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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 DLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, $ ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO ) * * -- LAPACK auxiliary routine (version 3.2) -- * Univ. of Tennessee, Univ. of California Berkeley, * Univ. of Colorado Denver and NAG Ltd.. * November 2006 */ #ifndef FLENS_LAPACK_LA_LAQR0_TCC #define FLENS_LAPACK_LA_LAQR0_TCC 1 #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { template <typename IndexType, typename MH> IndexType laqr0_wsq_impl(bool wantT, bool wantZ, IndexType iLo, IndexType iHi, const GeMatrix<MH> &H) { using std::max; using std::min; typedef typename GeMatrix<MH>::ElementType T; const IndexType nTiny = 11; const IndexType n = H.numRows(); if ((n==0) || (n<=nTiny)) { return 1; } char job[3]; job[0] = (wantT) ? 'S' : 'E'; job[1] = (wantZ) ? 'V' : 'N'; job[2] = 0; // // ==== NWR = recommended deflation window size. At this // . point, N .GT. NTINY = 11, so there is enough // . subdiagonal workspace for NWR.GE.2 as required. // . (In fact, there is enough subdiagonal space for // . NWR.GE.3.) ==== // IndexType nwr = ilaenv<T>(13, "LAQR0", job, n, iLo, iHi, -1); nwr = max(IndexType(2), nwr); nwr = min(min(IndexType(iHi-iLo+1), (n-1)/3), nwr); // // ==== NSR = recommended number of simultaneous shifts. // . At this point N .GT. NTINY = 11, so there is at // . enough subdiagonal workspace for NSR to be even // . and greater than or equal to two as required. ==== // IndexType nsr = ilaenv<T>(15, "LAQR0", job, n, iLo, iHi, -1); nsr = min(min(nsr, (n+6)/9), IndexType(iHi-iLo)); nsr = max(IndexType(2), nsr-(nsr%2)); // // ==== Estimate optimal workspace ==== // // ==== Workspace query call to DLAQR3 ==== // IndexType lWorkOpt = laqr3_wsq(IndexType(iLo), IndexType(iHi), nwr+1, H); // // ==== Optimal workspace = MAX(DLAQR5, DLAQR3) ==== // return max(3*nsr/2, lWorkOpt); } template <typename IndexType, typename MH, typename VWR, typename VWI, typename MZ, typename VWORK> IndexType laqr0_impl(bool wantT, bool wantZ, IndexType iLo, IndexType iHi, GeMatrix<MH> &H, DenseVector<VWR> &wr, DenseVector<VWI> &wi, IndexType iLoZ, IndexType iHiZ, GeMatrix<MZ> &Z, DenseVector<VWORK> &work) { using std::abs; using std::max; using std::min; using std::swap; typedef typename GeMatrix<MH>::ElementType T; const Underscore<IndexType> _; const IndexType n = H.numRows(); // ==== Matrices of order NTINY or smaller must be processed by // . DLAHQR because of insufficient subdiagonal scratch space. // . (This is a hard limit.) ==== const IndexType nTiny = 11; // ==== Exceptional deflation windows: try to cure rare // . slow convergence by varying the size of the // . deflation window after KEXNW iterations. ==== const IndexType kexNw = 5; // // ==== Exceptional shifts: try to cure rare slow convergence // . with ad-hoc exceptional shifts every KEXSH iterations. // . ==== const IndexType kexSh = 6; // // ==== The constants WILK1 and WILK2 are used to form the // . exceptional shifts. ==== const T wilk1 = T(0.75), wilk2 = T(-0.4375); const T Zero(0), One(1); IndexType info = 0; IndexType lWork, lWorkOpt; IndexType nDec = -1; // // ==== Perform and apply a workspace query if necessary ==== // if (work.length()==0) { lWorkOpt = laqr0_wsq(wantT, wantZ, iLo, iHi, H); work.resize(lWorkOpt); } lWork = work.length(); // // ==== Quick return for N = 0: nothing to do. ==== // if (n==0) { work(1) = One; return info; } if (n<=nTiny) { // // ==== Tiny matrices must use DLAHQR. ==== // lWorkOpt = 1; info = lahqr(wantT, wantZ, iLo, iHi, H, wr, wi, iLoZ, iHiZ, Z); } else { // // ==== Use small bulge multi-shift QR with aggressive early // . deflation on larger-than-tiny matrices. ==== // // ==== Hope for the best. ==== // info = 0; // // ==== Set up job flags for ILAENV. ==== // char job[3]; job[0] = (wantT) ? 'S' : 'E'; job[1] = (wantZ) ? 'V' : 'N'; job[2] = 0; // // ==== NWR = recommended deflation window size. At this // . point, N .GT. NTINY = 11, so there is enough // . subdiagonal workspace for NWR.GE.2 as required. // . (In fact, there is enough subdiagonal space for // . NWR.GE.3.) ==== // IndexType nwr = ilaenv<T>(13, "LAQR0", job, n, iLo, iHi, lWork); nwr = max(IndexType(2), nwr); nwr = min(min(IndexType(iHi-iLo+1), (n-1)/3), nwr); // // ==== NSR = recommended number of simultaneous shifts. // . At this point N .GT. NTINY = 11, so there is at // . enough subdiagonal workspace for NSR to be even // . and greater than or equal to two as required. ==== // IndexType nsr = ilaenv<T>(15, "LAQR0", job, n, iLo, iHi, lWork); nsr = min(min(nsr, (n+6)/9), IndexType(iHi-iLo)); nsr = max(IndexType(2), nsr - (nsr%2)); // // ==== Estimate optimal workspace ==== // // ==== Workspace query call to DLAQR3 ==== // lWorkOpt = laqr3_wsq(IndexType(iLo), IndexType(iHi), nwr+1, H); // // ==== Optimal workspace = MAX(DLAQR5, DLAQR3) ==== // lWorkOpt = max(3*nsr/2, lWorkOpt); // // ==== DLAHQR/DLAQR0 crossover point ==== // IndexType nMin = ilaenv<T>(12, "LAQR0", job, n, iLo, iHi, lWork); nMin = max(nTiny, nMin); // // ==== Nibble crossover point ==== // IndexType nibble = ilaenv<T>(14, "LAQR0", job, n, iLo, iHi, lWork); nibble = max(IndexType(0), nibble); // // ==== Accumulate reflections during ttswp? Use block // . 2-by-2 structure during matrix-matrix multiply? ==== // IndexType kacc22 = ilaenv<T>(16, "LAQR0", job, n, iLo, iHi, lWork); kacc22 = max(IndexType(0), kacc22); kacc22 = min(IndexType(2), kacc22); // // ==== NWMAX = the largest possible deflation window for // . which there is sufficient workspace. ==== // IndexType nwMax = min((n-1)/3, lWork/2); IndexType nw = nwMax; // // ==== NSMAX = the Largest number of simultaneous shifts // . for which there is sufficient workspace. ==== // IndexType nsMax = min((n+6 )/9, 2*lWork/3); nsMax = nsMax - (nsMax%2); // // ==== NDFL: an iteration count restarted at deflation. ==== // IndexType nDfl = 1; // // ==== ITMAX = iteration limit ==== // IndexType itMax = max(IndexType(30), 2*kexSh) * max(IndexType(10), IndexType(iHi-iLo+1)); // // ==== Last row and column in the active block ==== // IndexType kBot = iHi; // // ==== Main Loop ==== // IndexType it; for (it=1; it<=itMax; ++it) { // // ==== Done when KBOT falls below ILO ==== // if (kBot<iLo) { break; } // // ==== Locate active block ==== // IndexType k; for (k=kBot; k>=iLo+1; --k) { if (H(k,k-1)==Zero) { break; } } ASSERT(k==iLo || H(k,k-1)==Zero); const IndexType kTop = k; // // ==== Select deflation window size: // . Typical Case: // . If possible and advisable, nibble the entire // . active block. If not, use size MIN(NWR,NWMAX) // . or MIN(NWR+1,NWMAX) depending upon which has // . the smaller corresponding subdiagonal entry // . (a heuristic). // . // . Exceptional Case: // . If there have been no deflations in KEXNW or // . more iterations, then vary the deflation window // . size. At first, because, larger windows are, // . in general, more powerful than smaller ones, // . rapidly increase the window to the maximum possible. // . Then, gradually reduce the window size. ==== // IndexType nh = kBot - kTop + 1; IndexType nwUpBd = min(nh, nwMax); if (nDfl<kexNw) { nw = min(nwUpBd, nwr); } else { nw = min(nwUpBd, 2*nw); } if (nw<nwMax) { if (nw>=nh-1) { nw = nh; } else { const IndexType kwTop = kBot - nw + 1; if (abs(H(kwTop,kwTop-1))>abs(H(kwTop-1, kwTop-2))) { ++nw; } } } if (nDfl<kexNw) { nDec = -1; } else if (nDec>=0 || nw>=nwUpBd) { ++nDec; if (nw-nDec<2) { nDec = 0; } nw -= nDec; } // // ==== Aggressive early deflation: // . split workspace under the subdiagonal into // . - an nw-by-nw work array V in the lower // . left-hand-corner, // . - an NW-by-at-least-NW-but-more-is-better // . (NW-by-NHO) horizontal work array along // . the bottom edge, // . - an at-least-NW-but-more-is-better (NHV-by-NW) // . vertical work array along the left-hand-edge. // . ==== // auto _V = H(_(n-nw+1, n), _( 1, nw)); auto _T = H(_(n-nw+1, n), _(nw+1, n-nw-1)); auto _WV = H(_( nw+2, n-nw), _( 1, nw)); // // ==== Aggressive early deflation ==== // IndexType ls, ld; laqr3(wantT, wantZ, kTop, kBot, nw, H, IndexType(iLoZ), IndexType(iHiZ), Z, ls, ld, wr(_(1,kBot)), wi(_(1,kBot)), _V, _T, _WV, work); // // ==== Adjust KBOT accounting for new deflations. ==== // kBot -= ld; // // ==== KS points to the shifts. ==== // IndexType ks = kBot - ls + 1; // // ==== Skip an expensive QR sweep if there is a (partly // . heuristic) reason to expect that many eigenvalues // . will deflate without it. Here, the QR sweep is // . skipped if many eigenvalues have just been deflated // . or if the remaining active block is small. // if ((ld==0) || ((100*ld<=nw*nibble) && (kBot-kTop+1>min(nMin, nwMax)))) { // // ==== NS = nominal number of simultaneous shifts. // . This may be lowered (slightly) if DLAQR3 // . did not provide that many shifts. ==== // IndexType ns = min(min(nsMax, nsr), max(IndexType(2), kBot-kTop)); ns = ns - (ns % 2); // // ==== If there have been no deflations // . in a multiple of KEXSH iterations, // . then try exceptional shifts. // . Otherwise use shifts provided by // . DLAQR3 above or from the eigenvalues // . of a trailing principal submatrix. ==== // if (nDfl%kexSh==0) { ks = kBot - ns + 1; for (IndexType i=kBot; i>=max(ks+1,kTop+2); i-=2) { const T ss = abs(H(i,i-1)) + abs(H(i-1,i-2)); T aa = wilk1*ss + H(i,i); T bb = ss; T cc = wilk2*ss; T dd = aa; T cs, sn; lanv2(aa, bb, cc, dd, wr(i-1), wi(i-1), wr(i), wi(i), cs, sn); } if (ks==kTop) { wr(ks+1) = H(ks+1, ks+1); wi(ks+1) = Zero; wr(ks) = wr(ks+1); wi(ks) = wi(ks+1); } } else { // // ==== Got NS/2 or fewer shifts? Use DLAQR4 or // . DLAHQR on a trailing principal submatrix to // . get more. (Since NS.LE.NSMAX.LE.(N+6)/9, // . there is enough space below the subdiagonal // . to fit an NS-by-NS scratch array.) ==== // if (kBot-ks+1<=ns/2) { ks = kBot - ns +1; H(_(ks,kBot),_(1,ns)) = H(_(ks,kBot),_(ks,kBot)); if (ns>nMin) { // TODO: avoid the need for ZDummy typename GeMatrix<MZ>::NoView ZDummy; ks += laqr4(false, false, IndexType(1), ns, H(_(ks,kBot),_(1,ns)), wr(_(ks,kBot)), wi(_(ks,kBot)), IndexType(1), IndexType(1), ZDummy, work); } else { // TODO: avoid the need for ZDummy typename GeMatrix<MZ>::NoView ZDummy; ks += lahqr(false, false, IndexType(1), ns, H(_(ks,kBot),_(1,ns)), wr(_(ks,kBot)), wi(_(ks,kBot)), IndexType(1), IndexType(1), ZDummy); } // // ==== In case of a rare QR failure use // . eigenvalues of the trailing 2-by-2 // . principal submatrix. ==== // if (ks>=kBot) { T aa = H(kBot-1,kBot-1); T cc = H(kBot, kBot-1); T bb = H(kBot-1,kBot); T dd = H(kBot, kBot); T cs, sn; lanv2(aa, bb, cc, dd, wr(kBot-1), wi(kBot-1), wr(kBot), wi(kBot), cs, sn); ks = kBot - 1; } } if (kBot-ks+1>ns) { // // ==== Sort the shifts (Helps a little) // . Bubble sort keeps complex conjugate // . pairs together. ==== // bool sorted = false; for (IndexType k=kBot; k>=ks+1; --k) { if (sorted) { break; } sorted = true; for (IndexType i=ks; i<=k-1; ++i) { if (abs(wr(i))+abs(wi(i)) < abs(wr(i+1))+abs(wi(i+1))) { sorted = false; swap(wr(i), wr(i+1)); swap(wi(i), wi(i+1)); } } } } // // ==== Shuffle shifts into pairs of real shifts // . and pairs of complex conjugate shifts // . assuming complex conjugate shifts are // . already adjacent to one another. (Yes, // . they are.) ==== // for (IndexType i=kBot; i>=ks+2; i-=2) { if (wi(i)!=-wi(i-1)) { T tmp = wr(i); wr(i) = wr(i-1); wr(i-1) = wr(i-2); wr(i-2) = tmp; tmp = wi(i); wi(i) = wi(i-1); wi(i-1) = wi(i-2); wi(i-2) = tmp; } } } // // ==== If there are only two shifts and both are // . real, then use only one. ==== // if (kBot-ks+1==2) { if (wi(kBot)==0) { const T _H = H(kBot,kBot); if (abs(wr(kBot)-_H) < abs(wr(kBot-1)-_H)) { wr(kBot-1) = wr(kBot); } else { wr(kBot) = wr(kBot-1); } } } // // ==== Use up to NS of the the smallest magnatiude // . shifts. If there aren't NS shifts available, // . then use them all, possibly dropping one to // . make the number of shifts even. ==== // ns = min(ns, kBot-ks+1); ns = ns - (ns%2); ks = kBot - ns + 1; // // ==== Small-bulge multi-shift QR sweep: // . split workspace under the subdiagonal into // . - a KDU-by-KDU work array U in the lower // . left-hand-corner, // . - a KDU-by-at-least-KDU-but-more-is-better // . (KDU-by-NHo) horizontal work array WH along // . the bottom edge, // . - and an at-least-KDU-but-more-is-better-by-KDU // . (NVE-by-KDU) vertical work WV arrow along // . the left-hand-edge. ==== // IndexType kdu = 3*ns - 3; IndexType ku = n - kdu + 1; IndexType kmv = kdu + 4; IndexType nho = (n-kdu+1-4) - (kdu+1) + 1; typedef typename GeMatrix<MH>::View GeMatrixView; GeMatrixView _V(IndexType(3), ns/2, work(_(1,3*ns/2))); auto _U = H(_( ku, n), _( 1, kdu)); auto _WV = H(_(kmv,n-kdu), _( 1, kdu)); auto _WH = H(_( ku, n), _(kdu+1,kdu+nho)); // // ==== Small-bulge multi-shift QR sweep ==== // laqr5(wantT, wantZ, kacc22, kTop, kBot, ns, wr(_(ks,kBot)), wi(_(ks,kBot)), H, IndexType(iLoZ), IndexType(iHiZ), Z, _V, _U, _WV, _WH); } // // ==== Note progress (or the lack of it). ==== // if (ld>0) { nDfl = 1; } else { ++nDfl; } // // ==== End of main loop ==== // } // // ==== Iteration limit exceeded. Set INFO to show where // . the problem occurred and exit. ==== // if (it>itMax) { info = kBot; } } work(1) = lWorkOpt; return info; } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { template <typename IndexType, typename MH> IndexType laqr0_wsq_impl(bool wantT, bool wantZ, IndexType iLo, IndexType iHi, const GeMatrix<MH> &H) { typedef typename GeMatrix<MH>::ElementType T; T WORK, DUMMY; const IndexType LWORK = -1; cxxlapack::laqr0<IndexType>(wantT, wantZ, H.numRows(), iLo, iHi, &DUMMY, H.leadingDimension(), &DUMMY, &DUMMY, IndexType(1), IndexType(1), &DUMMY, IndexType(1), &WORK, LWORK); return WORK; } template <typename IndexType, typename MH, typename VWR, typename VWI, typename MZ, typename VWORK> IndexType laqr0_impl(bool wantT, bool wantZ, IndexType iLo, IndexType iHi, GeMatrix<MH> &H, DenseVector<VWR> &wr, DenseVector<VWI> &wi, IndexType iLoZ, IndexType iHiZ, GeMatrix<MZ> &Z, DenseVector<VWORK> &work) { IndexType info; info = cxxlapack::laqr0<IndexType>(wantT, wantZ, H.numRows(), iLo, iHi, H.data(), H.leadingDimension(), wr.data(), wi.data(), iLoZ, iHiZ, Z.data(), Z.leadingDimension(), work.data(), work.length()); ASSERT(info>=0); return info; } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== template <typename IndexType, typename MH> IndexType laqr0_wsq(bool wantT, bool wantZ, IndexType iLo, IndexType iHi, const GeMatrix<MH> &H) { using std::max; // // Test the input parameters // # ifndef NDEBUG ASSERT(H.firstRow()==1); ASSERT(H.firstCol()==1); ASSERT(H.numRows()==H.numCols()); const IndexType n = H.numRows(); if (n>0) { ASSERT(1<=iLo); ASSERT(iLo<=iHi); ASSERT(iHi<=n); } else { ASSERT(iLo==1); ASSERT(iHi==0); } # endif // // Call implementation // IndexType info = LAPACK_SELECT::laqr0_wsq_impl(wantT, wantZ, iLo, iHi, H); # ifdef CHECK_CXXLAPACK // // Compare results // IndexType _info = external::laqr0_wsq_impl(wantT, wantZ, iLo, iHi, H); if (info!=_info) { std::cerr << "CXXLAPACK: info = " << info << std::endl; std::cerr << "F77LAPACK: _info = " << _info << std::endl; ASSERT(0); } # endif return info; } template <typename IndexType, typename MH, typename VWR, typename VWI, typename MZ, typename VWORK> IndexType laqr0(bool wantT, bool wantZ, IndexType iLo, IndexType iHi, GeMatrix<MH> &H, DenseVector<VWR> &wr, DenseVector<VWI> &wi, IndexType iLoZ, IndexType iHiZ, GeMatrix<MZ> &Z, DenseVector<VWORK> &work) { LAPACK_DEBUG_OUT("laqr0"); using std::max; // // Test the input parameters // # ifndef NDEBUG ASSERT(H.firstRow()==1); ASSERT(H.firstCol()==1); ASSERT(H.numRows()==H.numCols()); const IndexType n = H.numRows(); if (n>0) { ASSERT(1<=iLo); ASSERT(iLo<=iHi); ASSERT(iHi<=n); } else { ASSERT(iLo==1); ASSERT(iHi==0); } ASSERT(wr.firstIndex()==1); ASSERT(wr.length()>=iHi); ASSERT(wi.firstIndex()==1); ASSERT(wi.length()>=iHi); ASSERT(1<=iLoZ); ASSERT(iLoZ<=iLo); ASSERT(iHi<=iHiZ); ASSERT(iHiZ<=n); ASSERT(Z.firstRow()==1); ASSERT(Z.firstCol()==1); ASSERT(Z.numRows()>=iHi); ASSERT(Z.numCols()>=iHi); ASSERT((work.length()==0) || (work.length()>=n)); # endif // // Make copies of output arguments // # ifdef CHECK_CXXLAPACK typename GeMatrix<MH>::NoView H_org = H; typename DenseVector<VWR>::NoView wr_org = wr; typename DenseVector<VWI>::NoView wi_org = wi; typename GeMatrix<MZ>::NoView Z_org = Z; typename DenseVector<VWORK>::NoView work_org = work; # endif // // Call implementation // IndexType info = LAPACK_SELECT::laqr0_impl(wantT, wantZ, iLo, iHi, H, wr, wi, iLoZ, iHiZ, Z, work); # ifdef CHECK_CXXLAPACK // // Make copies of results computed by the generic implementation // typename GeMatrix<MH>::NoView H_generic = H; typename DenseVector<VWR>::NoView wr_generic = wr; typename DenseVector<VWI>::NoView wi_generic = wi; typename GeMatrix<MZ>::NoView Z_generic = Z; typename DenseVector<VWORK>::NoView work_generic = work; // // restore output arguments // H = H_org; wr = wr_org; wi = wi_org; Z = Z_org; work = work_org; // // Compare generic results with results from the native implementation // IndexType _info = external::laqr0_impl(wantT, wantZ, iLo, iHi, H, wr, wi, iLoZ, iHiZ, Z, work); bool failed = false; if (! isIdentical(H_generic, H, "H_generic", "H")) { std::cerr << "CXXLAPACK: H_generic = " << H_generic << std::endl; std::cerr << "F77LAPACK: H = " << H << std::endl; failed = true; } if (! isIdentical(wr_generic, wr, "wr_generic", "wr")) { std::cerr << "CXXLAPACK: wr_generic = " << wr_generic << std::endl; std::cerr << "F77LAPACK: wr = " << wr << std::endl; failed = true; } if (! isIdentical(wi_generic, wi, "wi_generic", "wi")) { std::cerr << "CXXLAPACK: wi_generic = " << wi_generic << std::endl; std::cerr << "F77LAPACK: wi = " << wi << std::endl; failed = true; } if (! isIdentical(Z_generic, Z, "Z_generic", "Z")) { std::cerr << "CXXLAPACK: Z_generic = " << Z_generic << std::endl; std::cerr << "F77LAPACK: Z = " << Z << 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 (! isIdentical(work_generic, work, "work_generic", "work")) { std::cerr << "CXXLAPACK: work_generic = " << work_generic << std::endl; std::cerr << "F77LAPACK: work = " << work << std::endl; failed = true; } if (failed) { std::cerr << "error in: laqr0.tcc" << std::endl; ASSERT(0); } else { // std::cerr << "passed: laqr0.tcc" << std::endl; } # endif return info; } //-- forwarding ---------------------------------------------------------------- template <typename IndexType, typename MH> IndexType laqr0_wsq(bool wantT, bool wantZ, IndexType iLo, IndexType iHi, const MH &&H) { CHECKPOINT_ENTER; const IndexType info = laqr0_wsq(wantT, wantZ, iLo, iHi, H); CHECKPOINT_LEAVE; return info; } template <typename IndexType, typename MH, typename VWR, typename VWI, typename MZ, typename VWORK> IndexType laqr0(bool wantT, bool wantZ, IndexType iLo, IndexType iHi, MH &&H, VWR &&wr, VWI &&wi, IndexType iLoZ, IndexType iHiZ, MZ &&Z, VWORK &&work) { CHECKPOINT_ENTER; const IndexType info = laqr0(wantT, wantZ, iLo, iHi, H, wr, wi, iLoZ, iHiZ, Z, work); CHECKPOINT_LEAVE; return info; } } } // namespace lapack, flens #endif // FLENS_LAPACK_LA_LAQR0_TCC |