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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 DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, $ SR, SI, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, $ LDU, NV, WV, LDWV, NH, WH, LDWH ) * * -- LAPACK auxiliary routine (version 3.3.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2010 * */ #ifndef FLENS_LAPACK_LA_LAQR5_TCC #define FLENS_LAPACK_LA_LAQR5_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 VSR, typename VSI, typename MH, typename MZ, typename MV, typename MU, typename MWV, typename MWH> void laqr5_impl(bool wantT, bool wantZ, IndexType kacc22, IndexType kTop, IndexType kBot, IndexType nShifts, DenseVector<VSR> &sr, DenseVector<VSI> &si, GeMatrix<MH> &H, IndexType iLoZ, IndexType iHiZ, GeMatrix<MZ> &Z, GeMatrix<MV> &V, GeMatrix<MU> &U, GeMatrix<MWV> &WV, GeMatrix<MWH> &WH) { using std::abs; using std::max; using std::min; typedef typename GeMatrix<MH>::ElementType T; const T Zero(0), One(1); const Underscore<IndexType> _; const IndexType n = H.numRows(); const IndexType nv = WV.numRows(); const IndexType nh = WH.numCols(); typedef typename GeMatrix<MH>::VectorView VectorView; T vtBuffer[3]; VectorView vt = typename VectorView::Engine(3, vtBuffer); // // ==== If there are no shifts, then there is nothing to do. ==== // if (nShifts<2) { return; } // // ==== If the active block is empty or 1-by-1, then there // . is nothing to do. ==== // if (kTop>=kBot) { return; } // // ==== Shuffle shifts into pairs of real shifts and pairs // . of complex conjugate shifts assuming complex // . conjugate shifts are already adjacent to one // . another. ==== // for (IndexType i=1; i<=nShifts-2; i+=2) { if (si(i)!=-si(i+1)) { T tmp = sr(i); sr(i) = sr(i+1); sr(i+1) = sr(i+2); sr(i+2) = tmp; tmp = si(i); si(i) = si(i+1); si(i+1) = si(i+2); si(i+2) = tmp; } } // // ==== NSHFTS is supposed to be even, but if it is odd, // . then simply reduce it by one. The shuffle above // . ensures that the dropped shift is real and that // . the remaining shifts are paired. ==== // const IndexType ns = nShifts - (nShifts % 2); // // ==== Machine constants for deflation ==== // T safeMin = lamch<T>(SafeMin); T safeMax = One/safeMin; labad(safeMin, safeMax); const T ulp = lamch<T>(Precision); const T smallNum = safeMin*(T(n)/ulp); // // ==== Use accumulated reflections to update far-from-diagonal // . entries ? ==== // const bool accum = (kacc22==1) || (kacc22==2); // // ==== If so, exploit the 2-by-2 block structure? ==== // const bool blk22 = (ns>2) && (kacc22==2); // // ==== clear trash ==== // if (kTop+2<=kBot) { H(kTop+2,kTop) = Zero; } // // ==== NBMPS = number of 2-shift bulges in the chain ==== // const IndexType nBmps = ns/2; // // ==== KDU = width of slab ==== // const IndexType kdu = 6*nBmps - 3; // // ==== Create and chase chains of NBMPS bulges ==== // for (IndexType inCol=3*(1-nBmps)+kTop-1; inCol<=kBot-2; inCol+=3*nBmps-2) { IndexType ndCol = inCol + kdu; if (accum) { auto U_ = U(_(1,kdu),_(1,kdu)); U_ = Zero; U_.diag(0) = One; } // // ==== Near-the-diagonal bulge chase. The following loop // . performs the near-the-diagonal part of a small bulge // . multi-shift QR sweep. Each 6*NBMPS-2 column diagonal // . chunk extends from column INCOL to column NDCOL // . (including both column INCOL and column NDCOL). The // . following loop chases a 3*NBMPS column long chain of // . NBMPS bulges 3*NBMPS-2 columns to the right. (INCOL // . may be less than KTOP and and NDCOL may be greater than // . KBOT indicating phantom columns from which to chase // . bulges before they are actually introduced or to which // . to chase bulges beyond column KBOT.) ==== // const IndexType krColMax = min(inCol+3*nBmps-3, kBot-2); for (IndexType krCol=inCol; krCol<=krColMax; ++krCol) { // // ==== Bulges number MTOP to MBOT are active double implicit // . shift bulges. There may or may not also be small // . 2-by-2 bulge, if there is room. The inactive bulges // . (if any) must wait until the active bulges have moved // . down the diagonal to make room. The phantom matrix // . paradigm described above helps keep track. ==== // const IndexType mTop = max(IndexType(1), ((kTop-1)-krCol+2)/3+1); const IndexType mBot = min(nBmps, (kBot-krCol)/3); const IndexType m22 = mBot + 1; const bool bmp22 = (mBot<nBmps ) && (krCol+3*(m22-1))==(kBot-2); // // ==== Generate reflections to chase the chain right // . one column. (The minimum value of K is KTOP-1.) ==== // IndexType k; T alpha, beta; for (IndexType m=mTop; m<=mBot; ++m) { k = krCol + 3*(m-1); if (k==kTop-1) { laqr1(H(_(kTop,kTop+2),_(kTop,kTop+2)), sr(2*m-1), si(2*m-1), sr(2*m), si(2*m), V(_(1,3),m)); alpha = V(1,m); larfg(IndexType(3), alpha, V(_(2,3),m), V(1,m)); } else { beta = H(k+1,k); V(2,m) = H(k+2,k); V(3,m) = H(k+3,k); larfg(IndexType(3), beta, V(_(2,3),m), V(1,m)); // // ==== A Bulge may collapse because of vigilant // . deflation or destructive underflow. In the // . underflow case, try the two-small-subdiagonals // . trick to try to reinflate the bulge. ==== // if (H(k+3,k)!=Zero || H(k+3,k+1)!=Zero || H(k+3,k+2)==Zero) { // // ==== Typical case: not collapsed (yet). ==== // H(k+1, k) = beta; H(k+2, k) = Zero; H(k+3, k) = Zero; } else { // // ==== Atypical case: collapsed. Attempt to // . reintroduce ignoring H(K+1,K) and H(K+2,K). // . If the fill resulting from the new // . reflector is too large, then abandon it. // . Otherwise, use the new one. ==== // laqr1(H(_(k+1,k+3),_(k+1,k+3)), sr(2*m-1), si(2*m-1), sr(2*m), si(2*m), vt); alpha = vt(1); larfg(3, alpha, vt(_(2,3)), vt(1)); const T refSum = vt(1)*(H(k+1,k) + vt(2)*H(k+2,k)); if (abs(H(k+2,k)-refSum*vt(2)) + abs(refSum*vt(3)) > ulp*(abs(H(k,k))+abs(H(k+1,k+1))+abs(H(k+2,k+2)))) { // // ==== Starting a new bulge here would // . create non-negligible fill. Use // . the old one with trepidation. ==== // H(k+1, k) = beta; H(k+2, k) = Zero; H(k+3, k) = Zero; } else { // // ==== Stating a new bulge here would // . create only negligible fill. // . Replace the old reflector with // . the new one. ==== // H(k+1, k) -= refSum; H(k+2, k) = Zero; H(k+3, k) = Zero; V(1, m) = vt(1); V(2, m) = vt(2); V(3, m) = vt(3); } } } } // // ==== Generate a 2-by-2 reflection, if needed. ==== // k = krCol + 3*(m22-1); if (bmp22) { if (k==kTop-1) { laqr1(H(_(k+1,k+2),_(k+1,k+2)), sr(2*m22-1), si(2*m22-1), sr(2*m22), si(2*m22), V(_(1,2),m22)); beta = V(1, m22); larfg(IndexType(2), beta, V(_(2,2),m22), V(1,m22)); } else { beta = H(k+1, k); V(2, m22) = H(k+2,k); larfg(IndexType(2), beta, V(_(2,2),m22), V(1,m22)); H(k+1, k) = beta; H(k+2, k) = Zero; } } // // ==== Multiply H by reflections from the left ==== // IndexType jBot; if (accum) { jBot = min(ndCol, kBot); } else if (wantT) { jBot = n; } else { jBot = kBot; } for (IndexType j=max(kTop,krCol); j<=jBot; ++j) { IndexType mEnd = min(mBot, (j-krCol+2)/3); for (IndexType m=mTop; m<=mEnd; ++m) { k = krCol + 3*(m-1); const T refSum = V(1,m)*(H(k+1,j) + V(2,m)*H(k+2,j) + V(3,m)*H(k+3,j)); H(k+1,j) -= refSum; H(k+2,j) -= refSum*V(2,m); H(k+3,j) -= refSum*V(3,m); } } if (bmp22) { k = krCol + 3*(m22-1); for (IndexType j=max(k+1,kTop); j<=jBot; ++j) { const T refSum = V(1,m22)*(H(k+1,j)+V(2,m22)*H(k+2,j)); H(k+1,j) -= refSum; H(k+2,j) -= refSum*V(2,m22); } } // // ==== Multiply H by reflections from the right. // . Delay filling in the last row until the // . vigilant deflation check is complete. ==== // IndexType jTop; if (accum) { jTop = max(kTop, inCol); } else if (wantT) { jTop = 1; } else { jTop = kTop; } for (IndexType m=mTop; m<=mBot; ++m) { if (V(1,m)!=Zero) { k = krCol + 3*(m-1); for (IndexType j=jTop; j<=min(kBot,k+3); ++j) { const T refSum = V(1,m)*(H(j,k+1) + V(2,m)*H(j,k+2) + V(3,m)*H(j,k+3)); H(j, k+1) -= refSum; H(j, k+2) -= refSum*V(2, m); H(j, k+3) -= refSum*V(3, m); } if (accum) { // // ==== Accumulate U. (If necessary, update Z later // . with with an efficient matrix-matrix // . multiply.) ==== // IndexType kms = k - inCol; IndexType j1 = max(IndexType(1),kTop-inCol); for (IndexType j=j1; j<=kdu; ++j) { const T refSum = V(1,m)*(U(j,kms+1) + V(2,m)*U(j,kms+2) + V(3,m)*U(j,kms+3)); U(j, kms+1) -= refSum; U(j, kms+2) -= refSum*V(2, m); U(j, kms+3) -= refSum*V(3, m); } } else if (wantZ) { // // ==== U is not accumulated, so update Z // . now by multiplying by reflections // . from the right. ==== // for (IndexType j=iLoZ; j<=iHiZ; ++j) { const T refSum = V(1,m)*(Z(j,k+1) +V(2,m)*Z(j,k+2) +V(3,m)*Z(j,k+3)); Z(j,k+1) -= refSum; Z(j,k+2) -= refSum*V(2,m); Z(j,k+3) -= refSum*V(3,m); } } } } // // ==== Special case: 2-by-2 reflection (if needed) ==== // k = krCol + 3*(m22-1); if (bmp22) { if (V(1,m22)!=Zero) { for (IndexType j=jTop; j<=min(kBot,k+3); ++j) { const T refSum = V(1,m22)*(H(j,k+1)+V(2,m22)*H(j,k+2)); H(j,k+1) -= refSum; H(j,k+2) -= refSum*V(2,m22); } if (accum) { IndexType kms = k - inCol; IndexType j1 = max(IndexType(1),kTop-inCol); for (IndexType j=j1; j<=kdu; ++j) { const T refSum = V(1,m22)*(U(j,kms+1) + V(2,m22)*U(j,kms+2)); U(j,kms+1 ) -= refSum; U(j,kms+2 ) -= refSum*V(2,m22); } } else if (wantZ) { for (IndexType j=iLoZ; j<=iHiZ; ++j) { const T refSum = V(1,m22)*(Z(j,k+1) + V(2,m22)*Z(j,k+2)); Z(j,k+1) -= refSum; Z(j,k+2) -= refSum*V(2,m22); } } } } // // ==== Vigilant deflation check ==== // IndexType mStart = mTop; if (krCol+3*(mStart-1)<kTop) { ++mStart; } IndexType mEnd = mBot; if (bmp22) { ++mEnd; } if (krCol==kBot-2) { ++mEnd; } for (IndexType m=mStart; m<=mEnd; ++m) { k = min(kBot-1, krCol+3*(m-1)); // // ==== The following convergence test requires that // . the tradition small-compared-to-nearby-diagonals // . criterion and the Ahues & Tisseur (LAWN 122, 1997) // . criteria both be satisfied. The latter improves // . accuracy in some examples. Falling back on an // . alternate convergence criterion when TST1 or TST2 // . is zero (as done here) is traditional but probably // . unnecessary. ==== // if (H(k+1,k)!=Zero) { T test1 = abs(H(k,k)) + abs(H(k+1,k+1)); if (test1==Zero) { if (k>=kTop+1) { test1 += abs(H(k,k-1)); } if (k>=kTop+2) { test1 += abs(H(k,k-2)); } if (k>=kTop+3) { test1 += abs(H(k,k-3)); } if (k<=kBot-2) { test1 += abs(H(k+2,k+1)); } if (k<=kBot-3) { test1 += abs(H(k+3,k+1)); } if (k<=kBot-4) { test1 += abs(H(k+4,k+1)); } } if (abs(H(k+1,k))<=max(smallNum, ulp*test1)) { const T H12 = max(abs(H(k+1,k)), abs(H(k,k+1))); const T H21 = min(abs(H(k+1,k)), abs(H(k,k+1))); const T H11 = max(abs(H(k+1,k+1)), abs(H(k,k)-H(k+1,k+1))); const T H22 = min(abs(H(k+1,k+1)), abs(H(k,k)-H(k+1,k+1))); const T scal = H11 + H12; const T test2 = H22*(H11/scal); if (test2==Zero || H21*(H12/scal)<=max(smallNum,ulp*test2)) { H(k+1,k) = Zero; } } } } // // ==== Fill in the last row of each bulge. ==== // mEnd = min(nBmps, (kBot-krCol-1)/3); for (IndexType m=mTop; m<=mEnd; ++m) { k = krCol + 3*(m-1); const T refSum = V(1,m)*V(3,m)*H(k+4,k+3); H(k+4,k+1) = -refSum; H(k+4,k+2) = -refSum*V(2,m); H(k+4,k+3) -= refSum*V(3,m); } // // ==== End of near-the-diagonal bulge chase. ==== // } // // ==== Use U (if accumulated) to update far-from-diagonal // . entries in H. If required, use U to update Z as // . well. ==== // if (accum) { IndexType jTop, jBot; if (wantT) { jTop = 1; jBot = n; } else { jTop = kTop; jBot = kBot; } if ((!blk22) || (inCol<kTop) || (ndCol>kBot) || (ns<=2)) { // // ==== Updates not exploiting the 2-by-2 block // . structure of U. K1 and NU keep track of // . the location and size of U in the special // . cases of introducing bulges and chasing // . bulges off the bottom. In these special // . cases and in case the number of shifts // . is NS = 2, there is no 2-by-2 block // . structure to exploit. ==== // const IndexType k1 = max(IndexType(1), kTop-inCol); const IndexType nu = (kdu-max(IndexType(0), ndCol-kBot)) -k1+1; const IndexType _nu = (kdu-max(IndexType(0), ndCol-kBot)); // // ==== Horizontal Multiply ==== // for (IndexType jCol=min(ndCol,kBot)+1; jCol<=jBot; jCol+=nh) { const IndexType jLen = min(nh, jBot-jCol+1); auto _U = U(_(k1, _nu), _(k1, _nu)); auto _H = H(_(inCol+k1,inCol+_nu),_(jCol,jCol+jLen-1)); auto _WH = WH(_(1,nu),_(1,jLen)); blas::mm(ConjTrans, NoTrans, One, _U, _H, Zero, _WH); _H = _WH; } // // ==== Vertical multiply ==== // for (IndexType jRow=jTop; jRow<=max(kTop,inCol)-1; jRow+=nv) { const IndexType jLen = min(nv, max(kTop,inCol)-jRow); auto _H = H(_(jRow,jRow+jLen-1),_(inCol+k1,inCol+_nu)); auto _U = U(_(k1,_nu),_(k1,_nu)); auto _WV = WV(_(1,jLen),_(1,nu)); blas::mm(NoTrans, NoTrans, One, _H, _U, Zero, _WV); _H = _WV; } // // ==== Z multiply (also vertical) ==== // if (wantZ) { for (IndexType jRow=iLoZ; jRow<=iHiZ; jRow+=nv) { const IndexType jLen = min(nv, iHiZ-jRow+1); auto _Z = Z(_(jRow,jRow+jLen-1),_(inCol+k1,inCol+_nu)); auto _U = U(_(k1,_nu),_(k1,_nu)); auto _WV = WV(_(1,jLen),_(1,nu)); blas::mm(NoTrans, NoTrans, One, _Z, _U, Zero, _WV); _Z = _WV; } } } else { // // ==== Updates exploiting U's 2-by-2 block structure. // . (I2, I4, J2, J4 are the last rows and columns // . of the blocks.) ==== // const IndexType i2 = (kdu+1 ) / 2; const IndexType i4 = kdu; const IndexType j2 = i4 - i2; const IndexType j4 = kdu; // // ==== KZS and KNZ deal with the band of zeros // . along the diagonal of one of the triangular // . blocks. ==== // const IndexType kZs = (j4-j2) - (ns+1); const IndexType kNz = ns + 1; // // ==== Horizontal multiply ==== // for (IndexType jCol=min(ndCol, kBot)+1; jCol<=jBot; jCol+=nh) { const IndexType jLen = min(nh, jBot-jCol+1); // // ==== Copy bottom of H to top+KZS of scratch ==== // (The first KZS rows get multiplied by zero.) ==== // WH(_(kZs+1,kZs+kNz),_(1,jLen)) = H(_(inCol+j2+1,inCol+j2+kNz),_(jCol,jCol+jLen-1)); // // ==== Multiply by U21**T ==== // WH(_(1,kZs),_(1,jLen)) = Zero; blas::mm(Left, ConjTrans, One, U(_(j2+1,j2+kNz),_(kZs+1,kZs+kNz)).upper(), WH(_(kZs+1,kZs+kNz),_(1,jLen))); // // ==== Multiply top of H by U11**T ==== // blas::mm(ConjTrans, NoTrans, One, U(_(1,j2),_(1,i2)), H(_(inCol+1,inCol+j2),_(jCol,jCol+jLen-1)), One, WH(_(1,i2),_(1,jLen))); // // ==== Copy top of H to bottom of WH ==== // WH(_(i2+1,i2+j2),_(1,jLen)) = H(_(inCol+1,inCol+j2),_(jCol,jCol+jLen-1)); // // ==== Multiply by U21**T ==== // blas::mm(Left, ConjTrans, One, U(_(1,j2),_(i2+1,i2+j2)).lower(), WH(_(i2+1,i2+j2),_(1,jLen))); // // ==== Multiply by U22 ==== // blas::mm(ConjTrans, NoTrans, One, U(_(j2+1,j4),_(i2+1,i4)), H(_(inCol+j2+1,inCol+j4),_(jCol,jCol+jLen-1)), One, WH(_(i2+1,i4),_(1,jLen))); // // ==== Copy it back ==== // H(_(inCol+1,inCol+kdu),_(jCol,jCol+jLen-1)) = WH(_(1,kdu),_(1,jLen)); } // // ==== Vertical multiply ==== // for (IndexType jRow=jTop; jRow<=max(inCol,kTop)-1; jRow+=nv) { const IndexType jLen = min(nv, max(inCol,kTop) -jRow); // // ==== Copy right of H to scratch (the first KZS // . columns get multiplied by zero) ==== // WV(_(1,jLen),_(kZs+1,kZs+kNz)) = H(_(jRow,jRow+jLen-1),_(inCol+j2+1, inCol+j2+kNz)); // // ==== Multiply by U21 ==== // WV(_(1,jLen),_(1,kZs)) = Zero; blas::mm(Right, NoTrans, One, U(_(j2+1,j2+kNz),_(kZs+1,kZs+kNz)).upper(), WV(_(1,jLen),_(kZs+1,kZs+kNz))); // // ==== Multiply by U11 ==== // blas::mm(NoTrans, NoTrans, One, H(_(jRow,jRow+jLen-1),_(inCol+1,inCol+j2)), U(_(1,j2),_(1,i2)), One, WV(_(1,jLen),_(1,i2))); // // ==== Copy left of H to right of scratch ==== // WV(_(1,jLen),_(i2+1,i2+j2)) = H(_(jRow,jRow+jLen-1), _(inCol+1,inCol+j2)); // // ==== Multiply by U21 ==== // blas::mm(Right, NoTrans, One, U(_(1,i4-i2),_(i2+1,i4)).lower(), WV(_(1,jLen),_(i2+1,i4))); // // ==== Multiply by U22 ==== // blas::mm(NoTrans, NoTrans, One, H(_(jRow,jRow+jLen-1),_(inCol+j2+1,inCol+j4)), U(_(j2+1,j4),_(i2+1,i4)), One, WV(_(1,jLen),_(i2+1,i4))); // // ==== Copy it back ==== // H(_(jRow,jRow+jLen-1),_(inCol+1,inCol+kdu)) = WV(_(1,jLen),_(1,kdu)); } // // ==== Multiply Z (also vertical) ==== // if (wantZ) { for (IndexType jRow=iLoZ; jRow<=iHiZ; jRow+=nv) { const IndexType jLen = min(nv,iHiZ-jRow+1); // // ==== Copy right of Z to left of scratch (first // . KZS columns get multiplied by zero) ==== // WV(_(1,jLen),_(kZs+1,kZs+kNz)) = Z(_(jRow,jRow+jLen-1),_(inCol+j2+1,inCol+j2+kNz)); // // ==== Multiply by U12 ==== // WV(_(1,jLen),_(1,kZs)) = Zero; blas::mm(Right, NoTrans, One, U(_(j2+1,j2+kNz), _(kZs+1,kZs+kNz)).upper(), WV(_(1,jLen),_(kZs+1,kZs+kNz))); // // ==== Multiply by U11 ==== // blas::mm(NoTrans, NoTrans, One, Z(_(jRow,jRow+jLen-1), _(inCol+1,inCol+j2)), U(_(1,j2),_(1,i2)), One, WV(_(1,jLen),_(1,i2))); // // ==== Copy left of Z to right of scratch ==== // WV(_(1,jLen),_(i2+1,i2+j2)) = Z(_(jRow,jRow+jLen-1), _(inCol+1,inCol+j2)); // // ==== Multiply by U21 ==== // blas::mm(Right, NoTrans, One, U(_(1,i4-i2),_(i2+1,i4)).lower(), WV(_(1,jLen),_(i2+1,i4))); // // ==== Multiply by U22 ==== // blas::mm(NoTrans, NoTrans, One, Z(_(jRow,jRow+jLen-1),_(inCol+j2+1,inCol+j4)), U(_(j2+1,j4),_(i2+1,i4)), One, WV(_(1,jLen),_(i2+1,i4))); // // ==== Copy the result back to Z ==== // Z(_(jRow,jRow+jLen-1),_(inCol+1,inCol+kdu)) = WV(_(1,jLen),_(1,kdu)); } } } } } } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { template <typename IndexType, typename VSR, typename VSI, typename MH, typename MZ, typename MV, typename MU, typename MWV, typename MWH> void laqr5_impl(bool wantT, bool wantZ, IndexType kacc22, IndexType kTop, IndexType kBot, IndexType nShifts, DenseVector<VSR> &sr, DenseVector<VSI> &si, GeMatrix<MH> &H, IndexType iLoZ, IndexType iHiZ, GeMatrix<MZ> &Z, GeMatrix<MV> &V, GeMatrix<MU> &U, GeMatrix<MWV> &WV, GeMatrix<MWH> &WH) { cxxlapack::laqr5<IndexType>(wantT, wantZ, kacc22, H.numRows(), kTop, kBot, nShifts, sr.data(), si.data(), H.data(), H.leadingDimension(), iLoZ, iHiZ, Z.data(), Z.leadingDimension(), V.data(), V.leadingDimension(), U.data(), U.leadingDimension(), WV.numRows(), WV.data(), WV.leadingDimension(), WH.numCols(), WH.data(), WH.leadingDimension()); } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== template <typename IndexType, typename VSR, typename VSI, typename MH, typename MZ, typename MV, typename MU, typename MWV, typename MWH> void laqr5(bool wantT, bool wantZ, IndexType kacc22, IndexType kTop, IndexType kBot, IndexType nShifts, DenseVector<VSR> &sr, DenseVector<VSI> &si, GeMatrix<MH> &H, IndexType iLoZ, IndexType iHiZ, GeMatrix<MZ> &Z, GeMatrix<MV> &V, GeMatrix<MU> &U, GeMatrix<MWV> &WV, GeMatrix<MWH> &WH) { LAPACK_DEBUG_OUT("laqr5"); using std::max; // // Test the input parameters // # ifndef NDEBUG ASSERT((kacc22==0)||(kacc22==1)||(kacc22==2)); ASSERT(H.firstRow()==1); ASSERT(H.firstCol()==1); ASSERT(H.numRows()==H.numCols()); const IndexType n = H.numRows(); ASSERT(1<=kTop); ASSERT(kBot<=n); ASSERT(nShifts>0); ASSERT(nShifts % 2 == 0); ASSERT(sr.length()==nShifts); ASSERT(si.length()==nShifts); if (wantZ) { ASSERT(1<=iLoZ); ASSERT(iLoZ<=iHiZ); ASSERT(iHiZ<=n); } ASSERT(V.firstRow()==1); ASSERT(V.firstCol()==1); ASSERT(V.numRows()>=3); ASSERT(V.numCols()==nShifts/2); ASSERT(U.firstRow()==1); ASSERT(U.firstCol()==1); ASSERT(U.numRows()>=3*nShifts-3); ASSERT(WH.firstRow()==1); ASSERT(WH.firstCol()==1); ASSERT(WH.numRows()>=3*nShifts-3); ASSERT(WH.numCols()>=1); ASSERT(WV.firstRow()==1); ASSERT(WV.firstCol()==1); ASSERT(WV.numRows()>=1); ASSERT(WV.numCols()>=3*nShifts-3); # endif // // Make copies of output arguments // # ifdef CHECK_CXXLAPACK typename DenseVector<VSR>::NoView sr_org = sr; typename DenseVector<VSI>::NoView si_org = si; typename GeMatrix<MH>::NoView H_org = H; typename GeMatrix<MZ>::NoView Z_org = Z; typename GeMatrix<MV>::NoView V_org = V; typename GeMatrix<MU>::NoView U_org = U; typename GeMatrix<MWV>::NoView WV_org = WV; typename GeMatrix<MWH>::NoView WH_org = WH; # endif // // Call implementation // LAPACK_SELECT::laqr5_impl(wantT, wantZ, kacc22, kTop, kBot, nShifts, sr, si, H, iLoZ, iHiZ, Z, V, U, WV, WH); # ifdef CHECK_CXXLAPACK // // Make copies of results computed by the generic implementation // typename DenseVector<VSR>::NoView sr_generic = sr; typename DenseVector<VSI>::NoView si_generic = si; typename GeMatrix<MH>::NoView H_generic = H; typename GeMatrix<MZ>::NoView Z_generic = Z; typename GeMatrix<MV>::NoView V_generic = V; typename GeMatrix<MU>::NoView U_generic = U; typename GeMatrix<MWV>::NoView WV_generic = WV; typename GeMatrix<MWH>::NoView WH_generic = WH; // // restore output arguments // sr = sr_org; si = si_org; H = H_org; Z = Z_org; V = V_org; U = U_org; WV = WV_org; WH = WH_org; // // Compare generic results with results from the native implementation // external::laqr5_impl(wantT, wantZ, kacc22, kTop, kBot, nShifts, sr, si, H, iLoZ, iHiZ, Z, V, U, WV, WH); bool failed = false; if (! isIdentical(sr_generic, sr, "sr_generic", "sr")) { std::cerr << "CXXLAPACK: sr_generic = " << sr_generic << std::endl; std::cerr << "F77LAPACK: sr = " << sr << std::endl; failed = true; } if (! isIdentical(si_generic, si, "si_generic", "si")) { std::cerr << "CXXLAPACK: si_generic = " << si_generic << std::endl; std::cerr << "F77LAPACK: si = " << si << std::endl; failed = true; } 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(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(V_generic, V, "V_generic", "V")) { std::cerr << "CXXLAPACK: V_generic = " << V_generic << std::endl; std::cerr << "F77LAPACK: V = " << V << std::endl; failed = true; } if (! isIdentical(U_generic, U, "U_generic", "U")) { std::cerr << "CXXLAPACK: U_generic = " << U_generic << std::endl; std::cerr << "F77LAPACK: U = " << U << std::endl; failed = true; } if (! isIdentical(WV_generic, WV, "WV_generic", "WV")) { std::cerr << "CXXLAPACK: WV_generic = " << WV_generic << std::endl; std::cerr << "F77LAPACK: WV = " << WV << std::endl; failed = true; } if (! isIdentical(WH_generic, WH, "WH_generic", "WH")) { std::cerr << "CXXLAPACK: WH_generic = " << WH_generic << std::endl; std::cerr << "F77LAPACK: WH = " << WH << std::endl; failed = true; } if (failed) { std::cerr << "error in: laqr5.tcc" << std::endl; std::cerr << "N = H.numRows() = " << H.numRows() << std::endl; std::cerr << "H.numCols() = " << H.numCols() << std::endl; std::cerr << "NV = WV.numRows() = " << WV.numRows() << std::endl; std::cerr << "WV.numCols() = " << WV.numCols() << std::endl; std::cerr << "NH = WH.numRows() = " << WH.numRows() << std::endl; std::cerr << "WH.numCols() = " << WH.numCols() << std::endl; ASSERT(0); } else { // std::cerr << "passed: laqr5.tcc" << std::endl; } # endif } //-- forwarding ---------------------------------------------------------------- template <typename IndexType, typename VSR, typename VSI, typename MH, typename MZ, typename MV, typename MU, typename MWV, typename MWH> void laqr5(bool wantT, bool wantZ, IndexType kacc22, IndexType kTop, IndexType kBot, IndexType nShifts, VSR &&sr, VSI &&si, MH &&H, IndexType iLoZ, IndexType iHiZ, MZ &&Z, MV &&V, MU &&U, MWV &&WV, MWH &&WH) { CHECKPOINT_ENTER; laqr5(wantT, wantZ, kacc22, kTop, kBot, nShifts, sr, si, H, iLoZ, iHiZ, Z, V, U, WV, WH); CHECKPOINT_LEAVE; } } } // namespace lapack, flens #endif // FLENS_LAPACK_LA_LAQR5_TCC |