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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 DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
SUBROUTINE ZGEQRF( 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_GE_QRF_TCC
#define FLENS_LAPACK_GE_QRF_TCC 1
#include <flens/blas/blas.h>
#include <flens/lapack/lapack.h>
namespace flens { namespace lapack {
//== generic lapack implementation =============================================
namespace generic {
//-- (ge)qrf [real and complex variant] ----------------------------------------
template <typename MA, typename VTAU, typename VWORK>
void
qrf_impl(GeMatrix<MA> &A, DenseVector<VTAU> &tau, DenseVector<VWORK> &work)
{
using std::max;
using std::min;
typedef typename GeMatrix<MA>::ElementType T;
typedef typename GeMatrix<MA>::IndexType IndexType;
const Underscore<IndexType> _;
const IndexType m = A.numRows();
const IndexType n = A.numCols();
const IndexType k = min(m, n);
const Transpose adj = (IsComplex<T>::value) ? ConjTrans : Trans;
//
// Perform and apply workspace query
//
IndexType nb = ilaenv<T>(1, "GEQRF", "", m, n);
const IndexType lWorkOpt = n*nb;
if (work.length()==0) {
work.resize(max(lWorkOpt,IndexType(1)));
work(1)=lWorkOpt;
}
//
// Quick return if possible
//
if (k==0) {
work(1) = 1;
return;
}
IndexType nbMin = 2;
IndexType nx = 0;
IndexType iws = n;
IndexType ldWork = -1;
if ((nb>1) && (nb<k)) {
//
// Determine when to cross over from blocked to unblocked code.
//
nx = max(IndexType(0), IndexType(ilaenv<T>(3, "GEQRF", "", m, n)));
if (nx<k) {
//
// Determine if workspace is large enough for blocked code.
//
ldWork = n;
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),
IndexType(ilaenv<T>(2, "GEQRF", "", m, n)));
}
}
}
IndexType i;
if ((nb>=nbMin) && (nb<k) && (nx<k)) {
typename GeMatrix<MA>::View Work(n, nb, work);
//
// Use blocked code initially
//
for (i=1; i<=k-nx; i+=nb) {
const IndexType ib = min(k-i+1, nb);
//
// Compute the QR factorization of the current block
// A(i:m,i:i+ib-1)
//
qr2(A(_(i,m),_(i,i+ib-1)), tau(_(i,i+ib-1)), work(_(1,ib)));
if (i+ib<=n) {
//
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
//
auto Tr = Work(_(1,ib),_(1,ib)).upper();
larft(Forward, ColumnWise,
m-i+1,
A(_(i,m),_(i,i+ib-1)),
tau(_(i,i+ib-1)),
Tr);
//
// Apply H' to A(i:m,i+ib:n) from the left
//
larfb(Left, adj, Forward, ColumnWise,
A(_(i,m),_(i,i+ib-1)),
Tr,
A(_(i,m),_(i+ib,n)),
Work(_(ib+1,n),_(1,ib)));
}
}
} else {
i = 1;
}
//
// Use unblocked code to factor the last or only block.
//
if (i<=k) {
qr2(A(_(i,m),_(i,n)), tau(_(i,k)), work(_(1,n-i+1)));
}
work(1) = iws;
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
//-- (ge)qrf [real and complex variant] ----------------------------------------
template <typename MA, typename VTAU, typename VWORK>
void
qrf_impl(GeMatrix<MA> &A, DenseVector<VTAU> &tau, DenseVector<VWORK> &work)
{
typedef typename GeMatrix<MA>::ElementType ElementType;
typedef typename GeMatrix<MA>::IndexType IndexType;
if (work.length()==0) {
ElementType WORK;
IndexType LWORK = -1;
cxxlapack::geqrf<IndexType>(A.numRows(),
A.numCols(),
A.data(),
A.leadingDimension(),
tau.data(),
&WORK,
LWORK);
work.resize(real(WORK));
}
cxxlapack::geqrf<IndexType>(A.numRows(),
A.numCols(),
A.data(),
A.leadingDimension(),
tau.data(),
work.data(),
work.length());
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
//-- (ge)qrf [real/complex variant] --------------------------------------------
template <typename MA, typename VTAU, typename VWORK>
typename RestrictTo<(IsRealGeMatrix<MA>::value
&& IsRealDenseVector<VTAU>::value
&& IsRealDenseVector<VWORK>::value)
|| (IsComplexGeMatrix<MA>::value
&& IsComplexDenseVector<VTAU>::value
&& IsComplexDenseVector<VWORK>::value),
void>::Type
qrf(MA &&A, VTAU &&tau, VWORK &&work)
{
using std::min;
//
// Remove references from rvalue types
//
typedef typename RemoveRef<MA>::Type MatrixA;
typedef typename MatrixA::IndexType IndexType;
# ifdef CHECK_CXXLAPACK
typedef typename RemoveRef<VTAU>::Type VectorTau;
typedef typename RemoveRef<VWORK>::Type VectorWork;
# endif
const IndexType m = A.numRows();
const IndexType n = A.numCols();
const IndexType k = min(m,n);
# ifndef NDEBUG
//
// Test the input parameters
//
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
ASSERT(tau.firstIndex()==1);
ASSERT(work.firstIndex()==1);
ASSERT(tau.length()==0 || tau.length()==k);
ASSERT(work.length()>=n || work.length()==IndexType(0));
# endif
if (tau.length()==0) {
tau.resize(k);
}
# ifdef CHECK_CXXLAPACK
//
// Make copies of output arguments
//
typename MatrixA::NoView A_org = A;
typename VectorTau::NoView tau_org = tau;
typename VectorWork::NoView work_org = work;
# endif
//
// Call implementation
//
LAPACK_SELECT::qrf_impl(A, tau, work);
# ifdef CHECK_CXXLAPACK
//
// Restore output arguments
//
typename MatrixA::NoView A_generic = A;
typename VectorTau::NoView tau_generic = tau;
typename VectorWork::NoView work_generic = work;
A = A_org;
tau = tau_org;
// if the generic implementation resized work due to a work size query
// we must not restore the work array
if (work_org.length()>0) {
work = work_org;
} else {
work = 0;
}
//
// Compare results
//
external::qrf_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) {
ASSERT(0);
}
# endif
}
//-- (ge)tri [real/complex variant with temporary workspace] -------------------
template <typename MA, typename VTAU>
typename RestrictTo<(IsRealGeMatrix<MA>::value
&& IsRealDenseVector<VTAU>::value)
|| (IsComplexGeMatrix<MA>::value
&& IsComplexDenseVector<VTAU>::value),
void>::Type
qrf(MA &&A, VTAU &&tau)
{
typedef typename RemoveRef<MA>::Type::Vector WorkVector;
WorkVector work;
qrf(A, tau, work);
}
} } // namespace lapack, flens
#endif // FLENS_LAPACK_GE_QRF_TCC
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