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WilsonMG: Add a mixed precision version of FGMRES
This version does everything in double prec but accepts a preconditioner working in single precision.
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Daniel Richtmann
Daniel Richtmann
parent
11c4f5e32c
commit
4f41cd114d
@ -53,6 +53,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
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#include <Grid/algorithms/iterative/CommunicationAvoidingGeneralisedMinimalResidual.h>
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#include <Grid/algorithms/iterative/FlexibleGeneralisedMinimalResidual.h>
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#include <Grid/algorithms/iterative/FlexibleCommunicationAvoidingGeneralisedMinimalResidual.h>
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#include <Grid/algorithms/iterative/MixedPrecisionFlexibleGeneralisedMinimalResidual.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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@ -0,0 +1,272 @@
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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/MixedPrecisionFlexibleGeneralisedMinimalResidual.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_MIXED_PRECISION_FLEXIBLE_GENERALISED_MINIMAL_RESIDUAL_H
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#define GRID_MIXED_PRECISION_FLEXIBLE_GENERALISED_MINIMAL_RESIDUAL_H
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namespace Grid {
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template<class FieldD, class FieldF, typename std::enable_if<getPrecision<FieldD>::value == 2, int>::type = 0, typename std::enable_if< getPrecision<FieldF>::value == 1, int>::type = 0>
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class MixedPrecisionFlexibleGeneralisedMinimalResidual : public OperatorFunction<FieldD> {
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public:
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bool ErrorOnNoConverge; // Throw an assert when MPFGMRES 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 MaxNumberOfRestarts;
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Integer IterationCount; // Number of iterations the MPFGMRES 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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GridStopWatch ChangePrecTimer;
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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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GridBase* SinglePrecGrid;
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LinearFunction<FieldF> &Preconditioner;
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MixedPrecisionFlexibleGeneralisedMinimalResidual(RealD tol,
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Integer maxit,
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GridBase * sp_grid,
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LinearFunction<FieldF> &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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, MaxNumberOfRestarts(MaxIterations/RestartLength + ((MaxIterations%RestartLength == 0) ? 0 : 1))
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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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, SinglePrecGrid(sp_grid)
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, Preconditioner(Prec) {};
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void operator()(LinearOperatorBase<FieldD> &LinOp, const FieldD &src, FieldD &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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FieldD r(src._grid);
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std::cout << std::setprecision(4) << std::scientific;
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std::cout << GridLogIterative << "MPFGMRES: guess " << guess << std::endl;
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std::cout << GridLogIterative << "MPFGMRES: 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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ChangePrecTimer.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<MaxNumberOfRestarts; 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 << "MPFGMRES: Converged on iteration " << IterationCount
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<< " computed residual " << sqrt(cp / ssq)
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<< " true residual " << true_residual
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<< " target " << Tolerance << std::endl;
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std::cout << GridLogMessage << "MPFGMRES Time elapsed: Total " << SolverTimer.Elapsed() << std::endl;
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std::cout << GridLogMessage << "MPFGMRES Time elapsed: Precon " << PrecTimer.Elapsed() << std::endl;
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std::cout << GridLogMessage << "MPFGMRES Time elapsed: Matrix " << MatrixTimer.Elapsed() << std::endl;
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std::cout << GridLogMessage << "MPFGMRES Time elapsed: Linalg " << LinalgTimer.Elapsed() << std::endl;
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std::cout << GridLogMessage << "MPFGMRES Time elapsed: QR " << QrTimer.Elapsed() << std::endl;
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std::cout << GridLogMessage << "MPFGMRES Time elapsed: CompSol " << CompSolutionTimer.Elapsed() << std::endl;
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std::cout << GridLogMessage << "MPFGMRES Time elapsed: PrecChange " << ChangePrecTimer.Elapsed() << std::endl;
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return;
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}
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}
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std::cout << GridLogMessage << "MPFGMRES 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<FieldD> &LinOp, const FieldD &src, FieldD &psi, RealD rsq) {
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RealD cp = 0;
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FieldD w(src._grid);
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FieldD r(src._grid);
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std::vector<FieldD> v(RestartLength + 1, src._grid); // these should probably be made class members
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std::vector<FieldD> z(RestartLength + 1, src._grid); // so that they are only allocated once, not in every restart
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MatrixTimer.Start();
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LinOp.Op(psi, w);
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MatrixTimer.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 << "MPFGMRES: Iteration " << IterationCount
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<< " residual " << cp << " target " << rsq << std::endl;
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if ((i == RestartLength - 1) || (IterationCount == MaxIterations) || (cp <= rsq)) {
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computeSolution(z, 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<FieldD> &LinOp, std::vector<FieldD> &v, std::vector<FieldD> &z, FieldD &w, int iter) {
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FieldF v_f(SinglePrecGrid);
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FieldF z_f(SinglePrecGrid);
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ChangePrecTimer.Start();
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precisionChange(v_f, v[iter]);
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precisionChange(z_f, z[iter]);
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ChangePrecTimer.Stop();
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PrecTimer.Start();
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Preconditioner(v_f, z_f);
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PrecTimer.Stop();
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ChangePrecTimer.Start();
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precisionChange(z[iter], z_f);
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ChangePrecTimer.Stop();
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MatrixTimer.Start();
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LinOp.Op(z[iter], w);
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MatrixTimer.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<FieldD> const &z, FieldD &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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for (int i = 0; i <= iter; i++)
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psi = psi + z[i] * y[i];
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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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