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1225 lines
33 KiB
C++
1225 lines
33 KiB
C++
/*************************************************************************************
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Grid physics library, www.github.com/paboyle/Grid
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Source file: ./lib/algorithms/iterative/ImplicitlyRestartedLanczos.h
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Copyright (C) 2015
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Author: Peter Boyle <paboyle@ph.ed.ac.uk>
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Author: paboyle <paboyle@ph.ed.ac.uk>
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Author: Chulwoo Jung <chulwoo@bnl.gov>
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License along
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with this program; if not, write to the Free Software Foundation, Inc.,
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51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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See the full license in the file "LICENSE" in the top level distribution directory
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*************************************************************************************/
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/* END LEGAL */
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#ifndef GRID_IRL_CJ_H
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#define GRID_IRL_CJ_H
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#include <string.h> //memset
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#ifdef USE_LAPACK
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#ifdef USE_MKL
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#include<mkl_lapack.h>
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#else
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void LAPACK_dstegr(char *jobz, char *range, int *n, double *d, double *e,
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double *vl, double *vu, int *il, int *iu, double *abstol,
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int *m, double *w, double *z, int *ldz, int *isuppz,
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double *work, int *lwork, int *iwork, int *liwork,
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int *info);
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//#include <lapacke/lapacke.h>
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#endif
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#endif
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//#include <Grid/algorithms/densematrix/DenseMatrix.h>
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//#include <Grid/algorithms/iterative/EigenSort.h>
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// eliminate temorary vector in calc()
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#define MEM_SAVE
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namespace Grid {
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/////////////////////////////////////////////////////////////
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// Implicitly restarted lanczos
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/////////////////////////////////////////////////////////////
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// creating a seaprate instance to avoid conflicts for the time being
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template<class Field>
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class ImplicitlyRestartedLanczosCJ {
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const RealD small = 1.0e-16;
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public:
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int lock;
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int get;
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int Niter;
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int converged;
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int Nstop; // Number of evecs checked for convergence
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int Nk; // Number of converged sought
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int Np; // Np -- Number of spare vecs in kryloc space
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int Nm; // Nm -- total number of vectors
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RealD OrthoTime;
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RealD eresid;
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SortEigen<Field> _sort;
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LinearOperatorBase<Field> &_Linop;
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OperatorFunction<Field> &_poly;
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/////////////////////////
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// Constructor
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/////////////////////////
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void init(void){};
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void Abort(int ff, DenseVector<RealD> &evals, DenseVector<DenseVector<RealD> > &evecs);
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ImplicitlyRestartedLanczosCJ(
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LinearOperatorBase<Field> &Linop, // op
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OperatorFunction<Field> & poly, // polynmial
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int _Nstop, // sought vecs
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int _Nk, // sought vecs
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int _Nm, // spare vecs
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RealD _eresid, // resid in lmdue deficit
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int _Niter) : // Max iterations
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_Linop(Linop),
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_poly(poly),
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Nstop(_Nstop),
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Nk(_Nk),
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Nm(_Nm),
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eresid(_eresid),
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Niter(_Niter)
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{
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Np = Nm-Nk; assert(Np>0);
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};
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ImplicitlyRestartedLanczosCJ(
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LinearOperatorBase<Field> &Linop, // op
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OperatorFunction<Field> & poly, // polynmial
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int _Nk, // sought vecs
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int _Nm, // spare vecs
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RealD _eresid, // resid in lmdue deficit
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int _Niter) : // Max iterations
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_Linop(Linop),
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_poly(poly),
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Nstop(_Nk),
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Nk(_Nk),
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Nm(_Nm),
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eresid(_eresid),
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Niter(_Niter)
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{
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Np = Nm-Nk; assert(Np>0);
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};
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/////////////////////////
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// Sanity checked this routine (step) against Saad.
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/////////////////////////
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void RitzMatrix(DenseVector<Field>& evec,int k){
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if(1) return;
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GridBase *grid = evec[0]._grid;
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Field w(grid);
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std::cout<<GridLogMessage << "RitzMatrix "<<std::endl;
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for(int i=0;i<k;i++){
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_poly(_Linop,evec[i],w);
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std::cout<<GridLogMessage << "["<<i<<"] ";
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for(int j=0;j<k;j++){
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ComplexD in = innerProduct(evec[j],w);
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if ( fabs((double)i-j)>1 ) {
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if (abs(in) >1.0e-9 ) {
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std::cout<<GridLogMessage<<"oops"<<std::endl;
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abort();
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} else
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std::cout<<GridLogMessage << " 0 ";
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} else {
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std::cout<<GridLogMessage << " "<<in<<" ";
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}
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}
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std::cout<<GridLogMessage << std::endl;
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}
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}
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/* Saad PP. 195
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1. Choose an initial vector v1 of 2-norm unity. Set β1 ≡ 0, v0 ≡ 0
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2. For k = 1,2,...,m Do:
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3. wk:=Avk−βkv_{k−1}
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4. αk:=(wk,vk) //
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5. wk:=wk−αkvk // wk orthog vk
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6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
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7. vk+1 := wk/βk+1
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8. EndDo
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*/
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void step(DenseVector<RealD>& lmd,
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DenseVector<RealD>& lme,
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DenseVector<Field>& evec,
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Field& w,int Nm,int k, RealD &norm)
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{
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assert( k< Nm );
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_poly(_Linop,evec[k],w); // 3. wk:=Avk−βkv_{k−1}
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if(k>0){
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w -= lme[k-1] * evec[k-1];
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}
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ComplexD zalph = innerProduct(evec[k],w); // 4. αk:=(wk,vk)
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RealD alph = real(zalph);
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w = w - alph * evec[k];// 5. wk:=wk−αkvk
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RealD beta = normalise(w); // 6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
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// 7. vk+1 := wk/βk+1
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norm=beta;
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std::cout<<GridLogMessage << "alpha = " << zalph << " beta "<<beta<<std::endl;
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const RealD tiny = 1.0e-20;
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if ( beta < tiny ) {
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std::cout<<GridLogMessage << " beta is tiny "<<beta<<std::endl;
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}
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lmd[k] = alph;
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lme[k] = beta;
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if (k>0) {
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orthogonalize(w,evec,k); // orthonormalise
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}
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if(k < Nm-1) evec[k+1] = w;
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}
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void qr_decomp(DenseVector<RealD>& lmd,
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DenseVector<RealD>& lme,
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int Nk,
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int Nm,
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DenseVector<RealD>& Qt,
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RealD Dsh,
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int kmin,
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int kmax)
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{
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int k = kmin-1;
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RealD x;
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RealD Fden = 1.0/hypot(lmd[k]-Dsh,lme[k]);
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RealD c = ( lmd[k] -Dsh) *Fden;
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RealD s = -lme[k] *Fden;
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RealD tmpa1 = lmd[k];
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RealD tmpa2 = lmd[k+1];
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RealD tmpb = lme[k];
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lmd[k] = c*c*tmpa1 +s*s*tmpa2 -2.0*c*s*tmpb;
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lmd[k+1] = s*s*tmpa1 +c*c*tmpa2 +2.0*c*s*tmpb;
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lme[k] = c*s*(tmpa1-tmpa2) +(c*c-s*s)*tmpb;
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x =-s*lme[k+1];
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lme[k+1] = c*lme[k+1];
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for(int i=0; i<Nk; ++i){
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RealD Qtmp1 = Qt[i+Nm*k ];
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RealD Qtmp2 = Qt[i+Nm*(k+1)];
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Qt[i+Nm*k ] = c*Qtmp1 - s*Qtmp2;
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Qt[i+Nm*(k+1)] = s*Qtmp1 + c*Qtmp2;
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}
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// Givens transformations
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for(int k = kmin; k < kmax-1; ++k){
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RealD Fden = 1.0/hypot(x,lme[k-1]);
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RealD c = lme[k-1]*Fden;
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RealD s = - x*Fden;
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RealD tmpa1 = lmd[k];
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RealD tmpa2 = lmd[k+1];
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RealD tmpb = lme[k];
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lmd[k] = c*c*tmpa1 +s*s*tmpa2 -2.0*c*s*tmpb;
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lmd[k+1] = s*s*tmpa1 +c*c*tmpa2 +2.0*c*s*tmpb;
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lme[k] = c*s*(tmpa1-tmpa2) +(c*c-s*s)*tmpb;
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lme[k-1] = c*lme[k-1] -s*x;
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if(k != kmax-2){
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x = -s*lme[k+1];
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lme[k+1] = c*lme[k+1];
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}
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for(int i=0; i<Nk; ++i){
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RealD Qtmp1 = Qt[i+Nm*k ];
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RealD Qtmp2 = Qt[i+Nm*(k+1)];
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Qt[i+Nm*k ] = c*Qtmp1 -s*Qtmp2;
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Qt[i+Nm*(k+1)] = s*Qtmp1 +c*Qtmp2;
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}
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}
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}
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#ifdef USE_LAPACK
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#ifdef USE_MKL
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#define LAPACK_INT MKL_INT
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#else
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#define LAPACK_INT long long
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#endif
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void diagonalize_lapack(DenseVector<RealD>& lmd,
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DenseVector<RealD>& lme,
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int N1,
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int N2,
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DenseVector<RealD>& Qt,
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GridBase *grid){
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const int size = Nm;
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// tevals.resize(size);
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// tevecs.resize(size);
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LAPACK_INT NN = N1;
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// double evals_tmp[NN];
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// double evec_tmp[NN][NN];
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std::vector<double> evals_tmp(NN);
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std::vector<double> evec_tmp(NN*NN);
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memset(evec_tmp.data(),0,sizeof(double)*NN*NN);
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std::vector<double> DD(NN);
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std::vector<double> EE(NN);
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for (int i = 0; i< NN; i++)
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for (int j = i - 1; j <= i + 1; j++)
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if ( j < NN && j >= 0 ) {
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if (i==j) DD[i] = lmd[i];
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if (i==j) evals_tmp[i] = lmd[i];
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if (j==(i-1)) EE[j] = lme[j];
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}
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LAPACK_INT evals_found;
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// LAPACK_INT lwork = ( (18*NN) > (1+4*NN+NN*NN)? (18*NN):(1+4*NN+NN*NN)) ;
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LAPACK_INT lwork = 1+(18*NN) ;
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LAPACK_INT liwork = 3+NN*10 ;
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// LAPACK_INT iwork[liwork];
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// double work[lwork];
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// LAPACK_INT isuppz[2*NN];
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std::vector<LAPACK_INT> iwork(liwork);
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std::vector<double> work(lwork);
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std::vector<LAPACK_INT> isuppz(2*NN);
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char jobz = 'V'; // calculate evals & evecs
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char range = 'I'; // calculate all evals
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// char range = 'A'; // calculate all evals
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char uplo = 'U'; // refer to upper half of original matrix
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char compz = 'I'; // Compute eigenvectors of tridiagonal matrix
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int ifail[NN];
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LAPACK_INT info;
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// int total = QMP_get_number_of_nodes();
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// int node = QMP_get_node_number();
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// GridBase *grid = evec[0]._grid;
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int total = grid->_Nprocessors;
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int node = grid->_processor;
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int interval = (NN/total)+1;
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double vl = 0.0, vu = 0.0;
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LAPACK_INT il = interval*node+1 , iu = interval*(node+1);
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if (iu > NN) iu=NN;
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double tol = 0.0;
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if (1) {
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memset(evals_tmp.data(),0,sizeof(double)*NN);
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if ( il <= NN){
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printf("total=%d node=%d il=%d iu=%d\n",total,node,il,iu);
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#ifdef USE_MKL
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dstegr(&jobz, &range, &NN,
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#else
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LAPACK_dstegr(&jobz, &range, &NN,
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#endif
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DD.data(), EE.data(),
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&vl, &vu, &il, &iu, // these four are ignored if second parameteris 'A'
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&tol, // tolerance
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&evals_found, evals_tmp.data(), evec_tmp.data(), &NN,
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isuppz.data(),
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work.data(), &lwork, iwork.data(), &liwork,
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&info);
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for (int i = iu-1; i>= il-1; i--){
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printf("node=%d evals_found=%d evals_tmp[%d] = %g\n",node,evals_found, i - (il-1),evals_tmp[i - (il-1)]);
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evals_tmp[i] = evals_tmp[i - (il-1)];
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if (il>1) evals_tmp[i-(il-1)]=0.;
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for (int j = 0; j< NN; j++){
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evec_tmp[i*NN+j] = evec_tmp[(i - (il-1))*NN+j];
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if (il>1) evec_tmp[(i-(il-1))*NN+j]=0.;
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}
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}
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}
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{
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grid->GlobalSumVector(evals_tmp.data(),NN);
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grid->GlobalSumVector(evec_tmp.data(),NN*NN);
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}
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}
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// cheating a bit. It is better to sort instead of just reversing it, but the document of the routine says evals are sorted in increasing order. qr gives evals in decreasing order.
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for(int i=0;i<NN;i++){
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for(int j=0;j<NN;j++)
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Qt[(NN-1-i)*N2+j]=evec_tmp[i*NN+j];
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lmd [NN-1-i]=evals_tmp[i];
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}
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}
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#undef LAPACK_INT
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#endif
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void diagonalize(DenseVector<RealD>& lmd,
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DenseVector<RealD>& lme,
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int N2,
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int N1,
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DenseVector<RealD>& Qt,
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GridBase *grid)
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{
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#ifdef USE_LAPACK
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const int check_lapack=0; // just use lapack if 0, check against lapack if 1
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if(!check_lapack)
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return diagonalize_lapack(lmd,lme,N2,N1,Qt,grid);
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DenseVector <RealD> lmd2(N1);
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DenseVector <RealD> lme2(N1);
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DenseVector<RealD> Qt2(N1*N1);
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for(int k=0; k<N1; ++k){
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lmd2[k] = lmd[k];
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lme2[k] = lme[k];
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}
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for(int k=0; k<N1*N1; ++k)
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Qt2[k] = Qt[k];
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// diagonalize_lapack(lmd2,lme2,Nm2,Nm,Qt,grid);
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#endif
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int Niter = 10000*N1;
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int kmin = 1;
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int kmax = N2;
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// (this should be more sophisticated)
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for(int iter=0; ; ++iter){
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if ( (iter+1)%(100*N1)==0)
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std::cout<<GridLogMessage << "[QL method] Not converged - iteration "<<iter+1<<"\n";
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// determination of 2x2 leading submatrix
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RealD dsub = lmd[kmax-1]-lmd[kmax-2];
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RealD dd = sqrt(dsub*dsub + 4.0*lme[kmax-2]*lme[kmax-2]);
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RealD Dsh = 0.5*(lmd[kmax-2]+lmd[kmax-1] +dd*(dsub/fabs(dsub)));
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// (Dsh: shift)
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// transformation
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qr_decomp(lmd,lme,N2,N1,Qt,Dsh,kmin,kmax);
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// Convergence criterion (redef of kmin and kamx)
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for(int j=kmax-1; j>= kmin; --j){
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RealD dds = fabs(lmd[j-1])+fabs(lmd[j]);
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if(fabs(lme[j-1])+dds > dds){
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kmax = j+1;
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goto continued;
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}
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}
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Niter = iter;
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#ifdef USE_LAPACK
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if(check_lapack){
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const double SMALL=1e-8;
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diagonalize_lapack(lmd2,lme2,N2,N1,Qt2,grid);
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DenseVector <RealD> lmd3(N2);
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for(int k=0; k<N2; ++k) lmd3[k]=lmd[k];
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_sort.push(lmd3,N2);
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_sort.push(lmd2,N2);
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for(int k=0; k<N2; ++k){
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if (fabs(lmd2[k] - lmd3[k]) >SMALL) std::cout<<GridLogMessage <<"lmd(qr) lmd(lapack) "<< k << ": " << lmd2[k] <<" "<< lmd3[k] <<std::endl;
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// if (fabs(lme2[k] - lme[k]) >SMALL) std::cout<<GridLogMessage <<"lme(qr)-lme(lapack) "<< k << ": " << lme2[k] - lme[k] <<std::endl;
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}
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for(int k=0; k<N1*N1; ++k){
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// if (fabs(Qt2[k] - Qt[k]) >SMALL) std::cout<<GridLogMessage <<"Qt(qr)-Qt(lapack) "<< k << ": " << Qt2[k] - Qt[k] <<std::endl;
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}
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}
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#endif
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return;
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continued:
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for(int j=0; j<kmax-1; ++j){
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RealD dds = fabs(lmd[j])+fabs(lmd[j+1]);
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if(fabs(lme[j])+dds > dds){
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kmin = j+1;
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break;
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}
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}
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}
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std::cout<<GridLogMessage << "[QL method] Error - Too many iteration: "<<Niter<<"\n";
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abort();
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}
|
||
|
||
#if 1
|
||
static RealD normalise(Field& v)
|
||
{
|
||
RealD nn = norm2(v);
|
||
nn = sqrt(nn);
|
||
v = v * (1.0/nn);
|
||
return nn;
|
||
}
|
||
|
||
void orthogonalize(Field& w,
|
||
DenseVector<Field>& evec,
|
||
int k)
|
||
{
|
||
double t0=-usecond()/1e6;
|
||
typedef typename Field::scalar_type MyComplex;
|
||
MyComplex ip;
|
||
|
||
if ( 0 ) {
|
||
for(int j=0; j<k; ++j){
|
||
normalise(evec[j]);
|
||
for(int i=0;i<j;i++){
|
||
ip = innerProduct(evec[i],evec[j]); // are the evecs normalised? ; this assumes so.
|
||
evec[j] = evec[j] - ip *evec[i];
|
||
}
|
||
}
|
||
}
|
||
|
||
for(int j=0; j<k; ++j){
|
||
ip = innerProduct(evec[j],w); // are the evecs normalised? ; this assumes so.
|
||
w = w - ip * evec[j];
|
||
}
|
||
normalise(w);
|
||
t0+=usecond()/1e6;
|
||
OrthoTime +=t0;
|
||
}
|
||
|
||
void setUnit_Qt(int Nm, DenseVector<RealD> &Qt) {
|
||
for(int i=0; i<Qt.size(); ++i) Qt[i] = 0.0;
|
||
for(int k=0; k<Nm; ++k) Qt[k + k*Nm] = 1.0;
|
||
}
|
||
|
||
// needs more memory
|
||
void Rotate0(
|
||
// int _Nm,
|
||
DenseVector<RealD>& Qt,
|
||
DenseVector<Field>& evec,
|
||
int j0, int j1,
|
||
int _Nk
|
||
)
|
||
{
|
||
GridBase *grid = evec[0]._grid;
|
||
DenseVector<Field> B(Nm,grid); // waste of space replicating
|
||
if (0) { // old implementation without blocking
|
||
for(int i=0; i<(Nm); ++i) B[i] = 0.0;
|
||
|
||
for(int j=j0; j<j1; ++j){
|
||
for(int k=0; k<Nm; ++k){
|
||
B[j].checkerboard = evec[k].checkerboard;
|
||
B[j] += Qt[k+Nm*j] * evec[k];
|
||
}
|
||
}
|
||
}
|
||
{
|
||
for(int i=0; i<(Nm); ++i) {
|
||
B[i] = 0.0;
|
||
B[i].checkerboard = evec[0].checkerboard;
|
||
}
|
||
int j_block = 24; int k_block=24;
|
||
PARALLEL_FOR_LOOP
|
||
for(int ss=0;ss < grid->oSites();ss++){
|
||
for(int jj=j0; jj<j1; jj += j_block)
|
||
for(int kk=0; kk<Nm; kk += k_block)
|
||
for(int j=jj; (j<(j1)) && j<(jj+j_block); ++j){
|
||
for(int k=kk; (k<Nm) && k<(kk+k_block) ; ++k){
|
||
B[j]._odata[ss] +=Qt[k+Nm*j] * evec[k]._odata[ss];
|
||
}
|
||
}
|
||
}
|
||
}
|
||
for(int j=j0; j<j1; ++j) evec[j] = B[j];
|
||
}
|
||
|
||
void Rotate(
|
||
// int _Nm,
|
||
DenseVector<RealD>& Qt,
|
||
DenseVector<Field>& evec,
|
||
//int k1, int k2
|
||
int j0, int j1,
|
||
int _Nk
|
||
)
|
||
{
|
||
GridBase *grid = evec[0]._grid;
|
||
typedef typename Field::vector_object vobj;
|
||
assert(j0>=0);
|
||
assert(j1<Nm);
|
||
|
||
#pragma omp parallel
|
||
{
|
||
std::vector < vobj > B(Nm);
|
||
#pragma omp for
|
||
for(int ss=0;ss < grid->oSites();ss++){
|
||
for(int j=j0; j<j1; ++j)
|
||
zeroit(B[j]);
|
||
for(int j=j0; j<j1; ++j){
|
||
for(int k=0; k<_Nk ; ++k){
|
||
B[j] +=Qt[k+Nm*j] * evec[k]._odata[ss];
|
||
}
|
||
}
|
||
for(int j=j0; j<j1; ++j){
|
||
evec[j]._odata[ss] = B[j];
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
void Rotate2(
|
||
// int Nm,
|
||
DenseVector<RealD>& Qt,
|
||
DenseVector<Field>& evec,
|
||
int k1, int k2
|
||
)
|
||
{
|
||
GridBase *grid = evec[0]._grid;
|
||
int j_block = 24; int k_block=24;
|
||
|
||
assert(k2<Nm);
|
||
assert(k1>0);
|
||
int thr=GridThread::GetThreads();
|
||
int n_field = 1;
|
||
int each = 1;
|
||
if( (Nm*thr)>(grid->oSites()) ) {
|
||
each = (grid->oSites())/Nm ;
|
||
n_field = thr/each + 1;
|
||
}
|
||
std::cout<<GridLogMessage << "thr = " << thr << " n_field= "<< n_field << " each= "<<each << std::endl;
|
||
DenseVector<Field> B(n_field,grid);
|
||
PARALLEL_FOR_LOOP
|
||
for(int ss=0;ss < grid->oSites();ss++){
|
||
int me = GridThread::ThreadBarrier();
|
||
int i_field = me / each;
|
||
int k_field = me % each;
|
||
assert(i_field < n_field);
|
||
std::cout<<GridLogMessage << "me = " << me << " i_field= "<< i_field << " k_field= "<<k_field << std::endl;
|
||
// printf("thr=%d ss=%d me=%d\n",thr,ss,me);fflush(stdout);
|
||
// assert(Nm*thr<grid->oSites());
|
||
for(int j=0; j<Nm; ++j) B[i_field]._odata[j+Nm*k_field]=0.;
|
||
for(int j=k1-1; j<(k2+1); ++j){
|
||
for(int k=0; k<Nm ; ++k){
|
||
B[i_field]._odata[j+Nm*k_field] +=Qt[k+Nm*j] * evec[k]._odata[ss];
|
||
}
|
||
}
|
||
for(int j=k1-1; j<(k2+1); ++j){
|
||
evec[j]._odata[ss] = B[i_field]._odata[j+Nm*k_field];
|
||
}
|
||
}
|
||
}
|
||
|
||
void ConvCheck0( int _Nk,
|
||
DenseVector<RealD>& Qt,
|
||
DenseVector<Field>& evec,
|
||
DenseVector<RealD> &eval2,
|
||
DenseVector<int> &Iconv,
|
||
int &Nconv)
|
||
{
|
||
|
||
GridBase *grid = evec[0]._grid;
|
||
DenseVector<Field> B(Nm,grid); // waste of space replicating
|
||
Field v(grid);
|
||
if (0) {
|
||
for(int k = 0; k<_Nk; ++k) B[k]=0.0;
|
||
|
||
for(int j = 0; j<_Nk; ++j){
|
||
for(int k = 0; k<_Nk; ++k){
|
||
B[j].checkerboard = evec[k].checkerboard;
|
||
B[j] += Qt[k+j*Nm] * evec[k];
|
||
}
|
||
std::cout<<GridLogMessage << "norm(B["<<j<<"])="<<norm2(B[j])<<std::endl;
|
||
}
|
||
}
|
||
if (1) {
|
||
for(int i=0; i<(_Nk+1); ++i) {
|
||
B[i] = 0.0;
|
||
B[i].checkerboard = evec[0].checkerboard;
|
||
}
|
||
|
||
int j_block = 24; int k_block=24;
|
||
PARALLEL_FOR_LOOP
|
||
for(int ss=0;ss < grid->oSites();ss++){
|
||
for(int jj=0; jj<_Nk; jj += j_block)
|
||
for(int kk=0; kk<_Nk; kk += k_block)
|
||
for(int j=jj; (j<_Nk) && j<(jj+j_block); ++j){
|
||
for(int k=kk; (k<_Nk) && k<(kk+k_block) ; ++k){
|
||
B[j]._odata[ss] +=Qt[k+Nm*j] * evec[k]._odata[ss];
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
Nconv = 0;
|
||
// std::cout<<GridLogMessage << std::setiosflags(std::ios_base::scientific);
|
||
for(int i=0; i<_Nk; ++i){
|
||
|
||
// _poly(_Linop,B[i],v);
|
||
_Linop.HermOp(B[i],v);
|
||
|
||
RealD vnum = real(innerProduct(B[i],v)); // HermOp.
|
||
RealD vden = norm2(B[i]);
|
||
RealD vv0 = norm2(v);
|
||
eval2[i] = vnum/vden;
|
||
v -= eval2[i]*B[i];
|
||
RealD vv = norm2(v);
|
||
|
||
std::cout.precision(13);
|
||
std::cout<<GridLogMessage << "[" << std::setw(3)<< std::setiosflags(std::ios_base::right) <<i<<"] ";
|
||
std::cout<<"eval = "<<std::setw(25)<< std::setiosflags(std::ios_base::left)<< eval2[i];
|
||
std::cout<<"|H B[i] - eval[i]B[i]|^2 "<< std::setw(25)<< std::setiosflags(std::ios_base::right)<< vv;
|
||
std::cout<<" "<< vnum/(sqrt(vden)*sqrt(vv0)) << std::endl;
|
||
|
||
// change the criteria as evals are supposed to be sorted, all evals smaller(larger) than Nstop should have converged
|
||
if((vv<eresid*eresid) && (i == Nconv) ){
|
||
Iconv[Nconv] = i;
|
||
++Nconv;
|
||
}
|
||
|
||
} // i-loop end
|
||
// std::cout<<GridLogMessage << std::resetiosflags(std::ios_base::scientific);
|
||
}
|
||
|
||
void FinalCheck( int _Nk,
|
||
DenseVector<RealD>& eval,
|
||
DenseVector<Field>& evec
|
||
)
|
||
{
|
||
GridBase *grid = evec[0]._grid;
|
||
Field v(grid);
|
||
Field B(grid);
|
||
for(int j = 0; j<_Nk; ++j){
|
||
std::cout<<GridLogMessage << "norm(evec["<<j<<"])="<<norm2(evec[j])<<std::endl;
|
||
_Linop.HermOp(evec[j],v);
|
||
|
||
RealD vnum = real(innerProduct(evec[j],v)); // HermOp.
|
||
RealD vden = norm2(evec[j]);
|
||
RealD vv0 = norm2(v);
|
||
RealD eval2 = vnum/vden;
|
||
v -= eval2*evec[j];
|
||
RealD vv = norm2(v);
|
||
|
||
std::cout.precision(13);
|
||
std::cout<<GridLogMessage << "[" << std::setw(3)<< std::setiosflags(std::ios_base::right) <<j<<"] ";
|
||
std::cout<<"eval = "<<std::setw(25)<< std::setiosflags(std::ios_base::left)<< eval2;
|
||
std::cout<<"|H B[i] - eval[i]B[i]|^2 "<< std::setw(25)<< std::setiosflags(std::ios_base::right)<< vv;
|
||
std::cout<<" "<< vnum/(sqrt(vden)*sqrt(vv0)) << std::endl;
|
||
eval[j] = eval2;
|
||
|
||
}
|
||
}
|
||
|
||
void ConvCheck( int _Nk,
|
||
DenseVector<RealD>& Qt,
|
||
DenseVector<Field>& evec,
|
||
DenseVector<RealD> &eval2,
|
||
DenseVector<int> &Iconv,
|
||
int &Nconv)
|
||
{
|
||
GridBase *grid = evec[0]._grid;
|
||
Field v(grid);
|
||
Field B(grid);
|
||
Nconv = 0;
|
||
for(int j = 0; j<_Nk; ++j){
|
||
B=0.;
|
||
B.checkerboard = evec[0].checkerboard;
|
||
for(int k = 0; k<_Nk; ++k){
|
||
B += Qt[k+j*Nm] * evec[k];
|
||
}
|
||
std::cout<<GridLogMessage << "norm(B["<<j<<"])="<<norm2(B)<<std::endl;
|
||
// _poly(_Linop,B,v);
|
||
_Linop.HermOp(B,v);
|
||
|
||
RealD vnum = real(innerProduct(B,v)); // HermOp.
|
||
RealD vden = norm2(B);
|
||
RealD vv0 = norm2(v);
|
||
eval2[j] = vnum/vden;
|
||
v -= eval2[j]*B;
|
||
RealD vv = norm2(v);
|
||
|
||
std::cout.precision(13);
|
||
std::cout<<GridLogMessage << "[" << std::setw(3)<< std::setiosflags(std::ios_base::right) <<j<<"] ";
|
||
std::cout<<"eval = "<<std::setw(25)<< std::setiosflags(std::ios_base::left)<< eval2[j];
|
||
std::cout<<"|H B[i] - eval[i]B[i]|^2 "<< std::setw(25)<< std::setiosflags(std::ios_base::right)<< vv;
|
||
std::cout<<" "<< vnum/(sqrt(vden)*sqrt(vv0)) << std::endl;
|
||
|
||
// change the criteria as evals are supposed to be sorted, all evals smaller(larger) than Nstop should have converged
|
||
if((vv<eresid*eresid) && (j == Nconv) ){
|
||
Iconv[Nconv] = j;
|
||
++Nconv;
|
||
}
|
||
}
|
||
}
|
||
|
||
void ConvRotate2( int _Nk,
|
||
DenseVector<RealD>& Qt,
|
||
DenseVector<Field>& evec,
|
||
DenseVector<RealD> &eval,
|
||
DenseVector<RealD> &eval2,
|
||
DenseVector<int> &Iconv,
|
||
int &Nconv)
|
||
{
|
||
GridBase *grid = evec[0]._grid;
|
||
int thr=GridThread::GetThreads();
|
||
for(int i=0; i<Nconv; ++i)
|
||
eval[i] = eval2[Iconv[i]];
|
||
// int thr=GridThread::GetThreads();
|
||
// printf("thr=%d\n",thr);
|
||
Field B(grid);
|
||
PARALLEL_FOR_LOOP
|
||
for(int ss=0;ss < grid->oSites();ss++){
|
||
int me = GridThread::ThreadBarrier();
|
||
printf("thr=%d ss=%d me=%d\n",thr,ss,me);fflush(stdout);
|
||
assert( (Nm*thr)<grid->oSites());
|
||
// auto B2 = evec[0]._odata[0];
|
||
// std::vector < decltype( B2 ) > B(Nm,B2);
|
||
for(int j=0; j<Nconv; ++j) B._odata[Iconv[j]+Nm*me]=0.;
|
||
for(int j=0; j<Nconv; ++j){
|
||
for(int k=0; k<_Nk ; ++k){
|
||
B._odata[Iconv[j]+Nm*me] +=Qt[k+Nm*Iconv[j]] * evec[k]._odata[ss];
|
||
}
|
||
}
|
||
for(int j=0; j<Nconv; ++j){
|
||
evec[j]._odata[ss] = B._odata[Iconv[j]+Nm*me];
|
||
}
|
||
}
|
||
}
|
||
|
||
void ConvRotate( int _Nk,
|
||
DenseVector<RealD>& Qt,
|
||
DenseVector<Field>& evec,
|
||
DenseVector<RealD> &eval,
|
||
DenseVector<RealD> &eval2,
|
||
DenseVector<int> &Iconv,
|
||
int &Nconv)
|
||
{
|
||
GridBase *grid = evec[0]._grid;
|
||
typedef typename Field::vector_object vobj;
|
||
#pragma omp parallel
|
||
{
|
||
std::vector < vobj > B(Nm);
|
||
#pragma omp for
|
||
for(int ss=0;ss < grid->oSites();ss++){
|
||
// for(int j=0; j<Nconv; ++j) B[j]=0.;
|
||
for(int j=0; j<Nconv; ++j){
|
||
for(int k=0; k<_Nk ; ++k){
|
||
B[j] +=Qt[k+Nm*Iconv[j]] * evec[k]._odata[ss];
|
||
}
|
||
}
|
||
for(int j=0; j<Nconv; ++j){
|
||
evec[j]._odata[ss] = B[j];
|
||
}
|
||
}
|
||
}
|
||
for(int i=0; i<Nconv; ++i) eval[i] = eval2[Iconv[i]];
|
||
}
|
||
|
||
/* Rudy Arthur's thesis pp.137
|
||
------------------------
|
||
Require: M > K P = M − K †
|
||
Compute the factorization AVM = VM HM + fM eM
|
||
repeat
|
||
Q=I
|
||
for i = 1,...,P do
|
||
QiRi =HM −θiI Q = QQi
|
||
H M = Q †i H M Q i
|
||
end for
|
||
βK =HM(K+1,K) σK =Q(M,K)
|
||
r=vK+1βK +rσK
|
||
VK =VM(1:M)Q(1:M,1:K)
|
||
HK =HM(1:K,1:K)
|
||
→AVK =VKHK +fKe†K † Extend to an M = K + P step factorization AVM = VMHM + fMeM
|
||
until convergence
|
||
*/
|
||
|
||
// alternate implementation for minimizing memory usage. May affect the performance
|
||
void calc(
|
||
DenseVector<RealD>& eval,
|
||
DenseVector<Field>& evec,
|
||
const Field& src,
|
||
int& Nconv)
|
||
{
|
||
|
||
GridBase *grid = evec[0]._grid;
|
||
assert(grid == src._grid);
|
||
|
||
std::cout<<GridLogMessage << " -- Nk = " << Nk << " Np = "<< Np << std::endl;
|
||
std::cout<<GridLogMessage << " -- Nm = " << Nm << std::endl;
|
||
std::cout<<GridLogMessage << " -- size of eval = " << eval.size() << std::endl;
|
||
std::cout<<GridLogMessage << " -- size of evec = " << evec.size() << std::endl;
|
||
|
||
assert(Nm == evec.size() && Nm == eval.size());
|
||
|
||
DenseVector<RealD> lme(Nm);
|
||
DenseVector<RealD> lme2(Nm);
|
||
DenseVector<RealD> eval2(Nm);
|
||
DenseVector<RealD> Qt(Nm*Nm);
|
||
DenseVector<int> Iconv(Nm);
|
||
|
||
|
||
Field f(grid);
|
||
Field v(grid);
|
||
|
||
int k1 = 1;
|
||
int k2 = Nk;
|
||
|
||
Nconv = 0;
|
||
|
||
RealD beta_k;
|
||
|
||
// Set initial vector
|
||
// (uniform vector) Why not src??
|
||
// evec[0] = 1.0;
|
||
evec[0] = src;
|
||
std:: cout<<GridLogMessage <<"norm2(src)= " << norm2(src)<<std::endl;
|
||
// << src._grid << std::endl;
|
||
normalise(evec[0]);
|
||
std:: cout<<GridLogMessage <<"norm2(evec[0])= " << norm2(evec[0]) <<std::endl;
|
||
// << evec[0]._grid << std::endl;
|
||
|
||
// Initial Nk steps
|
||
OrthoTime=0.;
|
||
double t0=usecond()/1e6;
|
||
RealD norm; // sqrt norm of last vector
|
||
for(int k=0; k<Nk; ++k) step(eval,lme,evec,f,Nm,k,norm);
|
||
double t1=usecond()/1e6;
|
||
std::cout<<GridLogMessage <<"IRL::Initial steps: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
|
||
std::cout<<GridLogMessage <<"IRL::Initial steps:OrthoTime "<<OrthoTime<< "seconds"<<std::endl;
|
||
// std:: cout<<GridLogMessage <<"norm2(evec[1])= " << norm2(evec[1]) << std::endl;
|
||
// std:: cout<<GridLogMessage <<"norm2(evec[2])= " << norm2(evec[2]) << std::endl;
|
||
RitzMatrix(evec,Nk);
|
||
t1=usecond()/1e6;
|
||
std::cout<<GridLogMessage <<"IRL::RitzMatrix: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
|
||
for(int k=0; k<Nk; ++k){
|
||
// std:: cout<<GridLogMessage <<"eval " << k << " " <<eval[k] << std::endl;
|
||
// std:: cout<<GridLogMessage <<"lme " << k << " " << lme[k] << std::endl;
|
||
}
|
||
|
||
// Restarting loop begins
|
||
for(int iter = 0; iter<Niter; ++iter){
|
||
|
||
std::cout<<GridLogMessage<<"\n Restart iteration = "<< iter << std::endl;
|
||
|
||
//
|
||
// Rudy does a sort first which looks very different. Getting fed up with sorting out the algo defs.
|
||
// We loop over
|
||
//
|
||
OrthoTime=0.;
|
||
for(int k=Nk; k<Nm; ++k) step(eval,lme,evec,f,Nm,k,norm);
|
||
t1=usecond()/1e6;
|
||
std::cout<<GridLogMessage <<"IRL:: "<<Np <<" steps: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
|
||
std::cout<<GridLogMessage <<"IRL::Initial steps:OrthoTime "<<OrthoTime<< "seconds"<<std::endl;
|
||
f *= lme[Nm-1];
|
||
|
||
RitzMatrix(evec,k2);
|
||
t1=usecond()/1e6;
|
||
std::cout<<GridLogMessage <<"IRL:: RitzMatrix: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
|
||
|
||
// getting eigenvalues
|
||
for(int k=0; k<Nm; ++k){
|
||
eval2[k] = eval[k+k1-1];
|
||
lme2[k] = lme[k+k1-1];
|
||
}
|
||
setUnit_Qt(Nm,Qt);
|
||
diagonalize(eval2,lme2,Nm,Nm,Qt,grid);
|
||
t1=usecond()/1e6;
|
||
std::cout<<GridLogMessage <<"IRL:: diagonalize: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
|
||
int prelNconv=0;
|
||
for(int k=0; k<Nm; ++k){ //check all k's because QR can permutate eigenvectors
|
||
std::cout<<GridLogMessage <<"IRL:: Prel. conv. Test"<<k <<" " << norm<<" "<< fabs(Qt[Nm-1+Nm*k])<<std::endl;
|
||
// Arbitrarily add factor of 10 for now, to be conservative
|
||
if ( norm*fabs(Qt[Nm-1+Nm*k]) < eresid*10 ) prelNconv++;
|
||
}
|
||
|
||
// sorting
|
||
_sort.push(eval2,Nm);
|
||
t1=usecond()/1e6;
|
||
std::cout<<GridLogMessage <<"IRL:: eval sorting: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
|
||
|
||
// Implicitly shifted QR transformations
|
||
setUnit_Qt(Nm,Qt);
|
||
for(int ip=0; ip<k2; ++ip){
|
||
std::cout<<GridLogMessage << "eval "<< ip << " "<< eval2[ip] << std::endl;
|
||
}
|
||
for(int ip=k2; ip<Nm; ++ip){
|
||
std::cout<<GridLogMessage << "qr_decomp "<< ip << " "<< eval2[ip] << std::endl;
|
||
qr_decomp(eval,lme,Nm,Nm,Qt,eval2[ip],k1,Nm);
|
||
|
||
}
|
||
t1=usecond()/1e6;
|
||
std::cout<<GridLogMessage <<"IRL::qr_decomp: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
|
||
|
||
|
||
assert(k2<Nm);
|
||
|
||
// Uses more temorary
|
||
// Rotate0(Qt,evec,k1,k2,Nm);
|
||
// Uses minimal temporary, possibly with less speed
|
||
Rotate(Qt,evec,k1-1,k2+1,Nm);
|
||
// Try if Rotate() doesn't work
|
||
// Rotate2(Qt,evec,k1,k2);
|
||
t1=usecond()/1e6;
|
||
std::cout<<GridLogMessage <<"IRL::QR rotation: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
|
||
|
||
// Compressed vector f and beta(k2)
|
||
f *= Qt[Nm-1+Nm*(k2-1)];
|
||
f += lme[k2-1] * evec[k2];
|
||
beta_k = norm2(f);
|
||
beta_k = sqrt(beta_k);
|
||
std::cout<<GridLogMessage<<" beta(k) = "<<beta_k<<std::endl;
|
||
|
||
RealD betar = 1.0/beta_k;
|
||
evec[k2] = betar * f;
|
||
lme[k2-1] = beta_k;
|
||
|
||
// Convergence test
|
||
for(int k=0; k<Nm; ++k){
|
||
eval2[k] = eval[k];
|
||
lme2[k] = lme[k];
|
||
}
|
||
setUnit_Qt(Nm,Qt);
|
||
diagonalize(eval2,lme2,Nk,Nm,Qt,grid);
|
||
t1=usecond()/1e6;
|
||
std::cout<<GridLogMessage <<"IRL::diagonalize: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
|
||
|
||
if(prelNconv < Nstop)
|
||
std::cout<<GridLogMessage << "Prel. Convergence test ("<<prelNconv<<") failed, skipping a real(and expnesive) one" <<std::endl;
|
||
else
|
||
// ConvCheck0( Nk, Nm, Qt, evec, eval2, Iconv, Nconv);
|
||
ConvCheck( Nk, Qt, evec, eval2, Iconv, Nconv);
|
||
t1=usecond()/1e6;
|
||
std::cout<<GridLogMessage <<"IRL::convergence testing: "<<t1-t0<< "seconds"<<std::endl; t0=t1;
|
||
|
||
|
||
std::cout<<GridLogMessage<<" #modes converged: "<<Nconv<<std::endl;
|
||
|
||
if( Nconv>=Nstop ){
|
||
goto converged;
|
||
}
|
||
} // end of iter loop
|
||
|
||
std::cout<<GridLogMessage<<"\n NOT converged.\n";
|
||
abort();
|
||
|
||
converged:
|
||
// Sorting
|
||
eval.resize(Nconv);
|
||
#ifndef MEM_SAVE
|
||
evec.resize(Nconv,grid);
|
||
for(int i=0; i<Nconv; ++i){
|
||
eval[i] = eval2[Iconv[i]];
|
||
evec[i] = B[Iconv[i]];
|
||
}
|
||
#else
|
||
Rotate(Qt,evec,0,Nk,Nm);
|
||
FinalCheck( Nk, eval,evec);
|
||
//exit(-1);
|
||
// ConvRotate2( Nk, Nm, Qt, evec, eval,eval2,Iconv,Nconv);
|
||
#endif
|
||
// Skip sorting, as it doubles the memory usage(!) and can be avoided by diagonalizing "right away"
|
||
|
||
// _sort.push(eval,evec,Nconv);
|
||
|
||
std::cout<<GridLogMessage << "\n Converged\n Summary :\n";
|
||
std::cout<<GridLogMessage << " -- Iterations = "<< Nconv << "\n";
|
||
std::cout<<GridLogMessage << " -- beta(k) = "<< beta_k << "\n";
|
||
std::cout<<GridLogMessage << " -- Nconv = "<< Nconv << "\n";
|
||
}
|
||
|
||
|
||
void EigenSort(DenseVector<double> evals,
|
||
DenseVector<Field> evecs){
|
||
int N= evals.size();
|
||
_sort.push(evals,evecs, evals.size(),N);
|
||
}
|
||
|
||
|
||
|
||
|
||
|
||
|
||
/**
|
||
There is some matrix Q such that for any vector y
|
||
Q.e_1 = y and Q is unitary.
|
||
**/
|
||
template<class T>
|
||
static T orthQ(DenseMatrix<T> &Q, DenseVector<T> y){
|
||
int N = y.size(); //Matrix Size
|
||
Fill(Q,0.0);
|
||
T tau;
|
||
for(int i=0;i<N;i++){
|
||
Q[i][0]=y[i];
|
||
}
|
||
T sig = conj(y[0])*y[0];
|
||
T tau0 = fabs(sqrt(sig));
|
||
|
||
for(int j=1;j<N;j++){
|
||
sig += conj(y[j])*y[j];
|
||
tau = abs(sqrt(sig) );
|
||
|
||
if(abs(tau0) > 0.0){
|
||
|
||
T gam = conj( (y[j]/tau)/tau0 );
|
||
for(int k=0;k<=j-1;k++){
|
||
Q[k][j]=-gam*y[k];
|
||
}
|
||
Q[j][j]=tau0/tau;
|
||
} else {
|
||
Q[j-1][j]=1.0;
|
||
}
|
||
tau0 = tau;
|
||
}
|
||
return tau;
|
||
}
|
||
|
||
/**
|
||
There is some matrix Q such that for any vector y
|
||
Q.e_k = y and Q is unitary.
|
||
**/
|
||
template< class T>
|
||
static T orthU(DenseMatrix<T> &Q, DenseVector<T> y){
|
||
T tau = orthQ(Q,y);
|
||
SL(Q);
|
||
return tau;
|
||
}
|
||
|
||
|
||
/**
|
||
Wind up with a matrix with the first con rows untouched
|
||
|
||
say con = 2
|
||
Q is such that Qdag H Q has {x, x, val, 0, 0, 0, 0, ...} as 1st colum
|
||
and the matrix is upper hessenberg
|
||
and with f and Q appropriately modidied with Q is the arnoldi factorization
|
||
|
||
**/
|
||
|
||
template<class T>
|
||
static void Lock(DenseMatrix<T> &H, ///Hess mtx
|
||
DenseMatrix<T> &Q, ///Lock Transform
|
||
T val, ///value to be locked
|
||
int con, ///number already locked
|
||
RealD small,
|
||
int dfg,
|
||
bool herm)
|
||
{
|
||
//ForceTridiagonal(H);
|
||
|
||
int M = H.dim;
|
||
DenseVector<T> vec; Resize(vec,M-con);
|
||
|
||
DenseMatrix<T> AH; Resize(AH,M-con,M-con);
|
||
AH = GetSubMtx(H,con, M, con, M);
|
||
|
||
DenseMatrix<T> QQ; Resize(QQ,M-con,M-con);
|
||
|
||
Unity(Q); Unity(QQ);
|
||
|
||
DenseVector<T> evals; Resize(evals,M-con);
|
||
DenseMatrix<T> evecs; Resize(evecs,M-con,M-con);
|
||
|
||
Wilkinson<T>(AH, evals, evecs, small);
|
||
|
||
int k=0;
|
||
RealD cold = abs( val - evals[k]);
|
||
for(int i=1;i<M-con;i++){
|
||
RealD cnew = abs( val - evals[i]);
|
||
if( cnew < cold ){k = i; cold = cnew;}
|
||
}
|
||
vec = evecs[k];
|
||
|
||
ComplexD tau;
|
||
orthQ(QQ,vec);
|
||
//orthQM(QQ,AH,vec);
|
||
|
||
AH = Hermitian(QQ)*AH;
|
||
AH = AH*QQ;
|
||
|
||
for(int i=con;i<M;i++){
|
||
for(int j=con;j<M;j++){
|
||
Q[i][j]=QQ[i-con][j-con];
|
||
H[i][j]=AH[i-con][j-con];
|
||
}
|
||
}
|
||
|
||
for(int j = M-1; j>con+2; j--){
|
||
|
||
DenseMatrix<T> U; Resize(U,j-1-con,j-1-con);
|
||
DenseVector<T> z; Resize(z,j-1-con);
|
||
T nm = norm(z);
|
||
for(int k = con+0;k<j-1;k++){
|
||
z[k-con] = conj( H(j,k+1) );
|
||
}
|
||
normalise(z);
|
||
|
||
RealD tmp = 0;
|
||
for(int i=0;i<z.size()-1;i++){tmp = tmp + abs(z[i]);}
|
||
|
||
if(tmp < small/( (RealD)z.size()-1.0) ){ continue;}
|
||
|
||
tau = orthU(U,z);
|
||
|
||
DenseMatrix<T> Hb; Resize(Hb,j-1-con,M);
|
||
|
||
for(int a = 0;a<M;a++){
|
||
for(int b = 0;b<j-1-con;b++){
|
||
T sum = 0;
|
||
for(int c = 0;c<j-1-con;c++){
|
||
sum += H[a][con+1+c]*U[c][b];
|
||
}//sum += H(a,con+1+c)*U(c,b);}
|
||
Hb[b][a] = sum;
|
||
}
|
||
}
|
||
|
||
for(int k=con+1;k<j;k++){
|
||
for(int l=0;l<M;l++){
|
||
H[l][k] = Hb[k-1-con][l];
|
||
}
|
||
}//H(Hb[k-1-con][l] , l,k);}}
|
||
|
||
DenseMatrix<T> Qb; Resize(Qb,M,M);
|
||
|
||
for(int a = 0;a<M;a++){
|
||
for(int b = 0;b<j-1-con;b++){
|
||
T sum = 0;
|
||
for(int c = 0;c<j-1-con;c++){
|
||
sum += Q[a][con+1+c]*U[c][b];
|
||
}//sum += Q(a,con+1+c)*U(c,b);}
|
||
Qb[b][a] = sum;
|
||
}
|
||
}
|
||
|
||
for(int k=con+1;k<j;k++){
|
||
for(int l=0;l<M;l++){
|
||
Q[l][k] = Qb[k-1-con][l];
|
||
}
|
||
}//Q(Qb[k-1-con][l] , l,k);}}
|
||
|
||
DenseMatrix<T> Hc; Resize(Hc,M,M);
|
||
|
||
for(int a = 0;a<j-1-con;a++){
|
||
for(int b = 0;b<M;b++){
|
||
T sum = 0;
|
||
for(int c = 0;c<j-1-con;c++){
|
||
sum += conj( U[c][a] )*H[con+1+c][b];
|
||
}//sum += conj( U(c,a) )*H(con+1+c,b);}
|
||
Hc[b][a] = sum;
|
||
}
|
||
}
|
||
|
||
for(int k=0;k<M;k++){
|
||
for(int l=con+1;l<j;l++){
|
||
H[l][k] = Hc[k][l-1-con];
|
||
}
|
||
}//H(Hc[k][l-1-con] , l,k);}}
|
||
|
||
}
|
||
}
|
||
#endif
|
||
|
||
|
||
};
|
||
|
||
}
|
||
#endif
|
||
|