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First version of FGMRES; not working yet
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Daniel Richtmann
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8107b785cc
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0f75ea52b7
@ -49,6 +49,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
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#include <Grid/algorithms/iterative/ConjugateGradientReliableUpdate.h>
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#include <Grid/algorithms/iterative/MinimalResidual.h>
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#include <Grid/algorithms/iterative/GeneralisedMinimalResidual.h>
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#include <Grid/algorithms/iterative/FlexibleGeneralisedMinimalResidual.h>
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#include <Grid/algorithms/iterative/ImplicitlyRestartedLanczos.h>
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#include <Grid/algorithms/CoarsenedMatrix.h>
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#include <Grid/algorithms/FFT.h>
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284
lib/algorithms/iterative/FlexibleGeneralisedMinimalResidual.h
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284
lib/algorithms/iterative/FlexibleGeneralisedMinimalResidual.h
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@ -0,0 +1,284 @@
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/*************************************************************************************
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Grid physics library, www.github.com/paboyle/Grid
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Source file: ./lib/algorithms/iterative/FlexibleGeneralisedMinimalResidual.h
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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
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directory
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*************************************************************************************/
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/* END LEGAL */
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#ifndef GRID_FLEXIBLE_GENERALISED_MINIMAL_RESIDUAL_H
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#define GRID_FLEXIBLE_GENERALISED_MINIMAL_RESIDUAL_H
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// from Y. Saad - Iterative Methods for Sparse Linear Systems, PP 172
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// Compute r0 = b − Ax0 , β := ||r0||2 , and v1 := r0 /β
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// For j = 1, 2, ..., m Do:
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// Compute wj := Avj
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// For i = 1, ..., j Do:
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// hij := (wj , vi)
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// wj := wj − hij vi
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// EndDo
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// hj+1,j = ||wj||2 . If hj+1,j = 0 set m := j and go to HERE
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// vj+1 = wj /hj+1,j
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// EndDo
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// Define the (m + 1) × m Hessenberg matrix H̄m = {hij}1≤i≤m+1,1≤j≤m. [HERE]
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// Compute ym the minimizer of ||βe1 − H̄m y||2 and xm = x0 + Vm ym.
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///////////////////////////////////////////////////////////////////////////////////////////////////////
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// want to solve Ax = b -> A = LinOp, psi = x, b = src
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namespace Grid {
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template<class Field>
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class FlexibleGeneralisedMinimalResidual : public OperatorFunction<Field> {
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public:
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bool ErrorOnNoConverge; // Throw an assert when FGMRES fails to converge,
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// defaults to True.
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RealD Tolerance;
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Integer MaxIterations;
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Integer RestartLength;
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Integer IterationCount; // Number of iterations the FGMRES took to finish,
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// filled in upon completion
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GridStopWatch MatrixTimer;
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GridStopWatch PrecTimer;
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GridStopWatch LinalgTimer;
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GridStopWatch QrTimer;
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GridStopWatch CompSolutionTimer;
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Eigen::MatrixXcd H;
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std::vector<std::complex<double>> y;
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std::vector<std::complex<double>> gamma;
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std::vector<std::complex<double>> c;
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std::vector<std::complex<double>> s;
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LinearFunction<Field> &Preconditioner;
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FlexibleGeneralisedMinimalResidual(RealD tol,
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Integer maxit,
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LinearFunction<Field> &Prec,
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Integer restart_length,
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bool err_on_no_conv = true)
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: Tolerance(tol)
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, MaxIterations(maxit)
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, RestartLength(restart_length)
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, ErrorOnNoConverge(err_on_no_conv)
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, H(Eigen::MatrixXcd::Zero(RestartLength, RestartLength + 1)) // sizes taken from DD-αAMG code base
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, y(RestartLength + 1, 0.)
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, gamma(RestartLength + 1, 0.)
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, c(RestartLength + 1, 0.)
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, s(RestartLength + 1, 0.)
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, Preconditioner(Prec) {};
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void operator()(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi) {
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psi.checkerboard = src.checkerboard;
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conformable(psi, src);
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RealD guess = norm2(psi);
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assert(std::isnan(guess) == 0);
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RealD cp;
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RealD ssq = norm2(src);
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RealD rsq = Tolerance * Tolerance * ssq;
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Field r(src._grid);
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std::cout << std::setprecision(4) << std::scientific << std::endl;
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std::cout << GridLogIterative << "FlexibleGeneralisedMinimalResidual: guess " << guess << std::endl;
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std::cout << GridLogIterative << "FlexibleGeneralisedMinimalResidual: src " << ssq << std::endl;
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PrecTimer.Reset();
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MatrixTimer.Reset();
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LinalgTimer.Reset();
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QrTimer.Reset();
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CompSolutionTimer.Reset();
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GridStopWatch SolverTimer;
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SolverTimer.Start();
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IterationCount = 0;
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for (int k=0; k<MaxIterations; k++) {
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cp = outerLoopBody(LinOp, src, psi, rsq);
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// Stopping condition
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if (cp <= rsq) {
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SolverTimer.Stop();
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LinOp.Op(psi,r);
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axpy(r,-1.0,src,r);
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RealD srcnorm = sqrt(ssq);
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RealD resnorm = sqrt(norm2(r));
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RealD true_residual = resnorm / srcnorm;
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std::cout << GridLogMessage << "FlexibleGeneralisedMinimalResidual: Converged on iteration " << IterationCount << std::endl;
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std::cout << GridLogMessage << "\tComputed residual " << sqrt(cp / ssq) << std::endl;
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std::cout << GridLogMessage << "\tTrue residual " << true_residual << std::endl;
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std::cout << GridLogMessage << "\tTarget " << Tolerance << std::endl;
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std::cout << GridLogMessage << "FlexibleGeneralisedMinimalResidual Time breakdown" << std::endl;
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std::cout << GridLogMessage << "\tElapsed " << SolverTimer.Elapsed() << std::endl;
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std::cout << GridLogMessage << "\tPrecon " << PrecTimer.Elapsed() << std::endl;
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std::cout << GridLogMessage << "\tMatrix " << MatrixTimer.Elapsed() << std::endl;
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std::cout << GridLogMessage << "\tLinalg " << LinalgTimer.Elapsed() << std::endl;
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std::cout << GridLogMessage << "\tQR " << QrTimer.Elapsed() << std::endl;
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std::cout << GridLogMessage << "\tCompSol " << CompSolutionTimer.Elapsed() << std::endl;
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return;
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}
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}
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std::cout << GridLogMessage << "FlexibleGeneralisedMinimalResidual did NOT converge" << std::endl;
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if (ErrorOnNoConverge)
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assert(0);
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}
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RealD outerLoopBody(LinearOperatorBase<Field> &LinOp, const Field &src, Field &psi, RealD rsq) {
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RealD cp = 0;
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Field w(src._grid);
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Field r(src._grid);
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std::vector<Field> v(RestartLength + 1, src._grid);
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std::vector<Field> z(RestartLength + 1, src._grid);
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MatrixTimer.Start();
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LinOp.Op(psi, z[0]);
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MatrixTimer.Stop();
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PrecTimer.Start();
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Preconditioner(z[0], r);
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PrecTimer.Stop();
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LinalgTimer.Start();
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r = src - w;
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gamma[0] = sqrt(norm2(r));
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v[0] = (1. / gamma[0]) * r;
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LinalgTimer.Stop();
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for (int i=0; i<RestartLength; i++) {
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IterationCount++;
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arnoldiStep(LinOp, v, z, w, i);
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qrUpdate(i);
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cp = std::norm(gamma[i+1]);
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std::cout << GridLogIterative << "FlexibleGeneralisedMinimalResidual: Iteration " << IterationCount
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<< " residual " << cp << " target " << rsq << std::endl;
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if ((i == RestartLength - 1) || (cp <= rsq)) {
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computeSolution(v, psi, i);
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return cp;
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}
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}
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assert(0); // Never reached
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return cp;
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}
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void arnoldiStep(LinearOperatorBase<Field> &LinOp, std::vector<Field> &v, std::vector<Field> &z, Field &w, int iter) {
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MatrixTimer.Start();
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LinOp.Op(v[iter], z[0]);
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MatrixTimer.Stop();
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PrecTimer.Start();
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Preconditioner(z[0], w);
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PrecTimer.Stop();
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LinalgTimer.Start();
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for (int i = 0; i <= iter; ++i) {
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H(iter, i) = innerProduct(v[i], w);
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w = w - H(iter, i) * v[i];
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}
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H(iter, iter + 1) = sqrt(norm2(w));
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v[iter + 1] = (1. / H(iter, iter + 1)) * w;
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LinalgTimer.Stop();
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}
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void qrUpdate(int iter) {
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QrTimer.Start();
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for (int i = 0; i < iter ; ++i) {
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auto tmp = -s[i] * H(iter, i) + c[i] * H(iter, i + 1);
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H(iter, i) = std::conj(c[i]) * H(iter, i) + std::conj(s[i]) * H(iter, i + 1);
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H(iter, i + 1) = tmp;
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}
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// Compute new Givens Rotation
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ComplexD nu = sqrt(std::norm(H(iter, iter)) + std::norm(H(iter, iter + 1)));
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c[iter] = H(iter, iter) / nu;
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s[iter] = H(iter, iter + 1) / nu;
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// Apply new Givens rotation
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H(iter, iter) = nu;
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H(iter, iter + 1) = 0.;
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gamma[iter + 1] = -s[iter] * gamma[iter];
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gamma[iter] = std::conj(c[iter]) * gamma[iter];
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QrTimer.Stop();
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}
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void computeSolution(std::vector<Field> const &v, Field &psi, int iter) {
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CompSolutionTimer.Start();
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for (int i = iter; i >= 0; i--) {
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y[i] = gamma[i];
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for (int k = i + 1; k <= iter; k++)
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y[i] = y[i] - H(k, i) * y[k];
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y[i] = y[i] / H(i, i);
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}
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// TODO: Use axpys or similar for these
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// TODO: Fix the condition
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if (true) {
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for (int i = 0; i <= iter; i++)
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psi = psi + v[i] * y[i];
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}
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else {
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psi = y[0] * v[0];
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for (int i = 1; i <= iter; i++)
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psi = psi + v[i] * y[i];
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}
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CompSolutionTimer.Stop();
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}
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};
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}
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#endif
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// I took the version with p->kind == left from the WMG code base here. TODO: recheck if we need left or right
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