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Reunified the Lanczos implementations
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paboyle
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@ -7,8 +7,9 @@
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Copyright (C) 2015
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Author: Peter Boyle <paboyle@ph.ed.ac.uk>
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Author: Chulwoo Jung
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Author: Guido Cossu
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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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Author: Christoph Lehner <clehner@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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@ -27,125 +28,191 @@ Author: Guido Cossu
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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_H
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#define GRID_IRL_H
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#ifndef GRID_BIRL_H
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#define GRID_BIRL_H
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#include <string.h> //memset
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//#include <zlib.h>
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#include <sys/stat.h>
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namespace Grid {
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namespace Grid {
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enum IRLdiagonalisation {
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IRLdiagonaliseWithDSTEGR,
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IRLdiagonaliseWithQR,
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IRLdiagonaliseWithEigen
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};
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////////////////////////////////////////////////////////////////////////////////
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// Helper class for sorting the evalues AND evectors by Field
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// Use pointer swizzle on vectors
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////////////////////////////////////////////////////////////////////////////////
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template<class Field>
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class SortEigen {
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private:
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static bool less_lmd(RealD left,RealD right){
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return left > right;
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}
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static bool less_pair(std::pair<RealD,Field const*>& left,
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std::pair<RealD,Field const*>& right){
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return left.first > (right.first);
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}
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public:
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void push(std::vector<RealD>& lmd,std::vector<Field>& evec,int N) {
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////////////////////////////////////////////////////////////////////////
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// PAB: FIXME: VERY VERY VERY wasteful: takes a copy of the entire vector set.
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// : The vector reorder should be done by pointer swizzle somehow
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////////////////////////////////////////////////////////////////////////
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std::vector<Field> cpy(lmd.size(),evec[0]._grid);
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for(int i=0;i<lmd.size();i++) cpy[i] = evec[i];
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std::vector<std::pair<RealD, Field const*> > emod(lmd.size());
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void basisOrthogonalize(std::vector<Field> &basis,Field &w,int k)
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{
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for(int j=0; j<k; ++j){
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auto ip = innerProduct(basis[j],w);
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w = w - ip*basis[j];
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}
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}
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for(int i=0;i<lmd.size();++i) emod[i] = std::pair<RealD,Field const*>(lmd[i],&cpy[i]);
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partial_sort(emod.begin(),emod.begin()+N,emod.end(),less_pair);
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typename std::vector<std::pair<RealD, Field const*> >::iterator it = emod.begin();
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for(int i=0;i<N;++i){
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lmd[i]=it->first;
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evec[i]=*(it->second);
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++it;
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template<class Field>
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void basisRotate(std::vector<Field> &basis,Eigen::MatrixXd& Qt,int j0, int j1, int k0,int k1,int Nm)
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{
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typedef typename Field::vector_object vobj;
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GridBase* grid = basis[0]._grid;
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parallel_region
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{
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std::vector < vobj > B(Nm); // Thread private
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parallel_for_internal(int ss=0;ss < grid->oSites();ss++){
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for(int j=j0; j<j1; ++j) B[j]=0.;
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for(int j=j0; j<j1; ++j){
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for(int k=k0; k<k1; ++k){
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B[j] +=Qt(j,k) * basis[k]._odata[ss];
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}
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}
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for(int j=j0; j<j1; ++j){
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basis[j]._odata[ss] = B[j];
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}
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}
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}
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void push(std::vector<RealD>& lmd,int N) {
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std::partial_sort(lmd.begin(),lmd.begin()+N,lmd.end(),less_lmd);
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}
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template<class Field>
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void basisReorderInPlace(std::vector<Field> &_v,std::vector<RealD>& sort_vals, std::vector<int>& idx)
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{
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int vlen = idx.size();
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assert(vlen>=1);
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assert(vlen<=sort_vals.size());
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assert(vlen<=_v.size());
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for (size_t i=0;i<vlen;i++) {
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if (idx[i] != i) {
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assert(idx[i] > i);
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//////////////////////////////////////
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// idx[i] is a table of desired sources giving a permutation.
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//
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// Swap v[i] with v[idx[i]].
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//
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// Find j>i for which _vnew[j] = _vold[i],
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// track the move idx[j] => idx[i]
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// track the move idx[i] => i
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//////////////////////////////////////
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size_t j;
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for (j=i;j<idx.size();j++)
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if (idx[j]==i)
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break;
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assert(j!=idx.size());
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assert(idx[j]==i);
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std::swap(_v[i]._odata,_v[idx[i]]._odata); // should use vector move constructor, no data copy
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std::swap(sort_vals[i],sort_vals[idx[i]]);
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idx[j] = idx[i];
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idx[i] = i;
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}
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}
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bool saturated(RealD lmd, RealD thrs) {
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return fabs(lmd) > fabs(thrs);
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}
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inline std::vector<int> basisSortGetIndex(std::vector<RealD>& sort_vals)
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{
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std::vector<int> idx(sort_vals.size());
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std::iota(idx.begin(), idx.end(), 0);
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// sort indexes based on comparing values in v
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std::sort(idx.begin(), idx.end(), [&sort_vals](int i1, int i2) {
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return ::fabs(sort_vals[i1]) < ::fabs(sort_vals[i2]);
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});
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return idx;
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}
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template<class Field>
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void basisSortInPlace(std::vector<Field> & _v,std::vector<RealD>& sort_vals, bool reverse)
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{
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std::vector<int> idx = basisSortGetIndex(sort_vals);
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if (reverse)
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std::reverse(idx.begin(), idx.end());
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basisReorderInPlace(_v,sort_vals,idx);
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}
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// PAB: faster to compute the inner products first then fuse loops.
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// If performance critical can improve.
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template<class Field>
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void basisDeflate(const std::vector<Field> &_v,const std::vector<RealD>& eval,const Field& src_orig,Field& result) {
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result = zero;
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assert(_v.size()==eval.size());
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int N = (int)_v.size();
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for (int i=0;i<N;i++) {
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Field& tmp = _v[i];
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axpy(result,TensorRemove(innerProduct(tmp,src_orig)) / eval[i],tmp,result);
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}
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}
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enum IRLdiagonalisation {
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IRLdiagonaliseWithDSTEGR,
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IRLdiagonaliseWithQR,
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IRLdiagonaliseWithEigen
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};
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/////////////////////////////////////////////////////////////
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// Implicitly restarted lanczos
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/////////////////////////////////////////////////////////////
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template<class Field>
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class ImplicitlyRestartedLanczos {
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private:
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int MaxIter; // Max iterations
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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 Nm; // Nm -- total number of vectors
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RealD eresid;
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private:
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const RealD small = 1.0e-8;
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int MaxIter;
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int MinRestart; // Minimum number of restarts; only check for convergence after
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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 krylov space // == Nm - Nk
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int Nm; // Nm -- total number of vectors
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IRLdiagonalisation diagonalisation;
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////////////////////////////////////
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int orth_period;
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RealD OrthoTime;
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RealD eresid, betastp;
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////////////////////////////////
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// Embedded objects
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////////////////////////////////////
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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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LinearFunction<Field> &_HermOp;
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LinearFunction<Field> &_HermOpTest;
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/////////////////////////
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// Constructor
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/////////////////////////
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public:
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ImplicitlyRestartedLanczos(LinearOperatorBase<Field> &Linop, // op
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OperatorFunction<Field> & poly, // polynomial
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int _Nstop, // really sought vecs
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int _Nk, // sought vecs
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int _Nm, // total vecs
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RealD _eresid, // resid in lmd deficit
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int _MaxIter, // Max iterations
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IRLdiagonalisation _diagonalisation= IRLdiagonaliseWithEigen ) :
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_Linop(Linop), _poly(poly),
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Nstop(_Nstop), Nk(_Nk), Nm(_Nm),
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eresid(_eresid), MaxIter(_MaxIter),
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diagonalisation(_diagonalisation)
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{ };
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ImplicitlyRestartedLanczos(LinearFunction<Field> & HermOp,
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LinearFunction<Field> & HermOpTest,
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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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RealD _betastp, // if beta(k) < betastp: converged
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int _MaxIter, // Max iterations
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int _MinRestart, int _orth_period = 1,
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IRLdiagonalisation _diagonalisation= IRLdiagonaliseWithEigen) :
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_HermOp(HermOp), _HermOpTest(HermOpTest),
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Nstop(_Nstop) , Nk(_Nk), Nm(_Nm),
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eresid(_eresid), betastp(_betastp),
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MaxIter(_MaxIter) , MinRestart(_MinRestart),
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orth_period(_orth_period), diagonalisation(_diagonalisation) { };
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////////////////////////////////
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// Helpers
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////////////////////////////////
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static RealD normalise(Field& v)
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template<typename T> static RealD normalise(T& v)
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{
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RealD nn = norm2(v);
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nn = sqrt(nn);
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v = v * (1.0/nn);
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return nn;
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}
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void orthogonalize(Field& w, std::vector<Field>& evec, int k)
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void orthogonalize(Field& w, std::vector<Field>& evec,int k)
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{
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typedef typename Field::scalar_type MyComplex;
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MyComplex ip;
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for(int j=0; j<k; ++j){
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ip = innerProduct(evec[j],w);
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w = w - ip * evec[j];
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}
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OrthoTime-=usecond()/1e6;
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basisOrthogonalize(evec,w,k);
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normalise(w);
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OrthoTime+=usecond()/1e6;
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}
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/* Rudy Arthur's thesis pp.137
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@ -165,185 +232,265 @@ repeat
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→AVK =VKHK +fKe†K † Extend to an M = K + P step factorization AVM = VMHM + fMeM
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until convergence
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*/
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void calc(std::vector<RealD>& eval, std::vector<Field>& evec, const Field& src, int& Nconv)
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void calc(std::vector<RealD>& eval, std::vector<Field>& evec, const Field& src, int& Nconv, bool reverse, int SkipTest)
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{
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GridBase *grid = src._grid;
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assert(grid == evec[0]._grid);
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GridBase *grid = evec[0]._grid;
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assert(grid == src._grid);
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std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
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std::cout << GridLogMessage <<" ImplicitlyRestartedLanczos::calc() starting iteration 0 / "<< MaxIter<< std::endl;
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std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
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std::cout << GridLogMessage <<" -- seek Nk = " << Nk <<" vectors"<< std::endl;
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std::cout << GridLogMessage <<" -- accept Nstop = " << Nstop <<" vectors"<< std::endl;
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std::cout << GridLogMessage <<" -- total Nm = " << Nm <<" vectors"<< std::endl;
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std::cout << GridLogMessage <<" -- size of eval = " << eval.size() << std::endl;
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std::cout << GridLogMessage <<" -- size of evec = " << evec.size() << std::endl;
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GridLogIRL.TimingMode(1);
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std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
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std::cout << GridLogIRL <<" ImplicitlyRestartedLanczos::calc() starting iteration 0 / "<< MaxIter<< std::endl;
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std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
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std::cout << GridLogIRL <<" -- seek Nk = " << Nk <<" vectors"<< std::endl;
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std::cout << GridLogIRL <<" -- accept Nstop = " << Nstop <<" vectors"<< std::endl;
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std::cout << GridLogIRL <<" -- total Nm = " << Nm <<" vectors"<< std::endl;
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std::cout << GridLogIRL <<" -- size of eval = " << eval.size() << std::endl;
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std::cout << GridLogIRL <<" -- size of evec = " << evec.size() << std::endl;
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if ( diagonalisation == IRLdiagonaliseWithDSTEGR ) {
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std::cout << GridLogMessage << "Diagonalisation is DSTEGR "<<std::endl;
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std::cout << GridLogIRL << "Diagonalisation is DSTEGR "<<std::endl;
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} else if ( diagonalisation == IRLdiagonaliseWithQR ) {
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std::cout << GridLogMessage << "Diagonalisation is QR "<<std::endl;
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std::cout << GridLogIRL << "Diagonalisation is QR "<<std::endl;
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} else if ( diagonalisation == IRLdiagonaliseWithEigen ) {
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std::cout << GridLogMessage << "Diagonalisation is Eigen "<<std::endl;
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std::cout << GridLogIRL << "Diagonalisation is Eigen "<<std::endl;
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}
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std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
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std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
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assert(Nm <= evec.size() && Nm <= eval.size());
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assert(Nm == evec.size() && Nm == eval.size());
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// quickly get an idea of the largest eigenvalue to more properly normalize the residuum
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RealD evalMaxApprox = 0.0;
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{
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auto src_n = src;
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auto tmp = src;
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const int _MAX_ITER_IRL_MEVAPP_ = 50;
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for (int i=0;i<_MAX_ITER_IRL_MEVAPP_;i++) {
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_HermOpTest(src_n,tmp);
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RealD vnum = real(innerProduct(src_n,tmp)); // HermOp.
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RealD vden = norm2(src_n);
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RealD na = vnum/vden;
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if (fabs(evalMaxApprox/na - 1.0) < 0.05)
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i=_MAX_ITER_IRL_MEVAPP_;
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evalMaxApprox = na;
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std::cout << GridLogIRL << " Approximation of largest eigenvalue: " << evalMaxApprox << std::endl;
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src_n = tmp;
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}
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}
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std::vector<RealD> lme(Nm);
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std::vector<RealD> lme2(Nm);
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std::vector<RealD> eval2(Nm);
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std::vector<RealD> eval2_copy(Nm);
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Eigen::MatrixXd Qt = Eigen::MatrixXd::Zero(Nm,Nm);
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Eigen::MatrixXd Qt = Eigen::MatrixXd::Zero(Nm,Nm);
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std::vector<int> Iconv(Nm);
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std::vector<Field> B(Nm,grid); // waste of space replicating
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Field f(grid);
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Field v(grid);
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int k1 = 1;
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int k2 = Nk;
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Nconv = 0;
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RealD beta_k;
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Nconv = 0;
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// Set initial vector
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evec[0] = src;
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std::cout << GridLogMessage <<"norm2(src)= " << norm2(src)<<std::endl;
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normalise(evec[0]);
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std::cout << GridLogMessage <<"norm2(evec[0])= " << norm2(evec[0]) <<std::endl;
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// Initial Nk steps
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OrthoTime=0.;
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for(int k=0; k<Nk; ++k) step(eval,lme,evec,f,Nm,k);
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std::cout<<GridLogIRL <<"Initial "<< Nk <<"steps done "<<std::endl;
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std::cout<<GridLogIRL <<"Initial steps:OrthoTime "<<OrthoTime<< "seconds"<<std::endl;
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//////////////////////////////////
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// Restarting loop begins
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//////////////////////////////////
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int iter;
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for(iter = 0; iter<MaxIter; ++iter){
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OrthoTime=0.;
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std::cout<< GridLogMessage <<" **********************"<< std::endl;
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std::cout<< GridLogMessage <<" Restart iteration = "<< iter << std::endl;
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std::cout<< GridLogMessage <<" **********************"<< std::endl;
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std::cout<<GridLogIRL <<" running "<<Nm-Nk <<" steps: "<<std::endl;
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for(int k=Nk; k<Nm; ++k) step(eval,lme,evec,f,Nm,k);
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f *= lme[Nm-1];
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std::cout<<GridLogIRL <<" "<<Nm-Nk <<" steps done "<<std::endl;
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std::cout<<GridLogIRL <<"Initial steps:OrthoTime "<<OrthoTime<< "seconds"<<std::endl;
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//////////////////////////////////
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// getting eigenvalues
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//////////////////////////////////
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for(int k=0; k<Nm; ++k){
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eval2[k] = eval[k+k1-1];
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lme2[k] = lme[k+k1-1];
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}
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Qt = Eigen::MatrixXd::Identity(Nm,Nm);
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diagonalize(eval2,lme2,Nm,Nm,Qt,grid);
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std::cout<<GridLogIRL <<" diagonalized "<<std::endl;
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//////////////////////////////////
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// sorting
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_sort.push(eval2,Nm);
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// Implicitly shifted QR transformations
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Qt = Eigen::MatrixXd::Identity(Nm,Nm);
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//////////////////////////////////
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eval2_copy = eval2;
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// _sort.push(eval2,Nm);
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||||
std::partial_sort(eval2.begin(),eval2.begin()+Nm,eval2.end());
|
||||
|
||||
std::cout<<GridLogIRL <<" evals sorted "<<std::endl;
|
||||
for(int ip=0; ip<k2; ++ip) std::cout<<GridLogIRL << "eval "<< ip << " "<< eval2[ip] << std::endl;
|
||||
|
||||
//////////////////////////////////
|
||||
// Implicitly shifted QR transformations
|
||||
//////////////////////////////////
|
||||
Qt = Eigen::MatrixXd::Identity(Nm,Nm);
|
||||
std::cout<<GridLogIRL << "QR decompose " << std::endl;
|
||||
for(int ip=k2; ip<Nm; ++ip){
|
||||
// Eigen replacement for qr_decomp ???
|
||||
qr_decomp(eval,lme,Nm,Nm,Qt,eval2[ip],k1,Nm);
|
||||
QR_decomp(eval,lme,Nm,Nm,Qt,eval2[ip],k1,Nm);
|
||||
}
|
||||
|
||||
for(int i=0; i<(Nk+1); ++i) B[i] = 0.0;
|
||||
|
||||
for(int j=k1-1; j<k2+1; ++j){
|
||||
for(int k=0; k<Nm; ++k){
|
||||
B[j].checkerboard = evec[k].checkerboard;
|
||||
B[j] += Qt(j,k) * evec[k];
|
||||
}
|
||||
}
|
||||
for(int j=k1-1; j<k2+1; ++j) evec[j] = B[j];
|
||||
std::cout<<GridLogIRL <<"QR decompose done "<<std::endl;
|
||||
|
||||
assert(k2<Nm);
|
||||
assert(k2<Nm);
|
||||
assert(k1>0);
|
||||
basisRotate(evec,Qt,k1-1,k2+1,0,Nm,Nm); /// big constraint on the basis
|
||||
|
||||
std::cout<<GridLogIRL <<"QR rotation done "<<std::endl;
|
||||
|
||||
////////////////////////////////////////////////////
|
||||
// Compressed vector f and beta(k2)
|
||||
////////////////////////////////////////////////////
|
||||
f *= Qt(k2-1,Nm-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;
|
||||
|
||||
std::cout<<GridLogIRL<<" 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];
|
||||
// std::cout<<GridLogIRL << "eval2[" << k << "] = " << eval2[k] << std::endl;
|
||||
}
|
||||
Qt = Eigen::MatrixXd::Identity(Nm,Nm);
|
||||
diagonalize(eval2,lme2,Nk,Nm,Qt,grid);
|
||||
|
||||
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(j,k) * evec[k];
|
||||
}
|
||||
}
|
||||
|
||||
std::cout<<GridLogIRL <<" Diagonalized "<<std::endl;
|
||||
|
||||
Nconv = 0;
|
||||
for(int i=0; i<Nk; ++i){
|
||||
if (iter >= MinRestart) {
|
||||
std::cout << GridLogIRL << "Rotation to test convergence " << std::endl;
|
||||
|
||||
_Linop.HermOp(B[i],v);
|
||||
Field ev0_orig(grid);
|
||||
ev0_orig = evec[0];
|
||||
|
||||
RealD vnum = real(innerProduct(B[i],v)); // HermOp.
|
||||
RealD vden = norm2(B[i]);
|
||||
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::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 <<" #modes converged: "<<Nconv<<std::endl;
|
||||
basisRotate(evec,Qt,0,Nk,0,Nk,Nm);
|
||||
|
||||
if( Nconv>=Nstop ){
|
||||
goto converged;
|
||||
}
|
||||
} // end of iter loop
|
||||
|
||||
std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
|
||||
std::cout << GridLogError <<" ImplicitlyRestartedLanczos::calc() NOT converged.";
|
||||
std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
|
||||
{
|
||||
std::cout << GridLogIRL << "Test convergence" << std::endl;
|
||||
Field B(grid);
|
||||
|
||||
for(int j = 0; j<Nk; j+=SkipTest){
|
||||
B=evec[j];
|
||||
|
||||
//std::cout << "Checkerboard: " << evec[j].checkerboard << std::endl;
|
||||
B.checkerboard = evec[0].checkerboard;
|
||||
|
||||
_HermOpTest(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) / ::pow(evalMaxApprox,2.0);
|
||||
std::cout.precision(13);
|
||||
std::cout<<GridLogIRL << "[" << std::setw(3)<< std::setiosflags(std::ios_base::right) <<j<<"] "
|
||||
<<"eval = "<<std::setw(25)<< std::setiosflags(std::ios_base::left)<< eval2[j] << " (" << eval2_copy[j] << ")"
|
||||
<<" |H B[i] - eval[i]B[i]|^2 / evalMaxApprox^2 " << std::setw(25)<< std::setiosflags(std::ios_base::right)<< vv
|
||||
<<" "<< 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) ){
|
||||
Nconv+=SkipTest;
|
||||
}
|
||||
}
|
||||
|
||||
// test if we converged, if so, terminate
|
||||
std::cout<<GridLogIRL<<" #modes converged: "<<Nconv<<std::endl;
|
||||
if( Nconv>=Nstop || beta_k < betastp){
|
||||
goto converged;
|
||||
}
|
||||
|
||||
//B[j] +=Qt[k+_Nm*j] * _v[k]._odata[ss];
|
||||
{
|
||||
Eigen::MatrixXd qm = Eigen::MatrixXd::Zero(Nk,Nk); // Restrict Qt to Nk x Nk
|
||||
for (int k=0;k<Nk;k++)
|
||||
for (int j=0;j<Nk;j++)
|
||||
qm(j,k) = Qt(j,k);
|
||||
|
||||
Eigen::MatrixXd qmI = qm.inverse();
|
||||
|
||||
RealD res_check_rotate_inverse = (qm*qmI - Eigen::MatrixXd::Identity(Nk,Nk)).norm(); // sqrt( |X|^2 )
|
||||
|
||||
std::cout << GridLogIRL << "\tInverted ("<<Nk<<"x"<<Nk<<") Qt matrix " << " error = " << res_check_rotate_inverse <<std::endl;
|
||||
|
||||
assert(res_check_rotate_inverse < 1e-7);
|
||||
|
||||
basisRotate(evec,qmI,0,Nk,0,Nk,Nm);
|
||||
std::cout << GridLogIRL << "\t Basis rotation done "<<std::endl;
|
||||
|
||||
axpy(ev0_orig,-1.0,evec[0],ev0_orig);
|
||||
std::cout << GridLogIRL << " | evec[0] - evec[0]_orig | = " << ::sqrt(norm2(ev0_orig)) << std::endl;
|
||||
}
|
||||
}
|
||||
} else {
|
||||
std::cout << GridLogIRL << "iter < MinRestart: do not yet test for convergence\n";
|
||||
} // end of iter loop
|
||||
}
|
||||
|
||||
std::cout<<GridLogError<<"\n NOT converged.\n";
|
||||
abort();
|
||||
|
||||
converged:
|
||||
// Sorting
|
||||
eval.resize(Nconv);
|
||||
evec.resize(Nconv,grid);
|
||||
for(int i=0; i<Nconv; ++i){
|
||||
eval[i] = eval2[Iconv[i]];
|
||||
evec[i] = B[Iconv[i]];
|
||||
|
||||
if (SkipTest == 1) {
|
||||
eval = eval2;
|
||||
} else {
|
||||
//////////////////////////////////////////////
|
||||
// test quickly
|
||||
// PAB -- what precisely does this test? Don't like this eval2, eval2_copy etc...
|
||||
//////////////////////////////////////////////
|
||||
for (int j=0;j<Nstop;j+=SkipTest) {
|
||||
std::cout<<GridLogIRL << "Eigenvalue[" << j << "] = " << eval2[j] << " (" << eval2_copy[j] << ")" << std::endl;
|
||||
}
|
||||
eval2_copy.resize(eval2.size());
|
||||
eval = eval2_copy;
|
||||
}
|
||||
_sort.push(eval,evec,Nconv);
|
||||
|
||||
std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
|
||||
std::cout << GridLogMessage << "ImplicitlyRestartedLanczos CONVERGED ; Summary :\n";
|
||||
std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
|
||||
std::cout << GridLogMessage << " -- Iterations = "<< iter << "\n";
|
||||
std::cout << GridLogMessage << " -- beta(k) = "<< beta_k << "\n";
|
||||
std::cout << GridLogMessage << " -- Nconv = "<< Nconv << "\n";
|
||||
std::cout << GridLogMessage <<"**************************************************************************"<< std::endl;
|
||||
|
||||
basisSortInPlace(evec,eval,reverse);
|
||||
|
||||
for (int j=0;j<Nstop;j++) {
|
||||
std::cout<<GridLogIRL << " |e[" << j << "]|^2 = " << norm2(evec[j]) << std::endl;
|
||||
}
|
||||
|
||||
std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
|
||||
std::cout << GridLogIRL << "ImplicitlyRestartedLanczos CONVERGED ; Summary :\n";
|
||||
std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
|
||||
std::cout << GridLogIRL << " -- Iterations = "<< iter << "\n";
|
||||
std::cout << GridLogIRL << " -- beta(k) = "<< beta_k << "\n";
|
||||
std::cout << GridLogIRL << " -- Nconv = "<< Nconv << "\n";
|
||||
std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
|
||||
}
|
||||
|
||||
private:
|
||||
private:
|
||||
/* Saad PP. 195
|
||||
1. Choose an initial vector v1 of 2-norm unity. Set β1 ≡ 0, v0 ≡ 0
|
||||
2. For k = 1,2,...,m Do:
|
||||
@ -361,28 +508,41 @@ private:
|
||||
{
|
||||
const RealD tiny = 1.0e-20;
|
||||
assert( k< Nm );
|
||||
|
||||
_poly(_Linop,evec[k],w); // 3. wk:=Avk−βkv_{k−1}
|
||||
|
||||
|
||||
GridStopWatch gsw_op,gsw_o;
|
||||
|
||||
Field& evec_k = evec[k];
|
||||
|
||||
_HermOp(evec_k,w);
|
||||
std::cout<<GridLogIRL << "_HermOp (poly)" <<std::endl;
|
||||
|
||||
if(k>0) w -= lme[k-1] * evec[k-1];
|
||||
|
||||
ComplexD zalph = innerProduct(evec[k],w); // 4. αk:=(wk,vk)
|
||||
|
||||
ComplexD zalph = innerProduct(evec_k,w); // 4. αk:=(wk,vk)
|
||||
RealD alph = real(zalph);
|
||||
|
||||
w = w - alph * evec[k];// 5. wk:=wk−αkvk
|
||||
|
||||
|
||||
w = w - alph * evec_k;// 5. wk:=wk−αkvk
|
||||
|
||||
RealD beta = normalise(w); // 6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
|
||||
// 7. vk+1 := wk/βk+1
|
||||
|
||||
|
||||
lmd[k] = alph;
|
||||
lme[k] = beta;
|
||||
|
||||
if ( k > 0 ) orthogonalize(w,evec,k); // orthonormalise
|
||||
if ( k < Nm-1) evec[k+1] = w;
|
||||
|
||||
if ( beta < tiny ) std::cout << GridLogMessage << " beta is tiny "<<beta<<std::endl;
|
||||
|
||||
std::cout<<GridLogIRL << "linalg " <<std::endl;
|
||||
|
||||
if (k>0 && k % orth_period == 0) {
|
||||
orthogonalize(w,evec,k); // orthonormalise
|
||||
std::cout<<GridLogIRL << "orthogonalised " <<std::endl;
|
||||
}
|
||||
|
||||
if(k < Nm-1) evec[k+1] = w;
|
||||
|
||||
std::cout<<GridLogIRL << "alpha[" << k << "] = " << zalph << " beta[" << k << "] = "<<beta<<std::endl;
|
||||
if ( beta < tiny )
|
||||
std::cout<<GridLogIRL << " beta is tiny "<<beta<<std::endl;
|
||||
}
|
||||
|
||||
|
||||
void diagonalize_Eigen(std::vector<RealD>& lmd, std::vector<RealD>& lme,
|
||||
int Nk, int Nm,
|
||||
Eigen::MatrixXd & Qt, // Nm x Nm
|
||||
@ -405,11 +565,12 @@ private:
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
///////////////////////////////////////////////////////////////////////////
|
||||
// File could end here if settle on Eigen ???
|
||||
///////////////////////////////////////////////////////////////////////////
|
||||
|
||||
void qr_decomp(std::vector<RealD>& lmd, // Nm
|
||||
void QR_decomp(std::vector<RealD>& lmd, // Nm
|
||||
std::vector<RealD>& lme, // Nm
|
||||
int Nk, int Nm, // Nk, Nm
|
||||
Eigen::MatrixXd& Qt, // Nm x Nm matrix
|
||||
@ -576,51 +737,50 @@ void diagonalize_lapack(std::vector<RealD>& lmd,
|
||||
#endif
|
||||
}
|
||||
|
||||
void diagonalize_QR(std::vector<RealD>& lmd, std::vector<RealD>& lme,
|
||||
int Nk, int Nm,
|
||||
Eigen::MatrixXd & Qt,
|
||||
GridBase *grid)
|
||||
{
|
||||
int Niter = 100*Nm;
|
||||
int kmin = 1;
|
||||
int kmax = Nk;
|
||||
|
||||
// (this should be more sophisticated)
|
||||
for(int iter=0; iter<Niter; ++iter){
|
||||
|
||||
// determination of 2x2 leading submatrix
|
||||
RealD dsub = lmd[kmax-1]-lmd[kmax-2];
|
||||
RealD dd = sqrt(dsub*dsub + 4.0*lme[kmax-2]*lme[kmax-2]);
|
||||
RealD Dsh = 0.5*(lmd[kmax-2]+lmd[kmax-1] +dd*(dsub/fabs(dsub)));
|
||||
// (Dsh: shift)
|
||||
|
||||
// transformation
|
||||
qr_decomp(lmd,lme,Nk,Nm,Qt,Dsh,kmin,kmax); // Nk, Nm
|
||||
|
||||
// Convergence criterion (redef of kmin and kamx)
|
||||
for(int j=kmax-1; j>= kmin; --j){
|
||||
RealD dds = fabs(lmd[j-1])+fabs(lmd[j]);
|
||||
if(fabs(lme[j-1])+dds > dds){
|
||||
kmax = j+1;
|
||||
goto continued;
|
||||
}
|
||||
}
|
||||
Niter = iter;
|
||||
return;
|
||||
|
||||
continued:
|
||||
for(int j=0; j<kmax-1; ++j){
|
||||
RealD dds = fabs(lmd[j])+fabs(lmd[j+1]);
|
||||
if(fabs(lme[j])+dds > dds){
|
||||
kmin = j+1;
|
||||
break;
|
||||
}
|
||||
void diagonalize_QR(std::vector<RealD>& lmd, std::vector<RealD>& lme,
|
||||
int Nk, int Nm,
|
||||
Eigen::MatrixXd & Qt,
|
||||
GridBase *grid)
|
||||
{
|
||||
int QRiter = 100*Nm;
|
||||
int kmin = 1;
|
||||
int kmax = Nk;
|
||||
|
||||
// (this should be more sophisticated)
|
||||
for(int iter=0; iter<QRiter; ++iter){
|
||||
|
||||
// determination of 2x2 leading submatrix
|
||||
RealD dsub = lmd[kmax-1]-lmd[kmax-2];
|
||||
RealD dd = sqrt(dsub*dsub + 4.0*lme[kmax-2]*lme[kmax-2]);
|
||||
RealD Dsh = 0.5*(lmd[kmax-2]+lmd[kmax-1] +dd*(dsub/fabs(dsub)));
|
||||
// (Dsh: shift)
|
||||
|
||||
// transformation
|
||||
QR_decomp(lmd,lme,Nk,Nm,Qt,Dsh,kmin,kmax); // Nk, Nm
|
||||
|
||||
// Convergence criterion (redef of kmin and kamx)
|
||||
for(int j=kmax-1; j>= kmin; --j){
|
||||
RealD dds = fabs(lmd[j-1])+fabs(lmd[j]);
|
||||
if(fabs(lme[j-1])+dds > dds){
|
||||
kmax = j+1;
|
||||
goto continued;
|
||||
}
|
||||
}
|
||||
QRiter = iter;
|
||||
return;
|
||||
|
||||
continued:
|
||||
for(int j=0; j<kmax-1; ++j){
|
||||
RealD dds = fabs(lmd[j])+fabs(lmd[j+1]);
|
||||
if(fabs(lme[j])+dds > dds){
|
||||
kmin = j+1;
|
||||
break;
|
||||
}
|
||||
}
|
||||
std::cout << GridLogError << "[QL method] Error - Too many iteration: "<<Niter<<"\n";
|
||||
abort();
|
||||
}
|
||||
|
||||
};
|
||||
std::cout << GridLogError << "[QL method] Error - Too many iteration: "<<QRiter<<"\n";
|
||||
abort();
|
||||
}
|
||||
};
|
||||
}
|
||||
#endif
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user