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/*
* Copyright (c) 2012, 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 DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C ) * * -- LAPACK auxiliary 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 -- * */ #ifndef FLENS_LAPACK_LA_LAIC1_TCC #define FLENS_LAPACK_LA_LAIC1_TCC 1 #include <flens/lapack/lapack.h> #include <flens/matrixtypes/matrixtypes.h> #include <flens/vectortypes/vectortypes.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { //-- laic1 [real variant] ------------------------------------------------------ template <typename VX, typename SEST, typename VW, typename GAMMA, typename SESTPR, typename S, typename C> void laic1_impl(LAIC1::Job job, const DenseVector<VX> &x, SEST sEst, const DenseVector<VW> &w, const GAMMA &gamma, SESTPR &sEstPr, S &s, C &c) { using std::abs; using std::max; using std::sqrt; using cxxblas::conjugate; typedef typename DenseVector<VX>::ElementType ElementType; typedef typename DenseVector<VX>::IndexType IndexType; typedef typename ComplexTrait<ElementType>::PrimitiveType PrimitiveType; const PrimitiveType Zero(0), One(1), Two(2), Half(0.5), Four(4); const PrimitiveType eps = lamch<PrimitiveType>(Eps); const ElementType alpha = x*w; const PrimitiveType absAlpha = abs(alpha); const PrimitiveType absGamma = abs(gamma); const PrimitiveType absEst = abs(sEst); PrimitiveType s1, s2, tmp, zeta1, zeta2, b, t, scl, normA; ElementType cosine, sine; if (job==LAIC1::Max) { // // Estimating largest singular value // // special cases // if (sEst==Zero) { s1 =max(absGamma, absAlpha); if (s1==Zero) { s = Zero; c = One; sEstPr = Zero; } else { s = alpha / s1; c = gamma / s1; tmp = sqrt(s*conjugate(s) + c*conjugate(c)); s /= tmp; c /= tmp; sEstPr = s1*tmp; } return; } else if (absGamma<=eps*absEst) { s = One; c = Zero; tmp = max(absEst, absAlpha); s1 = absEst / tmp; s2 = absAlpha / tmp; sEstPr = tmp*sqrt(s1*s1 + s2*s2); return; } else if (absAlpha<=eps*absEst) { s1 = absGamma; s2 = absEst; if (s1<=s2) { s = One; c = Zero; sEstPr = s2; } else { s = Zero; c = One; sEstPr = s1; } return; } else if (absEst<=eps*absAlpha || absEst<=eps*absGamma) { s1 = absGamma; s2 = absAlpha; if (s1<=s2) { tmp = s1 / s2; if (IsComplex<ElementType>::value) { scl = sqrt(One + tmp*tmp); sEstPr = s2*scl; s = (alpha/s2) / scl; c = (gamma/s2) / scl; } else { s = sqrt(One + tmp*tmp); sEstPr = s2*s; c = (gamma/s2) / s; s = sign(One, alpha) / s; } } else { tmp = s2 / s1; if (IsComplex<ElementType>::value) { scl = sqrt(One + tmp*tmp); sEstPr = s1*scl; s = (alpha/s1) / scl; c = (gamma/s1) / scl; } else { c = sqrt(One + tmp*tmp); sEstPr = s1*c; s = (alpha/s1) / c; c = sign(One, gamma) / c; } } return; } else { // // normal case // if (IsComplex<ElementType>::value) { zeta1 = absAlpha / absEst; zeta2 = absGamma / absEst; } else { zeta1 = alpha / absEst; zeta2 = gamma / absEst; } b = (One - zeta1*zeta1 - zeta2*zeta2)*Half; c = zeta1*zeta1; if (b>Zero) { t = c / (b+sqrt(b*b+c)); } else { t = sqrt(b*b+c) - b; } if (IsComplex<ElementType>::value) { sine = -(alpha / absEst) / t; cosine = -(gamma / absEst) / (One +t); } else { sine = -zeta1 / t; cosine = -zeta2 / (One +t); } tmp = sqrt(sine*conjugate(sine) + cosine*conjugate(cosine)); s = sine / tmp; c = cosine / tmp; sEstPr = sqrt(t + One)*absEst; return; } } else if (job==LAIC1::Min) { // // Estimating smallest singular value // // special cases // if (sEst==Zero) { sEstPr = Zero; if (max(absGamma, absAlpha)==Zero) { sine = One; cosine = Zero; } else { sine = -gamma; cosine = alpha; } s1 = max(abs(sine), abs(cosine)); s = sine / s1; c = cosine / s1; tmp = sqrt(s*conjugate(s) + c*conjugate(c)); s /= tmp; c /= tmp; return; } else if (absGamma<=eps*absEst) { s = Zero; c = One; sEstPr = absGamma; return; } else if (absAlpha<=eps*absEst) { s1 = absGamma; s2 = absEst; if (s1<=s2) { s = Zero; c = One; sEstPr = s1; } else { s = One; c = Zero; sEstPr = s2; } return; } else if (absEst<=eps*absAlpha || absEst<=eps*absGamma) { s1 = absGamma; s2 = absAlpha; if (s1<=s2) { tmp = s1 / s2; if (IsComplex<ElementType>::value) { scl = sqrt(One + tmp*tmp); sEstPr = absEst*(tmp/scl); s = -(conjugate(gamma) / s2) / scl; c = (conjugate(alpha) / s2) / scl; } else { c = sqrt(One + tmp*tmp); sEstPr = absEst*(tmp/c); s = -(gamma / s2) / c; c = sign(One, alpha) / c; } } else { tmp = s2 / s1; if (IsComplex<ElementType>::value) { scl = sqrt(One + tmp*tmp); sEstPr = absEst / scl; s = -(conjugate(gamma) / s1) / scl; c = (conjugate(alpha) / s1) / scl; } else { s = sqrt(One + tmp*tmp); sEstPr = absEst / s; c = (alpha / s1) / s; s = -sign(One, gamma) / s; } } return; } else { // // normal case // if (IsComplex<ElementType>::value) { zeta1 = absAlpha / absEst; zeta2 = absGamma / absEst; } else { zeta1 = alpha / absEst; zeta2 = gamma / absEst; } normA = max(One + zeta1*zeta1 + abs(zeta1*zeta2), abs(zeta1*zeta2) + zeta2*zeta2); // // See if root is closer to zero or to ONE // PrimitiveType test = One + Two*(zeta1-zeta2)*(zeta1+zeta2); if (test>=Zero) { // // root is close to zero, compute directly // b = (zeta1*zeta1 + zeta2*zeta2 + One)*Half; c = zeta2*zeta2; t = c / (b + sqrt(abs(b*b-c))); if (IsComplex<ElementType>::value) { sine = (alpha/absEst) / (One - t); cosine = -(gamma/absEst) / t; } else { sine = zeta1 / (One - t); cosine = -zeta2 / t; } sEstPr = sqrt(t + Four*eps*eps*normA) * absEst; } else { // // root is closer to ONE, shift by that amount // b = (zeta2*zeta2 + zeta1*zeta1 - One)*Half; c = zeta1*zeta1; if (b>=Zero) { t = -c / (b + sqrt(b*b + c)); } else { t = b - sqrt(b*b + c); } if (IsComplex<ElementType>::value) { sine = -(alpha/absEst) / t; cosine = -(gamma/absEst) / (One + t); } else { sine = -zeta1 / t; cosine = -zeta2 / (One + t); } sEstPr = sqrt(One + t + Four*eps*eps*normA)*absEst; } tmp = sqrt(sine*conjugate(sine) + cosine*conjugate(cosine)); s = sine / tmp; c = cosine / tmp; return; } } } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { //-- laic1 [real variant] ------------------------------------------------------ template <typename VX, typename SEST, typename VW, typename GAMMA, typename SESTPR, typename S, typename C> void laic1_impl(LAIC1::Job job, const DenseVector<VX> &x, SEST sEst, const DenseVector<VW> &w, const GAMMA &gamma, SESTPR &sEstPr, S &s, C &c) { typedef typename DenseVector<VX>::IndexType IndexType; cxxlapack::laic1<IndexType>(IndexType(job), x.length(), x.data(), sEst, w.data(), gamma, sEstPr, s, c); } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== //-- laic1 [real variant] ------------------------------------------------------ template <typename VX, typename SEST, typename VW, typename GAMMA, typename SESTPR, typename S, typename C> void laic1(LAIC1::Job job, const DenseVector<VX> &x, SEST sEst, const DenseVector<VW> &w, const GAMMA &gamma, SESTPR &sEstPr, S &s, C &c) { // // Test the input parameters // # ifndef NDEBUG ASSERT(x.length()==w.length()); # endif // // Make copies of output arguments // # ifdef CHECK_CXXLAPACK SESTPR sEstPr_org = sEstPr; S s_org = s; C c_org = c; # endif // // Call implementation // LAPACK_SELECT::laic1_impl(job, x, sEst, w, gamma, sEstPr, s, c); # ifdef CHECK_CXXLAPACK // // Make copies of results computed by the generic implementation // SESTPR sEstPr_generic = sEstPr; S s_generic = s; C c_generic = c; // // restore output arguments // sEstPr = sEstPr_org; s = s_org; c = c_org; // // Compare generic results with results from the native implementation // external::laic1_impl(job, x, sEst, w, gamma, sEstPr, s, c); bool failed = false; if (! isIdentical(sEstPr_generic, sEstPr, "sEstPr_generic", "sEstPr")) { std::cerr << "CXXLAPACK: sEstPr_generic = " << sEstPr_generic << std::endl; std::cerr << "F77LAPACK: sEstPr = " << sEstPr << std::endl; failed = true; } if (! isIdentical(s_generic, s, "s_generic", "s")) { std::cerr << "CXXLAPACK: s_generic = " << s_generic << std::endl; std::cerr << "F77LAPACK: s = " << s << 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 (failed) { std::cerr << "error in: laic1.tcc" << std::endl; ASSERT(0); } else { // std::cerr << "passed: laic1.tcc" << std::endl; } # endif } } } // namespace lapack, flens #endif // FLENS_LAPACK_LA_LAIC1_TCC |