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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 DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) SUBROUTINE ZGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, 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 -- SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, INFO ) SUBROUTINE ZTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, 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_IMPL_TRS_TCC #define FLENS_LAPACK_IMPL_TRS_TCC 1 #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { //-- (ge)trs [real and complex variant] ---------------------------------------- template <typename MA, typename VP, typename MB> void trs_impl(Transpose trans, const GeMatrix<MA> &A, const DenseVector<VP> &piv, GeMatrix<MB> &B) { typedef typename GeMatrix<MA>::IndexType IndexType; typedef typename GeMatrix<MA>::ElementType T; const IndexType n = A.numCols(); const IndexType nRhs = B.numCols(); const T One(1); // // Quick return if possible // if ((n==0) || (nRhs==0)) { return; } if ((trans==NoTrans) || (trans==Conj)) { // // Solve A * X = B. // // Apply row interchanges to the right hand sides. // laswp(B, piv); // // Solve L*X = B, overwriting B with X. // blas::sm(Left, trans, One, A.lowerUnit(), B); // // Solve U*X = B, overwriting B with X. // blas::sm(Left, trans, One, A.upper(), B); } else { // // Solve A' * X = B. // // Solve U'*X = B, overwriting B with X. // blas::sm(Left, trans, One, A.upper(), B); // // Solve L'*X = B, overwriting B with X. // blas::sm(Left, trans, One, A.lowerUnit(), B); // // Apply row interchanges to the solution vectors. // laswp(B, piv.reverse()); } } //-- (tr)trs [real and complex variant] ---------------------------------------- template <typename MA, typename MB> typename TrMatrix<MA>::IndexType trs_impl(Transpose trans, const TrMatrix<MA> &A, GeMatrix<MB> &B) { typedef typename TrMatrix<MA>::IndexType IndexType; typedef typename TrMatrix<MA>::ElementType T; const IndexType n = A.dim(); const T Zero(0), One(1); IndexType info = 0; // // Quick return if possible // if (n==0) { return info; } // // Check for singularity. // if (A.diag()!=Unit) { for (info=1; info<=n; ++info) { if (A(info,info)==Zero) { return info; } } } info = 0; // // Solve A * x = b or A**T * x = b. // blas::sm(Left, trans, One, A, B); return info; } } // namespace generic //== interface for external lapack ============================================= #ifdef USE_CXXLAPACK namespace external { //-- (ge)trs [real and complex variant] ---------------------------------------- template <typename MA, typename VP, typename MB> void trs_impl(Transpose trans, const GeMatrix<MA> &A, const DenseVector<VP> &piv, GeMatrix<MB> &B) { typedef typename GeMatrix<MA>::IndexType IndexType; IndexType info; info = cxxlapack::getrs<IndexType>(getF77Char(trans), A.numRows(), B.numCols(), A.data(), A.leadingDimension(), piv.data(), B.data(), B.leadingDimension()); ASSERT(info==0); } //-- (tr)trs [real and complex variant] ---------------------------------------- template <typename MA, typename MB> typename TrMatrix<MA>::IndexType trs_impl(Transpose trans, const TrMatrix<MA> &A, GeMatrix<MB> &B) { typedef typename TrMatrix<MA>::IndexType IndexType; IndexType info; info = cxxlapack::trtrs<IndexType>(getF77Char(A.upLo()), getF77Char(trans), getF77Char(A.diag()), A.dim(), B.numCols(), A.data(), A.leadingDimension(), B.data(), B.leadingDimension()); ASSERT(info>=0); return info; } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== //-- (ge)trs [real and complex variant] ---------------------------------------- template <typename MA, typename VPIV, typename MB> typename RestrictTo<IsGeMatrix<MA>::value && IsIntegerDenseVector<VPIV>::value && IsGeMatrix<MB>::value, void>::Type trs(Transpose trans, const MA &A, const VPIV &piv, MB &&B) { LAPACK_DEBUG_OUT("(ge)trs [real/complex]"); // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename MatrixA::IndexType IndexType; typedef typename RemoveRef<MB>::Type MatrixB; // // Test the input parameters // # ifndef NDEBUG ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(A.numRows()==A.numCols()); const IndexType n = A.numRows(); ASSERT(piv.firstIndex()==1); ASSERT(piv.length()==n); ASSERT(B.firstRow()==1); ASSERT(B.firstCol()==1); ASSERT(B.numRows()==n); # endif // // Make copies of output arguments // typename MatrixB::NoView B_org = B; // // Call implementation // LAPACK_SELECT::trs_impl(trans, A, piv, B); // // Compare results // # ifdef CHECK_CXXLAPACK typename MatrixB::NoView B_generic = B; B = B_org; external::trs_impl(trans, A, piv, B); bool failed = false; if (! isIdentical(B_generic, B, "B_generic", "B")) { std::cerr << "CXXLAPACK: B_generic = " << B_generic << std::endl; std::cerr << "F77LAPACK: B = " << B << std::endl; failed = true; } if (failed) { ASSERT(0); } else { // std::cerr << "passed: (ge)trs.tcc" << std::endl; } # endif } //-- (ge)trs [variant if rhs is vector] ---------------------------------------- template <typename MA, typename VPIV, typename VB> typename RestrictTo<IsGeMatrix<MA>::value && IsIntegerDenseVector<VPIV>::value && IsDenseVector<VB>::value, void>::Type trs(Transpose trans, const MA &A, const VPIV &piv, VB &&b) { // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename RemoveRef<VB>::Type VectorB; // // Create matrix view from vector b and call above variant // typedef typename VectorB::ElementType ElementType; typedef typename VectorB::IndexType IndexType; const IndexType n = b.length(); const StorageOrder order = MatrixA::Engine::order; GeMatrix<FullStorageView<ElementType, order> > B(n, 1, b, n); trs(trans, A, piv, B); } //-- (tr)trs [real and complex variant] ---------------------------------------- template <typename MA, typename MB> typename RestrictTo<IsTrMatrix<MA>::value && IsGeMatrix<MB>::value, typename RemoveRef<MA>::Type::IndexType>::Type trs(Transpose trans, const MA &A, MB &&B) { LAPACK_DEBUG_OUT("(tr)trs [real/complex]"); // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename MatrixA::IndexType IndexType; typedef typename RemoveRef<MB>::Type MatrixB; // // Test the input parameters // # ifndef NDEBUG ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); const IndexType n = A.dim(); ASSERT(B.firstRow()==1); ASSERT(B.firstCol()==1); ASSERT(B.numRows()==n); # endif // // Make copies of output arguments // typename MatrixB::NoView B_org = B; // // Call implementation // IndexType info = LAPACK_SELECT::trs_impl(trans, A, B); // // Compare results // # ifdef CHECK_CXXLAPACK typename MatrixB::NoView B_generic = B; B = B_org; IndexType _info = external::trs_impl(trans, A, B); bool failed = false; if (! isIdentical(B_generic, B, "B_generic", "B")) { std::cerr << "CXXLAPACK: B_generic = " << B_generic << std::endl; std::cerr << "F77LAPACK: B = " << B << 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)trs.tcc" << std::endl; } # endif return info; } //-- (tr)trs [variant if rhs is vector] ---------------------------------------- template <typename MA, typename VB> typename RestrictTo<IsTrMatrix<MA>::value && IsDenseVector<VB>::value, typename RemoveRef<MA>::Type::IndexType>::Type trs(Transpose trans, const MA &A, VB &&b) { // // Remove references from rvalue types // typedef typename RemoveRef<MA>::Type MatrixA; typedef typename RemoveRef<VB>::Type VectorB; // // Create matrix view from vector b and call above variant // typedef typename VectorB::ElementType ElementType; typedef typename VectorB::IndexType IndexType; const IndexType n = b.length(); const StorageOrder order = MatrixA::Engine::order; GeMatrix<FullStorageView<ElementType, order> > B(n, 1, b, n); return trs(trans, A, B); } } } // namespace lapack, flens #endif // FLENS_LAPACK_IMPL_TRS_TCC |