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// @HEADER
// ***********************************************************************
//
// Teuchos: Common Tools Package
// Copyright (2004) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
//
// This library is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 2.1 of the
// License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
// USA
// Questions? Contact Michael A. Heroux (maherou@sandia.gov)
//
// ***********************************************************************
// @HEADER
// Kris
// 06.16.03 -- Start over from scratch
// 06.16.03 -- Initial templatization (Tpetra_BLAS.cpp is no longer needed)
// 06.18.03 -- Changed xxxxx_() function calls to XXXXX_F77()
// -- Added warning messages for generic calls
// 07.08.03 -- Move into Teuchos package/namespace
// 07.24.03 -- The first iteration of BLAS generics is nearing completion. Caveats:
// * TRSM isn't finished yet; it works for one case at the moment (left side, upper tri., no transpose, no unit diag.)
// * Many of the generic implementations are quite inefficient, ugly, or both. I wrote these to be easy to debug, not for efficiency or legibility. The next iteration will improve both of these aspects as much as possible.
// * Very little verification of input parameters is done, save for the character-type arguments (TRANS, etc.) which is quite robust.
// * All of the routines that make use of both an incx and incy parameter (which includes much of the L1 BLAS) are set up to work iff incx == incy && incx > 0. Allowing for differing/negative values of incx/incy should be relatively trivial.
// * All of the L2/L3 routines assume that the entire matrix is being used (that is, if A is mxn, lda = m); they don't work on submatrices yet. This *should* be a reasonably trivial thing to fix, as well.
// -- Removed warning messages for generic calls
// 08.08.03 -- TRSM now works for all cases where SIDE == L and DIAG == N. DIAG == U is implemented but does not work correctly; SIDE == R is not yet implemented.
// 08.14.03 -- TRSM now works for all cases and accepts (and uses) leading-dimension information.
// 09.26.03 -- character input replaced with enumerated input to cause compiling errors and not run-time errors ( suggested by RAB ).
#ifndef _TEUCHOS_BLAS_HPP_
#define _TEUCHOS_BLAS_HPP_
/*! \file Teuchos_BLAS.hpp
\brief Templated interface class to BLAS routines.
*/
/** \example BLAS/cxx_main.cpp
This is an example of how to use the Teuchos::BLAS class.
*/
/* for INTEL_CXML, the second arg may need to be changed to 'one'. If so
the appropriate declaration of one will need to be added back into
functions that include the macro:
*/
#if defined (INTEL_CXML)
unsigned int one=1;
#endif
#ifdef CHAR_MACRO
#undef CHAR_MACRO
#endif
#if defined (INTEL_CXML)
#define CHAR_MACRO(char_var) &char_var, one
#else
#define CHAR_MACRO(char_var) &char_var
#endif
#include "Teuchos_ConfigDefs.hpp"
#include "Teuchos_BLAS_wrappers.hpp"
#include "Teuchos_BLAS_types.hpp"
#include "Teuchos_ScalarTraits.hpp"
#include "Teuchos_OrdinalTraits.hpp"
/*! \class Teuchos::BLAS
\brief The Templated BLAS Wrapper Class.
The Teuchos::BLAS class provides functionality similar to the BLAS
(Basic Linear Algebra Subprograms). The BLAS provide portable, high-
performance implementations of kernels such as dense std::vector multiplication,
dot products, dense matrix-std::vector multiplication and dense matrix-matrix
multiplication.
The standard BLAS interface is Fortran-specific. Unfortunately, the
interface between C++ and Fortran is not standard across all computer
platforms. The Teuchos_BLAS class provides C++ bindings for the BLAS
kernels in order to insulate the rest of Petra from the details of
C++ to Fortran translation.
In addition to giving access the standard BLAS functionality.
Teuchos::BLAS also provide functionality for any <ScalarType> class that
defines the +, - * and / operators.
Teuchos::BLAS is a single memory image interface only. This is appropriate
since the standard BLAS are only specified for serial execution
(or shared memory parallel).
\note
<ol>
<li>These templates are specialized to use the Fortran BLAS routines for
scalar types \c float and \c double.
<li>If Teuchos is configured with \c --enable-teuchos-std::complex then these templates
are specialized for scalar types \c std::complex<float> and \c std::complex<double> also.
</ol>
*/
namespace Teuchos
{
extern const char ESideChar[];
extern const char ETranspChar[];
extern const char EUploChar[];
extern const char EDiagChar[];
template<typename OrdinalType, typename ScalarType>
class BLAS
{
typedef typename Teuchos::ScalarTraits<ScalarType>::magnitudeType MagnitudeType;
public:
//! @name Constructor/Destructor.
//@{
//! Default constructor.
inline BLAS(void) {}
//! Copy constructor.
inline BLAS(const BLAS<OrdinalType, ScalarType>& BLAS_source) {}
//! Destructor.
inline virtual ~BLAS(void) {}
//@}
//! @name Level 1 BLAS Routines.
//@{
//! Computes a Givens plane rotation.
void ROTG(ScalarType* da, ScalarType* db, MagnitudeType* c, ScalarType* s) const;
//! Applies a Givens plane rotation.
void ROT(const OrdinalType n, ScalarType* dx, const OrdinalType incx, ScalarType* dy, const OrdinalType incy, MagnitudeType* c, ScalarType* s) const;
//! Scale the std::vector \c x by the constant \c alpha.
void SCAL(const OrdinalType n, const ScalarType alpha, ScalarType* x, const OrdinalType incx) const;
//! Copy the std::vector \c x to the std::vector \c y.
void COPY(const OrdinalType n, const ScalarType* x, const OrdinalType incx, ScalarType* y, const OrdinalType incy) const;
//! Perform the operation: \c y \c <- \c y+alpha*x.
void AXPY(const OrdinalType n, const ScalarType alpha, const ScalarType* x, const OrdinalType incx, ScalarType* y, const OrdinalType incy) const;
//! Sum the absolute values of the entries of \c x.
typename ScalarTraits<ScalarType>::magnitudeType ASUM(const OrdinalType n, const ScalarType* x, const OrdinalType incx) const;
//! Form the dot product of the vectors \c x and \c y.
ScalarType DOT(const OrdinalType n, const ScalarType* x, const OrdinalType incx, const ScalarType* y, const OrdinalType incy) const;
//! Compute the 2-norm of the std::vector \c x.
typename ScalarTraits<ScalarType>::magnitudeType NRM2(const OrdinalType n, const ScalarType* x, const OrdinalType incx) const;
//! Return the index of the element of \c x with the maximum magnitude.
OrdinalType IAMAX(const OrdinalType n, const ScalarType* x, const OrdinalType incx) const;
//@}
//! @name Level 2 BLAS Routines.
//@{
//! Performs the matrix-std::vector operation: \c y \c <- \c alpha*A*x+beta*y or \c y \c <- \c alpha*A'*x+beta*y where \c A is a general \c m by \c n matrix.
void GEMV(ETransp trans, const OrdinalType m, const OrdinalType n, const ScalarType alpha, const ScalarType* A,
const OrdinalType lda, const ScalarType* x, const OrdinalType incx, const ScalarType beta, ScalarType* y, const OrdinalType incy) const;
//! Performs the matrix-std::vector operation: \c x \c <- \c A*x or \c x \c <- \c A'*x where \c A is a unit/non-unit \c n by \c n upper/lower triangular matrix.
void TRMV(EUplo uplo, ETransp trans, EDiag diag, const OrdinalType n, const ScalarType* A,
const OrdinalType lda, ScalarType* x, const OrdinalType incx) const;
//! Performs the rank 1 operation: \c A \c <- \c alpha*x*y'+A.
void GER(const OrdinalType m, const OrdinalType n, const ScalarType alpha, const ScalarType* x, const OrdinalType incx,
const ScalarType* y, const OrdinalType incy, ScalarType* A, const OrdinalType lda) const;
//@}
//! @name Level 3 BLAS Routines.
//@{
//! Performs the matrix-matrix operation: \c C \c <- \c alpha*op(A)*op(B)+beta*C where \c op(A) is either \c A or \c A', \c op(B) is either \c B or \c B', and C is an \c m by \c k matrix.
void GEMM(ETransp transa, ETransp transb, const OrdinalType m, const OrdinalType n, const OrdinalType k, const ScalarType alpha, const ScalarType* A, const OrdinalType lda, const ScalarType* B, const OrdinalType ldb, const ScalarType beta, ScalarType* C, const OrdinalType ldc) const;
//! Performs the matrix-matrix operation: \c C \c <- \c alpha*A*B+beta*C or \c C \c <- \c alpha*B*A+beta*C where \c A is an \c m by \c m or \c n by \c n symmetric matrix and \c B is a general matrix.
void SYMM(ESide side, EUplo uplo, const OrdinalType m, const OrdinalType n, const ScalarType alpha, const ScalarType* A, const OrdinalType lda, const ScalarType* B, const OrdinalType ldb, const ScalarType beta, ScalarType* C, const OrdinalType ldc) const;
//! Performs the matrix-matrix operation: \c C \c <- \c alpha*op(A)*B+beta*C or \c C \c <- \c alpha*B*op(A)+beta*C where \c op(A) is an unit/non-unit, upper/lower triangular matrix and \c B is a general matrix.
void TRMM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n,
const ScalarType alpha, const ScalarType* A, const OrdinalType lda, ScalarType* B, const OrdinalType ldb) const;
//! Solves the matrix equations: \c op(A)*X=alpha*B or \c X*op(A)=alpha*B where \c X and \c B are \c m by \c n matrices, \c A is a unit/non-unit, upper/lower triangular matrix and \c op(A) is \c A or \c A'. The matrix \c X is overwritten on \c B.
void TRSM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n,
const ScalarType alpha, const ScalarType* A, const OrdinalType lda, ScalarType* B, const OrdinalType ldb) const;
//@}
};
//------------------------------------------------------------------------------------------
// LEVEL 1 BLAS ROUTINES
//------------------------------------------------------------------------------------------
template<typename OrdinalType, typename ScalarType>
void BLAS<OrdinalType, ScalarType>::ROTG(ScalarType* da, ScalarType* db, MagnitudeType* c, ScalarType* s) const
{
ScalarType roe, scale, r;
ScalarType zero = ScalarTraits<ScalarType>::zero();
ScalarType one = ScalarTraits<ScalarType>::one();
if ( ScalarTraits<ScalarType>::magnitude( *da ) > ScalarTraits<ScalarType>::magnitude( *db ) ) { roe = *da; }
scale = ScalarTraits<ScalarType>::magnitude( *da ) + ScalarTraits<ScalarType>::magnitude( *db );
if ( scale == zero ) // There is nothing to do.
{
*c = one;
*s = zero;
*da = zero; *db = zero;
} else { // Compute the Givens rotation.
r = scale*ScalarTraits<ScalarType>::squareroot( ( *da/scale)*(*da/scale) + (*db/scale)*(*db/scale) );
if ( roe < zero ) { r *= -one; }
*c = *da / r;
*s = *db / r;
*db = ScalarTraits<ScalarType>::one();
if( ScalarTraits<ScalarType>::magnitude( *da ) > ScalarTraits<ScalarType>::magnitude( *db ) ){ *db = *s; }
if( ScalarTraits<ScalarType>::magnitude( *db ) >= ScalarTraits<ScalarType>::magnitude( *da ) &&
*c != ScalarTraits<ScalarType>::zero() ) { *db = one / *c; }
*da = r;
}
} /* end ROTG */
template<typename OrdinalType, typename ScalarType>
void BLAS<OrdinalType,ScalarType>::ROT(const OrdinalType n, ScalarType* dx, const OrdinalType incx, ScalarType* dy, const OrdinalType incy, MagnitudeType* c, ScalarType* s) const
{
// ToDo: Implement this.
}
template<typename OrdinalType, typename ScalarType>
void BLAS<OrdinalType, ScalarType>::SCAL(const OrdinalType n, const ScalarType alpha, ScalarType* x, const OrdinalType incx) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
OrdinalType i, ix = izero;
if ( n > izero ) {
// Set the initial index (ix).
if (incx < izero) { ix = (-n+ione)*incx; }
// Scale the std::vector.
for(i = izero; i < n; i++)
{
x[ix] *= alpha;
ix += incx;
}
}
} /* end SCAL */
template<typename OrdinalType, typename ScalarType>
void BLAS<OrdinalType, ScalarType>::COPY(const OrdinalType n, const ScalarType* x, const OrdinalType incx, ScalarType* y, const OrdinalType incy) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
OrdinalType i, ix = izero, iy = izero;
if ( n > izero ) {
// Set the initial indices (ix, iy).
if (incx < izero) { ix = (-n+ione)*incx; }
if (incy < izero) { iy = (-n+ione)*incy; }
for(i = izero; i < n; i++)
{
y[iy] = x[ix];
ix += incx;
iy += incy;
}
}
} /* end COPY */
template<typename OrdinalType, typename ScalarType>
void BLAS<OrdinalType, ScalarType>::AXPY(const OrdinalType n, const ScalarType alpha, const ScalarType* x, const OrdinalType incx, ScalarType* y, const OrdinalType incy) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
OrdinalType i, ix = izero, iy = izero;
if( n > izero && alpha != ScalarTraits<ScalarType>::zero())
{
// Set the initial indices (ix, iy).
if (incx < izero) { ix = (-n+ione)*incx; }
if (incy < izero) { iy = (-n+ione)*incy; }
for(i = izero; i < n; i++)
{
y[iy] += alpha * x[ix];
ix += incx;
iy += incy;
}
}
} /* end AXPY */
template<typename OrdinalType, typename ScalarType>
typename ScalarTraits<ScalarType>::magnitudeType BLAS<OrdinalType, ScalarType>::ASUM(const OrdinalType n, const ScalarType* x, const OrdinalType incx) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
typename ScalarTraits<ScalarType>::magnitudeType result =
ScalarTraits<typename ScalarTraits<ScalarType>::magnitudeType>::zero();
OrdinalType i, ix = izero;
if( n > izero ) {
// Set the initial indices
if (incx < izero) { ix = (-n+ione)*incx; }
for(i = izero; i < n; i++)
{
result += ScalarTraits<ScalarType>::magnitude(x[ix]);
ix += incx;
}
}
return result;
} /* end ASUM */
template<typename OrdinalType, typename ScalarType>
ScalarType BLAS<OrdinalType, ScalarType>::DOT(const OrdinalType n, const ScalarType* x, const OrdinalType incx, const ScalarType* y, const OrdinalType incy) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
ScalarType result = ScalarTraits<ScalarType>::zero();
OrdinalType i, ix = izero, iy = izero;
if( n > izero )
{
// Set the initial indices (ix,iy).
if (incx < izero) { ix = (-n+ione)*incx; }
if (incy < izero) { iy = (-n+ione)*incy; }
for(i = izero; i < n; i++)
{
result += ScalarTraits<ScalarType>::conjugate(x[ix]) * y[iy];
ix += incx;
iy += incy;
}
}
return result;
} /* end DOT */
template<typename OrdinalType, typename ScalarType>
typename ScalarTraits<ScalarType>::magnitudeType BLAS<OrdinalType, ScalarType>::NRM2(const OrdinalType n, const ScalarType* x, const OrdinalType incx) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
typename ScalarTraits<ScalarType>::magnitudeType result =
ScalarTraits<typename ScalarTraits<ScalarType>::magnitudeType>::zero();
OrdinalType i, ix = izero;
if ( n > izero )
{
// Set the initial index.
if (incx < izero) { ix = (-n+ione)*incx; }
for(i = izero; i < n; i++)
{
result += ScalarTraits<ScalarType>::conjugate(x[ix]) * x[ix];
ix += incx;
}
result = ScalarTraits<ScalarType>::squareroot(result);
}
return result;
} /* end NRM2 */
template<typename OrdinalType, typename ScalarType>
OrdinalType BLAS<OrdinalType, ScalarType>::IAMAX(const OrdinalType n, const ScalarType* x, const OrdinalType incx) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
OrdinalType result = izero, ix = izero, i;
ScalarType maxval;
if ( n > izero )
{
if (incx < izero) { ix = (-n+ione)*incx; }
maxval = ScalarTraits<ScalarType>::magnitude(x[ix]);
ix += incx;
for(i = ione; i < n; i++)
{
if(ScalarTraits<ScalarType>::magnitude(x[ix]) > maxval)
{
result = i;
maxval = ScalarTraits<ScalarType>::magnitude(x[ix]);
}
ix += incx;
}
}
return result + 1; // the BLAS I?AMAX functions return 1-indexed (Fortran-style) values
} /* end IAMAX */
//------------------------------------------------------------------------------------------
// LEVEL 2 BLAS ROUTINES
//------------------------------------------------------------------------------------------
template<typename OrdinalType, typename ScalarType>
void BLAS<OrdinalType, ScalarType>::GEMV(ETransp trans, const OrdinalType m, const OrdinalType n, const ScalarType alpha, const ScalarType* A, const OrdinalType lda, const ScalarType* x, const OrdinalType incx, const ScalarType beta, ScalarType* y, const OrdinalType incy) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
ScalarType zero = ScalarTraits<ScalarType>::zero();
ScalarType one = ScalarTraits<ScalarType>::one();
bool BadArgument = false;
// Quick return if there is nothing to do!
if( m == izero || n == izero || ( alpha == zero && beta == one ) ){ return; }
// Otherwise, we need to check the argument list.
if( m < izero ) {
std::cout << "BLAS::GEMV Error: M == " << m << std::endl;
BadArgument = true;
}
if( n < izero ) {
std::cout << "BLAS::GEMV Error: N == " << n << std::endl;
BadArgument = true;
}
if( lda < m ) {
std::cout << "BLAS::GEMV Error: LDA < MAX(1,M)"<< std::endl;
BadArgument = true;
}
if( incx == izero ) {
std::cout << "BLAS::GEMV Error: INCX == 0"<< std::endl;
BadArgument = true;
}
if( incy == izero ) {
std::cout << "BLAS::GEMV Error: INCY == 0"<< std::endl;
BadArgument = true;
}
if(!BadArgument) {
OrdinalType i, j, lenx, leny, ix, iy, jx, jy;
OrdinalType kx = izero, ky = izero;
ScalarType temp;
// Determine the lengths of the vectors x and y.
if(ETranspChar[trans] == 'N') {
lenx = n;
leny = m;
} else {
lenx = m;
leny = n;
}
// Set the starting pointers for the vectors x and y if incx/y < 0.
if (incx < izero ) { kx = (ione - lenx)*incx; }
if (incy < izero ) { ky = (ione - leny)*incy; }
// Form y = beta*y
ix = kx; iy = ky;
if(beta != one) {
if (incy == ione) {
if (beta == zero) {
for(i = izero; i < leny; i++) { y[i] = zero; }
} else {
for(i = izero; i < leny; i++) { y[i] *= beta; }
}
} else {
if (beta == zero) {
for(i = izero; i < leny; i++) {
y[iy] = zero;
iy += incy;
}
} else {
for(i = izero; i < leny; i++) {
y[iy] *= beta;
iy += incy;
}
}
}
}
// Return if we don't have to do anything more.
if(alpha == zero) { return; }
if( ETranspChar[trans] == 'N' ) {
// Form y = alpha*A*y
jx = kx;
if (incy == ione) {
for(j = izero; j < n; j++) {
if (x[jx] != zero) {
temp = alpha*x[jx];
for(i = izero; i < m; i++) {
y[i] += temp*A[j*lda + i];
}
}
jx += incx;
}
} else {
for(j = izero; j < n; j++) {
if (x[jx] != zero) {
temp = alpha*x[jx];
iy = ky;
for(i = izero; i < m; i++) {
y[iy] += temp*A[j*lda + i];
iy += incy;
}
}
jx += incx;
}
}
} else {
jy = ky;
if (incx == ione) {
for(j = izero; j < n; j++) {
temp = zero;
for(i = izero; i < m; i++) {
temp += A[j*lda + i]*x[i];
}
y[jy] += alpha*temp;
jy += incy;
}
} else {
for(j = izero; j < n; j++) {
temp = zero;
ix = kx;
for (i = izero; i < m; i++) {
temp += A[j*lda + i]*x[ix];
ix += incx;
}
y[jy] += alpha*temp;
jy += incy;
}
}
}
} /* if (!BadArgument) */
} /* end GEMV */
template<typename OrdinalType, typename ScalarType>
void BLAS<OrdinalType, ScalarType>::TRMV(EUplo uplo, ETransp trans, EDiag diag, const OrdinalType n, const ScalarType* A, const OrdinalType lda, ScalarType* x, const OrdinalType incx) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
ScalarType zero = ScalarTraits<ScalarType>::zero();
ScalarType one = ScalarTraits<ScalarType>::one();
bool BadArgument = false;
// Quick return if there is nothing to do!
if( n == izero ){ return; }
// Otherwise, we need to check the argument list.
if( n < izero ) {
std::cout << "BLAS::TRMV Error: N == " << n << std::endl;
BadArgument = true;
}
if( lda < n ) {
std::cout << "BLAS::TRMV Error: LDA < MAX(1,N)"<< std::endl;
BadArgument = true;
}
if( incx == izero ) {
std::cout << "BLAS::TRMV Error: INCX == 0"<< std::endl;
BadArgument = true;
}
if(!BadArgument) {
OrdinalType i, j, ix, jx, kx = izero;
ScalarType temp;
bool NoUnit = (EDiagChar[diag] == 'N');
// Set the starting pointer for the std::vector x if incx < 0.
if (incx < izero) { kx = (-n+ione)*incx; }
// Start the operations for a nontransposed triangular matrix
if (ETranspChar[trans] == 'N') {
/* Compute x = A*x */
if (EUploChar[uplo] == 'U') {
/* A is an upper triangular matrix */
if (incx == ione) {
for (j=izero; j<n; j++) {
if (x[j] != zero) {
temp = x[j];
for (i=izero; i<j; i++) {
x[i] += temp*A[j*lda + i];
}
if (NoUnit)
x[j] *= A[j*lda + j];
}
}
} else {
jx = kx;
for (j=izero; j<n; j++) {
if (x[jx] != zero) {
temp = x[jx];
ix = kx;
for (i=izero; i<j; i++) {
x[ix] += temp*A[j*lda + i];
ix += incx;
}
if (NoUnit)
x[jx] *= A[j*lda + j];
}
jx += incx;
}
} /* if (incx == ione) */
} else { /* A is a lower triangular matrix */
if (incx == ione) {
for (j=n-ione; j>-ione; j--) {
if (x[j] != zero) {
temp = x[j];
for (i=n-ione; i>j; i--) {
x[i] += temp*A[j*lda + i];
}
if (NoUnit)
x[j] *= A[j*lda + j];
}
}
} else {
kx += (n-ione)*incx;
jx = kx;
for (j=n-ione; j>-ione; j--) {
if (x[jx] != zero) {
temp = x[jx];
ix = kx;
for (i=n-ione; i>j; i--) {
x[ix] += temp*A[j*lda + i];
ix -= incx;
}
if (NoUnit)
x[jx] *= A[j*lda + j];
}
jx -= incx;
}
}
} /* if (EUploChar[uplo]=='U') */
} else { /* A is transposed/conjugated */
/* Compute x = A'*x */
if (EUploChar[uplo]=='U') {
/* A is an upper triangular matrix */
if (incx == ione) {
for (j=n-ione; j>-ione; j--) {
temp = x[j];
if (NoUnit)
temp *= A[j*lda + j];
for (i=j-ione; i>-ione; i--) {
temp += A[j*lda + i]*x[i];
}
x[j] = temp;
}
} else {
jx = kx + (n-ione)*incx;
for (j=n-ione; j>-ione; j--) {
temp = x[jx];
ix = jx;
if (NoUnit)
temp *= A[j*lda + j];
for (i=j-ione; i>-ione; i--) {
ix -= incx;
temp += A[j*lda + i]*x[ix];
}
x[jx] = temp;
jx -= incx;
}
}
} else {
/* A is a lower triangular matrix */
if (incx == ione) {
for (j=izero; j<n; j++) {
temp = x[j];
if (NoUnit)
temp *= A[j*lda + j];
for (i=j+ione; i<n; i++) {
temp += A[j*lda + i]*x[i];
}
x[j] = temp;
}
} else {
jx = kx;
for (j=izero; j<n; j++) {
temp = x[jx];
ix = jx;
if (NoUnit)
temp *= A[j*lda + j];
for (i=j+ione; i<n; i++) {
ix += incx;
temp += A[j*lda + i]*x[ix];
}
x[jx] = temp;
jx += incx;
}
}
} /* if (EUploChar[uplo]=='U') */
} /* if (ETranspChar[trans]=='N') */
} /* if (!BadArgument) */
} /* end TRMV */
template<typename OrdinalType, typename ScalarType>
void BLAS<OrdinalType, ScalarType>::GER(const OrdinalType m, const OrdinalType n, const ScalarType alpha, const ScalarType* x, const OrdinalType incx, const ScalarType* y, const OrdinalType incy, ScalarType* A, const OrdinalType lda) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
ScalarType zero = ScalarTraits<ScalarType>::zero();
ScalarType one = ScalarTraits<ScalarType>::one();
bool BadArgument = false;
// Quick return if there is nothing to do!
if( m == izero || n == izero || alpha == zero ){ return; }
// Otherwise, we need to check the argument list.
if( m < izero ) {
std::cout << "BLAS::GER Error: M == " << m << std::endl;
BadArgument = true;
}
if( n < izero ) {
std::cout << "BLAS::GER Error: N == " << n << std::endl;
BadArgument = true;
}
if( lda < m ) {
std::cout << "BLAS::GER Error: LDA < MAX(1,M)"<< std::endl;
BadArgument = true;
}
if( incx == 0 ) {
std::cout << "BLAS::GER Error: INCX == 0"<< std::endl;
BadArgument = true;
}
if( incy == 0 ) {
std::cout << "BLAS::GER Error: INCY == 0"<< std::endl;
BadArgument = true;
}
if(!BadArgument) {
OrdinalType i, j, ix, jy = izero, kx = izero;
ScalarType temp;
// Set the starting pointers for the vectors x and y if incx/y < 0.
if (incx < izero) { kx = (-m+ione)*incx; }
if (incy < izero) { jy = (-n+ione)*incy; }
// Start the operations for incx == 1
if( incx == ione ) {
for( j=izero; j<n; j++ ) {
if ( y[jy] != zero ) {
temp = alpha*y[jy];
for ( i=izero; i<m; i++ ) {
A[j*lda + i] += x[i]*temp;
}
}
jy += incy;
}
}
else { // Start the operations for incx != 1
for( j=izero; j<n; j++ ) {
if ( y[jy] != zero ) {
temp = alpha*y[jy];
ix = kx;
for( i=izero; i<m; i++ ) {
A[j*lda + i] += x[ix]*temp;
ix += incx;
}
}
jy += incy;
}
}
} /* if(!BadArgument) */
} /* end GER */
//------------------------------------------------------------------------------------------
// LEVEL 3 BLAS ROUTINES
//------------------------------------------------------------------------------------------
template<typename OrdinalType, typename ScalarType>
void BLAS<OrdinalType, ScalarType>::GEMM(ETransp transa, ETransp transb, const OrdinalType m, const OrdinalType n, const OrdinalType k, const ScalarType alpha, const ScalarType* A, const OrdinalType lda, const ScalarType* B, const OrdinalType ldb, const ScalarType beta, ScalarType* C, const OrdinalType ldc) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
ScalarType zero = ScalarTraits<ScalarType>::zero();
ScalarType one = ScalarTraits<ScalarType>::one();
OrdinalType i, j, p;
OrdinalType NRowA = m, NRowB = k;
ScalarType temp;
bool BadArgument = false;
// Change dimensions of matrix if either matrix is transposed
if( !(ETranspChar[transa]=='N') ) {
NRowA = k;
}
if( !(ETranspChar[transb]=='N') ) {
NRowB = n;
}
// Quick return if there is nothing to do!
if( (m==izero) || (n==izero) || (((alpha==zero)||(k==izero)) && (beta==one)) ){ return; }
if( m < izero ) {
std::cout << "BLAS::GEMM Error: M == " << m << std::endl;
BadArgument = true;
}
if( n < izero ) {
std::cout << "BLAS::GEMM Error: N == " << n << std::endl;
BadArgument = true;
}
if( k < izero ) {
std::cout << "BLAS::GEMM Error: K == " << k << std::endl;
BadArgument = true;
}
if( lda < NRowA ) {
std::cout << "BLAS::GEMM Error: LDA < MAX(1,M)"<< std::endl;
BadArgument = true;
}
if( ldb < NRowB ) {
std::cout << "BLAS::GEMM Error: LDB < MAX(1,K)"<< std::endl;
BadArgument = true;
}
if( ldc < m ) {
std::cout << "BLAS::GEMM Error: LDC < MAX(1,M)"<< std::endl;
BadArgument = true;
}
if(!BadArgument) {
// Only need to scale the resulting matrix C.
if( alpha == zero ) {
if( beta == zero ) {
for (j=izero; j<n; j++) {
for (i=izero; i<m; i++) {
C[j*ldc + i] = zero;
}
}
} else {
for (j=izero; j<n; j++) {
for (i=izero; i<m; i++) {
C[j*ldc + i] *= beta;
}
}
}
return;
}
//
// Now start the operations.
//
if ( ETranspChar[transb]=='N' ) {
if ( ETranspChar[transa]=='N' ) {
// Compute C = alpha*A*B + beta*C
for (j=izero; j<n; j++) {
if( beta == zero ) {
for (i=izero; i<m; i++){
C[j*ldc + i] = zero;
}
} else if( beta != one ) {
for (i=izero; i<m; i++){
C[j*ldc + i] *= beta;
}
}
for (p=izero; p<k; p++){
if (B[j*ldb + p] != zero ){
temp = alpha*B[j*ldb + p];
for (i=izero; i<m; i++) {
C[j*ldc + i] += temp*A[p*lda + i];
}
}
}
}
} else {
// Compute C = alpha*A'*B + beta*C
for (j=izero; j<n; j++) {
for (i=izero; i<m; i++) {
temp = zero;
for (p=izero; p<k; p++) {
temp += A[i*lda + p]*B[j*ldb + p];
}
if (beta == zero) {
C[j*ldc + i] = alpha*temp;
} else {
C[j*ldc + i] = alpha*temp + beta*C[j*ldc + i];
}
}
}
}
} else {
if ( ETranspChar[transa]=='N' ) {
// Compute C = alpha*A*B' + beta*C
for (j=izero; j<n; j++) {
if (beta == zero) {
for (i=izero; i<m; i++) {
C[j*ldc + i] = zero;
}
} else if ( beta != one ) {
for (i=izero; i<m; i++) {
C[j*ldc + i] *= beta;
}
}
for (p=izero; p<k; p++) {
if (B[p*ldb + j] != zero) {
temp = alpha*B[p*ldb + j];
for (i=izero; i<m; i++) {
C[j*ldc + i] += temp*A[p*lda + i];
}
}
}
}
} else {
// Compute C += alpha*A'*B' + beta*C
for (j=izero; j<n; j++) {
for (i=izero; i<m; i++) {
temp = zero;
for (p=izero; p<k; p++) {
temp += A[i*lda + p]*B[p*ldb + j];
}
if (beta == zero) {
C[j*ldc + i] = alpha*temp;
} else {
C[j*ldc + i] = alpha*temp + beta*C[j*ldc + i];
}
}
}
} // end if (ETranspChar[transa]=='N') ...
} // end if (ETranspChar[transb]=='N') ...
} // end if (!BadArgument) ...
} // end of GEMM
template<typename OrdinalType, typename ScalarType>
void BLAS<OrdinalType, ScalarType>::SYMM(ESide side, EUplo uplo, const OrdinalType m, const OrdinalType n, const ScalarType alpha, const ScalarType* A, const OrdinalType lda, const ScalarType* B, const OrdinalType ldb, const ScalarType beta, ScalarType* C, const OrdinalType ldc) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
ScalarType zero = ScalarTraits<ScalarType>::zero();
ScalarType one = ScalarTraits<ScalarType>::one();
OrdinalType i, j, k, NRowA = m;
ScalarType temp1, temp2;
bool BadArgument = false;
bool Upper = (EUploChar[uplo] == 'U');
if (ESideChar[side] == 'R') { NRowA = n; }
// Quick return.
if ( (m==izero) || (n==izero) || ( (alpha==zero)&&(beta==one) ) ) { return; }
if( m < 0 ) {
std::cout << "BLAS::SYMM Error: M == "<< m << std::endl;
BadArgument = true; }
if( n < 0 ) {
std::cout << "BLAS::SYMM Error: N == "<< n << std::endl;
BadArgument = true; }
if( lda < NRowA ) {
std::cout << "BLAS::SYMM Error: LDA == "<<lda<<std::endl;
BadArgument = true; }
if( ldb < m ) {
std::cout << "BLAS::SYMM Error: LDB == "<<ldb<<std::endl;
BadArgument = true; }
if( ldc < m ) {
std::cout << "BLAS::SYMM Error: LDC == "<<ldc<<std::endl;
BadArgument = true; }
if(!BadArgument) {
// Only need to scale C and return.
if (alpha == zero) {
if (beta == zero ) {
for (j=izero; j<n; j++) {
for (i=izero; i<m; i++) {
C[j*ldc + i] = zero;
}
}
} else {
for (j=izero; j<n; j++) {
for (i=izero; i<m; i++) {
C[j*ldc + i] *= beta;
}
}
}
return;
}
if ( ESideChar[side] == 'L') {
// Compute C = alpha*A*B + beta*C
if (Upper) {
// The symmetric part of A is stored in the upper triangular part of the matrix.
for (j=izero; j<n; j++) {
for (i=izero; i<m; i++) {
temp1 = alpha*B[j*ldb + i];
temp2 = zero;
for (k=izero; k<i; k++) {
C[j*ldc + k] += temp1*A[i*lda + k];
temp2 += B[j*ldb + k]*A[i*lda + k];
}
if (beta == zero) {
C[j*ldc + i] = temp1*A[i*lda + i] + alpha*temp2;
} else {
C[j*ldc + i] = beta*C[j*ldc + i] + temp1*A[i*lda + i] + alpha*temp2;
}
}
}
} else {
// The symmetric part of A is stored in the lower triangular part of the matrix.
for (j=izero; j<n; j++) {
for (i=m-ione; i>-ione; i--) {
temp1 = alpha*B[j*ldb + i];
temp2 = zero;
for (k=i+ione; k<m; k++) {
C[j*ldc + k] += temp1*A[i*lda + k];
temp2 += B[j*ldb + k]*A[i*lda + k];
}
if (beta == zero) {
C[j*ldc + i] = temp1*A[i*lda + i] + alpha*temp2;
} else {
C[j*ldc + i] = beta*C[j*ldc + i] + temp1*A[i*lda + i] + alpha*temp2;
}
}
}
}
} else {
// Compute C = alpha*B*A + beta*C.
for (j=izero; j<n; j++) {
temp1 = alpha*A[j*lda + j];
if (beta == zero) {
for (i=izero; i<m; i++) {
C[j*ldc + i] = temp1*B[j*ldb + i];
}
} else {
for (i=izero; i<m; i++) {
C[j*ldc + i] = beta*C[j*ldc + i] + temp1*B[j*ldb + i];
}
}
for (k=izero; k<j; k++) {
if (Upper) {
temp1 = alpha*A[j*lda + k];
} else {
temp1 = alpha*A[k*lda + j];
}
for (i=izero; i<m; i++) {
C[j*ldc + i] += temp1*B[k*ldb + i];
}
}
for (k=j+ione; k<n; k++) {
if (Upper) {
temp1 = alpha*A[k*lda + j];
} else {
temp1 = alpha*A[j*lda + k];
}
for (i=izero; i<m; i++) {
C[j*ldc + i] += temp1*B[k*ldb + i];
}
}
}
} // end if (ESideChar[side]=='L') ...
} // end if(!BadArgument) ...
} // end SYMM
template<typename OrdinalType, typename ScalarType>
void BLAS<OrdinalType, ScalarType>::TRMM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const ScalarType alpha, const ScalarType* A, const OrdinalType lda, ScalarType* B, const OrdinalType ldb) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
ScalarType zero = ScalarTraits<ScalarType>::zero();
ScalarType one = ScalarTraits<ScalarType>::one();
OrdinalType i, j, k, NRowA = m;
ScalarType temp;
bool BadArgument = false;
bool LSide = (ESideChar[side] == 'L');
bool NoUnit = (EDiagChar[diag] == 'N');
bool Upper = (EUploChar[uplo] == 'U');
if(!LSide) { NRowA = n; }
// Quick return.
if (n==izero || m==izero) { return; }
if( m < 0 ) {
std::cout << "BLAS::TRMM Error: M == "<< m <<std::endl;
BadArgument = true; }
if( n < 0 ) {
std::cout << "BLAS::TRMM Error: N == "<< n <<std::endl;
BadArgument = true; }
if( lda < NRowA ) {
std::cout << "BLAS::TRMM Error: LDA == "<< lda << std::endl;
BadArgument = true; }
if( ldb < m ) {
std::cout << "BLAS::TRMM Error: M == "<< ldb << std::endl;
BadArgument = true; }
if(!BadArgument) {
// B only needs to be zeroed out.
if( alpha == zero ) {
for( j=izero; j<n; j++ ) {
for( i=izero; i<m; i++ ) {
B[j*ldb + i] = zero;
}
}
return;
}
// Start the computations.
if ( LSide ) {
// A is on the left side of B.
if ( ETranspChar[transa]=='N' ) {
// Compute B = alpha*A*B
if ( Upper ) {
// A is upper triangular
for( j=izero; j<n; j++ ) {
for( k=izero; k<m; k++) {
if ( B[j*ldb + k] != zero ) {
temp = alpha*B[j*ldb + k];
for( i=izero; i<k; i++ ) {
B[j*ldb + i] += temp*A[k*lda + i];
}
if ( NoUnit )
temp *=A[k*lda + k];
B[j*ldb + k] = temp;
}
}
}
} else {
// A is lower triangular
for( j=izero; j<n; j++ ) {
for( k=m-ione; k>-ione; k-- ) {
if( B[j*ldb + k] != zero ) {
temp = alpha*B[j*ldb + k];
B[j*ldb + k] = temp;
if ( NoUnit )
B[j*ldb + k] *= A[k*lda + k];
for( i=k+ione; i<m; i++ ) {
B[j*ldb + i] += temp*A[k*lda + i];
}
}
}
}
}
} else {
// Compute B = alpha*A'*B
if( Upper ) {
for( j=izero; j<n; j++ ) {
for( i=m-ione; i>-ione; i-- ) {
temp = B[j*ldb + i];
if( NoUnit )
temp *= A[i*lda + i];
for( k=izero; k<i; k++ ) {
temp += A[i*lda + k]*B[j*ldb + k];
}
B[j*ldb + i] = alpha*temp;
}
}
} else {
for( j=izero; j<n; j++ ) {
for( i=izero; i<m; i++ ) {
temp = B[j*ldb + i];
if( NoUnit )
temp *= A[i*lda + i];
for( k=i+ione; k<m; k++ ) {
temp += A[i*lda + k]*B[j*ldb + k];
}
B[j*ldb + i] = alpha*temp;
}
}
}
}
} else {
// A is on the right hand side of B.
if( ETranspChar[transa] == 'N' ) {
// Compute B = alpha*B*A
if( Upper ) {
// A is upper triangular.
for( j=n-ione; j>-ione; j-- ) {
temp = alpha;
if( NoUnit )
temp *= A[j*lda + j];
for( i=izero; i<m; i++ ) {
B[j*ldb + i] *= temp;
}
for( k=izero; k<j; k++ ) {
if( A[j*lda + k] != zero ) {
temp = alpha*A[j*lda + k];
for( i=izero; i<m; i++ ) {
B[j*ldb + i] += temp*B[k*ldb + i];
}
}
}
}
} else {
// A is lower triangular.
for( j=izero; j<n; j++ ) {
temp = alpha;
if( NoUnit )
temp *= A[j*lda + j];
for( i=izero; i<m; i++ ) {
B[j*ldb + i] *= temp;
}
for( k=j+ione; k<n; k++ ) {
if( A[j*lda + k] != zero ) {
temp = alpha*A[j*lda + k];
for( i=izero; i<m; i++ ) {
B[j*ldb + i] += temp*B[k*ldb + i];
}
}
}
}
}
} else {
// Compute B = alpha*B*A'
if( Upper ) {
for( k=izero; k<n; k++ ) {
for( j=izero; j<k; j++ ) {
if( A[k*lda + j] != zero ) {
temp = alpha*A[k*lda + j];
for( i=izero; i<m; i++ ) {
B[j*ldb + i] += temp*B[k*ldb + i];
}
}
}
temp = alpha;
if( NoUnit )
temp *= A[k*lda + k];
if( temp != one ) {
for( i=izero; i<m; i++ ) {
B[k*ldb + i] *= temp;
}
}
}
} else {
for( k=n-ione; k>-ione; k-- ) {
for( j=k+ione; j<n; j++ ) {
if( A[k*lda + j] != zero ) {
temp = alpha*A[k*lda + j];
for( i=izero; i<m; i++ ) {
B[j*ldb + i] += temp*B[k*ldb + i];
}
}
}
temp = alpha;
if( NoUnit )
temp *= A[k*lda + k];
if( temp != one ) {
for( i=izero; i<m; i++ ) {
B[k*ldb + i] *= temp;
}
}
}
}
} // end if( ETranspChar[transa] == 'N' ) ...
} // end if ( LSide ) ...
} // end if (!BadArgument)
} // end TRMM
template<typename OrdinalType, typename ScalarType>
void BLAS<OrdinalType, ScalarType>::TRSM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const ScalarType alpha, const ScalarType* A, const OrdinalType lda, ScalarType* B, const OrdinalType ldb) const
{
OrdinalType izero = OrdinalTraits<OrdinalType>::zero();
OrdinalType ione = OrdinalTraits<OrdinalType>::one();
ScalarType zero = ScalarTraits<ScalarType>::zero();
ScalarType one = ScalarTraits<ScalarType>::one();
ScalarType temp;
OrdinalType NRowA = m;
bool BadArgument = false;
bool NoUnit = (EDiagChar[diag]=='N');
if (!(ESideChar[side] == 'L')) { NRowA = n; }
// Quick return.
if (n == izero || m == izero) { return; }
if( m < izero ) {
std::cout << "BLAS::TRSM Error: M == "<<m<<std::endl;
BadArgument = true; }
if( n < izero ) {
std::cout << "BLAS::TRSM Error: N == "<<n<<std::endl;
BadArgument = true; }
if( lda < NRowA ) {
std::cout << "BLAS::TRSM Error: LDA == "<<lda<<std::endl;
BadArgument = true; }
if( ldb < m ) {
std::cout << "BLAS::TRSM Error: LDB == "<<ldb<<std::endl;
BadArgument = true; }
if(!BadArgument)
{
int i, j, k;
// Set the solution to the zero std::vector.
if(alpha == zero) {
for(j = izero; j < n; j++) {
for( i = izero; i < m; i++) {
B[j*ldb+i] = zero;
}
}
}
else
{ // Start the operations.
if(ESideChar[side] == 'L') {
//
// Perform computations for OP(A)*X = alpha*B
//
if(ETranspChar[transa] == 'N') {
//
// Compute B = alpha*inv( A )*B
//
if(EUploChar[uplo] == 'U') {
// A is upper triangular.
for(j = izero; j < n; j++) {
// Perform alpha*B if alpha is not 1.
if(alpha != one) {
for( i = izero; i < m; i++) {
B[j*ldb+i] *= alpha;
}
}
// Perform a backsolve for column j of B.
for(k = (m - ione); k > -ione; k--) {
// If this entry is zero, we don't have to do anything.
if (B[j*ldb + k] != zero) {
if (NoUnit) {
B[j*ldb + k] /= A[k*lda + k];
}
for(i = izero; i < k; i++) {
B[j*ldb + i] -= B[j*ldb + k] * A[k*lda + i];
}
}
}
}
}
else
{ // A is lower triangular.
for(j = izero; j < n; j++) {
// Perform alpha*B if alpha is not 1.
if(alpha != one) {
for( i = izero; i < m; i++) {
B[j*ldb+i] *= alpha;
}
}
// Perform a forward solve for column j of B.
for(k = izero; k < m; k++) {
// If this entry is zero, we don't have to do anything.
if (B[j*ldb + k] != zero) {
if (NoUnit) {
B[j*ldb + k] /= A[k*lda + k];
}
for(i = k+ione; i < m; i++) {
B[j*ldb + i] -= B[j*ldb + k] * A[k*lda + i];
}
}
}
}
} // end if (uplo == 'U')
} // if (transa =='N')
else {
//
// Compute B = alpha*inv( A' )*B
//
if(EUploChar[uplo] == 'U') {
// A is upper triangular.
for(j = izero; j < n; j++) {
for( i = izero; i < m; i++) {
temp = alpha*B[j*ldb+i];
for(k = izero; k < i; k++) {
temp -= A[i*lda + k] * B[j*ldb + k];
}
if (NoUnit) {
temp /= A[i*lda + i];
}
B[j*ldb + i] = temp;
}
}
}
else
{ // A is lower triangular.
for(j = izero; j < n; j++) {
for(i = (m - ione) ; i > -ione; i--) {
temp = alpha*B[j*ldb+i];
for(k = i+ione; k < m; k++) {
temp -= A[i*lda + k] * B[j*ldb + k];
}
if (NoUnit) {
temp /= A[i*lda + i];
}
B[j*ldb + i] = temp;
}
}
}
}
} // if (side == 'L')
else {
// side == 'R'
//
// Perform computations for X*OP(A) = alpha*B
//
if (ETranspChar[transa] == 'N') {
//
// Compute B = alpha*B*inv( A )
//
if(EUploChar[uplo] == 'U') {
// A is upper triangular.
// Perform a backsolve for column j of B.
for(j = izero; j < n; j++) {
// Perform alpha*B if alpha is not 1.
if(alpha != one) {
for( i = izero; i < m; i++) {
B[j*ldb+i] *= alpha;
}
}
for(k = izero; k < j; k++) {
// If this entry is zero, we don't have to do anything.
if (A[j*lda + k] != zero) {
for(i = izero; i < m; i++) {
B[j*ldb + i] -= A[j*lda + k] * B[k*ldb + i];
}
}
}
if (NoUnit) {
temp = one/A[j*lda + j];
for(i = izero; i < m; i++) {
B[j*ldb + i] *= temp;
}
}
}
}
else
{ // A is lower triangular.
for(j = (n - ione); j > -ione; j--) {
// Perform alpha*B if alpha is not 1.
if(alpha != one) {
for( i = izero; i < m; i++) {
B[j*ldb+i] *= alpha;
}
}
// Perform a forward solve for column j of B.
for(k = j+ione; k < n; k++) {
// If this entry is zero, we don't have to do anything.
if (A[j*lda + k] != zero) {
for(i = izero; i < m; i++) {
B[j*ldb + i] -= A[j*lda + k] * B[k*ldb + i];
}
}
}
if (NoUnit) {
temp = one/A[j*lda + j];
for(i = izero; i < m; i++) {
B[j*ldb + i] *= temp;
}
}
}
} // end if (uplo == 'U')
} // if (transa =='N')
else {
//
// Compute B = alpha*B*inv( A' )
//
if(EUploChar[uplo] == 'U') {
// A is upper triangular.
for(k = (n - ione); k > -ione; k--) {
if (NoUnit) {
temp = one/A[k*lda + k];
for(i = izero; i < m; i++) {
B[k*ldb + i] *= temp;
}
}
for(j = izero; j < k; j++) {
if (A[k*lda + j] != zero) {
temp = A[k*lda + j];
for(i = izero; i < m; i++) {
B[j*ldb + i] -= temp*B[k*ldb + i];
}
}
}
if (alpha != one) {
for (i = izero; i < m; i++) {
B[k*ldb + i] *= alpha;
}
}
}
}
else
{ // A is lower triangular.
for(k = izero; k < n; k++) {
if (NoUnit) {
temp = one/A[k*lda + k];
for (i = izero; i < m; i++) {
B[k*ldb + i] *= temp;
}
}
for(j = k+ione; j < n; j++) {
if(A[k*lda + j] != zero) {
temp = A[k*lda + j];
for(i = izero; i < m; i++) {
B[j*ldb + i] -= temp*B[k*ldb + i];
}
}
}
if (alpha != one) {
for (i = izero; i < m; i++) {
B[k*ldb + i] *= alpha;
}
}
}
}
}
}
}
}
}
#ifndef DOXYGEN_SHOULD_SKIP_THIS
#ifdef HAVE_TEUCHOS_BLASFLOAT
template<typename OrdinalType>
class BLAS<OrdinalType, float>
{
public:
inline BLAS(void) {}
inline BLAS(const BLAS<OrdinalType, float>& BLAS_source) {}
inline virtual ~BLAS(void) {}
void ROTG(float* da, float* db, float* c, float* s) const;
void ROT(const OrdinalType n, float* dx, const OrdinalType incx, float* dy, const OrdinalType incy, float* c, float* s) const;
float ASUM(const OrdinalType n, const float* x, const OrdinalType incx) const;
void AXPY(const OrdinalType n, const float alpha, const float* x, const OrdinalType incx, float* y, const OrdinalType incy) const;
void COPY(const OrdinalType n, const float* x, const OrdinalType incx, float* y, const OrdinalType incy) const;
float DOT(const OrdinalType n, const float* x, const OrdinalType incx, const float* y, const OrdinalType incy) const;
float NRM2(const OrdinalType n, const float* x, const OrdinalType incx) const;
void SCAL(const OrdinalType n, const float alpha, float* x, const OrdinalType incx) const;
OrdinalType IAMAX(const OrdinalType n, const float* x, const OrdinalType incx) const;
void GEMV(ETransp trans, const OrdinalType m, const OrdinalType n, const float alpha, const float* A, const OrdinalType lda, const float* x, const OrdinalType incx, const float beta, float* y, const OrdinalType incy) const;
void TRMV(EUplo uplo, ETransp trans, EDiag diag, const OrdinalType n, const float* A, const OrdinalType lda, float* x, const OrdinalType incx) const;
void GER(const OrdinalType m, const OrdinalType n, const float alpha, const float* x, const OrdinalType incx, const float* y, const OrdinalType incy, float* A, const OrdinalType lda) const;
void GEMM(ETransp transa, ETransp transb, const OrdinalType m, const OrdinalType n, const OrdinalType k, const float alpha, const float* A, const OrdinalType lda, const float* B, const OrdinalType ldb, const float beta, float* C, const OrdinalType ldc) const;
void SYMM(ESide side, EUplo uplo, const OrdinalType m, const OrdinalType n, const float alpha, const float* A, const OrdinalType lda, const float *B, const OrdinalType ldb, const float beta, float *C, const OrdinalType ldc) const;
void TRMM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const float alpha, const float* A, const OrdinalType lda, float* B, const OrdinalType ldb) const;
void TRSM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const float alpha, const float* A, const OrdinalType lda, float* B, const OrdinalType ldb) const;
};
template<typename OrdinalType>
void BLAS<OrdinalType, float>::ROTG(float* da, float* db, float* c, float* s) const
{ SROTG_F77(da, db, c, s ); }
template<typename OrdinalType>
void BLAS<OrdinalType, float>::ROT(const OrdinalType n, float* dx, const OrdinalType incx, float* dy, const OrdinalType incy, float* c, float* s) const
{ SROT_F77(&n, dx, &incx, dy, &incy, c, s); }
template<typename OrdinalType>
float BLAS<OrdinalType, float>::ASUM(const OrdinalType n, const float* x, const OrdinalType incx) const
{
float tmp = SASUM_F77(&n, x, &incx);
return tmp;
}
template<typename OrdinalType>
void BLAS<OrdinalType, float>::AXPY(const OrdinalType n, const float alpha, const float* x, const OrdinalType incx, float* y, const OrdinalType incy) const
{ SAXPY_F77(&n, &alpha, x, &incx, y, &incy); }
template<typename OrdinalType>
void BLAS<OrdinalType, float>::COPY(const OrdinalType n, const float* x, const OrdinalType incx, float* y, const OrdinalType incy) const
{ SCOPY_F77(&n, x, &incx, y, &incy); }
template<typename OrdinalType>
float BLAS<OrdinalType, float>::DOT(const OrdinalType n, const float* x, const OrdinalType incx, const float* y, const OrdinalType incy) const
{ return SDOT_F77(&n, x, &incx, y, &incy); }
template<typename OrdinalType>
OrdinalType BLAS<OrdinalType, float>::IAMAX(const OrdinalType n, const float* x, const OrdinalType incx) const
{ return ISAMAX_F77(&n, x, &incx); }
template<typename OrdinalType>
float BLAS<OrdinalType, float>::NRM2(const OrdinalType n, const float* x, const OrdinalType incx) const
{ return SNRM2_F77(&n, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, float>::SCAL(const OrdinalType n, const float alpha, float* x, const OrdinalType incx) const
{ SSCAL_F77(&n, &alpha, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, float>::GEMV(ETransp trans, const OrdinalType m, const OrdinalType n, const float alpha, const float* A, const OrdinalType lda, const float* x, const OrdinalType incx, const float beta, float* y, const OrdinalType incy) const
{ SGEMV_F77(CHAR_MACRO(ETranspChar[trans]), &m, &n, &alpha, A, &lda, x, &incx, &beta, y, &incy); }
template<typename OrdinalType>
void BLAS<OrdinalType, float>::GER(const OrdinalType m, const OrdinalType n, const float alpha, const float* x, const OrdinalType incx, const float* y, const OrdinalType incy, float* A, const OrdinalType lda) const
{ SGER_F77(&m, &n, &alpha, x, &incx, y, &incy, A, &lda); }
template<typename OrdinalType>
void BLAS<OrdinalType, float>::TRMV(EUplo uplo, ETransp trans, EDiag diag, const OrdinalType n, const float* A, const OrdinalType lda, float* x, const OrdinalType incx) const
{ STRMV_F77(CHAR_MACRO(EUploChar[uplo]), CHAR_MACRO(ETranspChar[trans]), CHAR_MACRO(EDiagChar[diag]), &n, A, &lda, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, float>::GEMM(ETransp transa, ETransp transb, const OrdinalType m, const OrdinalType n, const OrdinalType k, const float alpha, const float* A, const OrdinalType lda, const float* B, const OrdinalType ldb, const float beta, float* C, const OrdinalType ldc) const
{ SGEMM_F77(CHAR_MACRO(ETranspChar[transa]), CHAR_MACRO(ETranspChar[transb]), &m, &n, &k, &alpha, A, &lda, B, &ldb, &beta, C, &ldc); }
template<typename OrdinalType>
void BLAS<OrdinalType, float>::SYMM(ESide side, EUplo uplo, const OrdinalType m, const OrdinalType n, const float alpha, const float* A, const OrdinalType lda, const float* B, const OrdinalType ldb, const float beta, float* C, const OrdinalType ldc) const
{ SSYMM_F77(CHAR_MACRO(ESideChar[side]), CHAR_MACRO(EUploChar[uplo]), &m, &n, &alpha, A, &lda, B, &ldb, &beta, C, &ldc); }
template<typename OrdinalType>
void BLAS<OrdinalType, float>::TRMM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const float alpha, const float* A, const OrdinalType lda, float* B, const OrdinalType ldb) const
{ STRMM_F77(CHAR_MACRO(ESideChar[side]), CHAR_MACRO(EUploChar[uplo]), CHAR_MACRO(ETranspChar[transa]), CHAR_MACRO(EDiagChar[diag]), &m, &n, &alpha, A, &lda, B, &ldb); }
template<typename OrdinalType>
void BLAS<OrdinalType, float>::TRSM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const float alpha, const float* A, const OrdinalType lda, float* B, const OrdinalType ldb) const
{ STRSM_F77(CHAR_MACRO(ESideChar[side]), CHAR_MACRO(EUploChar[uplo]), CHAR_MACRO(ETranspChar[transa]), CHAR_MACRO(EDiagChar[diag]), &m, &n, &alpha, A, &lda, B, &ldb); }
#endif // HAVE_TEUCHOS_BLASFLOAT
template<typename OrdinalType>
class BLAS<OrdinalType, double>
{
public:
inline BLAS(void) {}
inline BLAS(const BLAS<OrdinalType, double>& BLAS_source) {}
inline virtual ~BLAS(void) {}
void ROTG(double* da, double* db, double* c, double* s) const;
void ROT(const OrdinalType n, double* dx, const OrdinalType incx, double* dy, const OrdinalType incy, double* c, double* s) const;
double ASUM(const OrdinalType n, const double* x, const OrdinalType incx) const;
void AXPY(const OrdinalType n, const double alpha, const double* x, const OrdinalType incx, double* y, const OrdinalType incy) const;
void COPY(const OrdinalType n, const double* x, const OrdinalType incx, double* y, const OrdinalType incy) const;
double DOT(const OrdinalType n, const double* x, const OrdinalType incx, const double* y, const OrdinalType incy) const;
double NRM2(const OrdinalType n, const double* x, const OrdinalType incx) const;
void SCAL(const OrdinalType n, const double alpha, double* x, const OrdinalType incx) const;
OrdinalType IAMAX(const OrdinalType n, const double* x, const OrdinalType incx) const;
void GEMV(ETransp trans, const OrdinalType m, const OrdinalType n, const double alpha, const double* A, const OrdinalType lda, const double* x, const OrdinalType incx, const double beta, double* y, const OrdinalType incy) const;
void TRMV(EUplo uplo, ETransp trans, EDiag diag, const OrdinalType n, const double* A, const OrdinalType lda, double* x, const OrdinalType incx) const;
void GER(const OrdinalType m, const OrdinalType n, const double alpha, const double* x, const OrdinalType incx, const double* y, const OrdinalType incy, double* A, const OrdinalType lda) const;
void GEMM(ETransp transa, ETransp transb, const OrdinalType m, const OrdinalType n, const OrdinalType k, const double alpha, const double* A, const OrdinalType lda, const double* B, const OrdinalType ldb, const double beta, double* C, const OrdinalType ldc) const;
void SYMM(ESide side, EUplo uplo, const OrdinalType m, const OrdinalType n, const double alpha, const double* A, const OrdinalType lda, const double *B, const OrdinalType ldb, const double beta, double *C, const OrdinalType ldc) const;
void TRMM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const double alpha, const double* A, const OrdinalType lda, double* B, const OrdinalType ldb) const;
void TRSM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const double alpha, const double* A, const OrdinalType lda, double* B, const OrdinalType ldb) const;
};
template<typename OrdinalType>
void BLAS<OrdinalType, double>::ROTG(double* da, double* db, double* c, double* s) const
{ DROTG_F77(da, db, c, s); }
template<typename OrdinalType>
void BLAS<OrdinalType, double>::ROT(const OrdinalType n, double* dx, const OrdinalType incx, double* dy, const OrdinalType incy, double* c, double* s) const
{ DROT_F77(&n, dx, &incx, dy, &incy, c, s); }
template<typename OrdinalType>
double BLAS<OrdinalType, double>::ASUM(const OrdinalType n, const double* x, const OrdinalType incx) const
{ return DASUM_F77(&n, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, double>::AXPY(const OrdinalType n, const double alpha, const double* x, const OrdinalType incx, double* y, const OrdinalType incy) const
{ DAXPY_F77(&n, &alpha, x, &incx, y, &incy); }
template<typename OrdinalType>
void BLAS<OrdinalType, double>::COPY(const OrdinalType n, const double* x, const OrdinalType incx, double* y, const OrdinalType incy) const
{ DCOPY_F77(&n, x, &incx, y, &incy); }
template<typename OrdinalType>
double BLAS<OrdinalType, double>::DOT(const OrdinalType n, const double* x, const OrdinalType incx, const double* y, const OrdinalType incy) const
{ return DDOT_F77(&n, x, &incx, y, &incy); }
template<typename OrdinalType>
OrdinalType BLAS<OrdinalType, double>::IAMAX(const OrdinalType n, const double* x, const OrdinalType incx) const
{ return IDAMAX_F77(&n, x, &incx); }
template<typename OrdinalType>
double BLAS<OrdinalType, double>::NRM2(const OrdinalType n, const double* x, const OrdinalType incx) const
{ return DNRM2_F77(&n, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, double>::SCAL(const OrdinalType n, const double alpha, double* x, const OrdinalType incx) const
{ DSCAL_F77(&n, &alpha, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, double>::GEMV(ETransp trans, const OrdinalType m, const OrdinalType n, const double alpha, const double* A, const OrdinalType lda, const double* x, const OrdinalType incx, const double beta, double* y, const OrdinalType incy) const
{ DGEMV_F77(CHAR_MACRO(ETranspChar[trans]), &m, &n, &alpha, A, &lda, x, &incx, &beta, y, &incy); }
template<typename OrdinalType>
void BLAS<OrdinalType, double>::GER(const OrdinalType m, const OrdinalType n, const double alpha, const double* x, const OrdinalType incx, const double* y, const OrdinalType incy, double* A, const OrdinalType lda) const
{ DGER_F77(&m, &n, &alpha, x, &incx, y, &incy, A, &lda); }
template<typename OrdinalType>
void BLAS<OrdinalType, double>::TRMV(EUplo uplo, ETransp trans, EDiag diag, const OrdinalType n, const double* A, const OrdinalType lda, double* x, const OrdinalType incx) const
{ DTRMV_F77(CHAR_MACRO(EUploChar[uplo]), CHAR_MACRO(ETranspChar[trans]), CHAR_MACRO(EDiagChar[diag]), &n, A, &lda, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, double>::GEMM(ETransp transa, ETransp transb, const OrdinalType m, const OrdinalType n, const OrdinalType k, const double alpha, const double* A, const OrdinalType lda, const double* B, const OrdinalType ldb, const double beta, double* C, const OrdinalType ldc) const
{ DGEMM_F77(CHAR_MACRO(ETranspChar[transa]), CHAR_MACRO(ETranspChar[transb]), &m, &n, &k, &alpha, A, &lda, B, &ldb, &beta, C, &ldc); }
template<typename OrdinalType>
void BLAS<OrdinalType, double>::SYMM(ESide side, EUplo uplo, const OrdinalType m, const OrdinalType n, const double alpha, const double* A, const OrdinalType lda, const double *B, const OrdinalType ldb, const double beta, double *C, const OrdinalType ldc) const
{ DSYMM_F77(CHAR_MACRO(ESideChar[side]), CHAR_MACRO(EUploChar[uplo]), &m, &n, &alpha, A, &lda, B, &ldb, &beta, C, &ldc); }
template<typename OrdinalType>
void BLAS<OrdinalType, double>::TRMM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const double alpha, const double* A, const OrdinalType lda, double* B, const OrdinalType ldb) const
{ DTRMM_F77(CHAR_MACRO(ESideChar[side]), CHAR_MACRO(EUploChar[uplo]), CHAR_MACRO(ETranspChar[transa]), CHAR_MACRO(EDiagChar[diag]), &m, &n, &alpha, A, &lda, B, &ldb); }
template<typename OrdinalType>
void BLAS<OrdinalType, double>::TRSM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const double alpha, const double* A, const OrdinalType lda, double* B, const OrdinalType ldb) const
{ DTRSM_F77(CHAR_MACRO(ESideChar[side]), CHAR_MACRO(EUploChar[uplo]), CHAR_MACRO(ETranspChar[transa]), CHAR_MACRO(EDiagChar[diag]), &m, &n, &alpha, A, &lda, B, &ldb); }
#ifdef HAVE_TEUCHOS_COMPLEX
#ifdef HAVE_TEUCHOS_BLASFLOAT
template<typename OrdinalType>
class BLAS<OrdinalType, std::complex<float> >
{
public:
inline BLAS(void) {}
inline BLAS(const BLAS<OrdinalType, std::complex<float> >& BLAS_source) {}
inline virtual ~BLAS(void) {}
void ROTG(std::complex<float>* da, std::complex<float>* db, float* c, std::complex<float>* s) const;
void ROT(const OrdinalType n, std::complex<float>* dx, const OrdinalType incx, std::complex<float>* dy, const OrdinalType incy, float* c, std::complex<float>* s) const;
float ASUM(const OrdinalType n, const std::complex<float>* x, const OrdinalType incx) const;
void AXPY(const OrdinalType n, const std::complex<float> alpha, const std::complex<float>* x, const OrdinalType incx, std::complex<float>* y, const OrdinalType incy) const;
void COPY(const OrdinalType n, const std::complex<float>* x, const OrdinalType incx, std::complex<float>* y, const OrdinalType incy) const;
std::complex<float> DOT(const OrdinalType n, const std::complex<float>* x, const OrdinalType incx, const std::complex<float>* y, const OrdinalType incy) const;
float NRM2(const OrdinalType n, const std::complex<float>* x, const OrdinalType incx) const;
void SCAL(const OrdinalType n, const std::complex<float> alpha, std::complex<float>* x, const OrdinalType incx) const;
OrdinalType IAMAX(const OrdinalType n, const std::complex<float>* x, const OrdinalType incx) const;
void GEMV(ETransp trans, const OrdinalType m, const OrdinalType n, const std::complex<float> alpha, const std::complex<float>* A, const OrdinalType lda, const std::complex<float>* x, const OrdinalType incx, const std::complex<float> beta, std::complex<float>* y, const OrdinalType incy) const;
void TRMV(EUplo uplo, ETransp trans, EDiag diag, const OrdinalType n, const std::complex<float>* A, const OrdinalType lda, std::complex<float>* x, const OrdinalType incx) const;
void GER(const OrdinalType m, const OrdinalType n, const std::complex<float> alpha, const std::complex<float>* x, const OrdinalType incx, const std::complex<float>* y, const OrdinalType incy, std::complex<float>* A, const OrdinalType lda) const;
void GEMM(ETransp transa, ETransp transb, const OrdinalType m, const OrdinalType n, const OrdinalType k, const std::complex<float> alpha, const std::complex<float>* A, const OrdinalType lda, const std::complex<float>* B, const OrdinalType ldb, const std::complex<float> beta, std::complex<float>* C, const OrdinalType ldc) const;
void SYMM(ESide side, EUplo uplo, const OrdinalType m, const OrdinalType n, const std::complex<float> alpha, const std::complex<float>* A, const OrdinalType lda, const std::complex<float> *B, const OrdinalType ldb, const std::complex<float> beta, std::complex<float> *C, const OrdinalType ldc) const;
void TRMM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const std::complex<float> alpha, const std::complex<float>* A, const OrdinalType lda, std::complex<float>* B, const OrdinalType ldb) const;
void TRSM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const std::complex<float> alpha, const std::complex<float>* A, const OrdinalType lda, std::complex<float>* B, const OrdinalType ldb) const;
};
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<float> >::ROTG(std::complex<float>* da, std::complex<float>* db, float* c, std::complex<float>* s) const
{ CROTG_F77(da, db, c, s ); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<float> >::ROT(const OrdinalType n, std::complex<float>* dx, const OrdinalType incx, std::complex<float>* dy, const OrdinalType incy, float* c, std::complex<float>* s) const
{ CROT_F77(&n, dx, &incx, dy, &incy, c, s); }
template<typename OrdinalType>
float BLAS<OrdinalType, std::complex<float> >::ASUM(const OrdinalType n, const std::complex<float>* x, const OrdinalType incx) const
{ return CASUM_F77(&n, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<float> >::AXPY(const OrdinalType n, const std::complex<float> alpha, const std::complex<float>* x, const OrdinalType incx, std::complex<float>* y, const OrdinalType incy) const
{ CAXPY_F77(&n, &alpha, x, &incx, y, &incy); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<float> >::COPY(const OrdinalType n, const std::complex<float>* x, const OrdinalType incx, std::complex<float>* y, const OrdinalType incy) const
{ CCOPY_F77(&n, x, &incx, y, &incy); }
template<typename OrdinalType>
std::complex<float> BLAS<OrdinalType, std::complex<float> >::DOT(const OrdinalType n, const std::complex<float>* x, const OrdinalType incx, const std::complex<float>* y, const OrdinalType incy) const
{ return CDOT_F77(&n, x, &incx, y, &incy); }
template<typename OrdinalType>
OrdinalType BLAS<OrdinalType, std::complex<float> >::IAMAX(const OrdinalType n, const std::complex<float>* x, const OrdinalType incx) const
{ return ICAMAX_F77(&n, x, &incx); }
template<typename OrdinalType>
float BLAS<OrdinalType, std::complex<float> >::NRM2(const OrdinalType n, const std::complex<float>* x, const OrdinalType incx) const
{ return CNRM2_F77(&n, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<float> >::SCAL(const OrdinalType n, const std::complex<float> alpha, std::complex<float>* x, const OrdinalType incx) const
{ CSCAL_F77(&n, &alpha, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<float> >::GEMV(ETransp trans, const OrdinalType m, const OrdinalType n, const std::complex<float> alpha, const std::complex<float>* A, const OrdinalType lda, const std::complex<float>* x, const OrdinalType incx, const std::complex<float> beta, std::complex<float>* y, const OrdinalType incy) const
{ CGEMV_F77(CHAR_MACRO(ETranspChar[trans]), &m, &n, &alpha, A, &lda, x, &incx, &beta, y, &incy); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<float> >::GER(const OrdinalType m, const OrdinalType n, const std::complex<float> alpha, const std::complex<float>* x, const OrdinalType incx, const std::complex<float>* y, const OrdinalType incy, std::complex<float>* A, const OrdinalType lda) const
{ CGER_F77(&m, &n, &alpha, x, &incx, y, &incy, A, &lda); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<float> >::TRMV(EUplo uplo, ETransp trans, EDiag diag, const OrdinalType n, const std::complex<float>* A, const OrdinalType lda, std::complex<float>* x, const OrdinalType incx) const
{ CTRMV_F77(CHAR_MACRO(EUploChar[uplo]), CHAR_MACRO(ETranspChar[trans]), CHAR_MACRO(EDiagChar[diag]), &n, A, &lda, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<float> >::GEMM(ETransp transa, ETransp transb, const OrdinalType m, const OrdinalType n, const OrdinalType k, const std::complex<float> alpha, const std::complex<float>* A, const OrdinalType lda, const std::complex<float>* B, const OrdinalType ldb, const std::complex<float> beta, std::complex<float>* C, const OrdinalType ldc) const
{ CGEMM_F77(CHAR_MACRO(ETranspChar[transa]), CHAR_MACRO(ETranspChar[transb]), &m, &n, &k, &alpha, A, &lda, B, &ldb, &beta, C, &ldc); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<float> >::SYMM(ESide side, EUplo uplo, const OrdinalType m, const OrdinalType n, const std::complex<float> alpha, const std::complex<float>* A, const OrdinalType lda, const std::complex<float>* B, const OrdinalType ldb, const std::complex<float> beta, std::complex<float>* C, const OrdinalType ldc) const
{ CSYMM_F77(CHAR_MACRO(ESideChar[side]), CHAR_MACRO(EUploChar[uplo]), &m, &n, &alpha, A, &lda, B, &ldb, &beta, C, &ldc); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<float> >::TRMM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const std::complex<float> alpha, const std::complex<float>* A, const OrdinalType lda, std::complex<float>* B, const OrdinalType ldb) const
{ CTRMM_F77(CHAR_MACRO(ESideChar[side]), CHAR_MACRO(EUploChar[uplo]), CHAR_MACRO(ETranspChar[transa]), CHAR_MACRO(EDiagChar[diag]), &m, &n, &alpha, A, &lda, B, &ldb); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<float> >::TRSM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const std::complex<float> alpha, const std::complex<float>* A, const OrdinalType lda, std::complex<float>* B, const OrdinalType ldb) const
{ CTRSM_F77(CHAR_MACRO(ESideChar[side]), CHAR_MACRO(EUploChar[uplo]), CHAR_MACRO(ETranspChar[transa]), CHAR_MACRO(EDiagChar[diag]), &m, &n, &alpha, A, &lda, B, &ldb); }
#endif // HAVE_TEUCHOS_BLASFLOAT
template<typename OrdinalType>
class BLAS<OrdinalType, std::complex<double> >
{
public:
inline BLAS(void) {}
inline BLAS(const BLAS<OrdinalType, std::complex<double> >& BLAS_source) {}
inline virtual ~BLAS(void) {}
void ROTG(std::complex<double>* da, std::complex<double>* db, double* c, std::complex<double>* s) const;
void ROT(const OrdinalType n, std::complex<double>* dx, const OrdinalType incx, std::complex<double>* dy, const OrdinalType incy, double* c, std::complex<double>* s) const;
double ASUM(const OrdinalType n, const std::complex<double>* x, const OrdinalType incx) const;
void AXPY(const OrdinalType n, const std::complex<double> alpha, const std::complex<double>* x, const OrdinalType incx, std::complex<double>* y, const OrdinalType incy) const;
void COPY(const OrdinalType n, const std::complex<double>* x, const OrdinalType incx, std::complex<double>* y, const OrdinalType incy) const;
std::complex<double> DOT(const OrdinalType n, const std::complex<double>* x, const OrdinalType incx, const std::complex<double>* y, const OrdinalType incy) const;
double NRM2(const OrdinalType n, const std::complex<double>* x, const OrdinalType incx) const;
void SCAL(const OrdinalType n, const std::complex<double> alpha, std::complex<double>* x, const OrdinalType incx) const;
OrdinalType IAMAX(const OrdinalType n, const std::complex<double>* x, const OrdinalType incx) const;
void GEMV(ETransp trans, const OrdinalType m, const OrdinalType n, const std::complex<double> alpha, const std::complex<double>* A, const OrdinalType lda, const std::complex<double>* x, const OrdinalType incx, const std::complex<double> beta, std::complex<double>* y, const OrdinalType incy) const;
void TRMV(EUplo uplo, ETransp trans, EDiag diag, const OrdinalType n, const std::complex<double>* A, const OrdinalType lda, std::complex<double>* x, const OrdinalType incx) const;
void GER(const OrdinalType m, const OrdinalType n, const std::complex<double> alpha, const std::complex<double>* x, const OrdinalType incx, const std::complex<double>* y, const OrdinalType incy, std::complex<double>* A, const OrdinalType lda) const;
void GEMM(ETransp transa, ETransp transb, const OrdinalType m, const OrdinalType n, const OrdinalType k, const std::complex<double> alpha, const std::complex<double>* A, const OrdinalType lda, const std::complex<double>* B, const OrdinalType ldb, const std::complex<double> beta, std::complex<double>* C, const OrdinalType ldc) const;
void SYMM(ESide side, EUplo uplo, const OrdinalType m, const OrdinalType n, const std::complex<double> alpha, const std::complex<double>* A, const OrdinalType lda, const std::complex<double> *B, const OrdinalType ldb, const std::complex<double> beta, std::complex<double> *C, const OrdinalType ldc) const;
void TRMM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const std::complex<double> alpha, const std::complex<double>* A, const OrdinalType lda, std::complex<double>* B, const OrdinalType ldb) const;
void TRSM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const std::complex<double> alpha, const std::complex<double>* A, const OrdinalType lda, std::complex<double>* B, const OrdinalType ldb) const;
};
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<double> >::ROTG(std::complex<double>* da, std::complex<double>* db, double* c, std::complex<double>* s) const
{ ZROTG_F77(da, db, c, s); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<double> >::ROT(const OrdinalType n, std::complex<double>* dx, const OrdinalType incx, std::complex<double>* dy, const OrdinalType incy, double* c, std::complex<double>* s) const
{ ZROT_F77(&n, dx, &incx, dy, &incy, c, s); }
template<typename OrdinalType>
double BLAS<OrdinalType, std::complex<double> >::ASUM(const OrdinalType n, const std::complex<double>* x, const OrdinalType incx) const
{ return ZASUM_F77(&n, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<double> >::AXPY(const OrdinalType n, const std::complex<double> alpha, const std::complex<double>* x, const OrdinalType incx, std::complex<double>* y, const OrdinalType incy) const
{ ZAXPY_F77(&n, &alpha, x, &incx, y, &incy); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<double> >::COPY(const OrdinalType n, const std::complex<double>* x, const OrdinalType incx, std::complex<double>* y, const OrdinalType incy) const
{ ZCOPY_F77(&n, x, &incx, y, &incy); }
template<typename OrdinalType>
std::complex<double> BLAS<OrdinalType, std::complex<double> >::DOT(const OrdinalType n, const std::complex<double>* x, const OrdinalType incx, const std::complex<double>* y, const OrdinalType incy) const
{ return ZDOT_F77(&n, x, &incx, y, &incy); }
template<typename OrdinalType>
OrdinalType BLAS<OrdinalType, std::complex<double> >::IAMAX(const OrdinalType n, const std::complex<double>* x, const OrdinalType incx) const
{ return IZAMAX_F77(&n, x, &incx); }
template<typename OrdinalType>
double BLAS<OrdinalType, std::complex<double> >::NRM2(const OrdinalType n, const std::complex<double>* x, const OrdinalType incx) const
{ return ZNRM2_F77(&n, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<double> >::SCAL(const OrdinalType n, const std::complex<double> alpha, std::complex<double>* x, const OrdinalType incx) const
{ ZSCAL_F77(&n, &alpha, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<double> >::GEMV(ETransp trans, const OrdinalType m, const OrdinalType n, const std::complex<double> alpha, const std::complex<double>* A, const OrdinalType lda, const std::complex<double>* x, const OrdinalType incx, const std::complex<double> beta, std::complex<double>* y, const OrdinalType incy) const
{ ZGEMV_F77(CHAR_MACRO(ETranspChar[trans]), &m, &n, &alpha, A, &lda, x, &incx, &beta, y, &incy); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<double> >::GER(const OrdinalType m, const OrdinalType n, const std::complex<double> alpha, const std::complex<double>* x, const OrdinalType incx, const std::complex<double>* y, const OrdinalType incy, std::complex<double>* A, const OrdinalType lda) const
{ ZGER_F77(&m, &n, &alpha, x, &incx, y, &incy, A, &lda); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<double> >::TRMV(EUplo uplo, ETransp trans, EDiag diag, const OrdinalType n, const std::complex<double>* A, const OrdinalType lda, std::complex<double>* x, const OrdinalType incx) const
{ ZTRMV_F77(CHAR_MACRO(EUploChar[uplo]), CHAR_MACRO(ETranspChar[trans]), CHAR_MACRO(EDiagChar[diag]), &n, A, &lda, x, &incx); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<double> >::GEMM(ETransp transa, ETransp transb, const OrdinalType m, const OrdinalType n, const OrdinalType k, const std::complex<double> alpha, const std::complex<double>* A, const OrdinalType lda, const std::complex<double>* B, const OrdinalType ldb, const std::complex<double> beta, std::complex<double>* C, const OrdinalType ldc) const
{ ZGEMM_F77(CHAR_MACRO(ETranspChar[transa]), CHAR_MACRO(ETranspChar[transb]), &m, &n, &k, &alpha, A, &lda, B, &ldb, &beta, C, &ldc); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<double> >::SYMM(ESide side, EUplo uplo, const OrdinalType m, const OrdinalType n, const std::complex<double> alpha, const std::complex<double>* A, const OrdinalType lda, const std::complex<double> *B, const OrdinalType ldb, const std::complex<double> beta, std::complex<double> *C, const OrdinalType ldc) const
{ ZSYMM_F77(CHAR_MACRO(ESideChar[side]), CHAR_MACRO(EUploChar[uplo]), &m, &n, &alpha, A, &lda, B, &ldb, &beta, C, &ldc); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<double> >::TRMM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const std::complex<double> alpha, const std::complex<double>* A, const OrdinalType lda, std::complex<double>* B, const OrdinalType ldb) const
{ ZTRMM_F77(CHAR_MACRO(ESideChar[side]), CHAR_MACRO(EUploChar[uplo]), CHAR_MACRO(ETranspChar[transa]), CHAR_MACRO(EDiagChar[diag]), &m, &n, &alpha, A, &lda, B, &ldb); }
template<typename OrdinalType>
void BLAS<OrdinalType, std::complex<double> >::TRSM(ESide side, EUplo uplo, ETransp transa, EDiag diag, const OrdinalType m, const OrdinalType n, const std::complex<double> alpha, const std::complex<double>* A, const OrdinalType lda, std::complex<double>* B, const OrdinalType ldb) const
{ ZTRSM_F77(CHAR_MACRO(ESideChar[side]), CHAR_MACRO(EUploChar[uplo]), CHAR_MACRO(ETranspChar[transa]), CHAR_MACRO(EDiagChar[diag]), &m, &n, &alpha, A, &lda, B, &ldb); }
#endif // HAVE_TEUCHOS_COMPLEX
#endif // DOXYGEN_SHOULD_SKIP_THIS
} // namespace Teuchos
#endif // _TEUCHOS_BLAS_HPP_
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