lapack/clapack/trtrs.h

//=================================================================================================
/*!
//  \file blaze/math/lapack/clapack/trtrs.h
//  \brief Header file for the CLAPACK trtrs wrapper functions
//
//  Copyright (C) 2012-2020 Klaus Iglberger - All Rights Reserved
//
//  This file is part of the Blaze library. You can redistribute it and/or modify it under
//  the terms of the New (Revised) BSD License. Redistribution and use in source and binary
//  forms, with or without modification, are permitted provided that the following conditions
//  are met:
//
//  1. Redistributions of source code must retain the above copyright notice, this list of
//     conditions and the following disclaimer.
//  2. 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.
//  3. Neither the names of the Blaze development group 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 HOLDER 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.
*/
//=================================================================================================

#ifndef _BLAZE_MATH_LAPACK_CLAPACK_TRTRS_H_
#define _BLAZE_MATH_LAPACK_CLAPACK_TRTRS_H_


//*************************************************************************************************
// Includes
//*************************************************************************************************

#include <blaze/math/blas/Types.h>
#include <blaze/util/Complex.h>
#include <blaze/util/StaticAssert.h>
#include <blaze/util/Types.h>


//=================================================================================================
//
//  LAPACK FORWARD DECLARATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
#if !defined(INTEL_MKL_VERSION)
extern "C" {

void strtrs_( char* uplo, char* trans, char* diag, blaze::blas_int_t* n, blaze::blas_int_t* nrhs,
              float* A, blaze::blas_int_t* lda, float* B, blaze::blas_int_t* ldb,
              blaze::blas_int_t* info, blaze::fortran_charlen_t nuplo,
              blaze::fortran_charlen_t ntrans, blaze::fortran_charlen_t ndiag );
void dtrtrs_( char* uplo, char* trans, char* diag, blaze::blas_int_t* n, blaze::blas_int_t* nrhs,
              double* A, blaze::blas_int_t* lda, double* B, blaze::blas_int_t* ldb,
              blaze::blas_int_t* info, blaze::fortran_charlen_t nuplo,
              blaze::fortran_charlen_t ntrans, blaze::fortran_charlen_t ndiag );
void ctrtrs_( char* uplo, char* trans, char* diag, blaze::blas_int_t* n, blaze::blas_int_t* nrhs,
              float* A, blaze::blas_int_t* lda, float* B, blaze::blas_int_t* ldb,
              blaze::blas_int_t* info, blaze::fortran_charlen_t nuplo,
              blaze::fortran_charlen_t ntrans, blaze::fortran_charlen_t ndiag );
void ztrtrs_( char* uplo, char* trans, char* diag, blaze::blas_int_t* n, blaze::blas_int_t* nrhs,
              double* A, blaze::blas_int_t* lda, double* B, blaze::blas_int_t* ldb,
              blaze::blas_int_t* info, blaze::fortran_charlen_t nuplo,
              blaze::fortran_charlen_t ntrans, blaze::fortran_charlen_t ndiag );

}
#endif
/*! \endcond */
//*************************************************************************************************


namespace blaze {

//=================================================================================================
//
//  LAPACK TRIANGULAR SUBSTITUTION FUNCTIONS (TRTRS)
//
//=================================================================================================

//*************************************************************************************************
/*!\name LAPACK triangular substitution functions (trtrs) */
//@{
void trtrs( char uplo, char trans, char diag, blas_int_t n, blas_int_t nrhs,
            const float* A, blas_int_t lda, float* B, blas_int_t ldb,
            blas_int_t* info );

void trtrs( char uplo, char trans, char diag, blas_int_t n, blas_int_t nrhs,
            const double* A, blas_int_t lda, double* B, blas_int_t ldb,
            blas_int_t* info );

void trtrs( char uplo, char trans, char diag, blas_int_t n, blas_int_t nrhs,
            const complex<float>* A, blas_int_t lda, complex<float>* B,
            blas_int_t ldb, blas_int_t* info );

void trtrs( char uplo, char trans, char diag, blas_int_t n, blas_int_t nrhs,
            const complex<double>* A, blas_int_t lda, complex<double>* B,
            blas_int_t ldb, blas_int_t* info );
//@}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief LAPACK kernel for the substitution step of solving a triangular single precision linear
//        system of equations (\f$ A*X=B \f$).
// \ingroup lapack_substitution
//
// \param uplo \c 'L' in case of a lower matrix, \c 'U' in case of an upper matrix.
// \param trans \c 'N' for \f$ A*X=B \f$, \c 'T' for \f$ A^T*X=B \f$, and \c C for \f$ A^H*X=B \f$.
// \param diag \c 'U' in case of a unitriangular matrix, \c 'N' otherwise.
// \param n The number of rows/columns of the column-major matrix \f$[0..\infty)\f$.
// \param nrhs The number of right-hand side vectors \f$[0..\infty)\f$.
// \param A Pointer to the first element of the single precision column-major square matrix.
// \param lda The total number of elements between two columns of the matrix \f$[0..\infty)\f$.
// \param B Pointer to the first element of the column-major matrix.
// \param ldb The total number of elements between two columns of matrix \a B \f$[0..\infty)\f$.
// \param info Return code of the function call.
// \return void
//
// This function uses the LAPACK strtrs() function to perform the substitution step to compute
// the solution to the general system of linear equations \f$ A*X=B \f$, \f$ A^{T}*X=B \f$, or
// \f$ A^{H}*X=B \f$, where \a A is a \a n-by-\a n matrix and \a X and \a B are column-major
// \a n-by-\a nrhs matrices. The \a trans argument specifies the form of the linear system of
// equations:
//
//   - 'N': \f$ A*X=B \f$ (no transpose)
//   - 'T': \f$ A^{T}*X=B \f$ (transpose)
//   - 'C': \f$ A^{H}*X=B \f$ (conjugate transpose)
//
// The \a info argument provides feedback on the success of the function call:
//
//   - = 0: The function finished successfully.
//   - < 0: If info = -i, the i-th argument had an illegal value.
//
// For more information on the strtrs() function, see the LAPACK online documentation browser:
//
//        http://www.netlib.org/lapack/explore-html/
//
// \note This function can only be used if a fitting LAPACK library, which supports this function,
// is available and linked to the executable. Otherwise a call to this function will result in a
// linker error.
*/
inline void trtrs( char uplo, char trans, char diag, blas_int_t n, blas_int_t nrhs,
                   const float* A, blas_int_t lda, float* B, blas_int_t ldb,
                   blas_int_t* info )
{
#if defined(INTEL_MKL_VERSION)
   BLAZE_STATIC_ASSERT( sizeof( MKL_INT ) == sizeof( blas_int_t ) );
#endif

   strtrs_( &uplo, &trans, &diag, &n, &nrhs, const_cast<float*>( A ), &lda, B, &ldb, info
#if !defined(INTEL_MKL_VERSION)
          , blaze::fortran_charlen_t(1), blaze::fortran_charlen_t(1), blaze::fortran_charlen_t(1)
#endif
          );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief LAPACK kernel for the substitution step of solving a triangular double precision linear
//        system of equations (\f$ A*X=B \f$).
// \ingroup lapack_substitution
//
// \param uplo \c 'L' in case of a lower matrix, \c 'U' in case of an upper matrix.
// \param trans \c 'N' for \f$ A*X=B \f$, \c 'T' for \f$ A^T*X=B \f$, and \c C for \f$ A^H*X=B \f$.
// \param diag \c 'U' in case of a unitriangular matrix, \c 'N' otherwise.
// \param n The number of rows/columns of the column-major matrix \f$[0..\infty)\f$.
// \param nrhs The number of right-hand side vectors \f$[0..\infty)\f$.
// \param A Pointer to the first element of the double precision column-major square matrix.
// \param lda The total number of elements between two columns of the matrix \f$[0..\infty)\f$.
// \param B Pointer to the first element of the column-major matrix.
// \param ldb The total number of elements between two columns of matrix \a B \f$[0..\infty)\f$.
// \param info Return code of the function call.
// \return void
//
// This function uses the LAPACK dtrtrs() function to perform the substitution step to compute
// the solution to the general system of linear equations \f$ A*X=B \f$, \f$ A^{T}*X=B \f$, or
// \f$ A^{H}*X=B \f$, where \a A is a \a n-by-\a n matrix and \a X and \a B are column-major
// \a n-by-\a nrhs matrices. The \a trans argument specifies the form of the linear system of
// equations:
//
//   - 'N': \f$ A*X=B \f$ (no transpose)
//   - 'T': \f$ A^{T}*X=B \f$ (transpose)
//   - 'C': \f$ A^{H}*X=B \f$ (conjugate transpose)
//
// The \a info argument provides feedback on the success of the function call:
//
//   - = 0: The function finished successfully.
//   - < 0: If info = -i, the i-th argument had an illegal value.
//
// For more information on the dtrtrs() function, see the LAPACK online documentation browser:
//
//        http://www.netlib.org/lapack/explore-html/
//
// \note This function can only be used if a fitting LAPACK library, which supports this function,
// is available and linked to the executable. Otherwise a call to this function will result in a
// linker error.
*/
inline void trtrs( char uplo, char trans, char diag, blas_int_t n, blas_int_t nrhs,
                   const double* A, blas_int_t lda, double* B, blas_int_t ldb,
                   blas_int_t* info )
{
#if defined(INTEL_MKL_VERSION)
   BLAZE_STATIC_ASSERT( sizeof( MKL_INT ) == sizeof( blas_int_t ) );
#endif

   dtrtrs_( &uplo, &trans, &diag, &n, &nrhs, const_cast<double*>( A ), &lda, B, &ldb, info
#if !defined(INTEL_MKL_VERSION)
          , blaze::fortran_charlen_t(1), blaze::fortran_charlen_t(1), blaze::fortran_charlen_t(1)
#endif
          );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief LAPACK kernel for the substitution step of solving a triangular single precision complex
//        linear system of equations (\f$ A*X=B \f$).
// \ingroup lapack_substitution
//
// \param uplo \c 'L' in case of a lower matrix, \c 'U' in case of an upper matrix.
// \param trans \c 'N' for \f$ A*X=B \f$, \c 'T' for \f$ A^T*X=B \f$, and \c C for \f$ A^H*X=B \f$.
// \param diag \c 'U' in case of a unitriangular matrix, \c 'N' otherwise.
// \param n The number of rows/columns of the column-major matrix \f$[0..\infty)\f$.
// \param nrhs The number of right-hand side vectors \f$[0..\infty)\f$.
// \param A Pointer to the first element of the single precision complex column-major square matrix.
// \param lda The total number of elements between two columns of the matrix \f$[0..\infty)\f$.
// \param B Pointer to the first element of the column-major matrix.
// \param ldb The total number of elements between two columns of matrix \a B \f$[0..\infty)\f$.
// \param info Return code of the function call.
// \return void
//
// This function uses the LAPACK ctrtrs() function to perform the substitution step to compute
// the solution to the general system of linear equations \f$ A*X=B \f$, \f$ A^{T}*X=B \f$, or
// \f$ A^{H}*X=B \f$, where \a A is a \a n-by-\a n matrix and \a X and \a B are column-major
// \a n-by-\a nrhs matrices. The \a trans argument specifies the form of the linear system of
// equations:
//
//   - 'N': \f$ A*X=B \f$ (no transpose)
//   - 'T': \f$ A^{T}*X=B \f$ (transpose)
//   - 'C': \f$ A^{H}*X=B \f$ (conjugate transpose)
//
// The \a info argument provides feedback on the success of the function call:
//
//   - = 0: The function finished successfully.
//   - < 0: If info = -i, the i-th argument had an illegal value.
//
// For more information on the ctrtrs() function, see the LAPACK online documentation browser:
//
//        http://www.netlib.org/lapack/explore-html/
//
// \note This function can only be used if a fitting LAPACK library, which supports this function,
// is available and linked to the executable. Otherwise a call to this function will result in a
// linker error.
*/
inline void trtrs( char uplo, char trans, char diag, blas_int_t n, blas_int_t nrhs,
                   const complex<float>* A, blas_int_t lda, complex<float>* B,
                   blas_int_t ldb, blas_int_t* info )
{
   BLAZE_STATIC_ASSERT( sizeof( complex<float> ) == 2UL*sizeof( float ) );

#if defined(INTEL_MKL_VERSION)
   BLAZE_STATIC_ASSERT( sizeof( MKL_INT ) == sizeof( blas_int_t ) );
   BLAZE_STATIC_ASSERT( sizeof( MKL_Complex8 ) == sizeof( complex<float> ) );
   using ET = MKL_Complex8;
#else
   using ET = float;
#endif

   ctrtrs_( &uplo, &trans, &diag, &n, &nrhs, const_cast<ET*>( reinterpret_cast<const ET*>( A ) ),
            &lda, reinterpret_cast<ET*>( B ), &ldb, info
#if !defined(INTEL_MKL_VERSION)
          , blaze::fortran_charlen_t(1), blaze::fortran_charlen_t(1), blaze::fortran_charlen_t(1)
#endif
          );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief LAPACK kernel for the substitution step of solving a triangular double precision complex
//        linear system of equations (\f$ A*X=B \f$).
// \ingroup lapack_substitution
//
// \param uplo \c 'L' in case of a lower matrix, \c 'U' in case of an upper matrix.
// \param trans \c 'N' for \f$ A*X=B \f$, \c 'T' for \f$ A^T*X=B \f$, and \c C for \f$ A^H*X=B \f$.
// \param diag \c 'U' in case of a unitriangular matrix, \c 'N' otherwise.
// \param n The number of rows/columns of the column-major matrix \f$[0..\infty)\f$.
// \param nrhs The number of right-hand side vectors \f$[0..\infty)\f$.
// \param A Pointer to the first element of the double precision complex column-major square matrix.
// \param lda The total number of elements between two columns of the matrix \f$[0..\infty)\f$.
// \param B Pointer to the first element of the column-major matrix.
// \param ldb The total number of elements between two columns of matrix \a B \f$[0..\infty)\f$.
// \param info Return code of the function call.
// \return void
//
// This function uses the LAPACK ztrtrs() function to perform the substitution step to compute
// the solution to the general system of linear equations \f$ A*X=B \f$, \f$ A^{T}*X=B \f$, or
// \f$ A^{H}*X=B \f$, where \a A is a \a n-by-\a n matrix and \a X and \a B are column-major
// \a n-by-\a nrhs matrices. The \a trans argument specifies the form of the linear system of
// equations:
//
//   - 'N': \f$ A*X=B \f$ (no transpose)
//   - 'T': \f$ A^{T}*X=B \f$ (transpose)
//   - 'C': \f$ A^{H}*X=B \f$ (conjugate transpose)
//
// The \a info argument provides feedback on the success of the function call:
//
//   - = 0: The function finished successfully.
//   - < 0: If info = -i, the i-th argument had an illegal value.
//
// For more information on the ztrtrs() function, see the LAPACK online documentation browser:
//
//        http://www.netlib.org/lapack/explore-html/
//
// \note This function can only be used if a fitting LAPACK library, which supports this function,
// is available and linked to the executable. Otherwise a call to this function will result in a
// linker error.
*/
inline void trtrs( char uplo, char trans, char diag, blas_int_t n, blas_int_t nrhs,
                   const complex<double>* A, blas_int_t lda, complex<double>* B,
                   blas_int_t ldb, blas_int_t* info )
{
   BLAZE_STATIC_ASSERT( sizeof( complex<double> ) == 2UL*sizeof( double ) );

#if defined(INTEL_MKL_VERSION)
   BLAZE_STATIC_ASSERT( sizeof( MKL_INT ) == sizeof( blas_int_t ) );
   BLAZE_STATIC_ASSERT( sizeof( MKL_Complex16 ) == sizeof( complex<double> ) );
   using ET = MKL_Complex16;
#else
   using ET = double;
#endif

   ztrtrs_( &uplo, &trans, &diag, &n, &nrhs, const_cast<ET*>( reinterpret_cast<const ET*>( A ) ),
            &lda, reinterpret_cast<ET*>( B ), &ldb, info
#if !defined(INTEL_MKL_VERSION)
          , blaze::fortran_charlen_t(1), blaze::fortran_charlen_t(1), blaze::fortran_charlen_t(1)
#endif
          );
}
//*************************************************************************************************

} // namespace blaze

#endif