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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 DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO )
SUBROUTINE ZGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK, INFO )
*
* -- LAPACK routine (version 3.3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* -- April 2011 --
*/
#ifndef FLENS_LAPACK_GE_CON_TCC
#define FLENS_LAPACK_GE_CON_TCC 1
#include <flens/blas/blas.h>
#include <flens/lapack/lapack.h>
namespace flens { namespace lapack {
//== generic lapack implementation =============================================
namespace generic {
//-- (ge)con [real variant] ----------------------------------------------------
template <typename MA, typename NORMA, typename RCOND,
typename VWORK, typename VIWORK>
typename RestrictTo<IsReal<typename GeMatrix<MA>::ElementType>::value,
void>::Type
con_impl(Norm norm,
const GeMatrix<MA> &A,
const NORMA &normA,
RCOND &rCond,
DenseVector<VWORK> &work,
DenseVector<VIWORK> &iwork)
{
using std::abs;
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();
//
// Local Arrays
//
IndexType iSaveData[3] = {0, 0, 0};
DenseVectorView<IndexType>
iSave = typename DenseVectorView<IndexType>::Engine(3, iSaveData, 1);
//
// Quick return if possible
//
rCond = Zero;
if (n==0) {
rCond = One;
return;
} else if (normA==Zero) {
return;
}
const ElementType smallNum = lamch<ElementType>(SafeMin);
//
// Estimate the norm of inv(A).
//
ElementType normInvA = Zero;
bool normIn = false;
IndexType kase, kase1;
if (norm==OneNorm) {
kase1 = 1;
} else {
kase1 = 2;
}
kase = 0;
auto work1 = work(_(1,n));
auto work2 = work(_(n+1,2*n));
auto work3 = work(_(2*n+1,3*n));
auto work4 = work(_(3*n+1,4*n));
bool computeRCond = true;
while (true) {
lacn2(work2, work1, iwork, normInvA, kase, iSave);
if (kase==0) {
break;
}
ElementType sl, su;
if (kase==kase1) {
//
// Multiply by inv(L).
//
latrs(NoTrans, normIn, A.lowerUnit(), work1, sl, work3);
//
// Multiply by inv(U).
//
latrs(NoTrans, normIn, A.upper(), work1, su, work4);
} else {
//
// Multiply by inv(U**T).
//
latrs(Trans, normIn, A.upper(), work1, su, work4);
//
// Multiply by inv(L**T).
//
latrs(Trans, normIn, A.lowerUnit(), work1, sl, work3);
}
//
// Divide X by 1/(SL*SU) if doing so will not cause overflow.
//
const ElementType scale = sl*su;
normIn = true;
if (scale!=One) {
const IndexType ix = blas::iamax(work1);
if (scale<abs(work1(ix))*smallNum || scale==Zero) {
computeRCond = false;
break;
}
rscl(scale, work1);
}
}
//
// Compute the estimate of the reciprocal condition number.
//
if (computeRCond) {
if (normInvA!=Zero) {
rCond = (One/normInvA) / normA;
}
}
}
//-- (ge)con [complex variant] -------------------------------------------------
template <typename MA, typename NORMA, typename RCOND,
typename VWORK, typename VRWORK>
typename RestrictTo<IsComplex<typename GeMatrix<MA>::ElementType>::value,
void>::Type
con_impl(Norm norm,
const GeMatrix<MA> &A,
const NORMA &normA,
RCOND &rCond,
DenseVector<VWORK> &work,
DenseVector<VRWORK> &rwork)
{
using std::abs;
typedef typename GeMatrix<MA>::ElementType T;
typedef typename ComplexTrait<T>::PrimitiveType PT;
typedef typename GeMatrix<MA>::IndexType IndexType;
const PT Zero(0), One(1);
const Underscore<IndexType> _;
const IndexType n = A.numRows();
//
// Local Arrays
//
IndexType iSaveData[3] = {0, 0, 0};
DenseVectorView<IndexType>
iSave = typename DenseVectorView<IndexType>::Engine(3, iSaveData, 1);
//
// Quick return if possible
//
rCond = Zero;
if (n==0) {
rCond = One;
return;
} else if (normA==Zero) {
return;
}
const PT smallNum = lamch<PT>(SafeMin);
//
// Estimate the norm of inv(A).
//
PT normInvA = Zero;
bool normIn = false;
IndexType kase, kase1;
if (norm==OneNorm) {
kase1 = 1;
} else {
kase1 = 2;
}
kase = 0;
auto work1 = work(_(1,n));
auto work2 = work(_(n+1,2*n));
auto rwork1 = rwork(_(1 , n));
auto rwork2 = rwork(_(n+1,2*n));
bool computeRCond = true;
while (true) {
lacn2(work2, work1, normInvA, kase, iSave);
if (kase==0) {
break;
}
PT sl, su;
if (kase==kase1) {
//
// Multiply by inv(L).
//
latrs(NoTrans, normIn, A.lowerUnit(), work1, sl, rwork1);
//
// Multiply by inv(U).
//
latrs(NoTrans, normIn, A.upper(), work1, su, rwork2);
} else {
//
// Multiply by inv(U**T).
//
latrs(ConjTrans, normIn, A.upper(), work1, su, rwork2);
//
// Multiply by inv(L**T).
//
latrs(ConjTrans, normIn, A.lowerUnit(), work1, sl, rwork1);
}
//
// Divide X by 1/(SL*SU) if doing so will not cause overflow.
//
const PT scale = sl*su;
normIn = true;
if (scale!=One) {
const IndexType ix = blas::iamax(work1);
if (scale<(abs(real(work1(ix)))+abs(imag(work1(ix))))*smallNum
|| scale==Zero)
{
computeRCond = false;
break;
}
rscl(scale, work1);
}
}
//
// Compute the estimate of the reciprocal condition number.
//
if (computeRCond) {
if (normInvA!=Zero) {
rCond = (One/normInvA) / normA;
}
}
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
//-- (ge)con [real and complex variant] ----------------------------------------
template <typename MA, typename NORMA, typename RCOND,
typename VWORK, typename VWORK2>
void
con_impl(Norm norm,
const GeMatrix<MA> &A,
const NORMA &normA,
RCOND &rCond,
DenseVector<VWORK> &work,
DenseVector<VWORK2> &work2)
{
typedef typename GeMatrix<MA>::IndexType IndexType;
cxxlapack::gecon<IndexType>(char(norm),
A.numRows(), A.data(), A.leadingDimension(),
normA, rCond, work.data(), work2.data());
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
//-- (ge)con [real variant] ----------------------------------------------------
template <typename MA, typename NORMA, typename RCOND,
typename VWORK, typename VIWORK>
typename RestrictTo<IsRealGeMatrix<MA>::value
&& IsNotComplex<NORMA>::value
&& IsNotComplex<RCOND>::value
&& IsRealDenseVector<VWORK>::value
&& IsIntegerDenseVector<VIWORK>::value,
void>::Type
con(Norm norm,
const MA &A,
const NORMA &normA,
RCOND &rCond,
VWORK &&work,
VIWORK &&iwork)
{
LAPACK_DEBUG_OUT("(ge)con [real]");
//
// Test the input parameters
//
# ifndef NDEBUG
typedef typename MA::IndexType IndexType;
ASSERT(norm==InfinityNorm || norm==OneNorm);
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
ASSERT(A.numRows()==A.numCols());
const IndexType n = A.numRows();
ASSERT(work.firstIndex()==1);
ASSERT(work.length()==4*n);
ASSERT(iwork.firstIndex()==1);
ASSERT(iwork.length()==n);
# endif
# ifdef CHECK_CXXLAPACK
//
// Remove references from rvalue types
//
typedef typename RemoveRef<VWORK>::Type VectorWork;
typedef typename RemoveRef<VIWORK>::Type VectorIWork;
//
// Make copies of output arguments
//
RCOND rCond_org = rCond;
typename VectorWork::NoView work_org = work;
typename VectorIWork::NoView iwork_org = iwork;
# endif
//
// Call implementation
//
LAPACK_SELECT::con_impl(norm, A, normA, rCond, work, iwork);
# ifdef CHECK_CXXLAPACK
//
// Compare results
//
RCOND rCond_generic = rCond;
typename VectorWork::NoView work_generic = work;
typename VectorIWork::NoView iwork_generic = iwork;
rCond = rCond_org;
work = work_org;
iwork = iwork_org;
external::con_impl(norm, A, normA, rCond, work, iwork);
bool failed = false;
if (! isIdentical(rCond_generic, rCond, "rCond_generic", "rCond")) {
std::cerr << "CXXLAPACK: rCond_generic = "
<< rCond_generic << std::endl;
std::cerr << "F77LAPACK: rCond = " << rCond << std::endl;
failed = true;
}
if (! isIdentical(work_generic, work, "work_generic", "work")) {
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 << "CXXLAPACK: iwork_generic = "
<< iwork_generic << std::endl;
std::cerr << "F77LAPACK: iwork = " << iwork << std::endl;
failed = true;
}
if (failed) {
ASSERT(0);
}
# endif
}
//-- (ge)con [complex variant] -------------------------------------------------
template <typename MA, typename NORMA, typename RCOND,
typename VWORK, typename VRWORK>
typename RestrictTo<IsComplexGeMatrix<MA>::value
&& IsNotComplex<NORMA>::value
&& IsNotComplex<RCOND>::value
&& IsComplexDenseVector<VWORK>::value
&& IsRealDenseVector<VRWORK>::value,
void>::Type
con(Norm norm,
const MA &A,
const NORMA &normA,
RCOND &rCond,
VWORK &&work,
VRWORK &&rwork)
{
LAPACK_DEBUG_OUT("(ge)con [complex]");
//
// Test the input parameters
//
# ifndef NDEBUG
typedef typename MA::IndexType IndexType;
ASSERT(norm==InfinityNorm || norm==OneNorm);
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
ASSERT(A.numRows()==A.numCols());
const IndexType n = A.numRows();
ASSERT(work.firstIndex()==1);
ASSERT(work.length()==2*n);
ASSERT(rwork.firstIndex()==1);
ASSERT(rwork.length()==2*n);
# endif
# ifdef CHECK_CXXLAPACK
//
// Remove references from rvalue types
//
typedef typename RemoveRef<VWORK>::Type VectorWork;
typedef typename RemoveRef<VRWORK>::Type VectorRWork;
//
// Make copies of output arguments
//
RCOND rCond_org = rCond;
typename VectorWork::NoView work_org = work;
typename VectorRWork::NoView rwork_org = rwork;
# endif
//
// Call implementation
//
LAPACK_SELECT::con_impl(norm, A, normA, rCond, work, rwork);
# ifdef CHECK_CXXLAPACK
//
// Compare results
//
RCOND rCond_generic = rCond;
typename VectorWork::NoView work_generic = work;
typename VectorRWork::NoView rwork_generic = rwork;
rCond = rCond_org;
work = work_org;
rwork = rwork_org;
external::con_impl(norm, A, normA, rCond, work, rwork);
bool failed = false;
if (! isIdentical(rCond_generic, rCond, "rCond_generic", "rCond")) {
std::cerr << "CXXLAPACK: rCond_generic = "
<< rCond_generic << std::endl;
std::cerr << "F77LAPACK: rCond = " << rCond << std::endl;
failed = true;
}
if (! isIdentical(work_generic, work, "work_generic", "work")) {
std::cerr << "CXXLAPACK: work_generic = "
<< work_generic << std::endl;
std::cerr << "F77LAPACK: work = " << work << std::endl;
failed = true;
}
if (! isIdentical(rwork_generic, rwork, "rwork_generic", "rwork")) {
std::cerr << "CXXLAPACK: rwork_generic = "
<< rwork_generic << std::endl;
std::cerr << "F77LAPACK: rwork = " << rwork << std::endl;
failed = true;
}
if (failed) {
ASSERT(0);
}
# endif
}
} } // namespace lapack, flens
#endif // FLENS_LAPACK_GE_CON_TCC
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