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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 DGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, $ 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_GE_EQU_TCC #define FLENS_LAPACK_GE_EQU_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 VR, typename VC, typename ROWCOND, typename COLCOND, typename AMAX> typename GeMatrix<MA>::IndexType equ_impl(const GeMatrix<MA> &A, DenseVector<VR> &r, DenseVector<VC> &c, ROWCOND &rowCond, COLCOND &colCond, AMAX &amax) { using std::abs; using std::max; using std::min; typedef typename GeMatrix<MA>::ElementType T; typedef typename GeMatrix<MA>::IndexType IndexType; const T Zero(0), One(1); const Underscore<IndexType> _; const IndexType m = A.numRows(); const IndexType n = A.numCols(); IndexType info = 0; // // Quick return if possible // if (m==0 || n==0) { rowCond = One; colCond = One; amax = Zero; return info; } // // Get machine constants. // const T smallNum = lamch<T>(SafeMin); const T bigNum = One / smallNum; // // Compute row scale factors. // r = Zero; // // Find the maximum element in each row. // for (IndexType j=1; j<=n; ++j) { for (IndexType i=1; i<=m; ++i) { r(i) = max(r(i),abs(A(i,j))); } } // // Find the maximum and minimum scale factors. // T rcMin = bigNum; T rcMax = Zero; for (IndexType i=1; i<=m; ++i) { rcMax = max(rcMax, r(i)); rcMin = min(rcMin, r(i)); } amax = rcMax; if (rcMin==Zero) { // // Find the first zero scale factor and return an error code. // for (IndexType i=1; i<=m; ++i) { if (r(i)==Zero) { info = i; return info; } } } else { // // Invert the scale factors. // for (IndexType i=1; i<=m; ++i) { r(i) = One / min(max(r(i),smallNum), bigNum); } // // Compute ROWCND = min(R(I)) / max(R(I)) // rowCond = max(rcMin,smallNum) / min(rcMax,bigNum); } // Compute column scale factors // c = Zero; // // Find the maximum element in each column, // assuming the row scaling computed above. // for (IndexType j=1; j<=n; ++j) { for (IndexType i=1; i<=m; ++i) { c(j) = max(c(j),abs(A(i,j))*r(i)); } } // // Find the maximum and minimum scale factors. // rcMin = bigNum; rcMax = Zero; for (IndexType j=1; j<=n; ++j) { rcMin = min(rcMin, c(j)); rcMax = max(rcMax, c(j)); } if (rcMin==Zero) { // // Find the first zero scale factor and return an error code. // for (IndexType j=1; j<=n; ++j) { if (c(j)==Zero) { info = m+j; return info; } } } else { // // Invert the scale factors. // for (IndexType j=1; j<=n; ++j) { c(j) = One / min(max(c(j),smallNum), bigNum); } // // Compute COLCND = min(C(J)) / max(C(J)) // colCond = max(rcMin,smallNum) / min(rcMax,bigNum); } return info; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { template <typename MA, typename VR, typename VC, typename ROWCOND, typename COLCOND, typename AMAX> typename GeMatrix<MA>::IndexType equ_impl(const GeMatrix<MA> &A, DenseVector<VR> &r, DenseVector<VC> &c, ROWCOND &rowCond, COLCOND &colCond, AMAX &amax) { typedef typename GeMatrix<MA>::IndexType IndexType; IndexType info = cxxlapack::geequ<IndexType>(A.numRows(), A.numCols(), A.data(), A.leadingDimension(), r.data(), c.data(), rowCond, colCond, amax); ASSERT(info>=0); return info; } } // namespace external #endif // USE_CXXLAPACK //== (ge)equ =================================================================== // // Real Variant // template <typename MA, typename VR, typename VC, typename ROWCOND, typename COLCOND, typename AMAX> typename RestrictTo<IsRealGeMatrix<MA>::value && IsRealDenseVector<VR>::value && IsRealDenseVector<VC>::value && IsNotComplex<ROWCOND>::value && IsNotComplex<COLCOND>::value && IsNotComplex<AMAX>::value, typename MA::IndexType>::Type equ(const MA &A, VR &&r, VC &&c, ROWCOND &rowCond, COLCOND &colCond, AMAX &amax) { LAPACK_DEBUG_OUT("(ge)equ [real]"); typedef typename MA::IndexType IndexType; // // Remove references from rvalue types // typedef typename RemoveRef<VR>::Type VectorR; typedef typename RemoveRef<VC>::Type VectorC; // // Test the input parameters // # ifndef NDEBUG ASSERT(A.firstRow()==1); ASSERT(A.firstCol()==1); const IndexType m = A.numRows(); const IndexType n = A.numCols(); ASSERT(r.firstIndex()==1); ASSERT(r.length()==m); ASSERT(c.firstIndex()==1); ASSERT(c.length()==n); # endif # ifdef CHECK_CXXLAPACK // // Make copies of output arguments // typename VectorR::NoView r_org = r; typename VectorC::NoView c_org = c; ROWCOND rowCond_org = rowCond; COLCOND colCond_org = colCond; AMAX amax_org = amax; # endif // // Call implementation // const IndexType info = LAPACK_SELECT::equ_impl(A, r, c, rowCond, colCond, amax); # ifdef CHECK_CXXLAPACK // // Make copies of results computed by the generic implementation // typename VectorR::NoView r_generic = r; typename VectorC::NoView c_generic = c; ROWCOND rowCond_generic = rowCond; COLCOND colCond_generic = colCond; AMAX amax_generic = amax; // // restore output arguments // r = r_org; c = c_org; rowCond = rowCond_org; colCond = colCond_org; amax = amax_org; // // Compare generic results with results from the native implementation // const IndexType info_ = external::equ_impl(A, r, c, rowCond, colCond, amax); bool failed = false; if (! isIdentical(r_generic, r, "r_generic", "r")) { std::cerr << "CXXLAPACK: r_generic = " << r_generic << std::endl; std::cerr << "F77LAPACK: r = " << r << std::endl; failed = true; } if (! isIdentical(c_generic, c, "c_generic", "c")) { std::cerr << "CXXLAPACK: c_generic = " << c_generic << std::endl; std::cerr << "F77LAPACK: c = " << c << std::endl; failed = true; } if (! isIdentical(rowCond_generic, rowCond, "rowCond_generic", "rowCond")) { std::cerr << "CXXLAPACK: rowCond_generic = " << rowCond_generic << std::endl; std::cerr << "F77LAPACK: rowCond = " << rowCond << std::endl; failed = true; } if (! isIdentical(colCond_generic, colCond, "colCond_generic", "colCond")) { std::cerr << "CXXLAPACK: colCond_generic = " << colCond_generic << std::endl; std::cerr << "F77LAPACK: colCond = " << colCond << std::endl; failed = true; } if (! isIdentical(amax_generic, amax, "amax_generic", "amax")) { std::cerr << "CXXLAPACK: amax_generic = " << amax_generic << std::endl; std::cerr << "F77LAPACK: amax = " << amax << std::endl; failed = true; } if (info!=info_) { std::cerr << "CXXLAPACK: info = " << info << std::endl; std::cerr << "F77LAPACK: info_ = " << info_ << std::endl; failed = true; } if (failed) { std::cerr << "A = " << A << std::endl; std::cerr << "r = " << r << std::endl; std::cerr << "c = " << c << std::endl; ASSERT(0); } else { // std::cerr << "passed: equ.tcc" << std::endl; } # endif return info; } } } // namespace lapack, flens #endif // FLENS_LAPACK_GE_EQU_TCC |