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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 * DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK ) * * -- LAPACK auxiliary 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_LA_LAN_TCC #define FLENS_LAPACK_LA_LAN_TCC 1 #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { template <typename MA, typename VWORK> typename ComplexTrait<typename GeMatrix<MA>::ElementType>::PrimitiveType lan_impl(Norm norm, const GeMatrix<MA> &A, DenseVector<VWORK> &work) { using std::abs; using std::max; using std::min; using std::sqrt; typedef typename GeMatrix<MA>::ElementType ElementType; typedef typename ComplexTrait<ElementType>::PrimitiveType T; typedef typename GeMatrix<MA>::IndexType IndexType; const Underscore<IndexType> _; const IndexType m = A.numRows(); const IndexType n = A.numCols(); const T Zero(0), One(1); if (min(m,n)==T(0)) { return Zero; } else if (norm==MaximumNorm) { // // Find max(abs(A(i,j))). // T value = Zero; for (IndexType j=1; j<=n; ++j) { for (IndexType i=1; i<=m; ++i) { value = max(value, abs(A(i,j))); } } return value; } else if (norm==OneNorm) { // // Find norm1(A). // T value = Zero; for (IndexType j=1; j<=n; ++j) { T sum = Zero; for (IndexType i=1; i<=m; ++i) { sum += abs(A(i,j)); } value = max(value, sum); } return value; } else if (norm==InfinityNorm) { // // Find normI(A). // for (IndexType i=1; i<=m; ++i) { work(i) = Zero; } for (IndexType j=1; j<=n; ++j) { for (IndexType i=1; i<=m; ++i) { work(i) += abs(A(i,j)); } } T value = Zero; for (IndexType i=1; i<=m; ++i) { value = max(value, work(i)); } return value; } else if (norm==FrobeniusNorm) { // // Find normF(A). // T scale = Zero; T sum = One; for (IndexType j=1; j<=n; ++j) { lassq(A(_,j), scale, sum); } return scale*sqrt(sum); } ASSERT(0); return Zero; } template <typename MA, typename VWORK> typename ComplexTrait<typename TrMatrix<MA>::ElementType>::PrimitiveType lan_impl(Norm norm, const TrMatrix<MA> &A, DenseVector<VWORK> &work) { using std::abs; using std::max; using std::min; using std::sqrt; typedef typename TrMatrix<MA>::ElementType ElementType; typedef typename ComplexTrait<ElementType>::PrimitiveType T; typedef typename TrMatrix<MA>::IndexType IndexType; const Underscore<IndexType> _; const IndexType m = A.numRows(); const IndexType n = A.numCols(); const T Zero(0), One(1); T value = Zero; if (min(m,n)==0) { return value; } else if (norm==MaximumNorm) { // // Find max(abs(A(i,j))). // if (A.diag()==Unit) { value = One; if (A.upLo()==Upper) { for (IndexType j=1; j<=n; ++j) { for (IndexType i=1; i<=min(m,j-1); ++i) { value = max(value, abs(A(i,j))); } } } else { for (IndexType j=1; j<=n; ++j) { for (IndexType i=j+1; i<=m; ++i) { value = max(value, abs(A(i,j))); } } } } else { value = Zero; if (A.upLo()==Upper) { for (IndexType j=1; j<=n; ++j) { for (IndexType i=1; i<=min(m,j); ++i) { value = max(value, abs(A(i,j))); } } } else { for (IndexType j=1; j<=n; ++j) { for (IndexType i=j; i<=m; ++i) { value = max(value, abs(A(i,j))); } } } } } else if (norm==OneNorm) { // // Find norm1(A). // value = Zero; const bool unitDiag = (A.diag()==Unit); if (A.upLo()==Upper) { for (IndexType j=1; j<=n; ++j) { T sum; if (unitDiag && (j<=m)) { sum = One; for (IndexType i=1; i<=j-1; ++i) { sum += abs(A(i,j)); } } else { sum = Zero; for (IndexType i=1; i<=min(m,j); ++i) { sum += abs(A(i,j)); } } value = max(value, sum); } } else { for (IndexType j=1; j<=n; ++j) { T sum; if (unitDiag) { sum = One; for (IndexType i=j+1; i<=m; ++i) { sum += abs(A(i,j)); } } else { sum = Zero; for (IndexType i=j; i<=m; ++i) { sum += abs(A(i,j)); } } value = max(value, sum); } } } else if (norm==InfinityNorm) { // // Find normI(A). // if (A.upLo()==Upper) { if (A.diag()==Unit) { for (IndexType i=1; i<=m; ++i) { work(i) = One; } for (IndexType j=1; j<=n; ++j) { for (IndexType i=1; i<=min(m,j-1); ++i) { work(i) += abs(A(i,j)); } } } else { for (IndexType i=1; i<=m; ++i) { work(i) = Zero; } for (IndexType j=1; j<=n; ++j) { for (IndexType i=1; i<=min(m,j); ++j) { work(i) += abs(A(i,j)); } } } } else { if (A.diag()==Unit) { for (IndexType i=1; i<=n; ++i) { work(i) = One; } for (IndexType i=n+1; i<=m; ++i) { work(i) = Zero; } for (IndexType j=1; j<=n; ++j) { for (IndexType i=j+1; i<=m; ++i) { work(i) += abs(A(i,j)); } } } else { for (IndexType i=1; i<=m; ++i) { work(i) = Zero; } for (IndexType j=1; j<=n; ++j) { for (IndexType i=j; i<=m; ++i) { work(i) += abs(A(i,j)); } } } } value = Zero; for (IndexType i=1; i<=m; ++i) { value = max(value, work(i)); } } else if (norm==FrobeniusNorm) { // // Find normF(A). // T scale, sum; if (A.upLo()==Upper) { if (A.diag()==Unit) { scale = One; sum = min(m, n); for (IndexType j=2; j<=n; ++j) { const auto rows = _(1,min(m,j-1)); const auto Aj = A(rows,j); lassq(Aj, scale, sum); } } else { scale = Zero; sum = One; for (IndexType j=1; j<=n; ++j) { const auto rows = _(1,min(m,j)); const auto Aj = A(rows,j); lassq(Aj, scale, sum); } } } else { if (A.diag()==Unit) { scale = One, sum = min(m,n); for (IndexType j=1; j<=n; ++j) { const auto rows = _(min(m,j)+1,m); const auto Aj = A(rows,j); lassq(Aj, scale, sum); } } else { scale = Zero; sum = One; for (IndexType j=1; j<=n; ++j) { const auto rows = _(min(m+1,j),m); const auto Aj = A(rows,j); lassq(Aj, scale, sum); } } } value = scale*sqrt(sum); } return value; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { template <typename MA, typename VWORK> typename ComplexTrait<typename TrMatrix<MA>::ElementType>::PrimitiveType lan_impl(Norm norm, const GeMatrix<MA> &A, DenseVector<VWORK> &work) { typedef typename GeMatrix<MA>::IndexType IndexType; return cxxlapack::lange<IndexType>(getF77Char(norm), A.numRows(), A.numCols(), A.data(), A.leadingDimension(), work.data()); } template <typename MA, typename VWORK> typename ComplexTrait<typename TrMatrix<MA>::ElementType>::PrimitiveType lan_impl(Norm norm, const TrMatrix<MA> &A, DenseVector<VWORK> &work) { typedef typename TrMatrix<MA>::IndexType IndexType; return cxxlapack::lantr<IndexType>(getF77Char(norm), getF77Char(A.upLo()), getF77Char(A.diag()), A.numRows(), A.numCols(), A.data(), A.leadingDimension(), work.data()); } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== //-- lan(ge) template <typename MA> typename ComplexTrait<typename GeMatrix<MA>::ElementType>::PrimitiveType lan(Norm norm, const GeMatrix<MA> &A) { ASSERT(norm!=InfinityNorm); typedef typename ComplexTrait<typename GeMatrix<MA>::ElementType>::PrimitiveType T; DenseVector<Array<T> > dummy; return lan(norm, A, dummy); } template <typename MA, typename VWORK> typename ComplexTrait<typename GeMatrix<MA>::ElementType>::PrimitiveType lan(Norm norm, const GeMatrix<MA> &A, DenseVector<VWORK> &work) { typedef typename ComplexTrait<typename GeMatrix<MA>::ElementType>::PrimitiveType T; // // Test the input parameters // ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(norm!=InfinityNorm || work.length()>=A.numRows()); # ifdef CHECK_CXXLAPACK // // Make copies of output arguments // typename DenseVector<VWORK>::NoView _work = work; # endif // // Call implementation // T result = LAPACK_SELECT::lan_impl(norm, A, work); # ifdef CHECK_CXXLAPACK // // Compare results // if (_work.length()==0) { _work.resize(work.length()); } T _result = external::lan_impl(norm, A, _work); bool failed = false; if (! isIdentical(work, _work, " work", "_work")) { std::cerr << "CXXLAPACK: work = " << work << std::endl; std::cerr << "F77LAPACK: _work = " << _work << std::endl; failed = true; } if (! isIdentical(result, _result, " result", "_result")) { failed = true; } if (failed) { ASSERT(0); } # endif return result; } //-- lan(tr) template <typename MA> typename ComplexTrait<typename TrMatrix<MA>::ElementType>::PrimitiveType lan(Norm norm, const TrMatrix<MA> &A) { ASSERT(norm!=InfinityNorm); typedef typename ComplexTrait<typename TrMatrix<MA>::ElementType>::PrimitiveType T; DenseVector<Array<T> > dummy; return lan(norm, A, dummy); } template <typename MA, typename VWORK> typename ComplexTrait<typename TrMatrix<MA>::ElementType>::PrimitiveType lan(Norm norm, const TrMatrix<MA> &A, DenseVector<VWORK> &work) { typedef typename ComplexTrait<typename TrMatrix<MA>::ElementType>::PrimitiveType T; // // Test the input parameters // ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); ASSERT(norm!=InfinityNorm || work.length()>=A.numRows()); # ifdef CHECK_CXXLAPACK // // Make copies of output arguments // typename DenseVector<VWORK>::NoView _work = work; # endif // // Call implementation // T result = LAPACK_SELECT::lan_impl(norm, A, work); # ifdef CHECK_CXXLAPACK // // Compare results // if (_work.length()==0) { _work.resize(work.length()); } T _result = external::lan_impl(norm, A, _work); bool failed = false; if (! isIdentical(work, _work, " work", "_work")) { std::cerr << "CXXLAPACK: work = " << work << std::endl; std::cerr << "F77LAPACK: _work = " << _work << std::endl; failed = true; } if (! isIdentical(result, _result, " result", "_result")) { failed = true; } if (failed) { ASSERT(0); } # endif return result; } //-- forwarding ---------------------------------------------------------------- template <typename MA> typename ComplexTrait<typename MA::ElementType>::PrimitiveType lan(Norm norm, const MA &A) { typedef typename ComplexTrait<typename MA::ElementType>::PrimitiveType T; CHECKPOINT_ENTER; const T result = lan(norm, A); CHECKPOINT_LEAVE; return result; } template <typename MA, typename VWORK> typename ComplexTrait<typename MA::ElementType>::PrimitiveType lan(Norm norm, const MA &A, VWORK &&work) { typedef typename ComplexTrait<typename MA::ElementType>::PrimitiveType T; CHECKPOINT_ENTER; const T result = lan(norm, A, work); CHECKPOINT_LEAVE; return result; } } } // namespace lapack, flens #endif // FLENS_LAPACK_LA_LAN_TCC |