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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.
*/
/* Baesed on
*
SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO )
SUBROUTINE ZTRTRI( UPLO, DIAG, N, A, LDA, 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_TR_TRI_TCC
#define FLENS_LAPACK_TR_TRI_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 {
//-- (tr)tri [real and complex variant] ----------------------------------------
template <typename MA>
typename GeMatrix<MA>::IndexType
tri_impl(TrMatrix<MA> &A)
{
using std::min;
using cxxf77blas::getF77BlasChar;
typedef typename TrMatrix<MA>::ElementType ElementType;
typedef typename TrMatrix<MA>::IndexType IndexType;
const Underscore<IndexType> _;
const IndexType n = A.dim();
const bool upper = (A.upLo()==Upper);
const bool noUnit = (A.diag()==NonUnit);
const ElementType Zero(0), One(1);
IndexType info = 0;
//
// Quick return if possible
//
if (n==0) {
return info;
}
//
// Check for singularity if non-unit.
//
if (noUnit) {
for (info=1; info<=n; ++info) {
if (A(info,info)==Zero) {
return info;
}
}
info = 0;
}
//
// Determine the block size for this environment. //
const char upLoDiag[2] = { getF77BlasChar(A.upLo()),
getF77BlasChar(A.diag()) };
const IndexType nb = ilaenv<ElementType>(1, "TRTRI", upLoDiag, n);
if (nb<=1 || nb>=n) {
//
// Use unblocked code
//
info = ti2(A);
} else {
//
// Use blocked code
//
if (upper) {
//
// Compute inverse of upper triangular matrix
//
for (IndexType j=1; j<=n; j+=nb) {
const IndexType jb = min(nb, n-j+1);
//
// Compute rows 1:j-1 of current block column
//
const auto range1 = _(1,j-1);
const auto range2 = _(j,j+jb-1);
const auto U11 = (noUnit) ? A(range1, range1).upper()
: A(range1, range1).upperUnit();
auto U22 = (noUnit) ? A(range2, range2).upper()
: A(range2, range2).upperUnit();
auto U12 = A(range1, range2);
blas::mm(Left, NoTrans, One, U11, U12);
blas::sm(Right, NoTrans, -One, U22, U12);
//
// Compute inverse of current diagonal block
//
info = ti2(U22);
}
} else {
//
// Compute inverse of lower triangular matrix
//
const IndexType nn = ((n-1)/nb)*nb + 1;
for (IndexType j=nn; j>=1; j-=nb) {
const IndexType jb = min(nb, n-j+1);
const auto range1 = _(j,j+jb-1);
auto L11 = (noUnit) ? A(range1,range1).lower()
: A(range1,range1).lowerUnit();
if (j+jb<=n) {
//
// Compute rows j+jb:n of current block column
//
const auto range2 = _(j+jb,n);
const auto L22 = (noUnit) ? A(range2,range2).lower()
: A(range2,range2).lowerUnit();
auto L21 = A(range2, range1);
blas::mm(Left, NoTrans, One, L22, L21);
blas::sm(Right, NoTrans, -One, L11, L21);
}
//
// Compute inverse of current diagonal block
//
info = ti2(L11);
}
}
}
return info;
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
//-- (tr)tri [real and complex variant] ----------------------------------------
template <typename MA>
typename GeMatrix<MA>::IndexType
tri_impl(TrMatrix<MA> &A)
{
typedef typename TrMatrix<MA>::IndexType IndexType;
IndexType info = cxxlapack::trtri<IndexType>(getF77Char(A.upLo()),
getF77Char(A.diag()),
A.dim(),
A.data(),
A.leadingDimension());
ASSERT(info>=0);
return info;
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
//-- (tr)tri [real and complex variant] ----------------------------------------
template <typename MA>
typename RestrictTo<IsRealTrMatrix<MA>::value
|| IsComplexTrMatrix<MA>::value,
typename RemoveRef<MA>::Type::IndexType>::Type
tri(MA &&A)
{
//
// Remove references from rvalue types
//
typedef typename RemoveRef<MA>::Type MatrixA;
typedef typename MatrixA::IndexType IndexType;
//
// Test the input parameters
//
# ifndef NDEBUG
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
# endif
//
// Make copies of output arguments
//
# ifdef CHECK_CXXLAPACK
typename MatrixA::NoView A_org = A;
# endif
//
// Call implementation
//
const IndexType info = LAPACK_SELECT::tri_impl(A);
//
// Compare results
//
# ifdef CHECK_CXXLAPACK
typename MatrixA::NoView A_generic = A;
A = A_org;
const IndexType info_ = external::tri_impl(A);
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(info, info_, " info", "info_")) {
std::cerr << "CXXLAPACK: info = " << info << std::endl;
std::cerr << "F77LAPACK: info_ = " << info_ << std::endl;
failed = true;
}
if (failed) {
ASSERT(0);
} else {
// std::cerr << "passed: (tr)tri.tcc" << std::endl;
}
# endif
return info;
}
} } // namespace lapack, flens
#endif // FLENS_LAPACK_TR_TRI_TCC
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