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961 lines
41 KiB
C++
961 lines
41 KiB
C++
/*************************************************************************************
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Grid physics library, www.github.com/paboyle/Grid
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Source file: ./tests/Test_dwf_hdcr.cc
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Copyright (C) 2015
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Author: Daniel Richtmann <daniel.richtmann@ur.de>
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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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#include <Grid/Grid.h>
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#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h>
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//#include <algorithms/iterative/PrecConjugateResidual.h>
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using namespace std;
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using namespace Grid;
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using namespace Grid::QCD;
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template<class Field, int nbasis> class TestVectorAnalyzer {
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public:
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void operator()(LinearOperatorBase<Field> &Linop, std::vector<Field> const &vectors, int nn = nbasis) {
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// this function corresponds to testvector_analysis_PRECISION from the
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// DD-αAMG codebase
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auto positiveOnes = 0;
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std::vector<Field> tmp(4, vectors[0]._grid); // bit hacky?
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Gamma g5(Gamma::Algebra::Gamma5);
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std::cout << GridLogMessage << "Test vector analysis:" << std::endl;
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for(auto i = 0; i < nn; ++i) {
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Linop.Op(vectors[i], tmp[3]);
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tmp[0] = g5 * tmp[3]; // is this the same as coarse_gamma5_PRECISION?
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auto lambda = innerProduct(vectors[i], tmp[0]) / innerProduct(vectors[i], vectors[i]);
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tmp[1] = tmp[0] - lambda * vectors[i];
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auto mu = ::sqrt(norm2(tmp[1]) / norm2(vectors[i]));
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auto nrm = ::sqrt(norm2(vectors[i]));
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if(real(lambda) > 0)
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positiveOnes++;
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std::cout << GridLogMessage << std::scientific << std::setprecision(2) << std::setw(2) << std::showpos << "vector " << i << ": "
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<< "singular value: " << lambda << ", singular vector precision: " << mu << ", norm: " << nrm << std::endl;
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}
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std::cout << GridLogMessage << std::scientific << std::setprecision(2) << std::setw(2) << std::showpos << positiveOnes << " out of "
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<< nn << " vectors were positive" << std::endl;
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}
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};
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class myclass : Serializable {
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public:
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// clang-format off
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GRID_SERIALIZABLE_CLASS_MEMBERS(myclass,
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int, domaindecompose,
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int, domainsize,
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int, coarsegrids,
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int, order,
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int, Ls,
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double, mq,
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double, lo,
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double, hi,
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int, steps);
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// clang-format on
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myclass(){};
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};
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myclass params;
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RealD InverseApproximation(RealD x) {
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return 1.0 / x;
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}
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template<int nbasis> struct CoarseGrids {
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public:
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// typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
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// typedef CoarsenedMatrix<vSpinColourVector,vTComplex,nbasis>
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// CoarseOperator; typedef typename CoarseOperator::CoarseVector
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// CoarseVector;
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std::vector<std::vector<int>> LattSizes;
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std::vector<std::vector<int>> Seeds;
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std::vector<GridCartesian *> Grids;
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std::vector<GridParallelRNG> PRNGs;
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CoarseGrids(std::vector<std::vector<int>> const &blockSizes, int coarsegrids = 1) {
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assert(blockSizes.size() == coarsegrids);
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std::cout << GridLogMessage << "Constructing " << coarsegrids << " CoarseGrids" << std::endl;
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for(int cl = 0; cl < coarsegrids; ++cl) { // may be a bit ugly and slow but not perf critical
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// need to differentiate between first and other coarse levels in size calculation
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LattSizes.push_back({cl == 0 ? GridDefaultLatt() : LattSizes[cl - 1]});
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Seeds.push_back(std::vector<int>(LattSizes[cl].size()));
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for(int d = 0; d < LattSizes[cl].size(); ++d) {
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LattSizes[cl][d] = LattSizes[cl][d] / blockSizes[cl][d];
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Seeds[cl][d] = (cl + 1) * LattSizes[cl].size() + d + 1;
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// calculation unimportant, just to get. e.g., {5, 6, 7, 8} for first coarse level and so on
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}
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Grids.push_back(SpaceTimeGrid::makeFourDimGrid(LattSizes[cl], GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi()));
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PRNGs.push_back(GridParallelRNG(Grids[cl]));
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PRNGs[cl].SeedFixedIntegers(Seeds[cl]);
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std::cout << GridLogMessage << "cl = " << cl << ": LattSize = " << LattSizes[cl] << std::endl;
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std::cout << GridLogMessage << "cl = " << cl << ": Seeds = " << Seeds[cl] << std::endl;
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}
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}
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};
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// template < class Fobj, class CComplex, int coarseSpins, int nbasis, class Matrix >
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// class MultiGridPreconditioner : public LinearFunction< Lattice< Fobj > > {
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template<class Fobj, class CComplex, int nbasis, class Matrix> class MultiGridPreconditioner : public LinearFunction<Lattice<Fobj>> {
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public:
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typedef Aggregation<Fobj, CComplex, nbasis> Aggregates;
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typedef CoarsenedMatrix<Fobj, CComplex, nbasis> CoarseOperator;
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typedef typename Aggregation<Fobj, CComplex, nbasis>::siteVector siteVector;
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typedef typename Aggregation<Fobj, CComplex, nbasis>::CoarseScalar CoarseScalar;
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typedef typename Aggregation<Fobj, CComplex, nbasis>::CoarseVector CoarseVector;
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typedef typename Aggregation<Fobj, CComplex, nbasis>::CoarseMatrix CoarseMatrix;
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typedef typename Aggregation<Fobj, CComplex, nbasis>::FineField FineField;
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typedef LinearOperatorBase<FineField> FineOperator;
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Aggregates & _Aggregates;
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CoarseOperator &_CoarseOperator;
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Matrix & _FineMatrix;
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FineOperator & _FineOperator;
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Matrix & _SmootherMatrix;
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FineOperator & _SmootherOperator;
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// Constructor
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MultiGridPreconditioner(Aggregates & Agg,
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CoarseOperator &Coarse,
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FineOperator & Fine,
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Matrix & FineMatrix,
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FineOperator & Smooth,
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Matrix & SmootherMatrix)
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: _Aggregates(Agg)
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, _CoarseOperator(Coarse)
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, _FineOperator(Fine)
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, _FineMatrix(FineMatrix)
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, _SmootherOperator(Smooth)
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, _SmootherMatrix(SmootherMatrix) {}
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void PowerMethod(const FineField &in) {
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FineField p1(in._grid);
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FineField p2(in._grid);
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MdagMLinearOperator<Matrix, FineField> fMdagMOp(_FineMatrix);
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p1 = in;
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RealD absp2;
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for(int i = 0; i < 20; i++) {
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RealD absp1 = std::sqrt(norm2(p1));
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fMdagMOp.HermOp(p1, p2); // this is the G5 herm bit
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// _FineOperator.Op(p1,p2); // this is the G5 herm bit
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RealD absp2 = std::sqrt(norm2(p2));
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if(i % 10 == 9)
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std::cout << GridLogMessage << "Power method on mdagm " << i << " " << absp2 / absp1 << std::endl;
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p1 = p2 * (1.0 / std::sqrt(absp2));
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}
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}
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void operator()(const FineField &in, FineField &out) {
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if(params.domaindecompose) {
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operatorSAP(in, out);
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} else {
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operatorCheby(in, out);
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}
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}
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////////////////////////////////////////////////////////////////////////
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// ADEF2: [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
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// ADEF1: [MP+Q ] in = M [1 - A Q] in + Q in
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////////////////////////////////////////////////////////////////////////
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#if 1
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void operatorADEF2(const FineField &in, FineField &out) {
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CoarseVector Csrc(_CoarseOperator.Grid());
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CoarseVector Ctmp(_CoarseOperator.Grid());
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CoarseVector Csol(_CoarseOperator.Grid());
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ConjugateGradient<CoarseVector> CG(1.0e-10, 100000);
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ConjugateGradient<FineField> fCG(3.0e-2, 1000);
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HermitianLinearOperator<CoarseOperator, CoarseVector> HermOp(_CoarseOperator);
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MdagMLinearOperator<CoarseOperator, CoarseVector> MdagMOp(_CoarseOperator);
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MdagMLinearOperator<Matrix, FineField> fMdagMOp(_FineMatrix);
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FineField tmp(in._grid);
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FineField res(in._grid);
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FineField Min(in._grid);
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// Monitor completeness of low mode space
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_Aggregates.ProjectToSubspace(Csrc, in);
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_Aggregates.PromoteFromSubspace(Csrc, out);
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std::cout << GridLogMessage << "Coarse Grid Preconditioner\nCompleteness in: " << std::sqrt(norm2(out) / norm2(in)) << std::endl;
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// [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
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_FineOperator.Op(in, tmp); // this is the G5 herm bit
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fCG(fMdagMOp, tmp, Min); // solves MdagM = g5 M g5M
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// Monitor completeness of low mode space
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_Aggregates.ProjectToSubspace(Csrc, Min);
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_Aggregates.PromoteFromSubspace(Csrc, out);
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std::cout << GridLogMessage << "Completeness Min: " << std::sqrt(norm2(out) / norm2(Min)) << std::endl;
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_FineOperator.Op(Min, tmp);
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tmp = in - tmp; // in - A Min
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Csol = zero;
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_Aggregates.ProjectToSubspace(Csrc, tmp);
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HermOp.AdjOp(Csrc, Ctmp); // Normal equations
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CG(MdagMOp, Ctmp, Csol);
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HermOp.Op(Csol, Ctmp);
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Ctmp = Ctmp - Csrc;
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std::cout << GridLogMessage << "coarse space true residual " << std::sqrt(norm2(Ctmp) / norm2(Csrc)) << std::endl;
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_Aggregates.PromoteFromSubspace(Csol, out);
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_FineOperator.Op(out, res);
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res = res - tmp;
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std::cout << GridLogMessage << "promoted sol residual " << std::sqrt(norm2(res) / norm2(tmp)) << std::endl;
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_Aggregates.ProjectToSubspace(Csrc, res);
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std::cout << GridLogMessage << "coarse space proj of residual " << norm2(Csrc) << std::endl;
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out = out + Min; // additive coarse space correction
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// out = Min; // no additive coarse space correction
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_FineOperator.Op(out, tmp);
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tmp = tmp - in; // tmp is new residual
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std::cout << GridLogMessage << " Preconditioner in " << norm2(in) << std::endl;
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std::cout << GridLogMessage << " Preconditioner out " << norm2(out) << std::endl;
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std::cout << GridLogMessage << "preconditioner thinks residual is " << std::sqrt(norm2(tmp) / norm2(in)) << std::endl;
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}
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#endif
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// ADEF1: [MP+Q ] in = M [1 - A Q] in + Q in
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#if 1
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void operatorADEF1(const FineField &in, FineField &out) {
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CoarseVector Csrc(_CoarseOperator.Grid());
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CoarseVector Ctmp(_CoarseOperator.Grid());
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CoarseVector Csol(_CoarseOperator.Grid());
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Csol = zero;
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ConjugateGradient<CoarseVector> CG(1.0e-10, 100000);
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ConjugateGradient<FineField> fCG(3.0e-2, 1000);
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HermitianLinearOperator<CoarseOperator, CoarseVector> HermOp(_CoarseOperator);
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MdagMLinearOperator<CoarseOperator, CoarseVector> MdagMOp(_CoarseOperator);
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ShiftedMdagMLinearOperator<Matrix, FineField> fMdagMOp(_FineMatrix, 0.1);
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FineField tmp(in._grid);
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FineField res(in._grid);
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FineField Qin(in._grid);
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// Monitor completeness of low mode space
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// _Aggregates.ProjectToSubspace (Csrc,in);
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// _Aggregates.PromoteFromSubspace(Csrc,out);
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// std::cout<<GridLogMessage<<"Coarse Grid Preconditioner\nCompleteness in: "<<std::sqrt(norm2(out)/norm2(in))<<std::endl;
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_Aggregates.ProjectToSubspace(Csrc, in);
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HermOp.AdjOp(Csrc, Ctmp); // Normal equations
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CG(MdagMOp, Ctmp, Csol);
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_Aggregates.PromoteFromSubspace(Csol, Qin);
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// Qin=0;
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_FineOperator.Op(Qin, tmp); // A Q in
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tmp = in - tmp; // in - A Q in
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_FineOperator.Op(tmp, res); // this is the G5 herm bit
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fCG(fMdagMOp, res, out); // solves MdagM = g5 M g5M
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out = out + Qin;
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_FineOperator.Op(out, tmp);
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tmp = tmp - in; // tmp is new residual
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std::cout << GridLogMessage << "preconditioner thinks residual is " << std::sqrt(norm2(tmp) / norm2(in)) << std::endl;
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}
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#endif
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void SAP(const FineField &src, FineField &psi) {
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Lattice<iScalar<vInteger>> coor(src._grid);
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Lattice<iScalar<vInteger>> subset(src._grid);
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FineField r(src._grid);
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FineField zz(src._grid);
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zz = zero;
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FineField vec1(src._grid);
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FineField vec2(src._grid);
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const Integer block = params.domainsize;
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subset = zero;
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for(int mu = 0; mu < Nd; mu++) {
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LatticeCoordinate(coor, mu + 1);
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coor = div(coor, block);
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subset = subset + coor;
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}
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subset = mod(subset, (Integer)2);
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ShiftedMdagMLinearOperator<Matrix, FineField> fMdagMOp(_SmootherMatrix, 0.0);
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Chebyshev<FineField> Cheby(params.lo, params.hi, params.order, InverseApproximation);
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RealD resid;
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for(int i = 0; i < params.steps; i++) {
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// Even domain residual
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_FineOperator.Op(psi, vec1); // this is the G5 herm bit
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r = src - vec1;
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resid = norm2(r) / norm2(src);
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std::cout << "SAP " << i << " resid " << resid << std::endl;
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// Even domain solve
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r = where(subset == (Integer)0, r, zz);
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_SmootherOperator.AdjOp(r, vec1);
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Cheby(fMdagMOp, vec1, vec2); // solves MdagM = g5 M g5M
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psi = psi + vec2;
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// Odd domain residual
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_FineOperator.Op(psi, vec1); // this is the G5 herm bit
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r = src - vec1;
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r = where(subset == (Integer)1, r, zz);
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resid = norm2(r) / norm2(src);
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std::cout << "SAP " << i << " resid " << resid << std::endl;
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// Odd domain solve
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_SmootherOperator.AdjOp(r, vec1);
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Cheby(fMdagMOp, vec1, vec2); // solves MdagM = g5 M g5M
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psi = psi + vec2;
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_FineOperator.Op(psi, vec1); // this is the G5 herm bit
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r = src - vec1;
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resid = norm2(r) / norm2(src);
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std::cout << "SAP " << i << " resid " << resid << std::endl;
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}
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};
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void SmootherTest(const FineField &in) {
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FineField vec1(in._grid);
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FineField vec2(in._grid);
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RealD lo[3] = {0.5, 1.0, 2.0};
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// MdagMLinearOperator<Matrix,FineField> fMdagMOp(_FineMatrix);
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ShiftedMdagMLinearOperator<Matrix, FineField> fMdagMOp(_SmootherMatrix, 0.0);
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RealD Ni, r;
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Ni = norm2(in);
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for(int ilo = 0; ilo < 3; ilo++) {
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for(int ord = 5; ord < 50; ord *= 2) {
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_SmootherOperator.AdjOp(in, vec1);
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Chebyshev<FineField> Cheby(lo[ilo], 70.0, ord, InverseApproximation);
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Cheby(fMdagMOp, vec1, vec2); // solves MdagM = g5 M g5M
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_FineOperator.Op(vec2, vec1); // this is the G5 herm bit
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vec1 = in - vec1; // tmp = in - A Min
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r = norm2(vec1);
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std::cout << GridLogMessage << "Smoother resid " << std::sqrt(r / Ni) << std::endl;
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}
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}
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}
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void operatorCheby(const FineField &in, FineField &out) {
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CoarseVector Csrc(_CoarseOperator.Grid());
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CoarseVector Ctmp(_CoarseOperator.Grid());
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CoarseVector Csol(_CoarseOperator.Grid());
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Csol = zero;
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ConjugateGradient<CoarseVector> CG(3.0e-3, 100000);
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// ConjugateGradient<FineField> fCG(3.0e-2,1000);
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HermitianLinearOperator<CoarseOperator, CoarseVector> HermOp(_CoarseOperator);
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MdagMLinearOperator<CoarseOperator, CoarseVector> MdagMOp(_CoarseOperator);
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// MdagMLinearOperator<Matrix,FineField> fMdagMOp(_FineMatrix);
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ShiftedMdagMLinearOperator<Matrix, FineField> fMdagMOp(_SmootherMatrix, 0.0);
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FineField vec1(in._grid);
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FineField vec2(in._grid);
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// Chebyshev<FineField> Cheby (0.5,70.0,30,InverseApproximation);
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// Chebyshev<FineField> ChebyAccu(0.5,70.0,30,InverseApproximation);
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Chebyshev<FineField> Cheby(params.lo, params.hi, params.order, InverseApproximation);
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Chebyshev<FineField> ChebyAccu(params.lo, params.hi, params.order, InverseApproximation);
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// Cheby.JacksonSmooth();
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// ChebyAccu.JacksonSmooth();
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// _Aggregates.ProjectToSubspace (Csrc,in);
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// _Aggregates.PromoteFromSubspace(Csrc,out);
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// std::cout<<GridLogMessage<<"Completeness: "<<std::sqrt(norm2(out)/norm2(in))<<std::endl;
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// ofstream fout("smoother");
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// Cheby.csv(fout);
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// V11 multigrid.
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// Use a fixed chebyshev and hope hermiticity helps.
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// To make a working smoother for indefinite operator
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// must multiply by "Mdag" (ouch loses all low mode content)
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// and apply to poly approx of (mdagm)^-1.
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// so that we end up with an odd polynomial.
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RealD Ni = norm2(in);
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_SmootherOperator.AdjOp(in, vec1); // this is the G5 herm bit
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ChebyAccu(fMdagMOp, vec1, out); // solves MdagM = g5 M g5M
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|
||
std::cout << GridLogMessage << "Smoother norm " << norm2(out) << std::endl;
|
||
|
||
// Update with residual for out
|
||
_FineOperator.Op(out, vec1); // this is the G5 herm bit
|
||
vec1 = in - vec1; // tmp = in - A Min
|
||
|
||
RealD r = norm2(vec1);
|
||
|
||
std::cout << GridLogMessage << "Smoother resid " << std::sqrt(r / Ni) << " " << r << " " << Ni << std::endl;
|
||
|
||
_Aggregates.ProjectToSubspace(Csrc, vec1);
|
||
HermOp.AdjOp(Csrc, Ctmp); // Normal equations
|
||
CG(MdagMOp, Ctmp, Csol);
|
||
_Aggregates.PromoteFromSubspace(Csol, vec1); // Ass^{-1} [in - A Min]_s
|
||
// Q = Q[in - A Min]
|
||
out = out + vec1;
|
||
|
||
// Three preconditioner smoothing -- hermitian if C3 = C1
|
||
// Recompute error
|
||
_FineOperator.Op(out, vec1); // this is the G5 herm bit
|
||
vec1 = in - vec1; // tmp = in - A Min
|
||
r = norm2(vec1);
|
||
|
||
std::cout << GridLogMessage << "Coarse resid " << std::sqrt(r / Ni) << std::endl;
|
||
|
||
// Reapply smoother
|
||
_SmootherOperator.Op(vec1, vec2); // this is the G5 herm bit
|
||
ChebyAccu(fMdagMOp, vec2, vec1); // solves MdagM = g5 M g5M
|
||
|
||
out = out + vec1;
|
||
vec1 = in - vec1; // tmp = in - A Min
|
||
r = norm2(vec1);
|
||
std::cout << GridLogMessage << "Smoother resid " << std::sqrt(r / Ni) << std::endl;
|
||
}
|
||
|
||
void operatorSAP(const FineField &in, FineField &out) {
|
||
|
||
CoarseVector Csrc(_CoarseOperator.Grid());
|
||
CoarseVector Ctmp(_CoarseOperator.Grid());
|
||
CoarseVector Csol(_CoarseOperator.Grid());
|
||
Csol = zero;
|
||
|
||
ConjugateGradient<CoarseVector> CG(1.0e-3, 100000);
|
||
|
||
HermitianLinearOperator<CoarseOperator, CoarseVector> HermOp(_CoarseOperator);
|
||
MdagMLinearOperator<CoarseOperator, CoarseVector> MdagMOp(_CoarseOperator);
|
||
|
||
FineField vec1(in._grid);
|
||
FineField vec2(in._grid);
|
||
|
||
_Aggregates.ProjectToSubspace(Csrc, in);
|
||
_Aggregates.PromoteFromSubspace(Csrc, out);
|
||
std::cout << GridLogMessage << "Completeness: " << std::sqrt(norm2(out) / norm2(in)) << std::endl;
|
||
|
||
// To make a working smoother for indefinite operator
|
||
// must multiply by "Mdag" (ouch loses all low mode content)
|
||
// and apply to poly approx of (mdagm)^-1.
|
||
// so that we end up with an odd polynomial.
|
||
SAP(in, out);
|
||
|
||
// Update with residual for out
|
||
_FineOperator.Op(out, vec1); // this is the G5 herm bit
|
||
vec1 = in - vec1; // tmp = in - A Min
|
||
|
||
RealD r = norm2(vec1);
|
||
RealD Ni = norm2(in);
|
||
std::cout << GridLogMessage << "SAP resid " << std::sqrt(r / Ni) << " " << r << " " << Ni << std::endl;
|
||
|
||
_Aggregates.ProjectToSubspace(Csrc, vec1);
|
||
HermOp.AdjOp(Csrc, Ctmp); // Normal equations
|
||
CG(MdagMOp, Ctmp, Csol);
|
||
_Aggregates.PromoteFromSubspace(Csol, vec1); // Ass^{-1} [in - A Min]_s
|
||
// Q = Q[in - A Min]
|
||
out = out + vec1;
|
||
|
||
// Three preconditioner smoothing -- hermitian if C3 = C1
|
||
// Recompute error
|
||
_FineOperator.Op(out, vec1); // this is the G5 herm bit
|
||
vec1 = in - vec1; // tmp = in - A Min
|
||
r = norm2(vec1);
|
||
|
||
std::cout << GridLogMessage << "Coarse resid " << std::sqrt(r / Ni) << std::endl;
|
||
|
||
// Reapply smoother
|
||
SAP(vec1, vec2);
|
||
out = out + vec2;
|
||
|
||
// Update with residual for out
|
||
_FineOperator.Op(out, vec1); // this is the G5 herm bit
|
||
vec1 = in - vec1; // tmp = in - A Min
|
||
|
||
r = norm2(vec1);
|
||
Ni = norm2(in);
|
||
std::cout << GridLogMessage << "SAP resid(post) " << std::sqrt(r / Ni) << " " << r << " " << Ni << std::endl;
|
||
}
|
||
|
||
void runChecks(CoarseGrids<nbasis> &cGrids) {
|
||
|
||
/////////////////////////////////////////////
|
||
// Some stuff we need for the checks below //
|
||
/////////////////////////////////////////////
|
||
auto tolerance = 1e-13; // TODO: this obviously depends on the precision we use, current value is for double
|
||
|
||
std::vector<CoarseVector> cTmps(4, _CoarseOperator.Grid());
|
||
std::vector<FineField> fTmps(2, _Aggregates.subspace[0]._grid); // atm only for one coarser grid
|
||
|
||
// need to construct an operator, since _CoarseOperator is not a LinearOperator but only a matrix (the name is a bit misleading)
|
||
MdagMLinearOperator<CoarseOperator, CoarseVector> MdagMOp(_CoarseOperator);
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "MG correctness check: 0 == (1 - P R) v" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
for(auto i = 0; i < _Aggregates.subspace.size(); ++i) {
|
||
_Aggregates.ProjectToSubspace(cTmps[0], _Aggregates.subspace[i]); // R v_i
|
||
_Aggregates.PromoteFromSubspace(cTmps[0], fTmps[0]); // P R v_i
|
||
|
||
fTmps[1] = _Aggregates.subspace[i] - fTmps[0]; // v_i - P R v_i
|
||
auto deviation = std::sqrt(norm2(fTmps[1]) / norm2(_Aggregates.subspace[i]));
|
||
|
||
std::cout << GridLogMessage << "Vector " << i << ": norm2(v_i) = " << norm2(_Aggregates.subspace[i])
|
||
<< " | norm2(R v_i) = " << norm2(cTmps[0]) << " | norm2(P R v_i) = " << norm2(fTmps[0])
|
||
<< " | relative deviation = " << deviation << std::endl;
|
||
|
||
if(deviation > tolerance) {
|
||
std::cout << GridLogError << "Vector " << i << ": relative deviation check failed " << deviation << " > " << tolerance << std::endl;
|
||
abort();
|
||
}
|
||
}
|
||
std::cout << GridLogMessage << "Check passed!" << std::endl;
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "MG correctness check: 0 == (1 - R P) v_c" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
random(cGrids.PRNGs[0], cTmps[0]);
|
||
|
||
_Aggregates.PromoteFromSubspace(cTmps[0], fTmps[0]); // P v_c
|
||
_Aggregates.ProjectToSubspace(cTmps[1], fTmps[0]); // R P v_c
|
||
|
||
cTmps[2] = cTmps[0] - cTmps[1]; // v_c - R P v_c
|
||
auto deviation = std::sqrt(norm2(cTmps[2]) / norm2(cTmps[0]));
|
||
|
||
std::cout << GridLogMessage << "norm2(v_c) = " << norm2(cTmps[0]) << " | norm2(R P v_c) = " << norm2(cTmps[1])
|
||
<< " | norm2(P v_c) = " << norm2(fTmps[0]) << " | relative deviation = " << deviation << std::endl;
|
||
|
||
if(deviation > tolerance) {
|
||
std::cout << GridLogError << "relative deviation check failed " << deviation << " > " << tolerance << std::endl;
|
||
abort();
|
||
}
|
||
std::cout << GridLogMessage << "Check passed!" << std::endl;
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "MG correctness check: 0 == (R D P - D_c) v_c" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
random(cGrids.PRNGs[0], cTmps[0]);
|
||
|
||
_Aggregates.PromoteFromSubspace(cTmps[0], fTmps[0]); // P v_c
|
||
_FineOperator.Op(fTmps[0], fTmps[1]); // D P v_c
|
||
_Aggregates.ProjectToSubspace(cTmps[1], fTmps[1]); // R D P v_c
|
||
|
||
MdagMOp.Op(cTmps[0], cTmps[2]); // D_c v_c
|
||
|
||
cTmps[3] = cTmps[1] - cTmps[2]; // R D P v_c - D_c v_c
|
||
deviation = std::sqrt(norm2(cTmps[3]) / norm2(cTmps[1]));
|
||
|
||
std::cout << GridLogMessage << "norm2(R D P v_c) = " << norm2(cTmps[1]) << " | norm2(D_c v_c) = " << norm2(cTmps[2])
|
||
<< " | relative deviation = " << deviation << std::endl;
|
||
|
||
if(deviation > tolerance) {
|
||
std::cout << GridLogError << "relative deviation check failed " << deviation << " > " << tolerance << std::endl;
|
||
abort();
|
||
}
|
||
std::cout << GridLogMessage << "Check passed!" << std::endl;
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "MG correctness check: 0 == |(Im(v_c^dag D_c^dag D_c v_c)|" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
random(cGrids.PRNGs[0], cTmps[0]);
|
||
|
||
MdagMOp.Op(cTmps[0], cTmps[1]); // D_c v_c
|
||
MdagMOp.AdjOp(cTmps[1], cTmps[2]); // D_c^dag D_c v_c
|
||
|
||
// // alternative impl, which is better?
|
||
// MdagMOp.HermOp(cTmps[0], cTmps[2]); // D_c^dag D_c v_c
|
||
|
||
auto dot = innerProduct(cTmps[0], cTmps[2]); //v_c^dag D_c^dag D_c v_c
|
||
deviation = abs(imag(dot)) / abs(real(dot));
|
||
|
||
std::cout << GridLogMessage << "Re(v_c^dag D_c^dag D_c v_c) = " << real(dot) << " | Im(v_c^dag D_c^dag D_c v_c) = " << imag(dot)
|
||
<< " | relative deviation = " << deviation << std::endl;
|
||
|
||
if(deviation > tolerance) {
|
||
std::cout << GridLogError << "relative deviation check failed " << deviation << " > " << tolerance << std::endl;
|
||
abort();
|
||
}
|
||
std::cout << GridLogMessage << "Check passed!" << std::endl;
|
||
}
|
||
};
|
||
|
||
struct MGParams {
|
||
std::vector<std::vector<int>> blockSizes;
|
||
const int nbasis;
|
||
|
||
MGParams()
|
||
: blockSizes({{1, 1, 1, 2}})
|
||
// : blockSizes({{1,1,1,2}, {1,1,1,2}})
|
||
// : blockSizes({{1,1,1,2}, {1,1,1,2}, {1,1,1,2}})
|
||
, nbasis(20) {}
|
||
};
|
||
|
||
int main(int argc, char **argv) {
|
||
|
||
Grid_init(&argc, &argv);
|
||
|
||
params.domainsize = 1;
|
||
params.coarsegrids = 1;
|
||
params.domaindecompose = 0;
|
||
params.order = 30;
|
||
params.Ls = 1;
|
||
// params.mq = .13;
|
||
params.mq = .5;
|
||
params.lo = 0.5;
|
||
params.hi = 70.0;
|
||
params.steps = 1;
|
||
|
||
auto mgp = MGParams{};
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Params: " << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
std::cout << params << std::endl;
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Set up some fine level stuff: " << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
GridCartesian *FGrid = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(), GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi());
|
||
GridRedBlackCartesian *FrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(FGrid);
|
||
|
||
std::vector<int> fSeeds({1, 2, 3, 4});
|
||
GridParallelRNG fPRNG(FGrid);
|
||
fPRNG.SeedFixedIntegers(fSeeds);
|
||
|
||
Gamma g5(Gamma::Algebra::Gamma5);
|
||
|
||
// clang-format off
|
||
LatticeFermion src(FGrid); gaussian(fPRNG, src); // src=src + g5 * src;
|
||
LatticeFermion result(FGrid); result = zero;
|
||
LatticeFermion ref(FGrid); ref = zero;
|
||
LatticeFermion tmp(FGrid);
|
||
LatticeFermion err(FGrid);
|
||
LatticeGaugeField Umu(FGrid); SU3::HotConfiguration(fPRNG, Umu);
|
||
LatticeGaugeField UmuDD(FGrid);
|
||
LatticeColourMatrix U(FGrid);
|
||
LatticeColourMatrix zz(FGrid);
|
||
// clang-format on
|
||
|
||
if(params.domaindecompose) {
|
||
Lattice<iScalar<vInteger>> coor(FGrid);
|
||
zz = zero;
|
||
for(int mu = 0; mu < Nd; mu++) {
|
||
LatticeCoordinate(coor, mu);
|
||
U = PeekIndex<LorentzIndex>(Umu, mu);
|
||
U = where(mod(coor, params.domainsize) == (Integer)0, zz, U);
|
||
PokeIndex<LorentzIndex>(UmuDD, U, mu);
|
||
}
|
||
} else {
|
||
UmuDD = Umu;
|
||
}
|
||
|
||
RealD mass = params.mq;
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Set up some coarser levels stuff: " << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
std::vector<std::vector<int>> blockSizes({{1, 1, 1, 2}}); // corresponds to two level algorithm
|
||
// std::vector<std::vector<int>> blockSizes({{1, 1, 1, 2}, // corresponds to three level algorithm
|
||
// {1, 1, 1, 2}});
|
||
|
||
const int nbasis = 20; // we fix the number of test vector to the same
|
||
// number on every level for now
|
||
|
||
// // some stuff we need for every coarser lattice
|
||
// std::vector<std::vector<int>> cLattSizes({GridDefaultLatt()});;
|
||
// std::vector<GridCartesian *> cGrids(params.coarsegrids);
|
||
// std::vector<std::vector<int>> cSeeds({ {5,6,7,8} });
|
||
// std::vector<GridParallelRNG> cPRNGs;(params.coarsegrids);
|
||
|
||
// assert(cLattSizes.size() == params.coarsegrids);
|
||
// assert( cGrids.size() == params.coarsegrids);
|
||
// assert( cSeeds.size() == params.coarsegrids);
|
||
// assert( cPRNGs.size() == params.coarsegrids);
|
||
|
||
// for(int cl=0;cl<cLattSizes.size();cl++){
|
||
// for(int d=0;d<cLattSizes[cl].size();d++){
|
||
// // std::cout << cl << " " << d << " " << cLattSizes[cl][d] << " " <<
|
||
// blockSizes[cl][d] << std::endl; cLattSizes[cl][d] =
|
||
// cLattSizes[cl][d]/blockSizes[cl][d];
|
||
// }
|
||
// cGrids[cl] = SpaceTimeGrid::makeFourDimGrid(cLattSizes[cl],
|
||
// GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());;
|
||
// // std::cout << cLattSizes[cl] << std::endl;
|
||
// }
|
||
|
||
// GridParallelRNG cPRNG(CGrid); cPRNG.SeedFixedIntegers(cSeeds);
|
||
|
||
CoarseGrids<nbasis> cGrids(blockSizes);
|
||
|
||
// assert(0);
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Building the wilson operator on the fine grid" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
WilsonFermionR Dw(Umu, *FGrid, *FrbGrid, mass);
|
||
WilsonFermionR DwDD(UmuDD, *FGrid, *FrbGrid, mass);
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Some typedefs" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
typedef Aggregation<vSpinColourVector, vTComplex, nbasis> Subspace;
|
||
typedef CoarsenedMatrix<vSpinColourVector, vTComplex, nbasis> CoarseOperator;
|
||
typedef CoarseOperator::CoarseVector CoarseVector;
|
||
typedef TestVectorAnalyzer<LatticeFermion, nbasis> TVA;
|
||
|
||
// typedef Aggregation<vSpinColourVector,vTComplex,1,nbasis> Subspace;
|
||
// typedef CoarsenedMatrix<vSpinColourVector,vTComplex,1,nbasis> CoarseOperator;
|
||
// typedef CoarseOperator::CoarseVector CoarseVector;
|
||
|
||
// typedef CoarseOperator::CoarseG5PVector
|
||
// CoarseG5PVector; // P = preserving typedef
|
||
// CoarseOperator::CoarseG5PMatrix CoarseG5PMatrix;
|
||
|
||
#if 0
|
||
// clang-format off
|
||
std::cout << std::endl;
|
||
std::cout << "type_name<decltype(vTComplex{})>() = " << type_name<decltype(vTComplex{})>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<vTComplex>::scalar_type>() = " << type_name<GridTypeMapper<vTComplex>::scalar_type>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<vTComplex>::vector_type>() = " << type_name<GridTypeMapper<vTComplex>::vector_type>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<vTComplex>::vector_typeD>() = " << type_name<GridTypeMapper<vTComplex>::vector_typeD>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<vTComplex>::tensor_reduced>() = " << type_name<GridTypeMapper<vTComplex>::tensor_reduced>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<vTComplex>::scalar_object>() = " << type_name<GridTypeMapper<vTComplex>::scalar_object>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<vTComplex>::Complexified>() = " << type_name<GridTypeMapper<vTComplex>::Complexified>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<vTComplex>::Realified>() = " << type_name<GridTypeMapper<vTComplex>::Realified>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<vTComplex>::DoublePrecision>() = " << type_name<GridTypeMapper<vTComplex>::DoublePrecision>() << std::endl;
|
||
std::cout << std::endl;
|
||
|
||
std::cout << std::endl;
|
||
std::cout << "type_name<decltype(TComplex{})>() = " << type_name<decltype(TComplex{})>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<TComplex>::scalar_type>() = " << type_name<GridTypeMapper<TComplex>::scalar_type>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<TComplex>::vector_type>() = " << type_name<GridTypeMapper<TComplex>::vector_type>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<TComplex>::vector_typeD>() = " << type_name<GridTypeMapper<TComplex>::vector_typeD>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<TComplex>::tensor_reduced>() = " << type_name<GridTypeMapper<TComplex>::tensor_reduced>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<TComplex>::scalar_object>() = " << type_name<GridTypeMapper<TComplex>::scalar_object>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<TComplex>::Complexified>() = " << type_name<GridTypeMapper<TComplex>::Complexified>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<TComplex>::Realified>() = " << type_name<GridTypeMapper<TComplex>::Realified>() << std::endl;
|
||
std::cout << "type_name<GridTypeMapper<TComplex>::DoublePrecision>() = " << type_name<GridTypeMapper<TComplex>::DoublePrecision>() << std::endl;
|
||
std::cout << std::endl;
|
||
// clang-format on
|
||
#endif
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Calling Aggregation class to build subspaces" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
// • TODO: need some way to run the smoother on the "test vectors" for a few
|
||
// times before constructing the subspace from them
|
||
// • Maybe an application for an mrhs (true mrhs, no block) smoother?
|
||
// • In WMG, the vectors are normalized but not orthogonalized, but here they
|
||
// are constructed randomly and then orthogonalized (rather orthonormalized) against each other
|
||
MdagMLinearOperator<WilsonFermionR, LatticeFermion> HermOp(Dw);
|
||
Subspace Aggregates(cGrids.Grids[0], FGrid, 0);
|
||
assert((nbasis & 0x1) == 0);
|
||
int nb = nbasis / 2;
|
||
std::cout << GridLogMessage << " nbasis/2 = " << nb << std::endl;
|
||
|
||
Aggregates.CreateSubspace(fPRNG, HermOp /*, nb */); // Don't specify nb to see the orthogonalization check
|
||
|
||
TVA testVectorAnalyzer;
|
||
|
||
testVectorAnalyzer(HermOp, Aggregates.subspace, nb);
|
||
|
||
for(int n = 0; n < nb; n++) {
|
||
// multiply with g5 normally instead of G5R5 since this specific to DWF
|
||
Aggregates.subspace[n + nb] = g5 * Aggregates.subspace[n];
|
||
std::cout << GridLogMessage << n << " subspace " << norm2(Aggregates.subspace[n + nb]) << " " << norm2(Aggregates.subspace[n])
|
||
<< std::endl;
|
||
}
|
||
for(int n = 0; n < nbasis; n++) {
|
||
std::cout << GridLogMessage << "vec[" << n << "] = " << norm2(Aggregates.subspace[n]) << std::endl;
|
||
}
|
||
|
||
// tva(HermOp, Aggregates.subspace);
|
||
Aggregates.CheckOrthogonal();
|
||
testVectorAnalyzer(HermOp, Aggregates.subspace);
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Building coarse representation of Dirac operator" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
// using Gamma5HermitianLinearOperator corresponds to working with H = g5 * D
|
||
Gamma5HermitianLinearOperator<WilsonFermionR, LatticeFermion> HermIndefOp(Dw);
|
||
Gamma5HermitianLinearOperator<WilsonFermionR, LatticeFermion> HermIndefOpDD(DwDD);
|
||
CoarsenedMatrix<vSpinColourVector, vTComplex, nbasis> CoarseOp(*cGrids.Grids[0]);
|
||
CoarseOp.CoarsenOperator(FGrid, HermIndefOp, Aggregates); // uses only linop.OpDiag & linop.OpDir
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Building coarse vectors" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
CoarseVector c_src(cGrids.Grids[0]);
|
||
CoarseVector c_res(cGrids.Grids[0]);
|
||
gaussian(cGrids.PRNGs[0], c_src);
|
||
c_res = zero;
|
||
|
||
std::cout << "type_name<decltype(c_src)>() = " << type_name<decltype(c_src)>() << std::endl;
|
||
|
||
// c_res = g5 * c_src;
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Solving posdef-MR on coarse space " << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
MdagMLinearOperator<CoarseOperator, CoarseVector> PosdefLdop(CoarseOp);
|
||
MinimalResidual<CoarseVector> MR(5.0e-2, 100, false);
|
||
ConjugateGradient<CoarseVector> CG(5.0e-2, 100, false);
|
||
|
||
MR(PosdefLdop, c_src, c_res);
|
||
|
||
gaussian(cGrids.PRNGs[0], c_src);
|
||
c_res = zero;
|
||
CG(PosdefLdop, c_src, c_res);
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Dummy testing for building second coarse level" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
// typedef Aggregation< CoarseVector, vTComplex, nbasis > SubspaceAgain;
|
||
|
||
// SubspaceAgain AggregatesCoarsenedAgain(cGrids.Grids[1], cGrids.Grids[0], 0);
|
||
// AggregatesCoarsenedAgain.CreateSubspace(cGrids.PRNGs[0], PosdefLdop);
|
||
|
||
// for(int n=0;n<nb;n++){
|
||
// AggregatesCoarsenedAgain.subspace[n+nb] = g5 * AggregatesCoarsenedAgain.subspace[n]; // multiply with g5 normally instead of G5R5 since this specific to DWF
|
||
// std::cout<<GridLogMessage<<n<<" subspace "<<norm2(AggregatesCoarsenedAgain.subspace[n+nb])<<" "<<norm2(AggregatesCoarsenedAgain.subspace[n]) <<std::endl;
|
||
// }
|
||
|
||
// for(int n=0;n<nbasis;n++){
|
||
// std::cout<<GridLogMessage << "vec["<<n<<"] = "<<norm2(AggregatesCoarsenedAgain.subspace[n]) <<std::endl;
|
||
// }
|
||
|
||
// AggregatesCoarsenedAgain.CheckOrthogonal();
|
||
|
||
// std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
||
// std::cout<<GridLogMessage << "Solving indef-MCR on coarse space "<< std::endl;
|
||
// std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
||
// HermitianLinearOperator<CoarseOperator,CoarseVector> HermIndefLdop(CoarseOp);
|
||
// ConjugateResidual<CoarseVector> MCR(1.0e-6,100000);
|
||
// MCR(HermIndefLdop,c_src,c_res);
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Building deflation preconditioner " << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
MultiGridPreconditioner<vSpinColourVector, vTComplex, nbasis, WilsonFermionR> Precon(
|
||
Aggregates, CoarseOp, HermIndefOp, Dw, HermIndefOp, Dw);
|
||
|
||
MultiGridPreconditioner<vSpinColourVector, vTComplex, nbasis, WilsonFermionR> PreconDD(
|
||
Aggregates, CoarseOp, HermIndefOp, Dw, HermIndefOpDD, DwDD);
|
||
// MultiGridPreconditioner(Aggregates &Agg, CoarseOperator &Coarse,
|
||
// FineOperator &Fine,Matrix &FineMatrix,
|
||
// FineOperator &Smooth,Matrix &SmootherMatrix)
|
||
TrivialPrecon<LatticeFermion> Simple;
|
||
|
||
Precon.runChecks(cGrids);
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Building two level VPGCR and FGMRES solvers" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
PrecGeneralisedConjugateResidual<LatticeFermion> VPGCRMG(1.0e-12, 100, Precon, 8, 8);
|
||
FlexibleGeneralisedMinimalResidual<LatticeFermion> FGMRESMG(1.0e-12, 100, Precon, 8);
|
||
|
||
std::cout << GridLogMessage << "checking norm src " << norm2(src) << std::endl;
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Building unpreconditioned VPGCR and FGMRES solvers" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
PrecGeneralisedConjugateResidual<LatticeFermion> VPGCRT(1.0e-12, 4000000, Simple, 8, 8);
|
||
FlexibleGeneralisedMinimalResidual<LatticeFermion> FGMREST(1.0e-12, 4000000, Simple, 8);
|
||
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
std::cout << GridLogMessage << "Testing the four solvers" << std::endl;
|
||
std::cout << GridLogMessage << "**************************************************" << std::endl;
|
||
|
||
std::vector<OperatorFunction<LatticeFermion> *> solvers;
|
||
solvers.push_back(&VPGCRMG);
|
||
solvers.push_back(&FGMRESMG);
|
||
solvers.push_back(&VPGCRT);
|
||
solvers.push_back(&FGMREST);
|
||
|
||
for(auto elem : solvers) {
|
||
result = zero;
|
||
(*elem)(HermIndefOp, src, result);
|
||
}
|
||
|
||
Grid_finalize();
|
||
}
|