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787 lines
24 KiB
C++
787 lines
24 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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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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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_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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template<class Field>
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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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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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}
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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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}
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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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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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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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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(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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int _MaxIter, // Max iterations
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RealD _betastp=0.0, // if beta(k) < betastp: converged
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int _MinRestart=1, 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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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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{
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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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------------------------
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Require: M > K P = M − K †
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Compute the factorization AVM = VM HM + fM eM
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repeat
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Q=I
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for i = 1,...,P do
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QiRi =HM −θiI Q = QQi
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H M = Q †i H M Q i
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end for
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βK =HM(K+1,K) σK =Q(M,K)
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r=vK+1βK +rσK
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VK =VM(1:M)Q(1:M,1:K)
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HK =HM(1:K,1:K)
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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, bool reverse=true, int SkipTest=0)
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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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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 << GridLogIRL << "Diagonalisation is DSTEGR "<<std::endl;
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} else if ( diagonalisation == IRLdiagonaliseWithQR ) {
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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 << GridLogIRL << "Diagonalisation is Eigen "<<std::endl;
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}
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std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
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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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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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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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normalise(evec[0]);
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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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//////////////////////////////////
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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());
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std::cout<<GridLogIRL <<" evals sorted "<<std::endl;
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for(int ip=0; ip<k2; ++ip) std::cout<<GridLogIRL << "eval "<< ip << " "<< eval2[ip] << std::endl;
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//////////////////////////////////
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// Implicitly shifted QR transformations
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//////////////////////////////////
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Qt = Eigen::MatrixXd::Identity(Nm,Nm);
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std::cout<<GridLogIRL << "QR decompose " << std::endl;
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for(int ip=k2; ip<Nm; ++ip){
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QR_decomp(eval,lme,Nm,Nm,Qt,eval2[ip],k1,Nm);
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}
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std::cout<<GridLogIRL <<"QR decompose done "<<std::endl;
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assert(k2<Nm);
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assert(k2<Nm);
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assert(k1>0);
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basisRotate(evec,Qt,k1-1,k2+1,0,Nm,Nm); /// big constraint on the basis
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std::cout<<GridLogIRL <<"QR rotation done "<<std::endl;
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////////////////////////////////////////////////////
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// Compressed vector f and beta(k2)
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////////////////////////////////////////////////////
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f *= Qt(k2-1,Nm-1);
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f += lme[k2-1] * evec[k2];
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beta_k = norm2(f);
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beta_k = sqrt(beta_k);
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std::cout<<GridLogIRL<<" beta(k) = "<<beta_k<<std::endl;
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RealD betar = 1.0/beta_k;
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evec[k2] = betar * f;
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lme[k2-1] = beta_k;
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////////////////////////////////////////////////////
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// Convergence test
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////////////////////////////////////////////////////
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for(int k=0; k<Nm; ++k){
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eval2[k] = eval[k];
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lme2[k] = lme[k];
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// std::cout<<GridLogIRL << "eval2[" << k << "] = " << eval2[k] << std::endl;
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}
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Qt = Eigen::MatrixXd::Identity(Nm,Nm);
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diagonalize(eval2,lme2,Nk,Nm,Qt,grid);
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std::cout<<GridLogIRL <<" Diagonalized "<<std::endl;
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Nconv = 0;
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if (iter >= MinRestart) {
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std::cout << GridLogIRL << "Rotation to test convergence " << std::endl;
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Field ev0_orig(grid);
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ev0_orig = evec[0];
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basisRotate(evec,Qt,0,Nk,0,Nk,Nm);
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{
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std::cout << GridLogIRL << "Test convergence" << std::endl;
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Field B(grid);
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for(int j = 0; j<Nk; j+=SkipTest){
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B=evec[j];
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//std::cout << "Checkerboard: " << evec[j].checkerboard << std::endl;
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B.checkerboard = evec[0].checkerboard;
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_HermOpTest(B,v);
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RealD vnum = real(innerProduct(B,v)); // HermOp.
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RealD vden = norm2(B);
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RealD vv0 = norm2(v);
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eval2[j] = vnum/vden;
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v -= eval2[j]*B;
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RealD vv = norm2(v) / ::pow(evalMaxApprox,2.0);
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std::cout.precision(13);
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std::cout<<GridLogIRL << "[" << std::setw(3)<< std::setiosflags(std::ios_base::right) <<j<<"] "
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<<"eval = "<<std::setw(25)<< std::setiosflags(std::ios_base::left)<< eval2[j] << " (" << eval2_copy[j] << ")"
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<<" |H B[i] - eval[i]B[i]|^2 / evalMaxApprox^2 " << std::setw(25)<< std::setiosflags(std::ios_base::right)<< vv
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<<" "<< vnum/(sqrt(vden)*sqrt(vv0))
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<<std::endl;
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// change the criteria as evals are supposed to be sorted, all evals smaller(larger) than Nstop should have converged
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if((vv<eresid*eresid) && (j == Nconv) ){
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Nconv+=SkipTest;
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}
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}
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// test if we converged, if so, terminate
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std::cout<<GridLogIRL<<" #modes converged: "<<Nconv<<std::endl;
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if( Nconv>=Nstop || beta_k < betastp){
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goto converged;
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}
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//B[j] +=Qt[k+_Nm*j] * _v[k]._odata[ss];
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{
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Eigen::MatrixXd qm = Eigen::MatrixXd::Zero(Nk,Nk); // Restrict Qt to Nk x Nk
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for (int k=0;k<Nk;k++)
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for (int j=0;j<Nk;j++)
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qm(j,k) = Qt(j,k);
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Eigen::MatrixXd qmI = qm.inverse();
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RealD res_check_rotate_inverse = (qm*qmI - Eigen::MatrixXd::Identity(Nk,Nk)).norm(); // sqrt( |X|^2 )
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std::cout << GridLogIRL << "\tInverted ("<<Nk<<"x"<<Nk<<") Qt matrix " << " error = " << res_check_rotate_inverse <<std::endl;
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assert(res_check_rotate_inverse < 1e-7);
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basisRotate(evec,qmI,0,Nk,0,Nk,Nm);
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std::cout << GridLogIRL << "\t Basis rotation done "<<std::endl;
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axpy(ev0_orig,-1.0,evec[0],ev0_orig);
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std::cout << GridLogIRL << " | evec[0] - evec[0]_orig | = " << ::sqrt(norm2(ev0_orig)) << std::endl;
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}
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}
|
||
} 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:
|
||
|
||
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;
|
||
}
|
||
|
||
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:
|
||
/* 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:
|
||
3. wk:=Avk−βkv_{k−1}
|
||
4. αk:=(wk,vk) //
|
||
5. wk:=wk−αkvk // wk orthog vk
|
||
6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
|
||
7. vk+1 := wk/βk+1
|
||
8. EndDo
|
||
*/
|
||
void step(std::vector<RealD>& lmd,
|
||
std::vector<RealD>& lme,
|
||
std::vector<Field>& evec,
|
||
Field& w,int Nm,int k)
|
||
{
|
||
const RealD tiny = 1.0e-20;
|
||
assert( k< Nm );
|
||
|
||
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)
|
||
RealD alph = real(zalph);
|
||
|
||
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;
|
||
|
||
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
|
||
GridBase *grid)
|
||
{
|
||
Eigen::MatrixXd TriDiag = Eigen::MatrixXd::Zero(Nk,Nk);
|
||
|
||
for(int i=0;i<Nk;i++) TriDiag(i,i) = lmd[i];
|
||
for(int i=0;i<Nk-1;i++) TriDiag(i,i+1) = lme[i];
|
||
for(int i=0;i<Nk-1;i++) TriDiag(i+1,i) = lme[i];
|
||
|
||
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eigensolver(TriDiag);
|
||
|
||
for (int i = 0; i < Nk; i++) {
|
||
lmd[Nk-1-i] = eigensolver.eigenvalues()(i);
|
||
}
|
||
for (int i = 0; i < Nk; i++) {
|
||
for (int j = 0; j < Nk; j++) {
|
||
Qt(Nk-1-i,j) = eigensolver.eigenvectors()(j,i);
|
||
}
|
||
}
|
||
}
|
||
|
||
///////////////////////////////////////////////////////////////////////////
|
||
// File could end here if settle on Eigen ???
|
||
///////////////////////////////////////////////////////////////////////////
|
||
|
||
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
|
||
RealD Dsh, int kmin, int kmax)
|
||
{
|
||
int k = kmin-1;
|
||
RealD x;
|
||
|
||
RealD Fden = 1.0/hypot(lmd[k]-Dsh,lme[k]);
|
||
RealD c = ( lmd[k] -Dsh) *Fden;
|
||
RealD s = -lme[k] *Fden;
|
||
|
||
RealD tmpa1 = lmd[k];
|
||
RealD tmpa2 = lmd[k+1];
|
||
RealD tmpb = lme[k];
|
||
|
||
lmd[k] = c*c*tmpa1 +s*s*tmpa2 -2.0*c*s*tmpb;
|
||
lmd[k+1] = s*s*tmpa1 +c*c*tmpa2 +2.0*c*s*tmpb;
|
||
lme[k] = c*s*(tmpa1-tmpa2) +(c*c-s*s)*tmpb;
|
||
x =-s*lme[k+1];
|
||
lme[k+1] = c*lme[k+1];
|
||
|
||
for(int i=0; i<Nk; ++i){
|
||
RealD Qtmp1 = Qt(k,i);
|
||
RealD Qtmp2 = Qt(k+1,i);
|
||
Qt(k,i) = c*Qtmp1 - s*Qtmp2;
|
||
Qt(k+1,i)= s*Qtmp1 + c*Qtmp2;
|
||
}
|
||
|
||
// Givens transformations
|
||
for(int k = kmin; k < kmax-1; ++k){
|
||
|
||
RealD Fden = 1.0/hypot(x,lme[k-1]);
|
||
RealD c = lme[k-1]*Fden;
|
||
RealD s = - x*Fden;
|
||
|
||
RealD tmpa1 = lmd[k];
|
||
RealD tmpa2 = lmd[k+1];
|
||
RealD tmpb = lme[k];
|
||
|
||
lmd[k] = c*c*tmpa1 +s*s*tmpa2 -2.0*c*s*tmpb;
|
||
lmd[k+1] = s*s*tmpa1 +c*c*tmpa2 +2.0*c*s*tmpb;
|
||
lme[k] = c*s*(tmpa1-tmpa2) +(c*c-s*s)*tmpb;
|
||
lme[k-1] = c*lme[k-1] -s*x;
|
||
|
||
if(k != kmax-2){
|
||
x = -s*lme[k+1];
|
||
lme[k+1] = c*lme[k+1];
|
||
}
|
||
|
||
for(int i=0; i<Nk; ++i){
|
||
RealD Qtmp1 = Qt(k,i);
|
||
RealD Qtmp2 = Qt(k+1,i);
|
||
Qt(k,i) = c*Qtmp1 -s*Qtmp2;
|
||
Qt(k+1,i) = s*Qtmp1 +c*Qtmp2;
|
||
}
|
||
}
|
||
}
|
||
|
||
void diagonalize(std::vector<RealD>& lmd, std::vector<RealD>& lme,
|
||
int Nk, int Nm,
|
||
Eigen::MatrixXd & Qt,
|
||
GridBase *grid)
|
||
{
|
||
Qt = Eigen::MatrixXd::Identity(Nm,Nm);
|
||
if ( diagonalisation == IRLdiagonaliseWithDSTEGR ) {
|
||
diagonalize_lapack(lmd,lme,Nk,Nm,Qt,grid);
|
||
} else if ( diagonalisation == IRLdiagonaliseWithQR ) {
|
||
diagonalize_QR(lmd,lme,Nk,Nm,Qt,grid);
|
||
} else if ( diagonalisation == IRLdiagonaliseWithEigen ) {
|
||
diagonalize_Eigen(lmd,lme,Nk,Nm,Qt,grid);
|
||
} else {
|
||
assert(0);
|
||
}
|
||
}
|
||
|
||
#ifdef USE_LAPACK
|
||
void LAPACK_dstegr(char *jobz, char *range, int *n, double *d, double *e,
|
||
double *vl, double *vu, int *il, int *iu, double *abstol,
|
||
int *m, double *w, double *z, int *ldz, int *isuppz,
|
||
double *work, int *lwork, int *iwork, int *liwork,
|
||
int *info);
|
||
#endif
|
||
|
||
void diagonalize_lapack(std::vector<RealD>& lmd,
|
||
std::vector<RealD>& lme,
|
||
int Nk, int Nm,
|
||
Eigen::MatrixXd& Qt,
|
||
GridBase *grid)
|
||
{
|
||
#ifdef USE_LAPACK
|
||
const int size = Nm;
|
||
int NN = Nk;
|
||
double evals_tmp[NN];
|
||
double evec_tmp[NN][NN];
|
||
memset(evec_tmp[0],0,sizeof(double)*NN*NN);
|
||
double DD[NN];
|
||
double EE[NN];
|
||
for (int i = 0; i< NN; i++) {
|
||
for (int j = i - 1; j <= i + 1; j++) {
|
||
if ( j < NN && j >= 0 ) {
|
||
if (i==j) DD[i] = lmd[i];
|
||
if (i==j) evals_tmp[i] = lmd[i];
|
||
if (j==(i-1)) EE[j] = lme[j];
|
||
}
|
||
}
|
||
}
|
||
int evals_found;
|
||
int lwork = ( (18*NN) > (1+4*NN+NN*NN)? (18*NN):(1+4*NN+NN*NN)) ;
|
||
int liwork = 3+NN*10 ;
|
||
int iwork[liwork];
|
||
double work[lwork];
|
||
int isuppz[2*NN];
|
||
char jobz = 'V'; // calculate evals & evecs
|
||
char range = 'I'; // calculate all evals
|
||
// char range = 'A'; // calculate all evals
|
||
char uplo = 'U'; // refer to upper half of original matrix
|
||
char compz = 'I'; // Compute eigenvectors of tridiagonal matrix
|
||
int ifail[NN];
|
||
int info;
|
||
int total = grid->_Nprocessors;
|
||
int node = grid->_processor;
|
||
int interval = (NN/total)+1;
|
||
double vl = 0.0, vu = 0.0;
|
||
int il = interval*node+1 , iu = interval*(node+1);
|
||
if (iu > NN) iu=NN;
|
||
double tol = 0.0;
|
||
if (1) {
|
||
memset(evals_tmp,0,sizeof(double)*NN);
|
||
if ( il <= NN){
|
||
LAPACK_dstegr(&jobz, &range, &NN,
|
||
(double*)DD, (double*)EE,
|
||
&vl, &vu, &il, &iu, // these four are ignored if second parameteris 'A'
|
||
&tol, // tolerance
|
||
&evals_found, evals_tmp, (double*)evec_tmp, &NN,
|
||
isuppz,
|
||
work, &lwork, iwork, &liwork,
|
||
&info);
|
||
for (int i = iu-1; i>= il-1; i--){
|
||
evals_tmp[i] = evals_tmp[i - (il-1)];
|
||
if (il>1) evals_tmp[i-(il-1)]=0.;
|
||
for (int j = 0; j< NN; j++){
|
||
evec_tmp[i][j] = evec_tmp[i - (il-1)][j];
|
||
if (il>1) evec_tmp[i-(il-1)][j]=0.;
|
||
}
|
||
}
|
||
}
|
||
{
|
||
grid->GlobalSumVector(evals_tmp,NN);
|
||
grid->GlobalSumVector((double*)evec_tmp,NN*NN);
|
||
}
|
||
}
|
||
// Safer 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.
|
||
for(int i=0;i<NN;i++){
|
||
lmd [NN-1-i]=evals_tmp[i];
|
||
for(int j=0;j<NN;j++){
|
||
Qt((NN-1-i),j)=evec_tmp[i][j];
|
||
}
|
||
}
|
||
#else
|
||
assert(0);
|
||
#endif
|
||
}
|
||
|
||
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: "<<QRiter<<"\n";
|
||
abort();
|
||
}
|
||
};
|
||
}
|
||
#endif
|