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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 DGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM,
$ WR, WI, VS, LDVS, RCONDE, RCONDV, WORK, LWORK,
$ IWORK, LIWORK, BWORK, INFO )
SUBROUTINE ZGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,
$ VS, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK,
$ BWORK, INFO )
*
* -- LAPACK driver routine (version 3.2.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2010
*/
#ifndef FLENS_LAPACK_GE_ESX_TCC
#define FLENS_LAPACK_GE_ESX_TCC 1
#include <cxxstd/cmath.h>
#include <flens/blas/blas.h>
#include <flens/lapack/lapack.h>
namespace flens { namespace lapack {
//== generic lapack implementation =============================================
namespace generic {
//-- (ge)esx_wsq [real variant] ------------------------------------------------
template <typename MA>
Quadruple<typename GeMatrix<MA>::IndexType>
esx_wsq_impl(bool computeSchurVectors,
SENSE::Sense sense,
const GeMatrix<MA> &A)
{
using std::max;
typedef typename GeMatrix<MA>::ElementType T;
typedef typename GeMatrix<MA>::IndexType IndexType;
const IndexType n = A.numRows();
const bool wantSN = (sense==SENSE::None);
const bool wantSV = (sense==SENSE::InvariantSubspaceOnly);
const bool wantSB = (sense==SENSE::Both);
IndexType minWork, maxWork, liWork, lWork;
liWork = 1;
if (n==0) {
minWork = 1;
maxWork = 1;
lWork = 1;
} else {
maxWork = 2*n + n*ilaenv<T>(1, "GEHRD", "", n, 1, n, 0);
minWork = 3*n;
HSEQR::ComputeZ computeZ = (computeSchurVectors) ? HSEQR::NoInit
: HSEQR::No;
IndexType hsWork = hseqr_wsq(HSEQR::Schur, computeZ,
IndexType(1), n, A);
if (!computeSchurVectors) {
maxWork = max(maxWork, n + hsWork);
} else {
maxWork = max(maxWork,
2*n + (n-1)*ilaenv<T>(1, "ORGHR", "", n, 1, n));
maxWork = max(maxWork, n +hsWork);
}
lWork = maxWork;
if (!wantSN) {
lWork = max(lWork, n + (n*n)/2);
}
if (wantSV || wantSB) {
liWork = (n*n)/4;
}
}
return Quadruple<IndexType>(minWork, maxWork, lWork, liWork);
}
//-- (ge)esx [real variant] ----------------------------------------------------
template <typename SelectFunction, typename MA, typename IndexType,
typename VWR, typename VWI, typename MVS,
typename RCONDE, typename RCONDV,
typename VWORK, typename VIWORK, typename BWORK>
IndexType
esx_impl(bool computeSchurVectors,
bool sortEigenvalues,
SelectFunction selectFunction,
SENSE::Sense sense,
GeMatrix<MA> &A,
IndexType &sDim,
DenseVector<VWR> &wr,
DenseVector<VWI> &wi,
GeMatrix<MVS> &VS,
RCONDE &rCondE,
RCONDV &rCondV,
DenseVector<VWORK> &work,
DenseVector<VIWORK> &iWork,
DenseVector<BWORK> &bWork)
{
using std::sqrt;
typedef typename GeMatrix<MA>::ElementType T;
const Underscore<IndexType> _;
const IndexType n = A.numRows();
const T Zero(0), One(1);
//
// .. Local Arrays ..
// this array is used to save variables between calls to lacn2
//
T dum_[1];
DenseVectorView<T> dum = typename DenseVectorView<T>::Engine(1, dum_);
//
// Test the input arguments
//
IndexType info = 0;
const bool wantSN = (sense==SENSE::None);
const bool wantSV = (sense==SENSE::InvariantSubspaceOnly);
const bool wantSB = (sense==SENSE::Both);
//
// Compute workspace
// (Note: Comments in the code beginning "RWorkspace:" describe the
// minimal amount of real workspace needed at that point in the
// code, as well as the preferred amount for good performance.
// IWorkspace refers to integer workspace.
// NB refers to the optimal block size for the immediately
// following subroutine, as returned by ILAENV.
// HSWORK refers to the workspace preferred by DHSEQR, as
// calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
// the worst case.
// If SENSE = 'E', 'V' or 'B', then the amount of workspace needed
// depends on SDIM, which is computed by the routine DTRSEN later
// in the code.)
//
Quadruple<IndexType> wsQuery = esx_wsq(computeSchurVectors, sense, A);
IndexType minWork = wsQuery.first;
IndexType maxWork = wsQuery.second;
IndexType lWork = wsQuery.third;
IndexType liWork = wsQuery.forth;
if (work.length()!=0 && work.length()<minWork) {
ASSERT(0);
} else if (work.length()==0) {
work.resize(lWork);
}
work(1) = lWork;
if (iWork.length()!=0 && iWork.length()<liWork) {
ASSERT(0);
} else if (iWork.length()==0) {
iWork.resize(liWork);
}
iWork(1) = liWork;
//
// Quick return if possible
//
if (n==0) {
sDim = 0;
return info;
}
//
// Get machine constants
//
const T eps = lamch<T>(Precision);
T smallNum = lamch<T>(SafeMin);
T bigNum = One / smallNum;
labad(smallNum, bigNum);
smallNum = sqrt(smallNum) / eps;
bigNum = One / smallNum;
//
// Scale A if max element outside range [SMLNUM,BIGNUM]
//
const T normA = lan(MaximumNorm, A);
bool scaleA = false;
T cScale;
if (normA>Zero && normA<smallNum) {
scaleA = true;
cScale = smallNum;
} else if (normA>bigNum) {
scaleA = true;
cScale = bigNum;
}
if (scaleA) {
lascl(LASCL::FullMatrix, IndexType(0), IndexType(0), normA, cScale, A);
}
//
// Permute the matrix to make it more nearly triangular
// (RWorkspace: need N)
//
IndexType iBal = 1;
auto balWork = work(_(iBal,iBal+n-1));
IndexType iLo, iHi;
bal(BALANCE::PermuteOnly, A, iLo, iHi, balWork);
//
// Reduce to upper Hessenberg form
// (RWorkspace: need 3*N, prefer 2*N+N*NB)
//
IndexType iTau = iBal + n;
IndexType iWrk = iTau + n;
lWork = work.length();
auto tau = work(_(iTau, iTau+n-2));
auto hrdWork = work(_(iWrk, lWork));
hrd(iLo, iHi, A, tau, hrdWork);
if (computeSchurVectors) {
//
// Copy Householder vectors to VS
//
VS.lower() = A.lower();
//
// Generate orthogonal matrix in VS
// (RWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
//
orghr(iLo, iHi, VS, tau, hrdWork);
}
sDim = 0;
//
// Perform QR iteration, accumulating Schur vectors in VS if desired
// (RWorkspace: need N+1, prefer N+HSWORK (see comments) )
//
iWrk = iTau;
auto hseqrWork = work(_(iWrk, lWork));
HSEQR::ComputeZ computeZ = (computeSchurVectors) ? HSEQR::NoInit
: HSEQR::No;
IndexType iEval = hseqr(HSEQR::Schur, computeZ, iLo, iHi,
A, wr, wi, VS, hseqrWork);
if (iEval>0) {
info = iEval;
}
//
// Sort eigenvalues if desired
//
if (sortEigenvalues && info==0) {
if (scaleA) {
lascl(LASCL::FullMatrix, IndexType(0), IndexType(0),
cScale, normA, wr);
lascl(LASCL::FullMatrix, IndexType(0), IndexType(0),
cScale, normA, wi);
}
for (IndexType i=1; i<=n; ++i) {
bWork(i) = selectFunction(wr(i), wi(i));
}
//
// Reorder eigenvalues, transform Schur vectors, and compute
// reciprocal condition numbers
// (RWorkspace: if SENSE is not 'N', need N+2*SDIM*(N-SDIM)
// otherwise, need N )
// (IWorkspace: if SENSE is 'V' or 'B', need SDIM*(N-SDIM)
// otherwise, need 0 )
//
IndexType iCond = trsen(TRSEN::Job(sense), computeSchurVectors, bWork,
A, VS, wr, wi, sDim, rCondE, rCondV,
hseqrWork, iWork);
if (!wantSN) {
maxWork = max(maxWork, n+2*sDim*(n-sDim));
}
if (iCond>0) {
//
// DTRSEN failed to reorder or to restore standard Schur form
//
info = iCond + n;
}
}
if (computeSchurVectors) {
//
// Undo balancing
// (Workspace: need N)
//
bak(BALANCE::PermuteOnly, Right, iLo, iHi, balWork, VS);
}
if (scaleA) {
//
// Undo scaling for the Schur form of A
//
lascl(LASCL::UpperHessenberg, IndexType(0), IndexType(0),
cScale, normA, A);
wr = A.diag(0);
if ((wantSV || wantSB) && info==0) {
dum(1) = rCondV;
lascl(LASCL::FullMatrix, IndexType(0), IndexType(0),
cScale, normA, dum);
rCondV = dum(1);
}
if (cScale==smallNum) {
//
// If scaling back towards underflow, adjust WI if an
// offdiagonal element of a 2-by-2 block in the Schur form
// underflows.
//
IndexType i1, i2;
if (iEval>0) {
i1 = iEval + 1;
i2 = iHi - 1;
lascl(LASCL::FullMatrix, IndexType(0), IndexType(0),
cScale, normA, wi(_(1,iLo-1)));
} else if (sortEigenvalues) {
i1 = 1;
i2 = n - 1;
} else {
i1 = iLo;
i2 = iHi - 1;
}
IndexType iNext = i1-1;
for (IndexType i=i1; i<=i2; ++i) {
if (i<iNext) {
continue;
}
if (wi(i)==Zero) {
iNext = i + 1;
} else {
if (A(i+1,i)==Zero) {
wi(i) = Zero;
wi(i+1) = Zero;
} else if (A(i+1,i)!=Zero && A(i,i+1)==Zero) {
wi(i) = Zero;
wi(i+1) = Zero;
if (i>1) {
blas::swap(A(_(1,i-1),i), A(_(1,i-1),i+1));
}
if (n>i+1) {
blas::swap(A(i,_(i+2,n)), A(i+1,_(i+2,n)));
}
blas::swap(VS(_,i), VS(_,i+1));
A(i,i+1) = A(i+1,i);
A(i+1,i) = Zero;
}
iNext = i + 2;
}
}
}
lascl(LASCL::FullMatrix, IndexType(0), IndexType(0),
cScale, normA, wi(_(iEval+1,n)));
}
if (sortEigenvalues && info==0) {
//
// Check if reordering successful
//
bool lastSelect = true;
bool last2Select = true;
sDim = 0;
IndexType ip = 0;
for (IndexType i=1; i<=n; ++i) {
bool currentSelect = selectFunction(wr(i), wi(i));
if (wi(i)==Zero) {
if (currentSelect) {
++sDim;
}
ip = 0;
if (currentSelect && !lastSelect) {
info = n + 2;
}
} else {
if (ip==1) {
//
// Last eigenvalue of conjugate pair
//
currentSelect = currentSelect || lastSelect;
lastSelect = currentSelect;
if (currentSelect) {
sDim += 2;
}
ip = -1;
if (currentSelect && !last2Select) {
info = n + 2;
}
} else {
//
// First eigenvalue of conjugate pair
//
ip = 1;
}
}
last2Select = lastSelect;
lastSelect = currentSelect;
}
}
work(1) = maxWork;
if (wantSV || wantSB) {
iWork(1) = max(IndexType(1), sDim*(n-sDim));
} else {
iWork(1) = 1;
}
return info;
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
//-- (ge)esx_wsq [worksize query real variant] ---------------------------------
template <typename MA>
typename RestrictTo<IsNotComplex<typename MA::ElementType>::value,
Quadruple<typename MA::IndexType> >::Type
esx_wsq_impl(bool computeSchurVectors,
SENSE::Sense sense,
const GeMatrix<MA> &A)
{
using std::max;
typedef typename GeMatrix<MA>::ElementType T;
typedef typename GeMatrix<MA>::IndexType IndexType;
const IndexType n = A.numRows();
//const bool wantSN = (sense==SENSE::None);
const bool wantSV = (sense==SENSE::InvariantSubspaceOnly);
const bool wantSB = (sense==SENSE::Both);
IndexType minWork, liWork;
liWork = 1;
if (n==0) {
minWork = 1;
} else {
minWork = 3*n;
if (wantSV || wantSB) {
liWork = (n*n)/4;
}
}
//
// Compute optimal size for work
//
const IndexType LDVS = max(IndexType(1), A.numRows());
IndexType IDUMMY, IWORK;
T DUMMY;
const IndexType LWORK = -1;
T WORK;
cxxlapack::geesx<IndexType>(computeSchurVectors ? 'V' : 'N',
'S',
0,
getF77Char(sense),
n,
0,
A.leadingDimension(),
IDUMMY,
&DUMMY,
&DUMMY,
&DUMMY,
LDVS,
DUMMY,
DUMMY,
&WORK,
LWORK,
&IWORK,
IDUMMY,
&IDUMMY);
return Quadruple<IndexType>(minWork, WORK, WORK, liWork);
}
//-- (ge)esx_wsq [worksize query complex variant] ------------------------------
template <typename MA>
typename RestrictTo<IsComplex<typename MA::ElementType>::value,
Triple<typename MA::IndexType> >::Type
esx_wsq_impl(bool computeSchurVectors,
SENSE::Sense sense,
const GeMatrix<MA> &A)
{
using std::max;
typedef typename GeMatrix<MA>::ElementType T;
typedef typename ComplexTrait<T>::PrimitiveType RT;
typedef typename GeMatrix<MA>::IndexType IndexType;
const IndexType n = A.numRows();
//const bool wantSN = (sense==SENSE::None);
//const bool wantSV = (sense==SENSE::InvariantSubspaceOnly);
//const bool wantSB = (sense==SENSE::Both);
IndexType minWork;
if (n==0) {
minWork = 1;
} else {
minWork = 2*n;
}
//
// Compute optimal size for work
//
const IndexType LDVS = max(IndexType(1), A.numRows());
IndexType IDUMMY;
T DUMMY;
RT RDUMMY;
const IndexType LWORK = -1;
T WORK;
cxxlapack::geesx<IndexType>(computeSchurVectors ? 'V' : 'N',
'S',
0,
getF77Char(sense),
n,
0,
A.leadingDimension(),
IDUMMY,
&DUMMY,
&DUMMY,
LDVS,
RDUMMY,
RDUMMY,
&DUMMY,
LWORK,
&RDUMMY,
&IDUMMY);
return Triple<IndexType>(minWork, WORK.real(), WORK.real());
}
//-- (ge)esx [real variant] ----------------------------------------------------
template <typename SelectFunction, typename MA, typename IndexType,
typename VWR, typename VWI, typename MVS,
typename RCONDE, typename RCONDV,
typename VWORK, typename VIWORK, typename BWORK>
IndexType
esx_impl(bool computeSchurVectors,
bool sortEigenvalues,
SelectFunction selectFunction,
SENSE::Sense sense,
GeMatrix<MA> &A,
IndexType &sDim,
DenseVector<VWR> &wr,
DenseVector<VWI> &wi,
GeMatrix<MVS> &VS,
RCONDE &rCondE,
RCONDV &rCondV,
DenseVector<VWORK> &work,
DenseVector<VIWORK> &iWork,
DenseVector<BWORK> &bWork)
{
if (work.length()==0 || iWork.length()==0) {
const auto ws = esx_wsq_impl(computeSchurVectors, sense, A);
if (work.length()==0) {
work.resize(ws.third, 1);
}
if (iWork.length()==0) {
iWork.resize(ws.forth, 1);
}
}
IndexType info;
info = cxxlapack::geesx<IndexType>(computeSchurVectors ? 'V' : 'N',
sortEigenvalues ? 'S' : 'N',
selectFunction.select,
getF77Char(sense),
A.numRows(),
A.data(),
A.leadingDimension(),
sDim,
wr.data(),
wi.data(),
VS.data(),
VS.leadingDimension(),
rCondE,
rCondV,
work.data(),
work.length(),
iWork.data(),
iWork.length(),
bWork.data());
ASSERT(info>=0);
return info;
}
//-- (ge)esx [complex variant] -------------------------------------------------
template <typename SelectFunction, typename MA, typename IndexType,
typename VW, typename MVS, typename RCONDE, typename RCONDV,
typename VWORK, typename VRWORK, typename BWORK>
IndexType
esx_impl(bool computeSchurVectors,
bool sortEigenvalues,
SelectFunction selectFunction,
SENSE::Sense sense,
GeMatrix<MA> &A,
IndexType &sDim,
DenseVector<VW> &w,
GeMatrix<MVS> &VS,
RCONDE &rCondE,
RCONDV &rCondV,
DenseVector<VWORK> &work,
DenseVector<VRWORK> &rWork,
DenseVector<BWORK> &bWork)
{
if (work.length()==0) {
const auto ws = esx_wsq_impl(computeSchurVectors, sense, A);
work.resize(IndexType(ws.third), 1);
}
IndexType info;
info = cxxlapack::geesx<IndexType>(computeSchurVectors ? 'V' : 'N',
sortEigenvalues ? 'S' : 'N',
selectFunction.select,
getF77Char(sense),
A.numRows(),
A.data(),
A.leadingDimension(),
sDim,
w.data(),
VS.data(),
VS.leadingDimension(),
rCondE,
rCondV,
work.data(),
work.length(),
rWork.data(),
bWork.data());
ASSERT(info>=0);
return info;
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
//-- (ge)esx [real variant] ----------------------------------------------------
template <typename SelectFunction, typename MA, typename IndexType,
typename VWR, typename VWI, typename MVS,
typename RCONDE, typename RCONDV,
typename VWORK, typename VIWORK, typename VBWORK>
typename RestrictTo<IsRealGeMatrix<MA>::value
&& IsInteger<IndexType>::value
&& IsRealDenseVector<VWR>::value
&& IsRealDenseVector<VWI>::value
&& IsRealGeMatrix<MVS>::value
&& IsNotComplex<RCONDE>::value
&& IsNotComplex<RCONDV>::value
&& IsRealDenseVector<VWORK>::value
&& IsRealDenseVector<VIWORK>::value
&& IsRealDenseVector<VBWORK>::value,
IndexType>::Type
esx(bool computeSchurVectors,
bool sortEigenvalues,
SelectFunction selectFunction,
SENSE::Sense sense,
MA &&A,
IndexType &sDim,
VWR &&wr,
VWI &&wi,
MVS &&VS,
RCONDE &rCondE,
RCONDV &rCondV,
VWORK &&work,
VIWORK &&iWork,
VBWORK &&bWork)
{
LAPACK_DEBUG_OUT("(ge)esx [real]");
//
// Remove references from rvalue types
//
# ifdef CHECK_CXXLAPACK
typedef typename RemoveRef<MA>::Type MatrixA;
typedef typename RemoveRef<VWR>::Type VectorWR;
typedef typename RemoveRef<VWI>::Type VectorWI;
typedef typename RemoveRef<MVS>::Type MatrixVS;
typedef typename RemoveRef<VWORK>::Type VectorWork;
typedef typename RemoveRef<VIWORK>::Type VectorIWork;
typedef typename RemoveRef<VBWORK>::Type VectorBWork;
# endif
//
// Test the input parameters
//
IndexType n = A.numRows();
# ifndef NDEBUG
ASSERT(A.numRows()==A.numCols());
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
ASSERT(work.firstIndex()==1);
ASSERT(iWork.firstIndex()==1);
ASSERT(bWork.firstIndex()==1);
ASSERT(wr.firstIndex()==1);
ASSERT(wr.length()==0 || wr.length()==n);
ASSERT(wi.firstIndex()==1);
ASSERT(wi.length()==0 || wi.length()==n);
if (computeSchurVectors) {
ASSERT(VS.numRows()==VS.numCols());
ASSERT(VS.numRows()==0 || VS.numRows()==n);
ASSERT(VS.firstRow()==1);
ASSERT(VS.firstCol()==1);
}
if (sortEigenvalues) {
ASSERT(bWork.firstIndex()==1);
ASSERT(bWork.length()==0 || bWork.length()==n);
}
# endif
//
// Resize output arguments if they are empty and needed
//
if (wr.length()==0) {
wr.resize(n, 1);
}
if (wi.length()==0) {
wi.resize(n, 1);
}
if (computeSchurVectors && VS.numRows()==0) {
VS.resize(n, n, 1, 1);
}
if (sortEigenvalues && bWork.length()==0) {
bWork.resize(n, 1);
}
//
// Make copies of output arguments
//
# ifdef CHECK_CXXLAPACK
typename MatrixA::NoView A_org = A;
IndexType sDim_org = sDim;
typename VectorWR::NoView wr_org = wr;
typename VectorWI::NoView wi_org = wi;
typename MatrixVS::NoView VS_org = VS;
RCONDE rCondE_org = rCondE;
RCONDV rCondV_org = rCondV;
typename VectorWork::NoView work_org = work;
typename VectorIWork::NoView iWork_org = iWork;
typename VectorBWork::NoView bWork_org = bWork;
# endif
//
// Call implementation
//
IndexType result = LAPACK_SELECT::esx_impl(computeSchurVectors,
sortEigenvalues,
selectFunction,
sense,
A,
sDim,
wr,
wi,
VS,
rCondE,
rCondV,
work,
iWork,
bWork);
# ifdef CHECK_CXXLAPACK
//
// Make copies of results computed by the generic implementation
//
typename MatrixA::NoView A_generic = A;
IndexType sDim_generic = sDim;
typename VectorWR::NoView wr_generic = wr;
typename VectorWI::NoView wi_generic = wi;
typename MatrixVS::NoView VS_generic = VS;
RCONDE rCondE_generic = rCondE;
RCONDV rCondV_generic = rCondV;
typename VectorWork::NoView work_generic = work;
typename VectorIWork::NoView iWork_generic = iWork;
typename VectorBWork::NoView bWork_generic = bWork;
//
// restore output arguments
//
A = A_org;
sDim = sDim_org;
wr = wr_org;
wi = wi_org;
VS = VS_org;
rCondE = rCondE_org;
rCondV = rCondV_org;
work = work_org;
iWork = iWork_org;
bWork = bWork_org;
//
// Compare generic results with results from the native implementation
//
IndexType result_ = external::esx_impl(computeSchurVectors,
sortEigenvalues,
selectFunction,
sense,
A,
sDim,
wr,
wi,
VS,
rCondE,
rCondV,
work,
iWork,
bWork);
bool failed = false;
if (! isIdentical(A_generic, A, "A_generic", "A")) {
std::cerr << "CXXLAPACK: A_generic = " << A_generic << std::endl;
std::cerr << "F77LAPACK: A = " << A << std::endl;
failed = true;
}
if (! isIdentical(sDim_generic, sDim, "sDim_generic", "sDim")) {
std::cerr << "CXXLAPACK: sDim_generic = " << sDim_generic << std::endl;
std::cerr << "F77LAPACK: sDim = " << sDim << std::endl;
failed = true;
}
if (! isIdentical(wr_generic, wr, "wr_generic", "wr")) {
std::cerr << "CXXLAPACK: wr_generic = " << wr_generic << std::endl;
std::cerr << "F77LAPACK: wr = " << wr << std::endl;
failed = true;
}
if (! isIdentical(wi_generic, wi, "wi_generic", "wi")) {
std::cerr << "CXXLAPACK: wi_generic = " << wi_generic << std::endl;
std::cerr << "F77LAPACK: wi = " << wi << std::endl;
failed = true;
}
if (! isIdentical(VS_generic, VS, "VS_generic", "VS")) {
std::cerr << "CXXLAPACK: VS_generic = " << VS_generic << std::endl;
std::cerr << "F77LAPACK: VS = " << VS << std::endl;
failed = true;
}
if (! isIdentical(rCondE_generic, rCondE, "rCondE_generic", "rCondE")) {
std::cerr << "CXXLAPACK: rCondE_generic = "
<< rCondE_generic << std::endl;
std::cerr << "F77LAPACK: rCondE = " << rCondE << std::endl;
failed = true;
}
if (! isIdentical(rCondV_generic, rCondV, "rCondV_generic", "rCondV")) {
std::cerr << "CXXLAPACK: rCondV_generic = "
<< rCondV_generic << std::endl;
std::cerr << "F77LAPACK: rCondV = " << rCondV << 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 (! isIdentical(bWork_generic, bWork, "bWork_generic", "bWork")) {
std::cerr << "CXXLAPACK: bWork_generic = "
<< bWork_generic << std::endl;
std::cerr << "F77LAPACK: bWork = " << bWork << std::endl;
failed = true;
}
if (! isIdentical(result, result_, " result", "result_")) {
std::cerr << "CXXLAPACK: result = " << result << std::endl;
std::cerr << "F77LAPACK: result_ = " << result_ << std::endl;
failed = true;
}
if (failed) {
ASSERT(0);
} else {
// std::cerr << "passed: esx.tcc" << std::endl;
}
# endif
return result;
}
#ifdef USE_CXXLAPACK
//-- (ge)esx [complex variant] -------------------------------------------------
template <typename SelectFunction, typename MA, typename IndexType,
typename VW, typename MVS, typename RCONDE, typename RCONDV,
typename VWORK, typename VRWORK, typename VBWORK>
typename RestrictTo<IsComplexGeMatrix<MA>::value
&& IsInteger<IndexType>::value
&& IsComplexDenseVector<VW>::value
&& IsComplexGeMatrix<MVS>::value
&& IsNotComplex<RCONDE>::value
&& IsNotComplex<RCONDV>::value
&& IsComplexDenseVector<VWORK>::value
&& IsRealDenseVector<VRWORK>::value
&& IsRealDenseVector<VBWORK>::value,
IndexType>::Type
esx(bool computeSchurVectors,
bool sortEigenvalues,
SelectFunction selectFunction,
SENSE::Sense sense,
MA &&A,
IndexType &sDim,
VW &&w,
MVS &&VS,
RCONDE &rCondE,
RCONDV &rCondV,
VWORK &&work,
VRWORK &&rWork,
VBWORK &&bWork)
{
LAPACK_DEBUG_OUT("(ge)esx [complex]");
IndexType n = A.numRows();
//
// Test the input parameters
//
# ifndef NDEBUG
ASSERT(A.numRows()==A.numCols());
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
ASSERT(work.firstIndex()==1);
ASSERT(rWork.firstIndex()==1);
ASSERT(bWork.firstIndex()==1);
ASSERT(w.firstIndex()==1);
ASSERT(w.length()==0 || w.length()==n);
if (computeSchurVectors) {
ASSERT(VS.numRows()==VS.numCols());
ASSERT(VS.numRows()==0 || VS.numRows()==n);
ASSERT(VS.firstRow()==1);
ASSERT(VS.firstCol()==1);
}
if (sortEigenvalues) {
ASSERT(bWork.firstIndex()==1);
ASSERT(bWork.length()==0 || bWork.length()==n);
}
# endif
//
// Resize output arguments if they are empty and needed
//
if (w.length()==0) {
w.resize(n, 1);
}
if (computeSchurVectors && VS.numRows()==0) {
VS.resize(n, n, 1, 1);
}
if (sortEigenvalues && bWork.length()==0) {
bWork.resize(n, 1);
}
//
// Call external implementation
//
IndexType result = external::esx_impl(computeSchurVectors,
sortEigenvalues,
selectFunction,
sense,
A,
sDim,
w,
VS,
rCondE,
rCondV,
work,
rWork,
bWork);
return result;
}
#endif // USE_CXXLAPACK
//-- (ge)esx [worksize query, real variant] ------------------------------------
template <typename MA>
typename RestrictTo<IsNotComplex<typename MA::ElementType>::value,
Quadruple<typename MA::IndexType> >::Type
esx_wsq(bool computeSchurVectors,
SENSE::Sense sense,
const GeMatrix<MA> &A)
{
LAPACK_DEBUG_OUT("ev_wsq [real]");
//
// Test the input parameters
//
# ifndef NDEBUG
ASSERT(A.numRows()==A.numCols());
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
# endif
//
// Call implementation
//
const auto ws = LAPACK_SELECT::esx_wsq_impl(computeSchurVectors, sense, A);
# ifdef CHECK_CXXLAPACK
//
// Compare results
//
const auto ws_ = external::esx_wsq_impl(computeSchurVectors, sense, A);
if (! isIdentical(ws.first, ws_.first, "ws.first", "ws_.first")) {
ASSERT(0);
}
if (! isIdentical(ws.third, ws_.third, "ws.third", "ws_.third")) {
ASSERT(0);
}
if (! isIdentical(ws.forth, ws_.forth, "ws.forth", "ws_.forth")) {
ASSERT(0);
}
# endif
return ws;
}
#ifdef USE_CXXLAPACK
//-- (ge)esx [worksize query, complex variant] ---------------------------------
template <typename MA>
typename RestrictTo<IsComplex<typename MA::ElementType>::value,
Triple<typename MA::IndexType> >::Type
esx_wsq(bool computeSchurVectors,
SENSE::Sense sense,
const GeMatrix<MA> &A)
{
LAPACK_DEBUG_OUT("ev_wsq [complex]");
//
// Test the input parameters
//
# ifndef NDEBUG
ASSERT(A.numRows()==A.numCols());
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
# endif
//
// Call external implementation
//
const auto ws = external::esx_wsq_impl(computeSchurVectors, sense, A);
return ws;
}
#endif // USE_CXXLAPACK
} } // namespace lapack, flens
#endif // FLENS_LAPACK_GE_ESX_TCC
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