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/*
* Copyright (c) 2012, Klaus Pototzky
*
* 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 ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
$ INFO )
*
* -- LAPACK driver 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_HE_EV_TCC
#define FLENS_LAPACK_HE_EV_TCC 1
#include <flens/blas/blas.h>
#include <flens/lapack/lapack.h>
namespace flens { namespace lapack {
//== generic lapack implementation =============================================
namespace generic {
//-- (he)ev [worksize query hermitian variant] ---------------------------------
template <typename MA>
typename RestrictTo<IsComplex<typename MA::ElementType>::value,
Pair<typename MA::IndexType> >::Type
ev_wsq_impl(const HeMatrix<MA> &A)
{
using std::max;
typedef typename HeMatrix<MA>::ElementType T;
typedef typename HeMatrix<MA>::IndexType IndexType;
const IndexType n = A.numRows();
const char upLo[1] = { cxxf77blas::getF77BlasChar(A.upLo()) };
const IndexType nb = ilaenv<T>(1, "HETRD", upLo, n);
const IndexType lWorkOpt = max(IndexType(1), (nb+1)*n);
const IndexType minWork = (n==0) ? 1 : max(1,2*n-1);
return Pair<IndexType>(minWork, lWorkOpt);
}
template <typename MA, typename VW, typename VWORK, typename VRWORK>
typename HeMatrix<MA>::IndexType
ev_impl(bool computeV,
HeMatrix<MA> &A,
DenseVector<VW> &w,
DenseVector<VWORK> &work,
DenseVector<VRWORK> &rWork)
{
using std::real;
typedef typename HeMatrix<MA>::ElementType T;
typedef typename ComplexTrait<T>::PrimitiveType PT;
typedef typename GeMatrix<MA>::IndexType IndexType;
const Underscore<IndexType> _;
const bool upper = (A.upLo()==Upper);
const PT Zero(0), One(1);
const T COne(1);
Pair<IndexType> wsQuery = ev_wsq(A);
IndexType minWork = wsQuery.first;
IndexType maxWork = wsQuery.second;
//
// Perform and apply worksize query if requested
//
if (work.length()!=0 && work.length()<minWork) {
ASSERT(0);
} else if (work.length()==0) {
work.resize(maxWork);
}
const IndexType lWork = work.length();
const IndexType n = A.dim();
//
// Quick return if possible
//
if (n==0) {
return 0;
}
if (n==1) {
w(1) = real(A(1,1));
work(1) = 1;
if (computeV) {
A(1,1) = COne;
}
return 0;
}
//
// Get machine constants.
//
const PT safeMin = lamch<PT>(SafeMin);
const PT eps = lamch<PT>(Precision);
const PT smallNum = safeMin / eps;
const PT bigNum = One / smallNum;
const PT rMin = sqrt(smallNum);
const PT rMax = sqrt(bigNum);
//
// Scale matrix to allowable range, if necessary.
//
const PT ANorm = lan(MaximumNorm, A);
bool scaleA = false;
PT sigma;
if (ANorm>Zero && ANorm<rMin) {
scaleA = true;
sigma = rMin / ANorm;
} else if (ANorm>rMax) {
scaleA = true;
sigma = rMax / ANorm;
}
if (scaleA) {
lascl(upper ? LASCL::UpperTriangular : LASCL::LowerTriangular,
IndexType(0), IndexType(0), One, sigma, A);
}
//
// Call ZHETRD to reduce Hermitian matrix to tridiagonal form.
//
auto e_ = rWork(_(1,n-1));
auto tau_ = work(_(1,n-1));
auto work_ = work(_(n+1, lWork));
trd(A, w, e_, tau_, work_);
//
// For eigenvalues only, call DSTERF. For eigenvectors, first call
// ZUNGTR to generate the unitary matrix, then call ZSTEQR.
//
IndexType info = 0;
if (!computeV) {
info = sterf(w, e_);
} else {
ungtr(A, tau_, work_);
auto rWork_ = rWork(_(n+1, 3*n-2));
STEQR::ComputeZ jobZ = (computeV)
? STEQR::Orig
: STEQR::No;
steqr(jobZ, w, e_, A.general(), rWork_);
}
//
// If matrix was scaled, then rescale eigenvalues appropriately.
//
if (scaleA) {
if (info==0) {
w *= One/sigma;
} else {
w(_(1,info-1)) *= One/sigma;
}
}
//
// Set WORK(1) to optimal complex workspace size.
//
work(1) = maxWork;
return info;
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
//-- (he)ev [worksize query hermitian variant] ---------------------------------
template <typename MA>
typename RestrictTo<IsComplex<typename MA::ElementType>::value,
Pair<typename MA::IndexType> >::Type
ev_wsq_impl(const HeMatrix<MA> &A)
{
using std::max;
typedef typename HeMatrix<MA>::ElementType T;
typedef typename ComplexTrait<T>::PrimitiveType PT;
typedef typename HeMatrix<MA>::IndexType IndexType;
//
// Compute minimal workspace
//
IndexType n = A.dim();
IndexType minWork;
if (n==0) {
minWork = 1;
} else {
minWork = max(1,2*n-1);
}
//
// Get optimal workspace from external LAPACK
//
T DUMMY, WORK;
PT RDUMMY, RWORK;
IndexType LWORK = -1;
cxxlapack::heev('N',
getF77Char(A.upLo()),
A.dim(),
&DUMMY,
A.leadingDimension(),
&RDUMMY,
&WORK,
LWORK,
&RWORK);
return Pair<IndexType>(minWork,WORK.real());
}
//-- (he)ev [hermitian variant] ------------------------------------------------
template <typename MA, typename VW, typename VWORK, typename VRWORK>
typename HeMatrix<MA>::IndexType
ev_impl(bool computeV,
HeMatrix<MA> &A,
DenseVector<VW> &w,
DenseVector<VWORK> &work,
DenseVector<VRWORK> &rWork)
{
using std::max;
typedef typename HeMatrix<MA>::IndexType IndexType;
if (work.length()==0) {
const auto ws = ev_wsq_impl(A);
work.resize(ws.second, 1);
}
IndexType info;
info = cxxlapack::heev(computeV ? 'V' : 'N',
getF77Char(A.upLo()),
A.dim(),
A.data(),
A.leadingDimension(),
w.data(),
work.data(),
work.length(),
rWork.data());
ASSERT(info>=0);
return info;
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
//-- (he)ev [complex variant] --------------------------------------------------
template <typename MA, typename VW, typename VWORK, typename VRWORK>
typename RestrictTo<IsHeMatrix<MA>::value
&& IsRealDenseVector<VW>::value
&& IsComplexDenseVector<VWORK>::value
&& IsRealDenseVector<VRWORK>::value,
typename RemoveRef<MA>::Type::IndexType>::Type
ev(bool computeV,
MA &&A,
VW &&w,
VWORK &&work,
VRWORK &&rWork)
{
LAPACK_DEBUG_OUT("(he)ev [complex]");
using std::max;
//
// Remove references from rvalue types
//
typedef typename RemoveRef<MA>::Type MatrixA;
typedef typename MatrixA::IndexType IndexType;
const IndexType n = A.dim();
# ifdef CHECK_CXXLAPACK
typedef typename RemoveRef<VW>::Type VectorW;
typedef typename RemoveRef<VWORK>::Type VectorWork;
typedef typename RemoveRef<VRWORK>::Type VectorRWork;
# endif
//
// Test the input parameters
//
# ifndef NDEBUG
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
ASSERT(work.firstIndex()==1);
ASSERT(rWork.firstIndex()==1);
ASSERT(w.firstIndex()==1);
ASSERT(w.length()==0 || w.length()==n);
if (work.length()!=0) {
ASSERT(work.length()>=max(IndexType(1),2*n-1));
}
if (rWork.length()!=0) {
ASSERT(rWork.length()>=max(IndexType(1),3*n-2));
}
# endif
//
// Resize output arguments if they are empty and needed
//
if (w.length()==0) {
w.resize(n, 1);
}
if (rWork.length()==0) {
rWork.resize(max(IndexType(1),3*n-2));
}
//
// Make copies of output arguments
//
# ifdef CHECK_CXXLAPACK
typename MatrixA::NoView A_org = A;
typename VectorW::NoView w_org = w;
typename VectorWork::NoView work_org = work;
typename VectorRWork::NoView rWork_org = rWork;
# endif
//
// Call implementation
//
IndexType result = LAPACK_SELECT::ev_impl(computeV, A, w, work, rWork);
# ifdef CHECK_CXXLAPACK
//
// Compare results
//
typename MatrixA::NoView A_generic = A;
typename VectorW::NoView w_generic = w;
typename VectorWork::NoView work_generic = work;
typename VectorRWork::NoView rWork_generic = rWork;
A = A_org;
w = w_org;
work = work_org;
rWork = rWork_org;
IndexType result_ = external::ev_impl(computeV, A, w, work, rWork);
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(w_generic, w, " w_generic", "w")) {
std::cerr << "CXXLAPACK: w_generic = " << w_generic << std::endl;
std::cerr << "F77LAPACK: w = " << w << 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 (! isIdentical(result, result_, " result", "result_")) {
std::cerr << "CXXLAPACK: result = " << result << std::endl;
std::cerr << "F77LAPACK: result_ = " << result_ << std::endl;
failed = true;
}
if (failed) {
std::cerr << "computeV = " << computeV << std::endl;
ASSERT(0);
}
# endif
return result;
}
//-- (he)ev [worksize query] ---------------------------------------------------
template <typename MA>
typename RestrictTo<IsHeMatrix<MA>::value,
Pair<typename MA::IndexType> >::Type
ev_wsq(const MA &A)
{
LAPACK_DEBUG_OUT("(he)ev_wsq");
//
// Test the input parameters
//
# ifndef NDEBUG
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
# endif
//
// Call implementation
//
const auto ws = LAPACK_SELECT::ev_wsq_impl(A);
# ifdef CHECK_CXXLAPACK
//
// Compare results
//
const auto optWorkSize = external::ev_wsq_impl(A);
if (! isIdentical(optWorkSize.first, ws.first,
"optWorkSize.first", "ws.first"))
{
ASSERT(0);
}
if (! isIdentical(optWorkSize.second, ws.second,
"optWorkSize.second", "ws.second"))
{
ASSERT(0);
}
# endif
return ws;
}
//-- (he)ev [real variant with temporary workspace] ----------------------------
template <typename MA, typename VW>
typename RestrictTo<IsHeMatrix<MA>::value
&& IsRealDenseVector<VW>::value,
typename RemoveRef<MA>::Type::IndexType>::Type
ev(bool computeV,
MA &&A,
VW &&w)
{
//
// Remove references from rvalue types
//
typedef typename RemoveRef<MA>::Type::Vector WorkVector;
typedef typename RemoveRef<MA>::Type::ElementType T;
typedef typename ComplexTrait<T>::PrimitiveType PT;
typedef DenseVector<Array<PT> > RealWorkVector;
WorkVector work;
RealWorkVector rWork;
return ev(computeV, A, w, work, rWork);
}
} } // namespace lapack, flens
#endif // FLENS_LAPACK_HE_EV_TCC
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