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/*
* Copyright (c) 2012, 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 DGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )
SUBROUTINE ZGBTRF( 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_TRF_TCC
#define FLENS_LAPACK_GB_TRF_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)trf [real and complex variant] ----------------------------------------
template <typename MA, typename VP>
typename GbMatrix<MA>::IndexType
trf_impl(GbMatrix<MA> &A, DenseVector<VP> &piv)
{
using std::min;
using std::max;
typedef typename GbMatrix<MA>::GeNoView GeNoView;
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 = A.leadingDimension();
const ElementType zero(0), one(1);
const Underscore<IndexType> _;
IndexType nbmax = 64, ldWork = nbmax+1;
IndexType nb = lapack::ilaenv<ElementType>(1, "GBTRF", "", m, n, kl, ku);
//
// The block size must not exceed the limit set by the size of the
// local arrays Work13 and Work31.
//
nb = min( nb, nbmax );
if( nb<=1 || nb>kl ) {
//
// Use unblocked code
//
return lapack::tf2(A, piv);
} else {
GeNoView Work13(ldWork, nbmax), Work31(ldWork, nbmax);
//
// Use blocked code
//
//
// 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+=nb) {
IndexType jb = min( nb, min( m, n )-j+1 );
//
// The active part of the matrix is partitioned
//
// A11 A12 A13
// A21 A22 A23
// A31 A32 A33
//
// Here A11, A21 and A31 denote the current block of jB columns
// which is about to be factorized. The number of rows in the
// partitioning are jb, i2, i3 respectively, and the numbers
// of columns are jB, j2, Jj3. The superdiagonal elements of A13
// and the subdiagonal elements of A31 lie outside the band.
//
IndexType i2 = min( kl-jb, m-j-jb+1 );
IndexType i3 = min( jb, m-j-kl+1 );
//
// j2 and j3 are computed after ju has been updated.
//
// Factorize the current block of jb columns
//
for (IndexType jj = j; jj<=j + jb - 1; ++jj) {
//
// Set fill-in elements in column JJ+KV to zero
//
if( jj+kv<=n ) {
AB(_(1,kl),jj+kv) = zero;
}
//
// Find pivot and test for singularity. km is the number of
// subdiagonal elements in the current column.
//
IndexType km = min( kl, m-jj );
IndexType jp = blas::iamax(AB(_(kv+1,kv+km+1),jj));
piv( jj ) = jp + jj - j;
if( AB( kv+jp, jj )!=zero ) {
ju = max( ju, min( jj+ku+jp-1, n ) );
if( jp!=1 ) {
//
// Apply interchange to columns j to j+jb-1
//
if( jp+jj-1<j+kl ) {
blas::swap(A(jj,_(j,j+jb-1)),
A(jj+jp-1,_(j,j+jb-1)));
} else {
//
// The interchange affects columns j to jj-1 of A31
// which are stored in the work array WORK31
//
blas::swap(A(jj,_(j,jj-1)),
Work31(jp+jj-j-kl, _(1, jj-j)));
blas::swap(A(jj,_(jj,j+jb-1)),
A(jj+jp-1,_(jj,j+jb-1)));
}
}
//
// Compute multipliers
//
blas::scal(one / AB( kv+1, jj ), AB( _(kv+2,kv+km+1), jj ));
//
// Update trailing submatrix within the band and within
// the current block. jm is the index of the last column
// which needs to be updated.
//
IndexType jm = min( ju, j+jb-1 );
if( jm>jj ) {
GeMatrixView AB_tmp = FullStorageView(km, jm-jj, ldAB-1,
&AB( kv+1, jj+1));
blas::r(-one, AB( _(kv+2, kv+km+1), jj ),
A(jj,_(jj+1,jm)), AB_tmp);
}
} else {
//
// If pivot is zero, return index
//
return jj;
}
//
// Copy current column of A31 into the work array WORK31
//
IndexType NW = min( jj-j+1, i3 );
if( NW>0 ) {
blas::copy(AB( _(kv+kl+1-jj+j,kv+kl-jj+j+NW), jj ),
Work31( _(1,NW), jj-j+1 ));
}
}
if( j+jb<=n ) {
//
// Apply the row interchanges to the other blocks.
//
IndexType j2 = min( ju-j+1, kv ) - jb;
IndexType j3 = max( 0, ju-j-kv+1 );
//
// Use DLASWP to apply the row interchanges to A12, A22, and
// A32.
//
const IndexType mAB_tmp = min(ldAB-1, AB.numRows()-kv+jb);
GeMatrixView AB_tmp = FullStorageView(mAB_tmp, j2, ldAB-1,
&AB( kv+1-jb, j+jb ));
lapack::laswp(AB_tmp, piv(_(j,j+jb-1)));
//
// Adjust the pivot indices.
//
for(IndexType i = j; i<=j + jb - 1; ++i) {
piv( i ) = piv( i ) + j - 1;
}
//
// Apply the row interchanges to A13, A23, and A33
// columnwise.
//
IndexType k2 = j - 1 + jb + j2;
for (IndexType i = 1; i<=j3; ++i) {
IndexType jj = k2 + i;
for (IndexType ii = j + i - 1; ii<=j + jb - 1; ++ii) {
IndexType ip = piv( ii );
if ( ip!=ii ) {
ElementType TEMP = AB( kv+1+ii-jj, jj );
AB( kv+1+ii-jj, jj ) = AB( kv+1+ip-jj, jj );
AB( kv+1+ip-jj, jj ) = TEMP;
}
}
}
//
// Update the relevant part of the trailing submatrix
//
if( j2>0 ) {
//
// Update A12
//
GeMatrixView AB_tmp_1 = FullStorageView(jb, jb, ldAB-1,
&AB(kv+1, j));
GeMatrixView AB_tmp_2 = FullStorageView(jb, j2, ldAB-1,
&AB(kv+1-jb, j+jb));
blas::sm(Left, NoTrans, one, AB_tmp_1.lowerUnit(),
AB_tmp_2);
if( i2>0 ) {
//
// Update A22
//
GeMatrixView AB_tmp_1 = FullStorageView(i2, jb, ldAB-1,
&AB(kv+1+jb, j));
GeMatrixView AB_tmp_2 = FullStorageView(jb, j2, ldAB-1,
&AB( kv+1-jb, j+jb));
GeMatrixView AB_tmp_3 = FullStorageView(i2, j2, ldAB-1,
&AB( kv+1, j+jb));
AB_tmp_3 -= AB_tmp_1*AB_tmp_2;
}
if( i3>0 ) {
//
// Update A32
//
GeMatrixView AB_tmp_1 = FullStorageView(jb, j2, ldAB-1,
&AB(kv+1-jb, j+jb));
GeMatrixView AB_tmp_2 = FullStorageView(i3, j2, ldAB-1,
&AB( kv+kl+1-jb, j+jb));
AB_tmp_2 -= Work31(_(1,i3),_(1,jb))*AB_tmp_1;
}
}
if( j3>0 ) {
//
// Copy the lower triangle of A13 into the work array
// WORK13
//
for (IndexType jj=1; jj<=j3; ++jj) {
Work13(_(jj,jb), jj) = AB(_(1,jb-jj+1), jj+j+kv-1);
}
//
// Update A13 in the work array
//
GeMatrixView AB_tmp = FullStorageView(jb, jb, ldAB-1,
&AB(kv+1, j));
blas::sm(Left, NoTrans, one, AB_tmp.lowerUnit(),
Work13(_(1,jb),_(1,j3)));
if( i2>0 ) {
//
// Update A23
//
GeMatrixView AB_tmp_1 = FullStorageView(i2, jb, ldAB-1,
&AB(kv+1+jb,j));
GeMatrixView AB_tmp_3 = FullStorageView(i2, j3, ldAB-1,
&AB(1+jb,j+kv));
AB_tmp_3 -= AB_tmp_1*Work13(_(1,jb),_(1,j3));
}
if( i3>0 ) {
//
// Update A33
//
GeMatrixView AB_tmp = FullStorageView(i3, j3, ldAB-1,
&AB( 1+kl, j+kv));
AB_tmp -= Work31(_(1,i3),_(1,jb))
*Work13(_(1,jb),_(1,j3));
}
//
// Copy the lower triangle of A13 back into place
//
for (IndexType jj = 1; jj<=j3; ++jj) {
AB(_(1,jb-jj+1), jj+j+kv-1) = Work13(_(jj,jb),jj) ;
}
}
} else {
//
// Adjust the pivot indices.
//
for (IndexType i = j; i<= j + jb - 1; ++i) {
piv( i ) = piv( i ) + j - 1;
}
}
//
// Partially undo the interchanges in the current block to
// restore the upper triangular form of A31 and copy the upper
// triangle of A31 back into place
//
for (IndexType jj = j + jb - 1; jj>= j; --jj) {
IndexType jp = piv( jj ) - jj + 1;
if( jp!=1 ) {
//
// Apply interchange to columns j to jj-1
//
if( jp+jj-1<j+kl ) {
//
// The interchange does not affect A31
//
blas::swap(A(jj,_(j,jj-1)),A(jj+jp-1,_(j,jj-1)));
} else {
//
// The interchange does affect A31
//
blas::swap(A(jj,_(j,jj-1)), Work31(jp+jj-j-kl, _(1,jj-j)));
}
}
//
// Copy the current column of A31 back into place
//
IndexType nw = min( i3, jj-j+1 );
if( nw>0 ) {
blas::copy(Work31(_(1,nw), jj-j+1),
AB( _(kv+kl+1-jj+j,kv+kl-jj+j+nw), jj ));
}
}
}
}
return 0;
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
//-- (gb)trf [real and complex variant] ----------------------------------------
template <typename MA, typename VP>
typename GbMatrix<MA>::IndexType
trf_impl(GbMatrix<MA> &A, DenseVector<VP> &piv)
{
typedef typename GeMatrix<MA>::IndexType IndexType;
const IndexType k = A.numSuperDiags()-A.numSubDiags();
return cxxlapack::gbtrf<IndexType>(A.numRows(), A.numCols(),
A.numSubDiags(), k,
A.data(), A.leadingDimension(),
piv.data());
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
//-- (gb)trf [real and complex variant] ----------------------------------------
template <typename MA, typename VPIV>
typename RestrictTo<IsGbMatrix<MA>::value
&& IsIntegerDenseVector<VPIV>::value,
typename RemoveRef<MA>::Type::IndexType>::Type
trf(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::trf_impl(A, piv);
# ifdef CHECK_CXXLAPACK
//
// Compare results
//
IndexType info_ = external::trf_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_TRF_TCC
|