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/*
* Copyright (c) 2011, Michael Lehn
*
* All rights reserved.
*
* 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 name of the FLENS 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
* 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.
*/
/* Based on
*
SUBROUTINE DGESVX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV,
$ EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR,
$ WORK, IWORK, INFO )
*
* -- LAPACK driver routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2006
*/
#ifndef FLENS_LAPACK_GE_SVX_TCC
#define FLENS_LAPACK_GE_SVX_TCC 1
#include <flens/blas/blas.h>
#include <flens/lapack/lapack.h>
namespace flens { namespace lapack {
//== generic lapack implementation =============================================
namespace generic {
template <typename MA, typename MAF, typename VPIV, typename VR, typename VC,
typename MB, typename MX, typename RCOND, typename FERR,
typename BERR, typename VWORK, typename VIWORK>
typename GeMatrix<MA>::IndexType
svx_impl(SVX::Fact fact,
Transpose trans,
GeMatrix<MA> &A,
GeMatrix<MAF> &AF,
DenseVector<VPIV> &piv,
SVX::Equilibration equed,
DenseVector<VR> &r,
DenseVector<VC> &c,
GeMatrix<MB> &B,
GeMatrix<MX> &X,
RCOND &rCond,
DenseVector<FERR> &fErr,
DenseVector<BERR> &bErr,
DenseVector<VWORK> &work,
DenseVector<VIWORK> &iwork)
{
using std::max;
using std::min;
using namespace SVX;
typedef typename GeMatrix<MA>::ElementType ElementType;
typedef typename GeMatrix<MA>::IndexType IndexType;
const ElementType Zero(0), One(1);
const Underscore<IndexType> _;
const IndexType n = A.numRows();
const IndexType nRhs = B.numCols();
IndexType info = 0;
const ElementType smallNum = lamch<ElementType>(SafeMin);
const ElementType bigNum = One / smallNum;
bool rowEqu, colEqu;
ElementType rPivGrowth;
if (fact==NotFactored || fact==Equilibrate) {
equed = None;
rowEqu = false;
colEqu = false;
} else {
rowEqu = (equed==Row || equed==Both);
colEqu = (equed==Column || equed==Both);
}
//
// Test the input parameters.
//
ElementType rowCond, colCond;
if (rowEqu) {
ElementType rcMin = bigNum;
ElementType rcMax = Zero;
for (IndexType j=1; j<=n; ++j) {
rcMin = min(rcMin, r(j));
rcMax = max(rcMax, r(j));
}
ASSERT(rcMin>Zero);
if (n>0) {
rowCond = max(rcMin,smallNum) / min(rcMax,bigNum);
} else {
rowCond = One;
}
}
if (colEqu) {
ElementType rcMin = bigNum;
ElementType rcMax = Zero;
for (IndexType j=1; j<=n; ++j) {
rcMin = min(rcMin, c(j));
rcMax = max(rcMax, c(j));
}
ASSERT(rcMin>Zero);
if (n>0) {
colCond = max(rcMin,smallNum) / min(rcMax,bigNum);
} else {
colCond = One;
}
}
if (fact==Equilibrate) {
ElementType amax;
//
// Compute row and column scalings to equilibrate the matrix A.
//
if (equ(A, r, c, rowCond, colCond, amax)==0) {
//
// Equilibrate the matrix.
//
equed = Equilibration(laq(A, r, c, rowCond, colCond, amax));
rowEqu = (equed==Row || equed==Both);
colEqu = (equed==Column || equed==Both);
}
}
//
// Scale the right hand side.
//
if (trans==NoTrans) {
if (rowEqu) {
for (IndexType j=1; j<=nRhs; ++j) {
for (IndexType i=1; i<=n; ++i) {
B(i,j) *= r(i);
}
}
}
} else if (colEqu) {
for (IndexType j=1; j<=nRhs; ++j) {
for (IndexType i=1; i<=n; ++i) {
B(i,j) *= c(i);
}
}
}
if ((fact==NotFactored) || (fact==Equilibrate)) {
//
// Compute the LU factorization of A.
//
AF = A;
info = trf(AF, piv);
//
// Return if INFO is non-zero.
//
if (info>0) {
//
// Compute the reciprocal pivot growth factor of the
// leading rank-deficient INFO columns of A.
//
const auto range = _(1,info);
rPivGrowth = lan(MaximumNorm, AF(range,range).upper());
if (rPivGrowth==Zero) {
rPivGrowth = One;
} else {
rPivGrowth = lan(MaximumNorm, A) / rPivGrowth;
}
work(1) = rPivGrowth;
rCond = Zero;
return info;
}
}
//
// Compute the norm of the matrix A and the
// reciprocal pivot growth factor RPVGRW.
//
const Norm norm = (trans==NoTrans) ? OneNorm : InfinityNorm;
const ElementType normA = lan(norm, A, work);
rPivGrowth = lan(MaximumNorm, AF.upper());
if (rPivGrowth==Zero) {
rPivGrowth = One;
} else {
rPivGrowth = lan(MaximumNorm, A) / rPivGrowth;
}
//
// Compute the reciprocal of the condition number of A.
//
con(norm, AF, normA, rCond, work, iwork);
//
// Compute the solution matrix X.
//
X = B;
trs(trans, AF, piv, X);
//
// Use iterative refinement to improve the computed solution and
// compute error bounds and backward error estimates for it.
//
rfs(trans, A, AF, piv, B, X, fErr, bErr, work(_(1,3*n)), iwork);
//
// Transform the solution matrix X to a solution of the original
// system.
//
if (trans==NoTrans) {
if (colEqu) {
for (IndexType j=1; j<=nRhs; ++j) {
for (IndexType i=1; i<=n; ++i) {
X(i,j) *= c(i);
}
}
for (IndexType j=1; j<=nRhs; ++j) {
fErr(j) /= colCond;
}
}
} else if (rowEqu) {
for (IndexType j=1; j<=nRhs; ++j) {
for (IndexType i=1; i<=n; ++i) {
X(i,j) *= r(i);
}
}
for (IndexType j=1; j<=nRhs; ++j) {
fErr(j) /= rowCond;
}
}
work(1) = rPivGrowth;
//
// Set INFO = N+1 if the matrix is singular to working precision.
//
const ElementType eps = lamch<ElementType>(Eps);
if (rCond<eps) {
info = n+1;
}
return info;
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
template <typename MA, typename MAF, typename VPIV, typename VR, typename VC,
typename MB, typename MX, typename RCOND, typename FERR,
typename BERR, typename VWORK, typename VIWORK>
typename GeMatrix<MA>::IndexType
svx_impl(SVX::Fact fact,
Transpose trans,
GeMatrix<MA> &A,
GeMatrix<MAF> &AF,
DenseVector<VPIV> &piv,
SVX::Equilibration equed,
DenseVector<VR> &r,
DenseVector<VC> &c,
GeMatrix<MB> &B,
GeMatrix<MX> &X,
RCOND &rCond,
DenseVector<FERR> &fErr,
DenseVector<BERR> &bErr,
DenseVector<VWORK> &work,
DenseVector<VIWORK> &iwork)
{
typedef typename GeMatrix<MA>::IndexType IndexType;
IndexType info;
info = cxxlapack::gesvx<IndexType>(getF77Char(fact),
getF77Char(trans),
A.numRows(),
B.numCols(),
A.data(),
A.leadingDimension(),
AF.data(),
AF.leadingDimension(),
piv.data(),
getF77Char(equed),
r.data(),
c.data(),
B.data(),
B.leadingDimension(),
X.data(),
X.leadingDimension(),
rCond,
fErr.data(),
bErr.data(),
work.data(),
iwork.data());
ASSERT(info>=0);
return info;
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
template <typename MA, typename MAF, typename VPIV, typename VR, typename VC,
typename MB, typename MX, typename RCOND, typename FERR,
typename BERR, typename VWORK, typename VIWORK>
typename GeMatrix<MA>::IndexType
svx(SVX::Fact fact,
Transpose trans,
GeMatrix<MA> &A,
GeMatrix<MAF> &AF,
DenseVector<VPIV> &piv,
SVX::Equilibration equed,
DenseVector<VR> &r,
DenseVector<VC> &c,
GeMatrix<MB> &B,
GeMatrix<MX> &X,
RCOND &rCond,
DenseVector<FERR> &fErr,
DenseVector<BERR> &bErr,
DenseVector<VWORK> &work,
DenseVector<VIWORK> &iwork)
{
typedef typename GeMatrix<MA>::IndexType IndexType;
//
// Test the input parameters
//
# ifndef NDEBUG
# endif
# ifdef CHECK_CXXLAPACK
//
// Make copies of output arguments
//
typename GeMatrix<MA>::NoView A_org = A;
typename GeMatrix<MAF>::NoView AF_org = AF;
typename DenseVector<VPIV>::NoView piv_org = piv;
SVX::Equilibration equed_org = equed;
typename DenseVector<VR>::NoView r_org = r;
typename DenseVector<VC>::NoView c_org = c;
typename GeMatrix<MB>::NoView B_org = B;
typename GeMatrix<MX>::NoView X_org = X;
RCOND rCond_org = rCond;
typename DenseVector<FERR>::NoView fErr_org = fErr;
typename DenseVector<BERR>::NoView bErr_org = bErr;
typename DenseVector<VWORK>::NoView work_org = work;
typename DenseVector<VIWORK>::NoView iwork_org = iwork;
# endif
//
// Call implementation
//
IndexType info = LAPACK_SELECT::svx_impl(fact, trans, A, AF, piv, equed,
r, c, B, X, rCond, fErr, bErr,
work, iwork);
# ifdef CHECK_CXXLAPACK
//
// Compare results
//
typename GeMatrix<MA>::NoView A_generic = A;
typename GeMatrix<MAF>::NoView AF_generic = AF;
typename DenseVector<VPIV>::NoView piv_generic = piv;
SVX::Equilibration equed_generic = equed;
typename DenseVector<VR>::NoView r_generic = r;
typename DenseVector<VC>::NoView c_generic = c;
typename GeMatrix<MB>::NoView B_generic = B;
typename GeMatrix<MX>::NoView X_generic = X;
RCOND rCond_generic = rCond;
typename DenseVector<FERR>::NoView fErr_generic = fErr;
typename DenseVector<BERR>::NoView bErr_generic = bErr;
typename DenseVector<VWORK>::NoView work_generic = work;
typename DenseVector<VIWORK>::NoView iwork_generic = iwork;
A = A_org;
AF = AF_org;
piv = piv_org;
equed = equed_org;
r = r_org;
c = c_org;
B = B_org;
X = X_org;
rCond = rCond_org;
fErr = fErr_org;
bErr = bErr_org;
work = work_org;
iwork = iwork_org;
IndexType info_ = external::svx_impl(fact, trans, A, AF, piv, equed,
r, c, B, X, rCond, fErr, bErr,
work, iwork);
bool failed = false;
if (! isIdentical(A_generic, A, "A_generic", "A")) {
std::cerr << "A_org = " << A_org << std::endl;
std::cerr << "CXXLAPACK: A_generic = " << A_generic << std::endl;
std::cerr << "F77LAPACK: A = " << A << std::endl;
failed = true;
}
if (! isIdentical(AF_generic, AF, "AF_generic", "AF")) {
std::cerr << "AF_org = " << AF_org << std::endl;
std::cerr << "CXXLAPACK: AF_generic = " << AF_generic << std::endl;
std::cerr << "F77LAPACK: AF = " << AF << std::endl;
failed = true;
}
if (! isIdentical(piv_generic, piv, "piv_generic", "piv")) {
std::cerr << "piv_org = " << piv_org << std::endl;
std::cerr << "CXXLAPACK: piv_generic = " << piv_generic << std::endl;
std::cerr << "F77LAPACK: piv = " << piv << std::endl;
failed = true;
}
if (equed_generic!=equed) {
std::cerr << "equed_org = " << equed_org << std::endl;
std::cerr << "CXXLAPACK: equed_generic = "
<< equed_generic << std::endl;
std::cerr << "F77LAPACK: equed = " << equed << std::endl;
failed = true;
}
if (! isIdentical(r_generic, r, "r_generic", "r")) {
std::cerr << "r_org = " << r_org << std::endl;
std::cerr << "CXXLAPACK: r_generic = " << r_generic << std::endl;
std::cerr << "F77LAPACK: r = " << r << std::endl;
failed = true;
}
if (! isIdentical(c_generic, c, "c_generic", "c")) {
std::cerr << "c_org = " << c_org << std::endl;
std::cerr << "CXXLAPACK: c_generic = " << c_generic << std::endl;
std::cerr << "F77LAPACK: c = " << piv << std::endl;
failed = true;
}
if (! isIdentical(B_generic, B, "B_generic", "B")) {
std::cerr << "B_org = " << B_org << std::endl;
std::cerr << "CXXLAPACK: B_generic = " << B_generic << std::endl;
std::cerr << "F77LAPACK: B = " << B << std::endl;
failed = true;
}
if (! isIdentical(X_generic, X, "X_generic", "X")) {
std::cerr << "X_org = " << X_org << std::endl;
std::cerr << "CXXLAPACK: X_generic = " << X_generic << std::endl;
std::cerr << "F77LAPACK: X = " << X << std::endl;
failed = true;
}
if (! isIdentical(rCond_generic, rCond, "rCond_generic", "rCond")) {
std::cerr << "rCond_org = " << rCond_org << std::endl;
std::cerr << "CXXLAPACK: rCond_generic = "
<< rCond_generic << std::endl;
std::cerr << "F77LAPACK: rCond = " << rCond << std::endl;
failed = true;
}
if (! isIdentical(fErr_generic, fErr, "fErr_generic", "fErr")) {
std::cerr << "fErr_org = " << fErr_org << std::endl;
std::cerr << "CXXLAPACK: fErr_generic = " << fErr_generic << std::endl;
std::cerr << "F77LAPACK: fErr = " << fErr << std::endl;
failed = true;
}
if (! isIdentical(bErr_generic, bErr, "bErr_generic", "bErr")) {
std::cerr << "bErr_org = " << bErr_org << std::endl;
std::cerr << "CXXLAPACK: bErr_generic = " << bErr_generic << std::endl;
std::cerr << "F77LAPACK: bErr = " << bErr << std::endl;
failed = true;
}
if (! isIdentical(work_generic, work, "work_generic", "work")) {
std::cerr << "work_org = " << work_org << std::endl;
std::cerr << "CXXLAPACK: work_generic = " << work_generic << std::endl;
std::cerr << "F77LAPACK: work = " << work << std::endl;
failed = true;
}
if (! isIdentical(iwork_generic, iwork, "iwork_generic", "iwork")) {
std::cerr << "iwork_org = " << iwork_org << std::endl;
std::cerr << "CXXLAPACK: iwork_generic = "
<< iwork_generic << std::endl;
std::cerr << "F77LAPACK: iwork = " << iwork << std::endl;
failed = true;
}
if (! isIdentical(info, info_, " info", "info_")) {
std::cerr << "CXXLAPACK: info = " << info << std::endl;
std::cerr << "F77LAPACK: info_ = " << info_ << std::endl;
failed = true;
}
if (failed) {
ASSERT(0);
}
# endif
return info;
}
} } // namespace lapack, flens
#endif // FLENS_LAPACK_GE_SVX_TCC
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