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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 DGELQ2( M, N, A, LDA, TAU, WORK, INFO )
SUBROUTINE ZGELQ2( M, N, A, LDA, TAU, WORK, 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_LQ2_TCC
#define FLENS_LAPACK_GE_LQ2_TCC 1
#include <flens/blas/blas.h>
#include <flens/lapack/lapack.h>
namespace flens { namespace lapack {
//== generic lapack implementation =============================================
namespace generic {
//-- [lq2, real version] -------------------------------------------------------
template <typename MA, typename VTAU, typename VWORK>
typename
RestrictTo<IsRealGeMatrix<GeMatrix<MA> >::value,
void>::Type
lq2_impl(GeMatrix<MA> &A, DenseVector<VTAU> &tau, DenseVector<VWORK> &work)
{
typedef typename GeMatrix<MA>::ElementType ElementType;
typedef typename GeMatrix<MA>::IndexType IndexType;
const Underscore<IndexType> _;
const IndexType m = A.numRows();
const IndexType n = A.numCols();
const IndexType k = std::min(m, n);
const ElementType One(1);
for (IndexType i=1; i<=k; ++i) {
//
// Generate elementary reflector H(i) to annihilate A(i,i+1:n)
//
larfg(n-i+1, A(i,i), A(i,_(std::min(i+1,n),n)), tau(i));
if (i<m) {
//
// Apply H(i) to A(i+1:m,i:n) from the right
//
const ElementType Aii = A(i,i);
A(i,i) = One;
auto work_ = work(_(1, m-i));
larf(Right, A(i,_(i,n)), tau(i), A(_(i+1,m), _(i,n)), work_);
A(i,i) = Aii;
}
}
}
//-- [lq2, complex version] ----------------------------------------------------
template <typename MA, typename VTAU, typename VWORK>
typename
RestrictTo<IsComplexGeMatrix<GeMatrix<MA> >::value,
void>::Type
lq2_impl(GeMatrix<MA> &A, DenseVector<VTAU> &tau, DenseVector<VWORK> &work)
{
typedef typename GeMatrix<MA>::ElementType ElementType;
typedef typename GeMatrix<MA>::IndexType IndexType;
const Underscore<IndexType> _;
const IndexType m = A.numRows();
const IndexType n = A.numCols();
const IndexType k = std::min(m, n);
const ElementType One(1);
ElementType alpha;
for (IndexType i=1; i<=k; ++i) {
//
// Generate elementary reflector H(i) to annihilate A(i,i+1:n)
//
A(i, _(i,n)) = conjugate(A(i, _(i,n)));
alpha = A(i,i);
larfg(n-i+1, alpha, A(i,_(std::min(i+1,n),n)), tau(i));
if (i<m) {
//
// Apply H(i) to A(i+1:m,i:n) from the right
//
A(i,i) = One;
auto work_ = work(_(1, m-i));
larf(Right, A(i,_(i,n)), tau(i), A(_(i+1,m), _(i,n)), work_);
}
A(i,i) = alpha;
A(i, _(i,n)) = conjugate(A(i, _(i,n)));
}
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
template <typename MA, typename VTAU, typename VWORK>
void
lq2_impl(GeMatrix<MA> &A, DenseVector<VTAU> &tau, DenseVector<VWORK> &work)
{
typedef typename GeMatrix<MA>::IndexType IndexType;
IndexType info = cxxlapack::gelq2<IndexType>(A.numRows(),
A.numCols(),
A.data(),
A.leadingDimension(),
tau.data(),
work.data());
ASSERT(info==0);
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
template <typename MA, typename VTAU, typename VWORK>
void
lq2(GeMatrix<MA> &A, DenseVector<VTAU> &tau, DenseVector<VWORK> &work)
{
//
// Test the input parameters
//
# ifndef NDEBUG
typedef typename GeMatrix<MA>::IndexType IndexType;
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
ASSERT(tau.firstIndex()==1);
ASSERT(work.firstIndex()==1);
const IndexType m = A.numRows();
const IndexType n = A.numCols();
const IndexType k = std::min(m, n);
ASSERT(tau.length()>=k);
ASSERT(work.length()>=m);
# endif
# ifdef CHECK_CXXLAPACK
//
// Make copies of output arguments
//
typename GeMatrix<MA>::NoView A_org = A;
typename DenseVector<VTAU>::NoView tau_org = tau;
typename DenseVector<VTAU>::NoView work_org = work;
# endif
//
// Call implementation
//
LAPACK_SELECT::lq2_impl(A, tau, work);
# ifdef CHECK_CXXLAPACK
//
// Restore output arguments
//
typename GeMatrix<MA>::NoView A_generic = A;
typename DenseVector<VTAU>::NoView tau_generic = tau;
typename DenseVector<VTAU>::NoView work_generic = work;
A = A_org;
tau = tau_org;
work = work_org;
//
// Compare results
//
external::lq2_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
}
//-- forwarding ----------------------------------------------------------------
template <typename MA, typename VTAU, typename VWORK>
void
lq2(MA &&A, VTAU &&tau, VWORK &&work)
{
CHECKPOINT_ENTER;
lq2(A, tau, work);
CHECKPOINT_LEAVE;
}
} } // namespace lapack, flens
#endif // FLENS_LAPACK_GE_LQ2_TCC
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