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/*
* Copyright (c) 2013, Michael Lehn, 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 DGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )
SUBROUTINE ZGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )
*
* -- LAPACK routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2006
*/
#ifndef FLENS_LAPACK_GB_TF2_TCC
#define FLENS_LAPACK_GB_TF2_TCC 1
#include <cxxstd/algorithm.h>
#include <flens/blas/blas.h>
#include <flens/lapack/lapack.h>
namespace flens { namespace lapack {
//== generic lapack implementation =============================================
namespace generic {
//-- (gb)tf2 [real and complex variant] ----------------------------------------
template <typename MA, typename VP>
typename GbMatrix<MA>::IndexType
tf2_impl(GbMatrix<MA> &A, DenseVector<VP> &piv)
{
using std::min;
using std::max;
typedef typename GbMatrix<MA>::GeView GeMatrixView;
typedef typename GbMatrix<MA>::FullStorageView FullStorageView;
typedef typename GbMatrix<MA>::IndexType IndexType;
typedef typename GbMatrix<MA>::ElementType ElementType;
GeMatrixView AB = A.viewStorageGeMatrix();
const IndexType m = A.numRows();
const IndexType n = A.numCols();
const IndexType kl = A.numSubDiags();
const IndexType ku = A.numSuperDiags()-A.numSubDiags();
const IndexType kv = kl + ku;
const IndexType ldAB = AB.leadingDimension();
const ElementType zero(0), one(1);
const Underscore<IndexType> _;
//
// Gaussian elimination with partial pivoting
//
// Set fill-in elements in columns ku+2 to kv to zero.
//
for( IndexType j = ku + 2; j<=min( kv, n ); ++j) {
AB(_( kv - j + 2, kl), j) = zero;
}
//
// ju is the index of the last column affected by the current stage
// of the factorization.
//
IndexType ju = 1;
for (IndexType j = 1; j<= min( m, n ); ++j) {
//
// Set fill-in elements in column j+kv to zero.
//
if( j+kv<=n ) {;
AB(_(1,kl),j+kv) = zero;
}
//
// Find pivot and test for singularity. km is the number of
// subdiagonal elements in the current column.
//
IndexType km = min( kl, m-j );
IndexType jp = blas::iamax(AB( _(kv+1,kv+km+1), j ));
piv( j ) = jp + j - 1;
if( AB( kv+jp, j ) != zero ) {
ju = max( ju, min( j+ku+jp-1, n ) );
//
// Apply interchange to columns j to ju.
//
if( jp!=1 ) {
blas::swap(A(jp+j-1,_(j,ju)), A(j,_(j,ju)));
}
if( km>0 ) {
//
// Compute multipliers.
//
blas::scal(one / AB( kv+1, j ), AB(_(kv+2, kv+km+1), j ));
//
// Update trailing submatrix within the band.
//
if( ju>j ) {
GeMatrixView ABtmp = FullStorageView(km, ju-j, ldAB-1,
&AB(kv+1, j+1));
blas::r(-one, AB(_(kv+2,kv+km+1),j), A(j,_(j+1,ju)), ABtmp);
}
}
} else {
//
// If pivot is zero, return the index
//
return j;
}
}
return 0;
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
//-- (gb)tf2 [real and complex variant] ----------------------------------------
template <typename MA, typename VP>
typename GbMatrix<MA>::IndexType
tf2_impl(GbMatrix<MA> &A, DenseVector<VP> &piv)
{
typedef typename GeMatrix<MA>::IndexType IndexType;
const IndexType k = A.numSuperDiags()-A.numSubDiags();
return cxxlapack::gbtf2<IndexType>(A.numRows(), A.numCols(),
A.numSubDiags(), k,
A.data(), A.leadingDimension(),
piv.data());
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
//-- (gb)tf2 [real and complex variant] ----------------------------------------
template <typename MA, typename VPIV>
typename RestrictTo<IsGbMatrix<MA>::value
&& IsIntegerDenseVector<VPIV>::value,
typename RemoveRef<MA>::Type::IndexType>::Type
tf2(MA &&A, VPIV &&piv)
{
using std::min;
//
// Remove references from rvalue types
//
typedef typename RemoveRef<MA>::Type MatrixA;
typedef typename MatrixA::IndexType IndexType;
const IndexType mn = min(A.numRows(), A.numCols());
if (piv.length()!=mn) {
piv.resize(mn);
}
ASSERT(piv.length()==mn);
# ifndef NDEBUG
//
// Test the input parameters
//
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
ASSERT((piv.inc()>0 && piv.firstIndex()==1)
|| (piv.inc()<0 && piv.firstIndex()==A.numRows()));
# endif
# ifdef CHECK_CXXLAPACK
typedef typename RemoveRef<VPIV>::Type VectorPiv;
//
// Make copies of output arguments
//
typename MatrixA::NoView A_ = A;
typename VectorPiv::NoView piv_ = piv;
# endif
//
// Call implementation
//
IndexType info = LAPACK_SELECT::tf2_impl(A, piv);
# ifdef CHECK_CXXLAPACK
//
// Compare results
//
IndexType info_ = external::tf2_impl(A_, piv_);
bool failed = false;
if (! isIdentical(A, A_, " A", "A_")) {
std::cerr << "CXXLAPACK: A = " << A << std::endl;
std::cerr << "F77LAPACK: A_ = " << A_ << std::endl;
failed = true;
}
if (! isIdentical(piv, piv_, " piv", "piv_")) {
std::cerr << "CXXLAPACK: piv = " << piv << std::endl;
std::cerr << "F77LAPACK: piv_ = " << piv_ << std::endl;
failed = true;
}
if (! isIdentical(info, info_, " info", "info_")) {
std::cerr << "CXXLAPACK: info = " << info << std::endl;
std::cerr << "F77LAPACK: info_ = " << info_ << std::endl;
failed = true;
}
if (failed) {
ASSERT(0);
}
# endif
return info;
}
} } // namespace lapack, flens
#endif // FLENS_LAPACK_GB_TF2_TCC
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