0, InnerStride<> > rhs(_rhs,cols,InnerStride<>(rhsIncr)); \
     VectorRhs x_tmp; \
     if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
     x = x_tmp.data(); \
  \
  /* Square part handling */\
  \
     char trans, uplo, diag; \
     MKL_INT m, n, lda, incx, incy; \
     EIGTYPE const *a; \
     MKLTYPE alpha_, beta_; \
     assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
     assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(beta_, EIGTYPE(1)); \
  \
  /* Set m, n */ \
     n = (MKL_INT)size; \
     lda = lhsStride; \
     incx = 1; \
     incy = resIncr; \
  \
  /* Set uplo, trans and diag*/ \
     trans = ConjLhs ? 'C' : 'T'; \
     uplo = IsLower ? 'U' : 'L'; \
     diag = IsUnitDiag ? 'U' : 'N'; \
  \
  /* call ?TRMV*/ \
     MKLPREFIX##trmv(&uplo, &trans, &diag, &n, (const MKLTYPE*)_lhs, &lda, (MKLTYPE*)x, &incx); \
  \
  /* Add op(a_tr)rhs into res*/ \
     MKLPREFIX##axpy(&n, &alpha_,(const MKLTYPE*)x, &incx, (MKLTYPE*)_res, &incy); \
  /* Non-square case - doesn't fit to MKL ?TRMV. Fall to default triangular product*/ \
     if (size<(std::max)(rows,cols)) { \
       typedef Matrix<EIGTYPE, Dynamic, Dynamic> MatrixLhs; \
       if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \
       x = x_tmp.data(); \
       if (size<rows) { \
         y = _res + size*resIncr; \
         a = _lhs + size*lda; \
         m = rows-size; \
         n = size; \
       } \
       else { \
         x += size; \
         y = _res; \
         a = _lhs + size; \
         m = size; \
         n = cols-size; \
       } \
       MKLPREFIX##gemv(&trans, &n, &m, &alpha_, (const MKLTYPE*)a, &lda, (const MKLTYPE*)x, &incx, &beta_, (MKLTYPE*)y, &incy); \
     } \
    } \
  };
  
  EIGEN_MKL_TRMV_RM(double, double, d, d)
  EIGEN_MKL_TRMV_RM(dcomplex, MKL_Complex16, cd, z)
  EIGEN_MKL_TRMV_RM(float, float, f, s)
  EIGEN_MKL_TRMV_RM(scomplex, MKL_Complex8, cf, c)
  
  } // end namespase internal
  
  } // end namespace Eigen
  
  #endif // EIGEN_TRIANGULAR_MATRIX_VECTOR_MKL_H
  