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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 DTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, $ LDVR, MM, M, WORK, INFO ) * * -- LAPACK 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_IMPL_TREVC_TCC #define FLENS_LAPACK_IMPL_TREVC_TCC 1 #include <flens/auxiliary/auxiliary.h> #include <flens/blas/blas.h> #include <flens/lapack/lapack.h> namespace flens { namespace lapack { //== generic lapack implementation ============================================= namespace generic { template <typename VSELECT, typename MT, typename MVL, typename MVR, typename IndexType, typename VWORK> void trevc_impl(bool computeVL, bool computeVR, TREVC::Job howMany, DenseVector<VSELECT> &select, const GeMatrix<MT> &T, GeMatrix<MVL> &VL, GeMatrix<MVR> &VR, IndexType mm, IndexType &m, DenseVector<VWORK> &work) { using std::abs; using flens::max; typedef typename GeMatrix<MT>::ElementType ElementType; // TODO: define a colmajor GeMatrixView typedef typename GeMatrix<MT>::View GeMatrixView; const ElementType Zero(0), One(1); const Underscore<IndexType> _; const IndexType n = T.numCols(); // // .. Local Arrays .. // ElementType _xData[4]; GeMatrixView X = typename GeMatrixView::Engine(2, 2, _xData, 2); GeMatrixView Work(n, 3, work, n); // // Decode and test the input parameters // const bool over = howMany==TREVC::Backtransform; const bool someV = howMany==TREVC::Selected; // // Set M to the number of columns required to store the selected // eigenvectors, standardize the array SELECT if necessary, and // test MM. // if (someV) { m = 0; bool pair = false; for (IndexType j=1; j<=n; ++j) { if (pair) { pair = false; select(j) = false; } else { if (j<n) { if (T(j+1,j)==Zero) { if (select(j)) { ++m; } } else { pair = true; if (select(j) || select(j+1)) { select(j) = true; m += 2; } } } else { if (select(n)) { ++m; } } } } } else { m = n; } if (mm<m) { ASSERT(0); } // // Quick return if possible. // if (n==0) { return; } // // Set the constants to control overflow. // ElementType underflow = lamch<ElementType>(SafeMin); ElementType overflow = One / underflow; labad(underflow, overflow); const ElementType ulp = lamch<ElementType>(Precision); const ElementType smallNum = underflow*(n/ulp); const ElementType bigNum = (One-ulp)/smallNum; // // Compute 1-norm of each column of strictly upper triangular // part of T to control overflow in triangular solver. // work(1) = Zero; for (IndexType j=2; j<=n; ++j) { work(j) = Zero; for (IndexType i=1; i<=j-1; ++i) { work(j) += abs(T(i,j)); } } // // Index IP is used to specify the real or complex eigenvalue: // IP = 0, real eigenvalue, // 1, first of conjugate complex pair: (wr,wi) // -1, second of conjugate complex pair: (wr,wi) // const IndexType n2 = 2*n; ElementType scale, xNorm, wr, wi; if (computeVR) { // // Compute right eigenvectors. // IndexType ip = 0; IndexType is = m; for (IndexType ki=n; ki>=1; --ki) { if (ip==1) { ip = 0; continue; } if (ki!=1 && T(ki,ki-1)!=Zero) { ip = -1; } if (someV) { if (ip==0) { if (!select(ki)) { if (ip==1) { ip = 0; } if (ip==-1) { ip = 1; } continue; } } else { if (!select(ki-1)) { if (ip==1) { ip = 0; } if (ip==-1) { ip = 1; } continue; } } } // // Compute the KI-th eigenvalue (WR,WI). // wr = T(ki,ki); wi = Zero; if (ip!=0) { wi = sqrt(abs(T(ki,ki-1)))*sqrt(abs(T(ki-1,ki))); } const ElementType safeMin = max(ulp*(abs(wr)+abs(wi)), smallNum); if (ip==0) { // // Real right eigenvector // work(ki+n) = One; // // Form right-hand side // TODO: do this by work(_(...)) = -T(_(...),ki) // for (IndexType k=1; k<=ki-1; ++k) { work(k+n) = -T(k,ki); } // // Solve the upper quasi-triangular system: // (T(1:KI-1,1:KI-1) - WR)*X = SCALE*WORK. // IndexType jNext = ki - 1; for (IndexType j=ki-1; j>=1; --j) { if (j>jNext) { continue; } IndexType j1 = j; IndexType j2 = j; jNext = j - 1; if (j>1) { if (T(j,j-1)!=Zero) { j1 = j - 1; jNext = j - 2; } } if (j1==j2) { // // 1-by-1 diagonal block // laln2(false, IndexType(1), safeMin, One, T(_(j,j),_(j,j)), One, One, Work(_(j,j), _(2,2)), wr, Zero, X(_(1,1),_(1,1)), scale, xNorm); // // Scale X(1,1) to avoid overflow when updating // the right-hand side. // if (xNorm>One) { if (work(j)>bigNum/xNorm) { X(1,1) /= xNorm; scale /= xNorm; } } // // Scale if necessary // if (scale!=One) { work(_(1+n,ki+n)) *= scale; } work(j+n) = X(1,1); // // Update right-hand side // work(_(1+n,j-1+n)) -= X(1,1)*T(_(1,j-1),j); } else { // // 2-by-2 diagonal block // laln2(false, IndexType(1), safeMin, One, T(_(j-1,j),_(j-1,j)), One, One, Work(_(j-1,j), _(2,2)), wr, Zero, X(_(1,2),_(1,1)), scale, xNorm); // // Scale X(1,1) and X(2,1) to avoid overflow when // updating the right-hand side. // if (xNorm>One) { const ElementType beta = max(work(j-1), work(j)); if (beta>bigNum/xNorm) { X(1,1) /= xNorm; X(2,1) /= xNorm; scale /= xNorm; } } // // Scale if necessary // if (scale!=One) { work(_(1+n,ki+n)) *= scale; } work(j-1+n) = X(1,1); work(j+n) = X(2,1); // // Update right-hand side // work(_(1+n,j-2+n)) -= X(1,1)*T(_(1,j-2),j-1); work(_(1+n,j-2+n)) -= X(2,1)*T(_(1,j-2),j); } } // // Copy the vector x or Q*x to VR and normalize. // if (!over) { VR(_(1,ki),is) = work(_(1+n,ki+n)); const IndexType ii = blas::iamax(VR(_(1,ki),is)); const ElementType reMax = One / abs(VR(ii,is)); VR(_(1,ki),is) *= reMax; VR(_(ki+1,n),is) = Zero; } else { if (ki>1) { blas::mv(NoTrans, One, VR(_,_(1,ki-1)), work(_(1+n,n+ki-1)), work(ki+n), VR(_,ki)); } const IndexType ii = blas::iamax(VR(_,ki)); const ElementType reMax = One / abs(VR(ii,ki)); VR(_,ki) *= reMax; } } else { // // Complex right eigenvector. // // Initial solve // [ (T(KI-1,KI-1) T(KI-1,KI) ) - (WR + I* WI)]*X = 0. // [ (T(KI,KI-1) T(KI,KI) ) ] // if (abs(T(ki-1,ki))>=abs(T(ki,ki-1))) { work(ki-1+n) = One; work(ki+n2) = wi / T(ki-1,ki); } else { work(ki-1+n ) = -wi / T(ki,ki-1); work(ki+n2 ) = One; } work(ki+n) = Zero; work(ki-1+n2) = Zero; // // Form right-hand side // for (IndexType k=1; k<=ki-2; ++k) { work(k+n) = -work(ki-1+n) * T(k,ki-1); work(k+n2) = -work(ki+n2) * T(k,ki); } // // Solve upper quasi-triangular system: // (T(1:KI-2,1:KI-2) - (WR+i*WI))*X = SCALE*(WORK+i*WORK2) // IndexType jNext = ki - 2; for (IndexType j=ki-2; j>=1; --j) { if (j>jNext) { continue; } IndexType j1 = j; IndexType j2 = j; jNext = j - 1; if (j>1) { if (T(j,j-1)!=Zero) { j1 = j - 1; jNext = j - 2; } } if (j1==j2) { // // 1-by-1 diagonal block // laln2(false, IndexType(2), safeMin, One, T(_(j,j),_(j,j)), One, One, Work(_(j,j), _(2,3)), wr, wi, X(_(1,1),_(1,2)), scale, xNorm); // // Scale X(1,1) and X(1,2) to avoid overflow when // updating the right-hand side. // if (xNorm>One) { if (work(j)>bigNum/xNorm) { X(1,1) /= xNorm; X(1,2) /= xNorm; scale /= xNorm; } } // // Scale if necessary // if (scale!=One) { work(_(1+n,ki+n)) *= scale; work(_(1+n2,ki+n2)) *= scale; } work(j+n) = X(1,1); work(j+n2) = X(1,2); // // Update the right-hand side // work(_(1+n,j-1+n)) -= X(1,1)*T(_(1,j-1),j); work(_(1+n2,j-1+n2)) -= X(1,2)*T(_(1,j-1),j); } else { // // 2-by-2 diagonal block // laln2(false, IndexType(2), safeMin, One, T(_(j-1,j),_(j-1,j)), One, One, Work(_(j-1,j), _(2,3)), wr, wi, X(_(1,2),_(1,2)), scale, xNorm); // // Scale X to avoid overflow when updating // the right-hand side. // if (xNorm>One) { const ElementType beta = max(work(j-1), work(j)); if (beta>bigNum/xNorm) { const ElementType rec = One / xNorm; X(1,1) *= rec; X(1,2) *= rec; X(2,1) *= rec; X(2,2) *= rec; scale *= rec; } } // // Scale if necessary // if (scale!=One) { work(_(1+n,ki+n)) *= scale; work(_(1+n2,ki+n2)) *= scale; } work(j-1+n) = X(1,1); work(j+n) = X(2,1); work(j-1+n2) = X(1,2); work(j+n2) = X(2,2); // // Update the right-hand side // work(_(1+n,j-2+n)) -= X(1,1)*T(_(1,j-2),j-1); work(_(1+n,j-2+n)) -= X(2,1)*T(_(1,j-2),j); work(_(1+n2,j-2+n2)) -= X(1,2)*T(_(1,j-2),j-1); work(_(1+n2,j-2+n2)) -= X(2,2)*T(_(1,j-2),j); } } // // Copy the vector x or Q*x to VR and normalize. // if (!over) { VR(_(1,ki),is-1) = work(_(1+n,ki+n)); VR(_(1,ki),is) = work(_(1+n2,ki+n2)); ElementType eMax = Zero; for (IndexType k=1; k<=ki; ++k) { eMax = max(eMax, abs(VR(k,is-1))+abs(VR(k,is))); } const ElementType reMax = One / eMax; VR(_(1,ki),is-1) *= reMax; VR(_(1,ki),is) *= reMax; VR(_(ki+1,n),is-1) = Zero; VR(_(ki+1,n),is) = Zero; } else { if (ki>2) { blas::mv(NoTrans, One, VR(_,_(1,ki-2)), work(_(1+n,ki-2+n)), work(ki-1+n), VR(_,ki-1)); blas::mv(NoTrans, One, VR(_,_(1,ki-2)), work(_(n2+1,n2+ki-2)), work(ki+n2), VR(_,ki)); } else { VR(_,ki-1) *= work(ki-1+n); VR(_,ki) *= work(ki+n2); } ElementType eMax = Zero; for (IndexType k=1; k<=n; ++k) { eMax = max(eMax, abs(VR(k,ki-1)) + abs(VR(k,ki))); } const ElementType reMax = One / eMax; VR(_,ki-1) *= reMax; VR(_,ki) *= reMax; } } --is; if (ip!=0) { --is; } if (ip==1) { ip = 0; } if (ip==-1) { ip = 1; } } } if (computeVL) { // // Compute left eigenvectors. // IndexType ip = 0; IndexType is = 1; for (IndexType ki=1; ki<=n; ++ki) { if (ip==-1) { ip = 0; continue; } if (ki!=n && T(ki+1,ki)!=Zero) { ip = 1; } if (someV) { if (!select(ki)) { if (ip==-1) { ip = 0; } if (ip==1) { ip = -1; } continue; } } // // Compute the KI-th eigenvalue (WR,WI). // ElementType wr = T(ki,ki); ElementType wi = Zero; if (ip!=0) { wi = sqrt(abs(T(ki,ki+1))) * sqrt(abs(T(ki+1,ki))); } const ElementType safeMin = max(ulp*(abs(wr)+abs(wi)), smallNum); if (ip==0) { // // Real left eigenvector. // work(ki+n) = One; // // Form right-hand side // for (IndexType k=ki+1; k<=n; ++k) { work(k+n) = -T(ki,k); } // // Solve the quasi-triangular system: // (T(KI+1:N,KI+1:N) - WR)**T*X = SCALE*WORK // ElementType vMax = One; ElementType vCrit = bigNum; IndexType jNext = ki + 1; for (IndexType j=ki+1; j<=n; ++j) { if (j<jNext) { continue; } IndexType j1 = j; IndexType j2 = j; jNext = j + 1; if (j<n) { if (T(j+1,j)!=Zero) { j2 = j + 1; jNext = j + 2; } } if (j1==j2) { // // 1-by-1 diagonal block // // Scale if necessary to avoid overflow when forming // the right-hand side. // if (work(j)>vCrit) { const ElementType rec = One / vMax; work(_(ki+n,n2)) *= rec; vMax = One; vCrit = bigNum; } work(j+n) -= T(_(ki+1,j-1),j)*work(_(ki+1+n,n+j-1)); // // Solve (T(J,J)-WR)**T*X = WORK // laln2(false, IndexType(1), safeMin, One, T(_(j,j),_(j,j)), One, One, Work(_(j,j), _(2,2)), wr, Zero, X(_(1,1),_(1,1)), scale, xNorm); // // Scale if necessary // if (scale!=One) { work(_(ki+n,n2)) *= scale; } work(j+n) = X(1,1); vMax = max(abs(work(j+n)), vMax); vCrit = bigNum / vMax; } else { // // 2-by-2 diagonal block // // Scale if necessary to avoid overflow when forming // the right-hand side. // const ElementType beta = max(work(j), work(j+1)); if (beta>vCrit) { const ElementType rec = One / vMax; work(_(ki+n,n2)) *= rec; vMax = One; vCrit = bigNum; } work(j+n) -= T(_(ki+1,j-1),j)*work(_(ki+1+n,n+j-1)); work(j+1+n) -= T(_(ki+1,j-1),j+1)*work(_(ki+1+n,n+j-1)); // // Solve // [T(J,J)-WR T(J,J+1) ]**T * X = SCALE*( WORK1 ) // [T(J+1,J) T(J+1,J+1)-WR] ( WORK2 ) // laln2(true, IndexType(1), safeMin, One, T(_(j,j+1),_(j,j+1)), One, One, Work(_(j,j+1), _(2,2)), wr, Zero, X(_(1,2),_(1,1)), scale, xNorm); // // Scale if necessary // if (scale!=One) { work(_(ki+n,n2)) *= scale; } work(j+n) = X(1,1); work(j+1+n) = X(2,1); vMax = max(abs(work(j+n)), abs(work(j+1+n)), vMax); vCrit = bigNum / vMax; } } // // Copy the vector x or Q*x to VL and normalize. // if (!over) { VL(_(ki,n),is) = work(_(ki+n,n2)); const IndexType ii = blas::iamax(VL(_(ki,n),is)) + ki - 1; const ElementType reMax = One / abs(VL(ii,is)); VL(_(ki,n),is) *= reMax; VL(_(1,ki-1),is) = Zero; } else { if (ki<n) { blas::mv(NoTrans, One, VL(_,_(ki+1,n)), work(_(ki+1+n,n2)), work(ki+n), VL(_,ki)); } const IndexType ii = blas::iamax(VL(_,ki)); const ElementType reMax = One / abs(VL(ii,ki)); VL(_,ki) *= reMax; } } else { // // Complex left eigenvector. // // Initial solve: // ((T(KI,KI) T(KI,KI+1) )**T - (WR - I* WI))*X = 0. // ((T(KI+1,KI) T(KI+1,KI+1)) ) // if (abs(T(ki,ki+1))>=abs(T(ki+1,ki))) { work(ki+n) = wi / T(ki,ki+1); work(ki+1+n2) = One; } else { work(ki+n) = One; work(ki+1+n2) = -wi / T(ki+1,ki); } work(ki+1+n) = Zero; work(ki+n2) = Zero; // // Form right-hand side // for (IndexType k=ki+2; k<=n; ++k) { work(k+n) = -work(ki+n)*T(ki,k); work(k+n2) = -work(ki+1+n2)*T(ki+1,k); } // // Solve complex quasi-triangular system: // ( T(KI+2,N:KI+2,N) - (WR-i*WI) )*X = WORK1+i*WORK2 // ElementType vMax = One; ElementType vCrit = bigNum; IndexType jNext = ki + 2; for (IndexType j=ki+2; j<=n; ++j) { if (j<jNext) { continue; } IndexType j1 = j; IndexType j2 = j; jNext = j + 1; if (j<n) { if (T(j+1,j)!=Zero) { j2 = j + 1; jNext = j + 2; } } if (j1==j2) { // // 1-by-1 diagonal block // // Scale if necessary to avoid overflow when // forming the right-hand side elements. // if (work(j)>vCrit) { const ElementType rec = One / vMax; work(_(ki+n,n2)) *= rec; work(_(ki+n2,n2+n)) *= rec; vMax = One; vCrit = bigNum; } work(j+n) -= T(_(ki+2,j-1),j)*work(_(ki+2+n,n+j-1)); work(j+n2) -= T(_(ki+2,j-1),j)*work(_(ki+2+n2,n2+j-1)); // // Solve (T(J,J)-(WR-i*WI))*(X11+i*X12)= WK+I*WK2 // laln2(true, IndexType(2), safeMin, One, T(_(j,j),_(j,j)), One, One, Work(_(j,j), _(2,3)), wr, -wi, X(_(1,1),_(1,2)), scale, xNorm); // // Scale if necessary // if (scale!=One) { work(_(ki+n,n2)) *= scale; work(_(ki+n2,n2+n)) *= scale; } work(j+n) = X(1,1); work(j+n2) = X(1,2); vMax = max(abs(work(j+n)), abs(work(j+n2)), vMax); vCrit = bigNum / vMax; } else { // // 2-by-2 diagonal block // // Scale if necessary to avoid overflow when forming // the right-hand side elements. // const ElementType beta = max(work(j), work(j+1)); if (beta>vCrit) { const ElementType rec = One / vMax; work(_(ki+n,n2)) *= rec; work(_(ki+n2,n2+n)) *= rec; vMax = One; vCrit = bigNum; } const auto _work1 = work(_(ki+2+n,n+j-1)); const auto _work2 = work(_(ki+2+n2,n2+j-1)); work(j+n) -= T(_(ki+2,j-1),j) * _work1; work(j+n2) -= T(_(ki+2,j-1),j) * _work2; work(j+1+n) -= T(_(ki+2,j-1),j+1) * _work1; work(j+1+n2)-= T(_(ki+2,j-1),j+1) * _work2; // // Solve 2-by-2 complex linear equation // ([T(j,j) T(j,j+1) ]**T-(wr-i*wi)*I)*X = SCALE*B // ([T(j+1,j) T(j+1,j+1)] ) // laln2(true, IndexType(2), safeMin, One, T(_(j,j+1),_(j,j+1)), One, One, Work(_(j,j+1), _(2,3)), wr, -wi, X(_(1,2),_(1,2)), scale, xNorm); // // Scale if necessary // if (scale!=One) { work(_(ki+n,n2)) *= scale; work(_(ki+n2,n2+n)) *= scale; } work(j+n) = X(1,1); work(j+n2) = X(1,2); work(j+1+n) = X(2,1); work(j+1+n2) = X(2,2); vMax = max(abs(X(1,1)), abs(X(1,2)), abs(X(2,1)), abs(X(2,2)), vMax); vCrit = bigNum / vMax; } } // // Copy the vector x or Q*x to VL and normalize. // if (!over) { VL(_(ki,n),is) = work(_(ki+n,n2)); VL(_(ki,n),is+1) = work(_(ki+n2,n2+n)); ElementType eMax = Zero; for (IndexType k=ki; k<=n; ++k) { eMax = max(eMax, abs(VL(k,is)) + abs(VL(k,is+1))); } const ElementType reMax = One / eMax; VL(_(ki,n),is) *= reMax; VL(_(ki,n),is+1) *= reMax; VL(_(1,ki-1),is) = Zero; VL(_(1,ki-1),is+1) = Zero; } else { if (ki<n-1) { blas::mv(NoTrans, One, VL(_,_(ki+2,n)), work(_(ki+2+n,n2)), work(ki+n), VL(_,ki)); blas::mv(NoTrans, One, VL(_,_(ki+2,n)), work(_(ki+2+n2,n2+n)), work(ki+1+n2), VL(_,ki+1)); } else { VL(_,ki) *= work(ki+n); VL(_,ki+1) *= work(ki+1+n2); } ElementType eMax = Zero; for (IndexType k=1; k<=n; ++k) { eMax = max(eMax, abs(VL(k,ki)) + abs(VL(k,ki+1))); } const ElementType reMax = One / eMax; VL(_,ki) *= reMax; VL(_,ki+1) *= reMax; } } ++is; if (ip!=0) { ++is; } if (ip==-1) { ip = 0; } if (ip==1) { ip = -1; } } } } } // namespace generic //== interface for native lapack =============================================== #ifdef USE_CXXLAPACK namespace external { template <typename VSELECT, typename MT, typename MVL, typename MVR, typename IndexType, typename VWORK> void trevc_impl(bool computeVL, bool computeVR, TREVC::Job howMany, DenseVector<VSELECT> &select, const GeMatrix<MT> &T, GeMatrix<MVL> &VL, GeMatrix<MVR> &VR, IndexType mm, IndexType &m, DenseVector<VWORK> &work) { typedef typename GeMatrix<MT>::ElementType ElementType; char side = 'N'; if (computeVL && computeVR) { side = 'B'; } else if (computeVL) { side = 'L'; } else if (computeVR) { side = 'R'; } else { ASSERT(0); } DenseVector<Array<IndexType> > _select = select; cxxlapack::trevc<IndexType>(side, getF77Char(howMany), _select.data(), T.numRows(), T.data(), T.leadingDimension(), VL.data(), VL.leadingDimension(), VR.data(), VR.leadingDimension(), mm, m, work.data()); } } // namespace external #endif // USE_CXXLAPACK //== public interface ========================================================== template <typename VSELECT, typename MT, typename MVL, typename MVR, typename IndexType, typename VWORK> void trevc(bool computeVL, bool computeVR, TREVC::Job howMany, DenseVector<VSELECT> &select, const GeMatrix<MT> &T, GeMatrix<MVL> &VL, GeMatrix<MVR> &VR, IndexType mm, IndexType &m, DenseVector<VWORK> &work) { LAPACK_DEBUG_OUT("BEGIN: trevc"); typedef typename GeMatrix<MT>::ElementType ElementType; // // Test the input parameters // ASSERT(T.firstRow()==1); ASSERT(T.firstCol()==1); ASSERT(T.numRows()==T.numCols()); ASSERT(VL.firstRow()==1); ASSERT(VL.firstCol()==1); ASSERT(VR.firstRow()==1); ASSERT(VR.firstCol()==1); # ifdef CHECK_CXXLAPACK // // Make copies of output arguments // typename DenseVector<VSELECT>::NoView select_org = select; typename GeMatrix<MVL>::NoView VL_org = VL; typename GeMatrix<MVR>::NoView VR_org = VR; typename DenseVector<VWORK>::NoView work_org = work; # endif // // Call implementation // LAPACK_SELECT::trevc_impl(computeVL, computeVR, howMany, select, T, VL, VR, mm, m, work); # ifdef CHECK_CXXLAPACK // // Make copies of results computed by the generic implementation // typename DenseVector<VSELECT>::NoView select_generic = select; typename GeMatrix<MVL>::NoView VL_generic = VL; typename GeMatrix<MVR>::NoView VR_generic = VR; typename DenseVector<VWORK>::NoView work_generic = work; // // restore output arguments // select = select_org; VL = VL_org; VR = VR_org; work = work_org; // // Compare results // external::trevc_impl(computeVL, computeVR, howMany, select, T, VL, VR, mm, m, work); bool failed = false; if (! isIdentical(VL_generic, VL, "VL_generic", "VL")) { std::cerr << "CXXLAPACK: VL_generic = " << VL_generic << std::endl; std::cerr << "F77LAPACK: VL = " << VL << std::endl; failed = true; } if (! isIdentical(VR_generic, VR, "VR_generic", "_VR")) { std::cerr << "CXXLAPACK: VR_generic = " << VR_generic << std::endl; std::cerr << "F77LAPACK: VR = " << VR << 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) { ASSERT(0); } # endif LAPACK_DEBUG_OUT("END: trevc"); } //-- forwarding ---------------------------------------------------------------- template <typename VSELECT, typename MT, typename MVL, typename MVR, typename IndexType, typename VWORK> void trevc(bool computeVL, bool computeVR, TREVC::Job howMany, VSELECT &&select, const MT &T, MVL &&VL, MVR &&VR, IndexType &&m, VWORK &&work) { CHECKPOINT_ENTER; trevc(computeVL, computeVR, howMany, select, T, VL, VR, m, work); CHECKPOINT_LEAVE; } } } // namespace lapack, flens #endif // FLENS_LAPACK_IMPL_TREVC_TCC |