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/*
* Copyright (c) 2012, 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 DTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, 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_IMPL_TZRZF_TCC
#define FLENS_LAPACK_IMPL_TZRZF_TCC 1
#include <flens/blas/blas.h>
#include <flens/lapack/lapack.h>
namespace flens { namespace lapack {
//== generic lapack implementation =============================================
namespace generic {
//-- tzrzf [real variant] ------------------------------------------------------
template <typename MA, typename VTAU, typename VWORK>
void
tzrzf_impl(GeMatrix<MA> &A,
DenseVector<VTAU> &tau,
DenseVector<VWORK> &work)
{
using std::max;
using std::min;
typedef typename GeMatrix<MA>::ElementType ElementType;
typedef typename GeMatrix<MA>::IndexType IndexType;
typedef GeMatrixView<ElementType> GeView;
const Underscore<IndexType> _;
const ElementType Zero(0);
const IndexType m = A.numRows();
const IndexType n = A.numCols();
IndexType lWorkMin, lWorkOpt, nb;
if (m==0 || m==n) {
nb = 0;
lWorkOpt = 1;
lWorkMin = 1;
} else {
//
// Determine the block size.
//
nb = ilaenv<ElementType>(1, "GERQF", "", m, n);
lWorkOpt = m*nb;
lWorkMin = max(IndexType(1), m);
}
if (work.length()==0) {
work.resize(lWorkOpt);
}
work(1) = lWorkOpt;
ASSERT(work.length()>=lWorkMin);
//
// Quick return if possible
//
if (m==0) {
return;
} else if (m==n) {
tau = Zero;
return;
}
IndexType nbMin = 2;
IndexType nx = 1;
IndexType iws = m;
IndexType ldWork = -1;
if (nb>1 && nb<m) {
//
// Determine when to cross over from blocked to unblocked code.
//
nx = max(IndexType(0), ilaenv<ElementType>(3, "GERQF", "", m, n));
if (nx<m) {
//
// Determine if workspace is large enough for blocked code.
//
ldWork = m;
iws = ldWork*nb;
if (work.length()<iws) {
//
// Not enough workspace to use optimal NB: reduce NB and
// determine the minimum value of NB.
//
nb = work.length()/ldWork;
nbMin = max(IndexType(2),
ilaenv<ElementType>(2, "GERQF", "", m, n));
}
}
}
IndexType mu = 0;
if (nb>=nbMin && nb<m && nx<m) {
//
// Use blocked code initially.
// The last kk rows are handled by the block method.
//
IndexType m1 = min(m+1, n);
IndexType ki = ((m-nx-1)/nb)*nb;
IndexType kk = min(m, ki+nb);
IndexType i;
for (i=m-kk+ki+1; i>=m-kk+1; i-=nb) {
const IndexType ib = min(m-i+1, nb);
GeView Work(ldWork, ib, work, ldWork);
auto Tr = Work(_(1,ib),_(1,ib)).lower();
//
// Compute the TZ factorization of the current block
// A(i:i+ib-1,i:n)
//
auto tau_ = tau(_(i,i+ib-1));
auto work_ = work(_(1,ib));
latrz(n-m, A(_(i,i+ib-1),_(i,n)), tau_, work_);
if (i>1) {
//
// Form the triangular factor of the block reflector
// H = H(i+ib-1) . . . H(i+1) H(i)
//
larzt(Backward, RowWise, A(_(i,i+ib-1),_(m1,n)), tau_, Tr);
//
// Apply H to A(1:i-1,i:n) from the right
//
larzb(Right, NoTrans, Backward, RowWise,
A(_(i,i+ib-1),_(m1,n)), Tr, A(_(1,i-1),_(i,n)),
Work(_(ib+1,ib+i-1),_));
}
}
mu = i + nb - 1;
} else {
mu = m;
}
//
// Use unblocked code to factor the last or only block
//
if (mu>0) {
latrz(n-m, A(_(1,mu),_), tau(_(1,mu)), work(_(1,mu)));
}
work(1) = lWorkOpt;
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
//-- tzrzf [real and complex variant] -----------------------------------------
template <typename MA, typename VTAU, typename VWORK>
void
tzrzf_impl(GeMatrix<MA> &A,
DenseVector<VTAU> &tau,
DenseVector<VWORK> &work)
{
typedef typename GeMatrix<MA>::IndexType IndexType;
cxxlapack::tzrzf<IndexType>(A.numRows(),
A.numCols(),
A.data(),
A.leadingDimension(),
tau.data(),
work.data(),
work.length());
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
//-- tzrzf [real and complex variant] ------------------------------------------
template <typename MA, typename VTAU, typename VWORK>
typename RestrictTo<IsGeMatrix<MA>::value
&& IsDenseVector<VTAU>::value
&& IsDenseVector<VWORK>::value,
void>::Type
tzrzf(MA &&A,
VTAU &&tau,
VWORK &&work)
{
using std::max;
using std::min;
LAPACK_DEBUG_OUT("tzrzf [real]");
//
// Test the input parameters
//
//
// Remove references from rvalue types
//
# if defined(CHECK_CXXLAPACK) || !defined(NDEBUG)
typedef typename RemoveRef<MA>::Type MatrixA;
# endif
# ifndef NDEBUG
typedef typename MatrixA::IndexType IndexType;
const IndexType m = A.numRows();
const IndexType n = A.numCols();
ASSERT(n>=m);
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
ASSERT(tau.firstIndex()==1);
ASSERT(work.firstIndex()==1);
ASSERT(tau.length()==m);
if (work.length()>0) {
ASSERT(work.length()>=max(IndexType(1),m));
}
# endif
//
// Make copies of output arguments
//
# ifdef CHECK_CXXLAPACK
typedef typename RemoveRef<VTAU>::Type VectorTau;
typedef typename RemoveRef<VWORK>::Type VectorWork;
typename MatrixA::NoView A_org = A;
typename VectorTau::NoView tau_org = tau;
typename VectorWork::NoView work_org = work;
# endif
//
// Call implementation
//
LAPACK_SELECT::tzrzf_impl(A, tau, work);
# ifdef CHECK_CXXLAPACK
//
// Make copies of results computed by the generic implementation
//
typename MatrixA::NoView A_generic = A;
typename VectorTau::NoView tau_generic = tau;
typename VectorWork::NoView work_generic = work;
//
// restore output arguments
//
A = A_org;
tau = tau_org;
work = work_org;
//
// Compare generic results with results from the native implementation
//
external::tzrzf_impl(A, tau, work);
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(tau_generic, tau, "tau_generic", "tau")) {
std::cerr << "CXXLAPACK: tau_generic = " << tau_generic << std::endl;
std::cerr << "F77LAPACK: tau = " << tau << 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 (failed) {
std::cerr << "error in: tzrzf.tcc" << std::endl;
ASSERT(0);
} else {
// std::cerr << "passed: tzrzf.tcc" << std::endl;
}
# endif
}
} } // namespace lapack, flens
#endif // FLENS_LAPACK_IMPL_TZRZF_TCC
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