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Added a mixed precision multishift algorithm for which the matrix multiplies are performed in single precision but the search directions are accumulated in double precision.
A reliable update step is performed at a tunable frequency to correct the residual. A final mixed-prec single-shift solve is performed on each pole to perform cleanup if necessary. A test is provided to demonstrate the algorithm.
This commit is contained in:
Christopher Kelly
@@ -54,6 +54,7 @@ NAMESPACE_CHECK(BiCGSTAB);
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#include <Grid/algorithms/iterative/SchurRedBlack.h>
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#include <Grid/algorithms/iterative/ConjugateGradientMultiShift.h>
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#include <Grid/algorithms/iterative/ConjugateGradientMixedPrec.h>
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#include <Grid/algorithms/iterative/ConjugateGradientMultiShiftMixedPrec.h>
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#include <Grid/algorithms/iterative/BiCGSTABMixedPrec.h>
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#include <Grid/algorithms/iterative/BlockConjugateGradient.h>
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#include <Grid/algorithms/iterative/ConjugateGradientReliableUpdate.h>
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410
Grid/algorithms/iterative/ConjugateGradientMultiShiftMixedPrec.h
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410
Grid/algorithms/iterative/ConjugateGradientMultiShiftMixedPrec.h
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@@ -0,0 +1,410 @@
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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/ConjugateGradientMultiShift.h
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Copyright (C) 2015
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Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
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Author: Peter Boyle <paboyle@ph.ed.ac.uk>
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Author: Christopher Kelly <ckelly@bnl.gov>
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License along
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with this program; if not, write to the Free Software Foundation, Inc.,
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51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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See the full license in the file "LICENSE" in the top level distribution directory
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*************************************************************************************/
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/* END LEGAL */
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#ifndef GRID_CONJUGATE_GRADIENT_MULTI_SHIFT_MIXEDPREC_H
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#define GRID_CONJUGATE_GRADIENT_MULTI_SHIFT_MIXEDPREC_H
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NAMESPACE_BEGIN(Grid);
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//CK 2020: A variant of the multi-shift conjugate gradient with the matrix multiplication in single precision.
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//The residual is stored in single precision, but the search directions and solution are stored in double precision.
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//Every update_freq iterations the residual is corrected in double precision.
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//For safety the a final regular CG is applied to clean up if necessary
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//Linop to add shift to input linop, used in cleanup CG
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namespace ConjugateGradientMultiShiftMixedPrecSupport{
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template<typename Field>
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class ShiftedLinop: public LinearOperatorBase<Field>{
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public:
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LinearOperatorBase<Field> &linop_base;
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RealD shift;
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ShiftedLinop(LinearOperatorBase<Field> &_linop_base, RealD _shift): linop_base(_linop_base), shift(_shift){}
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void OpDiag (const Field &in, Field &out){ assert(0); }
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void OpDir (const Field &in, Field &out,int dir,int disp){ assert(0); }
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void OpDirAll (const Field &in, std::vector<Field> &out){ assert(0); }
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void Op (const Field &in, Field &out){ assert(0); }
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void AdjOp (const Field &in, Field &out){ assert(0); }
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void HermOp(const Field &in, Field &out){
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linop_base.HermOp(in, out);
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axpy(out, shift, in, out);
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}
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void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
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HermOp(in,out);
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ComplexD dot = innerProduct(in,out);
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n1=real(dot);
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n2=norm2(out);
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}
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};
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};
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template<class FieldD, class FieldF,
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typename std::enable_if< getPrecision<FieldD>::value == 2, int>::type = 0,
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typename std::enable_if< getPrecision<FieldF>::value == 1, int>::type = 0>
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class ConjugateGradientMultiShiftMixedPrec : public OperatorMultiFunction<FieldD>,
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public OperatorFunction<FieldD>
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{
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public:
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using OperatorFunction<FieldD>::operator();
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RealD Tolerance;
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Integer MaxIterations;
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Integer IterationsToComplete; //Number of iterations the CG took to finish. Filled in upon completion
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std::vector<int> IterationsToCompleteShift; // Iterations for this shift
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int verbose;
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MultiShiftFunction shifts;
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std::vector<RealD> TrueResidualShift;
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int ReliableUpdateFreq; //number of iterations between reliable updates
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GridBase* SinglePrecGrid; //Grid for single-precision fields
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LinearOperatorBase<FieldF> &Linop_f; //single precision
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ConjugateGradientMultiShiftMixedPrec(Integer maxit, MultiShiftFunction &_shifts,
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GridBase* _SinglePrecGrid, LinearOperatorBase<FieldF> &_Linop_f,
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int _ReliableUpdateFreq
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) :
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MaxIterations(maxit), shifts(_shifts), SinglePrecGrid(_SinglePrecGrid), Linop_f(_Linop_f), ReliableUpdateFreq(_ReliableUpdateFreq)
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{
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verbose=1;
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IterationsToCompleteShift.resize(_shifts.order);
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TrueResidualShift.resize(_shifts.order);
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}
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void operator() (LinearOperatorBase<FieldD> &Linop, const FieldD &src, FieldD &psi)
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{
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GridBase *grid = src.Grid();
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int nshift = shifts.order;
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std::vector<FieldD> results(nshift,grid);
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(*this)(Linop,src,results,psi);
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}
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void operator() (LinearOperatorBase<FieldD> &Linop, const FieldD &src, std::vector<FieldD> &results, FieldD &psi)
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{
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int nshift = shifts.order;
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(*this)(Linop,src,results);
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psi = shifts.norm*src;
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for(int i=0;i<nshift;i++){
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psi = psi + shifts.residues[i]*results[i];
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}
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return;
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}
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void operator() (LinearOperatorBase<FieldD> &Linop_d, const FieldD &src_d, std::vector<FieldD> &psi_d)
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{
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GridBase *DoublePrecGrid = src_d.Grid();
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precisionChangeWorkspace wk_f_from_d(SinglePrecGrid, DoublePrecGrid);
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precisionChangeWorkspace wk_d_from_f(DoublePrecGrid, SinglePrecGrid);
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////////////////////////////////////////////////////////////////////////
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// Convenience references to the info stored in "MultiShiftFunction"
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////////////////////////////////////////////////////////////////////////
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int nshift = shifts.order;
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std::vector<RealD> &mass(shifts.poles); // Make references to array in "shifts"
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std::vector<RealD> &mresidual(shifts.tolerances);
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std::vector<RealD> alpha(nshift,1.0);
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//Double precision search directions
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FieldD p_d(DoublePrecGrid);
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std::vector<FieldD> ps_d(nshift, DoublePrecGrid);// Search directions (double precision)
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FieldD tmp_d(DoublePrecGrid);
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FieldD r_d(DoublePrecGrid);
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FieldD mmp_d(DoublePrecGrid);
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assert(psi_d.size()==nshift);
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assert(mass.size()==nshift);
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assert(mresidual.size()==nshift);
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// dynamic sized arrays on stack; 2d is a pain with vector
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RealD bs[nshift];
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RealD rsq[nshift];
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RealD z[nshift][2];
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int converged[nshift];
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const int primary =0;
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//Primary shift fields CG iteration
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RealD a,b,c,d;
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RealD cp,bp,qq; //prev
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// Matrix mult fields
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FieldF r_f(SinglePrecGrid);
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FieldF p_f(SinglePrecGrid);
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FieldF tmp_f(SinglePrecGrid);
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FieldF mmp_f(SinglePrecGrid);
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FieldF src_f(SinglePrecGrid);
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precisionChange(src_f, src_d, wk_f_from_d);
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// Check lightest mass
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for(int s=0;s<nshift;s++){
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assert( mass[s]>= mass[primary] );
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converged[s]=0;
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}
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// Wire guess to zero
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// Residuals "r" are src
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// First search direction "p" is also src
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cp = norm2(src_d);
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// Handle trivial case of zero src.
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if( cp == 0. ){
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for(int s=0;s<nshift;s++){
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psi_d[s] = Zero();
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IterationsToCompleteShift[s] = 1;
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TrueResidualShift[s] = 0.;
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}
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return;
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}
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for(int s=0;s<nshift;s++){
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rsq[s] = cp * mresidual[s] * mresidual[s];
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std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrec: shift "<< s <<" target resid "<<rsq[s]<<std::endl;
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ps_d[s] = src_d;
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}
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// r and p for primary
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r_f=src_f; //residual maintained in single
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p_f=src_f;
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p_d = src_d; //primary copy --- make this a reference to ps_d to save axpys
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//MdagM+m[0]
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Linop_f.HermOpAndNorm(p_f,mmp_f,d,qq); // mmp = MdagM p d=real(dot(p, mmp)), qq=norm2(mmp)
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axpy(mmp_f,mass[0],p_f,mmp_f);
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RealD rn = norm2(p_f);
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d += rn*mass[0];
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b = -cp /d;
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// Set up the various shift variables
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int iz=0;
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z[0][1-iz] = 1.0;
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z[0][iz] = 1.0;
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bs[0] = b;
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for(int s=1;s<nshift;s++){
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z[s][1-iz] = 1.0;
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z[s][iz] = 1.0/( 1.0 - b*(mass[s]-mass[0]));
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bs[s] = b*z[s][iz];
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}
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// r += b[0] A.p[0]
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// c= norm(r)
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c=axpy_norm(r_f,b,mmp_f,r_f);
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for(int s=0;s<nshift;s++) {
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axpby(psi_d[s],0.,-bs[s]*alpha[s],src_d,src_d);
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}
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///////////////////////////////////////
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// Timers
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///////////////////////////////////////
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GridStopWatch AXPYTimer, ShiftTimer, QRTimer, MatrixTimer, SolverTimer, PrecChangeTimer, CleanupTimer;
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SolverTimer.Start();
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// Iteration loop
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int k;
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for (k=1;k<=MaxIterations;k++){
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a = c /cp;
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//Update double precision search direction by residual
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PrecChangeTimer.Start();
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precisionChange(r_d, r_f, wk_d_from_f);
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PrecChangeTimer.Stop();
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AXPYTimer.Start();
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axpy(p_d,a,p_d,r_d);
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for(int s=0;s<nshift;s++){
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if ( ! converged[s] ) {
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if (s==0){
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axpy(ps_d[s],a,ps_d[s],r_d);
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} else{
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RealD as =a *z[s][iz]*bs[s] /(z[s][1-iz]*b);
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axpby(ps_d[s],z[s][iz],as,r_d,ps_d[s]);
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}
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}
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}
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AXPYTimer.Stop();
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PrecChangeTimer.Start();
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precisionChange(p_f, p_d, wk_f_from_d); //get back single prec search direction for linop
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PrecChangeTimer.Stop();
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cp=c;
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MatrixTimer.Start();
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Linop_f.HermOp(p_f,mmp_f);
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d=real(innerProduct(p_f,mmp_f));
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MatrixTimer.Stop();
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AXPYTimer.Start();
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axpy(mmp_f,mass[0],p_f,mmp_f);
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AXPYTimer.Stop();
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RealD rn = norm2(p_f);
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d += rn*mass[0];
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bp=b;
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b=-cp/d;
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// Toggle the recurrence history
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bs[0] = b;
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iz = 1-iz;
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ShiftTimer.Start();
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for(int s=1;s<nshift;s++){
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if((!converged[s])){
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RealD z0 = z[s][1-iz];
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RealD z1 = z[s][iz];
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z[s][iz] = z0*z1*bp
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/ (b*a*(z1-z0) + z1*bp*(1- (mass[s]-mass[0])*b));
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bs[s] = b*z[s][iz]/z0; // NB sign rel to Mike
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}
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}
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ShiftTimer.Stop();
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//Update double precision solutions
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AXPYTimer.Start();
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for(int s=0;s<nshift;s++){
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int ss = s;
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if( (!converged[s]) ) {
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axpy(psi_d[ss],-bs[s]*alpha[s],ps_d[s],psi_d[ss]);
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}
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}
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//Perform reliable update if necessary; otherwise update residual from single-prec mmp
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RealD c_f = axpy_norm(r_f,b,mmp_f,r_f);
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AXPYTimer.Stop();
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c = c_f;
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if(k % ReliableUpdateFreq == 0){
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//Replace r with true residual
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MatrixTimer.Start();
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Linop_d.HermOp(psi_d[0],mmp_d);
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MatrixTimer.Stop();
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AXPYTimer.Start();
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axpy(mmp_d,mass[0],psi_d[0],mmp_d);
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RealD c_d = axpy_norm(r_d, -1.0, mmp_d, src_d);
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AXPYTimer.Stop();
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std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrec k="<<k<< ", replaced |r|^2 = "<<c_f <<" with |r|^2 = "<<c_d<<std::endl;
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PrecChangeTimer.Start();
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precisionChange(r_f, r_d, wk_f_from_d);
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PrecChangeTimer.Stop();
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c = c_d;
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}
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// Convergence checks
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int all_converged = 1;
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for(int s=0;s<nshift;s++){
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if ( (!converged[s]) ){
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IterationsToCompleteShift[s] = k;
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RealD css = c * z[s][iz]* z[s][iz];
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if(css<rsq[s]){
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if ( ! converged[s] )
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std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrec k="<<k<<" Shift "<<s<<" has converged"<<std::endl;
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converged[s]=1;
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} else {
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all_converged=0;
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}
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}
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}
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if ( all_converged ){
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SolverTimer.Stop();
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std::cout<<GridLogMessage<< "ConjugateGradientMultiShiftMixedPrec: All shifts have converged iteration "<<k<<std::endl;
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std::cout<<GridLogMessage<< "ConjugateGradientMultiShiftMixedPrec: Checking solutions"<<std::endl;
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// Check answers
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for(int s=0; s < nshift; s++) {
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Linop_d.HermOpAndNorm(psi_d[s],mmp_d,d,qq);
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axpy(tmp_d,mass[s],psi_d[s],mmp_d);
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axpy(r_d,-alpha[s],src_d,tmp_d);
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RealD rn = norm2(r_d);
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RealD cn = norm2(src_d);
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TrueResidualShift[s] = std::sqrt(rn/cn);
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std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrec: shift["<<s<<"] true residual "<< TrueResidualShift[s] << " target " << mresidual[s] << std::endl;
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//If we have not reached the desired tolerance, do a (mixed precision) CG cleanup
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if(rn >= rsq[s]){
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CleanupTimer.Start();
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std::cout<<GridLogMessage<<"ConjugateGradientMultiShiftMixedPrec: performing cleanup step for shift " << s << std::endl;
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//Setup linear operators for final cleanup
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ConjugateGradientMultiShiftMixedPrecSupport::ShiftedLinop<FieldD> Linop_shift_d(Linop_d, mass[s]);
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ConjugateGradientMultiShiftMixedPrecSupport::ShiftedLinop<FieldF> Linop_shift_f(Linop_f, mass[s]);
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MixedPrecisionConjugateGradient<FieldD,FieldF> cg(mresidual[s], MaxIterations, MaxIterations, SinglePrecGrid, Linop_shift_f, Linop_shift_d);
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cg(src_d, psi_d[s]);
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TrueResidualShift[s] = cg.TrueResidual;
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CleanupTimer.Stop();
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}
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}
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std::cout << GridLogMessage << "ConjugateGradientMultiShiftMixedPrec: Time Breakdown for body"<<std::endl;
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std::cout << GridLogMessage << "\tElapsed " << SolverTimer.Elapsed() <<std::endl;
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std::cout << GridLogMessage << "\tAXPY " << AXPYTimer.Elapsed() <<std::endl;
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std::cout << GridLogMessage << "\tMatrix " << MatrixTimer.Elapsed() <<std::endl;
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std::cout << GridLogMessage << "\tShift " << ShiftTimer.Elapsed() <<std::endl;
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std::cout << GridLogMessage << "\tPrecision Change " << PrecChangeTimer.Elapsed() <<std::endl;
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std::cout << GridLogMessage << "\tFinal Cleanup " << CleanupTimer.Elapsed() <<std::endl;
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IterationsToComplete = k;
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return;
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}
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}
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// ugly hack
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std::cout<<GridLogMessage<<"CG multi shift did not converge"<<std::endl;
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// assert(0);
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}
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};
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NAMESPACE_END(Grid);
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#endif
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93
tests/solver/Test_dwf_multishift_mixedprec.cc
Normal file
93
tests/solver/Test_dwf_multishift_mixedprec.cc
Normal file
@@ -0,0 +1,93 @@
|
||||
/*************************************************************************************
|
||||
|
||||
Grid physics library, www.github.com/paboyle/Grid
|
||||
|
||||
Source file: ./tests/Test_dwf_multishift_mixedprec.cc
|
||||
|
||||
Copyright (C) 2015
|
||||
|
||||
Author: Christopher Kelly <ckelly@bnl.gov>
|
||||
|
||||
This program is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
This program is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License along
|
||||
with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
See the full license in the file "LICENSE" in the top level distribution directory
|
||||
*************************************************************************************/
|
||||
/* END LEGAL */
|
||||
#include <Grid/Grid.h>
|
||||
|
||||
using namespace Grid;
|
||||
|
||||
int main (int argc, char ** argv)
|
||||
{
|
||||
Grid_init(&argc, &argv);
|
||||
|
||||
const int Ls = 16;
|
||||
GridCartesian* UGrid_d = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(), GridDefaultSimd(Nd, vComplexD::Nsimd()), GridDefaultMpi());
|
||||
GridRedBlackCartesian* UrbGrid_d = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid_d);
|
||||
GridCartesian* FGrid_d = SpaceTimeGrid::makeFiveDimGrid(Ls, UGrid_d);
|
||||
GridRedBlackCartesian* FrbGrid_d = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls, UGrid_d);
|
||||
|
||||
GridCartesian* UGrid_f = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(), GridDefaultSimd(Nd, vComplexF::Nsimd()), GridDefaultMpi());
|
||||
GridRedBlackCartesian* UrbGrid_f = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid_f);
|
||||
GridCartesian* FGrid_f = SpaceTimeGrid::makeFiveDimGrid(Ls, UGrid_f);
|
||||
GridRedBlackCartesian* FrbGrid_f = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls, UGrid_f);
|
||||
|
||||
std::vector<int> seeds4({1, 2, 3, 4});
|
||||
std::vector<int> seeds5({5, 6, 7, 8});
|
||||
GridParallelRNG RNG5(FGrid_d);
|
||||
RNG5.SeedFixedIntegers(seeds5);
|
||||
GridParallelRNG RNG4(UGrid_d);
|
||||
RNG4.SeedFixedIntegers(seeds4);
|
||||
|
||||
LatticeFermionD src_d(FGrid_d);
|
||||
random(RNG5, src_d);
|
||||
|
||||
LatticeGaugeFieldD Umu_d(UGrid_d);
|
||||
SU<Nc>::HotConfiguration(RNG4, Umu_d);
|
||||
|
||||
LatticeGaugeFieldF Umu_f(UGrid_f);
|
||||
precisionChange(Umu_f, Umu_d);
|
||||
|
||||
std::cout << GridLogMessage << "Lattice dimensions: " << GridDefaultLatt() << " Ls: " << Ls << std::endl;
|
||||
|
||||
RealD mass = 0.01;
|
||||
RealD M5 = 1.8;
|
||||
DomainWallFermionD Ddwf_d(Umu_d, *FGrid_d, *FrbGrid_d, *UGrid_d, *UrbGrid_d, mass, M5);
|
||||
DomainWallFermionF Ddwf_f(Umu_f, *FGrid_f, *FrbGrid_f, *UGrid_f, *UrbGrid_f, mass, M5);
|
||||
|
||||
LatticeFermionD src_o_d(FrbGrid_d);
|
||||
pickCheckerboard(Odd, src_o_d, src_d);
|
||||
|
||||
SchurDiagMooeeOperator<DomainWallFermionD, LatticeFermionD> HermOpEO_d(Ddwf_d);
|
||||
SchurDiagMooeeOperator<DomainWallFermionF, LatticeFermionF> HermOpEO_f(Ddwf_f);
|
||||
|
||||
AlgRemez remez(1e-4, 64, 50);
|
||||
int order = 15;
|
||||
remez.generateApprox(order, 1, 2); //sqrt
|
||||
|
||||
MultiShiftFunction shifts(remez, 1e-10, false);
|
||||
|
||||
int relup_freq = 50;
|
||||
double t1=usecond();
|
||||
ConjugateGradientMultiShiftMixedPrec<LatticeFermionD,LatticeFermionF> mcg(10000, shifts, FrbGrid_f, HermOpEO_f, relup_freq);
|
||||
|
||||
std::vector<LatticeFermionD> results_o_d(order, FrbGrid_d);
|
||||
mcg(HermOpEO_d, src_o_d, results_o_d);
|
||||
double t2=usecond();
|
||||
|
||||
std::cout<<GridLogMessage << "Test: Total usec = "<< (t2-t1)<<std::endl;
|
||||
|
||||
Grid_finalize();
|
||||
}
|
||||
Reference in New Issue
Block a user