mirror of
https://github.com/paboyle/Grid.git
synced 2025-11-04 05:54:32 +00:00
multishift conjugate gradient added and a strong test: take a diagonal
but non-identity matrix l1 0 0 0 .... 0 l2 0 0 .... 0 0 l3 0 ... . . . . . . . . . And apply the multishift CG to it. Sum the poles and residues. Insist that this be the same as the exactly taken square root where l1,l2,l3 >= 0.
This commit is contained in:
Azusa Yamaguchi
@@ -4,13 +4,16 @@
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#include <algorithms/SparseMatrix.h>
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#include <algorithms/LinearOperator.h>
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#include <algorithms/approx/Zolotarev.h>
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#include <algorithms/approx/Chebyshev.h>
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#include <algorithms/approx/Remez.h>
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#include <algorithms/approx/MultiShiftFunction.h>
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#include <algorithms/iterative/ConjugateGradient.h>
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#include <algorithms/iterative/NormalEquations.h>
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#include <algorithms/iterative/SchurRedBlack.h>
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#include <algorithms/approx/Zolotarev.h>
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#include <algorithms/approx/Chebyshev.h>
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#include <algorithms/approx/Remez.h>
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#include <algorithms/iterative/ConjugateGradientMultiShift.h>
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// Eigen/lanczos
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// EigCg
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@@ -1,4 +1,4 @@
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HFILES=./algorithms/approx/bigfloat.h ./algorithms/approx/bigfloat_double.h ./algorithms/approx/Chebyshev.h ./algorithms/approx/Remez.h ./algorithms/approx/Zolotarev.h ./algorithms/iterative/ConjugateGradient.h ./algorithms/iterative/NormalEquations.h ./algorithms/iterative/SchurRedBlack.h ./algorithms/LinearOperator.h ./algorithms/SparseMatrix.h ./Algorithms.h ./AlignedAllocator.h ./cartesian/Cartesian_base.h ./cartesian/Cartesian_full.h ./cartesian/Cartesian_red_black.h ./Cartesian.h ./communicator/Communicator_base.h ./Communicator.h ./Comparison.h ./cshift/Cshift_common.h ./cshift/Cshift_mpi.h ./cshift/Cshift_none.h ./Cshift.h ./Grid.h ./GridConfig.h ./lattice/Lattice_arith.h ./lattice/Lattice_base.h ./lattice/Lattice_comparison.h ./lattice/Lattice_conformable.h ./lattice/Lattice_coordinate.h ./lattice/Lattice_ET.h ./lattice/Lattice_local.h ./lattice/Lattice_overload.h ./lattice/Lattice_peekpoke.h ./lattice/Lattice_reality.h ./lattice/Lattice_reduction.h ./lattice/Lattice_rng.h ./lattice/Lattice_trace.h ./lattice/Lattice_transfer.h ./lattice/Lattice_transpose.h ./lattice/Lattice_where.h ./Lattice.h ./parallelIO/NerscIO.h ./qcd/action/Actions.h ./qcd/action/fermion/CayleyFermion5D.h ./qcd/action/fermion/ContinuedFractionFermion5D.h ./qcd/action/fermion/DomainWallFermion.h ./qcd/action/fermion/FermionOperator.h ./qcd/action/fermion/MobiusFermion.h ./qcd/action/fermion/MobiusZolotarevFermion.h ./qcd/action/fermion/OverlapWilsonCayleyTanhFermion.h ./qcd/action/fermion/OverlapWilsonCayleyZolotarevFermion.h ./qcd/action/fermion/OverlapWilsonContfracTanhFermion.h ./qcd/action/fermion/OverlapWilsonContfracZolotarevFermion.h ./qcd/action/fermion/OverlapWilsonPartialFractionTanhFermion.h ./qcd/action/fermion/OverlapWilsonPartialFractionZolotarevFermion.h ./qcd/action/fermion/PartialFractionFermion5D.h ./qcd/action/fermion/ScaledShamirFermion.h ./qcd/action/fermion/ShamirZolotarevFermion.h ./qcd/action/fermion/WilsonCompressor.h ./qcd/action/fermion/WilsonFermion.h ./qcd/action/fermion/WilsonFermion5D.h ./qcd/action/fermion/WilsonKernels.h ./qcd/action/gauge/GaugeActionBase.h ./qcd/action/gauge/WilsonGaugeAction.h ./qcd/Dirac.h ./qcd/LinalgUtils.h ./qcd/QCD.h ./qcd/SpaceTimeGrid.h ./qcd/TwoSpinor.h ./qcd/utils/CovariantCshift.h ./qcd/utils/WilsonLoops.h ./simd/Grid_avx.h ./simd/Grid_avx512.h ./simd/Grid_qpx.h ./simd/Grid_sse4.h ./simd/Grid_vector_types.h ./simd/Old/Grid_vComplexD.h ./simd/Old/Grid_vComplexF.h ./simd/Old/Grid_vInteger.h ./simd/Old/Grid_vRealD.h ./simd/Old/Grid_vRealF.h ./Simd.h ./stencil/Lebesgue.h ./Stencil.h ./tensors/Tensor_arith.h ./tensors/Tensor_arith_add.h ./tensors/Tensor_arith_mac.h ./tensors/Tensor_arith_mul.h ./tensors/Tensor_arith_scalar.h ./tensors/Tensor_arith_sub.h ./tensors/Tensor_class.h ./tensors/Tensor_extract_merge.h ./tensors/Tensor_inner.h ./tensors/Tensor_outer.h ./tensors/Tensor_peek.h ./tensors/Tensor_poke.h ./tensors/Tensor_reality.h ./tensors/Tensor_Ta.h ./tensors/Tensor_trace.h ./tensors/Tensor_traits.h ./tensors/Tensor_transpose.h ./Tensors.h ./Threads.h
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HFILES=./algorithms/approx/bigfloat.h ./algorithms/approx/bigfloat_double.h ./algorithms/approx/Chebyshev.h ./algorithms/approx/MultiShiftFunction.h ./algorithms/approx/Remez.h ./algorithms/approx/Zolotarev.h ./algorithms/iterative/ConjugateGradient.h ./algorithms/iterative/ConjugateGradientMultiShift.h ./algorithms/iterative/NormalEquations.h ./algorithms/iterative/SchurRedBlack.h ./algorithms/LinearOperator.h ./algorithms/SparseMatrix.h ./Algorithms.h ./AlignedAllocator.h ./cartesian/Cartesian_base.h ./cartesian/Cartesian_full.h ./cartesian/Cartesian_red_black.h ./Cartesian.h ./communicator/Communicator_base.h ./Communicator.h ./Comparison.h ./cshift/Cshift_common.h ./cshift/Cshift_mpi.h ./cshift/Cshift_none.h ./Cshift.h ./Grid.h ./GridConfig.h ./lattice/Lattice_arith.h ./lattice/Lattice_base.h ./lattice/Lattice_comparison.h ./lattice/Lattice_conformable.h ./lattice/Lattice_coordinate.h ./lattice/Lattice_ET.h ./lattice/Lattice_local.h ./lattice/Lattice_overload.h ./lattice/Lattice_peekpoke.h ./lattice/Lattice_reality.h ./lattice/Lattice_reduction.h ./lattice/Lattice_rng.h ./lattice/Lattice_trace.h ./lattice/Lattice_transfer.h ./lattice/Lattice_transpose.h ./lattice/Lattice_where.h ./Lattice.h ./parallelIO/NerscIO.h ./qcd/action/Actions.h ./qcd/action/fermion/CayleyFermion5D.h ./qcd/action/fermion/ContinuedFractionFermion5D.h ./qcd/action/fermion/DomainWallFermion.h ./qcd/action/fermion/FermionOperator.h ./qcd/action/fermion/MobiusFermion.h ./qcd/action/fermion/MobiusZolotarevFermion.h ./qcd/action/fermion/OverlapWilsonCayleyTanhFermion.h ./qcd/action/fermion/OverlapWilsonCayleyZolotarevFermion.h ./qcd/action/fermion/OverlapWilsonContfracTanhFermion.h ./qcd/action/fermion/OverlapWilsonContfracZolotarevFermion.h ./qcd/action/fermion/OverlapWilsonPartialFractionTanhFermion.h ./qcd/action/fermion/OverlapWilsonPartialFractionZolotarevFermion.h ./qcd/action/fermion/PartialFractionFermion5D.h ./qcd/action/fermion/ScaledShamirFermion.h ./qcd/action/fermion/ShamirZolotarevFermion.h ./qcd/action/fermion/WilsonCompressor.h ./qcd/action/fermion/WilsonFermion.h ./qcd/action/fermion/WilsonFermion5D.h ./qcd/action/fermion/WilsonKernels.h ./qcd/action/gauge/GaugeActionBase.h ./qcd/action/gauge/WilsonGaugeAction.h ./qcd/Dirac.h ./qcd/LinalgUtils.h ./qcd/QCD.h ./qcd/SpaceTimeGrid.h ./qcd/TwoSpinor.h ./qcd/utils/CovariantCshift.h ./qcd/utils/WilsonLoops.h ./simd/Grid_avx.h ./simd/Grid_avx512.h ./simd/Grid_qpx.h ./simd/Grid_sse4.h ./simd/Grid_vector_types.h ./simd/Old/Grid_vComplexD.h ./simd/Old/Grid_vComplexF.h ./simd/Old/Grid_vInteger.h ./simd/Old/Grid_vRealD.h ./simd/Old/Grid_vRealF.h ./Simd.h ./stencil/Lebesgue.h ./Stencil.h ./tensors/Tensor_arith.h ./tensors/Tensor_arith_add.h ./tensors/Tensor_arith_mac.h ./tensors/Tensor_arith_mul.h ./tensors/Tensor_arith_scalar.h ./tensors/Tensor_arith_sub.h ./tensors/Tensor_class.h ./tensors/Tensor_extract_merge.h ./tensors/Tensor_inner.h ./tensors/Tensor_outer.h ./tensors/Tensor_peek.h ./tensors/Tensor_poke.h ./tensors/Tensor_reality.h ./tensors/Tensor_Ta.h ./tensors/Tensor_trace.h ./tensors/Tensor_traits.h ./tensors/Tensor_transpose.h ./Tensors.h ./Threads.h
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CCFILES=./algorithms/approx/Remez.cc ./algorithms/approx/Zolotarev.cc ./GridInit.cc ./qcd/action/fermion/CayleyFermion5D.cc ./qcd/action/fermion/ContinuedFractionFermion5D.cc ./qcd/action/fermion/PartialFractionFermion5D.cc ./qcd/action/fermion/WilsonFermion.cc ./qcd/action/fermion/WilsonFermion5D.cc ./qcd/action/fermion/WilsonKernels.cc ./qcd/action/fermion/WilsonKernelsHand.cc ./qcd/Dirac.cc ./qcd/SpaceTimeGrid.cc ./stencil/Lebesgue.cc ./stencil/Stencil_common.cc
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CCFILES=./algorithms/approx/MultiShiftFunction.cc ./algorithms/approx/Remez.cc ./algorithms/approx/Zolotarev.cc ./GridInit.cc ./qcd/action/fermion/CayleyFermion5D.cc ./qcd/action/fermion/ContinuedFractionFermion5D.cc ./qcd/action/fermion/PartialFractionFermion5D.cc ./qcd/action/fermion/WilsonFermion.cc ./qcd/action/fermion/WilsonFermion5D.cc ./qcd/action/fermion/WilsonKernels.cc ./qcd/action/fermion/WilsonKernelsHand.cc ./qcd/Dirac.cc ./qcd/SpaceTimeGrid.cc ./stencil/Lebesgue.cc ./stencil/Stencil_common.cc
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@@ -167,6 +167,14 @@ namespace Grid {
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virtual void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) = 0;
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};
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/////////////////////////////////////////////////////////////
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// Base classes for Multishift solvers for operators
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/////////////////////////////////////////////////////////////
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template<class Field> class OperatorMultiFunction {
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public:
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virtual void operator() (LinearOperatorBase<Field> &Linop, const Field &in, std::vector<Field> &out) = 0;
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};
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// FIXME : To think about
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// Chroma functionality list defining LinearOperator
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29
lib/algorithms/approx/MultiShiftFunction.cc
Normal file
29
lib/algorithms/approx/MultiShiftFunction.cc
Normal file
@@ -0,0 +1,29 @@
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#include <Grid.h>
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namespace Grid {
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double MultiShiftFunction::approx(double x)
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{
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double a = norm;
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for(int n=0;n<poles.size();n++){
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a = a + residues[n]/(x+poles[n]);
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}
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return a;
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}
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void MultiShiftFunction::gnuplot(std::ostream &out)
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{
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out<<"f(x) = "<<norm<<"";
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for(int n=0;n<poles.size();n++){
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out<<"+("<<residues[n]<<"/(x+"<<poles[n]<<"))";
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}
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out<<";"<<std::endl;
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}
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void MultiShiftFunction::csv(std::ostream &out)
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{
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for (double x=lo; x<hi; x*=1.05) {
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double f = approx(x);
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double r = sqrt(x);
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out<< x<<","<<r<<","<<f<<","<<r-f<<std::endl;
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}
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return;
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}
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}
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28
lib/algorithms/approx/MultiShiftFunction.h
Normal file
28
lib/algorithms/approx/MultiShiftFunction.h
Normal file
@@ -0,0 +1,28 @@
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#ifndef MULTI_SHIFT_FUNCTION
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#define MULTI_SHIFT_FUNCTION
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namespace Grid {
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class MultiShiftFunction {
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public:
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int order;
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std::vector<RealD> poles;
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std::vector<RealD> residues;
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std::vector<RealD> tolerances;
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RealD norm;
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RealD lo,hi;
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MultiShiftFunction(int n,RealD _lo,RealD _hi): poles(n), residues(n), lo(_lo), hi(_hi) {;};
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RealD approx(RealD x);
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void csv(std::ostream &out);
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void gnuplot(std::ostream &out);
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MultiShiftFunction(AlgRemez & remez,double tol,bool inverse) :
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order(remez.getDegree()),
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tolerances(remez.getDegree(),tol),
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poles(remez.getDegree()),
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residues(remez.getDegree())
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{
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remez.getBounds(lo,hi);
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if ( inverse ) remez.getIPFE (&residues[0],&poles[0],&norm);
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else remez.getPFE (&residues[0],&poles[0],&norm);
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}
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};
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}
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#endif
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@@ -125,8 +125,17 @@ class AlgRemez
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// Destructor
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virtual ~AlgRemez();
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int getDegree(void){
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assert(n==d);
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return n;
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}
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// Reset the bounds of the approximation
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void setBounds(double lower, double upper);
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// Reset the bounds of the approximation
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void getBounds(double &lower, double &upper) {
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lower=(double)apstrt;
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upper=(double)apend;
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}
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// Generate the rational approximation x^(pnum/pden)
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double generateApprox(int num_degree, int den_degree,
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250
lib/algorithms/iterative/ConjugateGradientMultiShift.h
Normal file
250
lib/algorithms/iterative/ConjugateGradientMultiShift.h
Normal file
@@ -0,0 +1,250 @@
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#ifndef GRID_CONJUGATE_MULTI_SHIFT_GRADIENT_H
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#define GRID_CONJUGATE_MULTI_SHIFT_GRADIENT_H
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namespace Grid {
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/////////////////////////////////////////////////////////////
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// Base classes for iterative processes based on operators
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// single input vec, single output vec.
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/////////////////////////////////////////////////////////////
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template<class Field>
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class ConjugateGradientMultiShift : public OperatorMultiFunction<Field>,
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public OperatorFunction<Field>
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{
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public:
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RealD Tolerance;
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Integer MaxIterations;
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int verbose;
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MultiShiftFunction shifts;
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ConjugateGradientMultiShift(Integer maxit,MultiShiftFunction &_shifts) :
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MaxIterations(maxit),
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shifts(_shifts)
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{
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verbose=1;
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}
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void operator() (LinearOperatorBase<Field> &Linop, const Field &src, Field &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<Field> results(nshift,grid);
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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<Field> &Linop, const Field &src, std::vector<Field> &psi)
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{
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GridBase *grid = src._grid;
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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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std::vector<Field> ps(nshift,grid);// Search directions
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assert(psi.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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Field r(grid);
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Field p(grid);
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Field tmp(grid);
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Field mmp(grid);
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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);
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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<<"ConjugateGradientMultiShift: shift "<<s
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<<" target resid "<<rsq[s]<<std::endl;
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ps[s] = src;
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}
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// r and p for primary
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r=src;
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p=src;
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//MdagM+m[0]
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Linop.HermOpAndNorm(p,mmp,d,qq);
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axpy(mmp,mass[0],p,mmp);
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RealD rn = norm2(p);
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d += rn*mass[0];
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// have verified that inner product of
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// p and mmp is equal to d after this since
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// the d computation is tricky
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// qq = real(innerProduct(p,mmp));
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// std::cout << "debug equal ? qq "<<qq<<" d "<< d<<std::endl;
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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,b,mmp,r);
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for(int s=0;s<nshift;s++) {
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axpby(psi[s],0.,-bs[s]*alpha[s],src,src);
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}
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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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axpy(p,a,p,r);
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// Note to self - direction ps is iterated seperately
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// for each shift. Does not appear to have any scope
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// for avoiding linear algebra in "single" case.
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//
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// However SAME r is used. Could load "r" and update
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// ALL ps[s]. 2/3 Bandwidth saving
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// New Kernel: Load r, vector of coeffs, vector of pointers ps
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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[s],a,ps[s],r);
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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[s],z[s][iz],as,r,ps[s]);
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}
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}
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}
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cp=c;
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Linop.HermOpAndNorm(p,mmp,d,qq);
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axpy(mmp,mass[0],p,mmp);
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RealD rn = norm2(p);
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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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c=axpy_norm(r,b,mmp,r);
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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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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));
|
||||
bs[s] = b*z[s][iz]/z0; // NB sign rel to Mike
|
||||
}
|
||||
}
|
||||
|
||||
for(int s=0;s<nshift;s++){
|
||||
int ss = s;
|
||||
// Scope for optimisation here in case of "single".
|
||||
// Could load psi[0] and pull all ps[s] in.
|
||||
// if ( single ) ss=primary;
|
||||
// Bandwith saving in single case is Ls * 3 -> 2+Ls, so ~ 3x saving
|
||||
// Pipelined CG gain:
|
||||
//
|
||||
// New Kernel: Load r, vector of coeffs, vector of pointers ps
|
||||
// New Kernel: Load psi[0], vector of coeffs, vector of pointers ps
|
||||
// If can predict the coefficient bs then we can fuse these and avoid write reread cyce
|
||||
// on ps[s].
|
||||
// Before: 3 x npole + 3 x npole
|
||||
// After : 2 x npole (ps[s]) => 3x speed up of multishift CG.
|
||||
|
||||
if( (!converged[s]) ) {
|
||||
axpy(psi[ss],-bs[s]*alpha[s],ps[s],psi[ss]);
|
||||
}
|
||||
}
|
||||
|
||||
// Convergence checks
|
||||
int all_converged = 1;
|
||||
for(int s=0;s<nshift;s++){
|
||||
|
||||
if ( (!converged[s]) ){
|
||||
|
||||
RealD css = c * z[s][iz]* z[s][iz];
|
||||
|
||||
if(css<rsq[s]){
|
||||
if ( ! converged[s] )
|
||||
std::cout<<"ConjugateGradientMultiShift k="<<k<<" Shift "<<s<<" has converged"<<std::endl;
|
||||
converged[s]=1;
|
||||
} else {
|
||||
all_converged=0;
|
||||
}
|
||||
|
||||
}
|
||||
}
|
||||
|
||||
if ( all_converged ){
|
||||
|
||||
std::cout<< "CGMultiShift: All shifts have converged iteration "<<k<<std::endl;
|
||||
std::cout<< "CGMultiShift: Checking solutions"<<std::endl;
|
||||
|
||||
// Check answers
|
||||
for(int s=0; s < nshift; s++) {
|
||||
Linop.HermOpAndNorm(psi[s],mmp,d,qq);
|
||||
axpy(tmp,mass[s],psi[s],mmp);
|
||||
axpy(r,-alpha[s],src,tmp);
|
||||
RealD rn = norm2(r);
|
||||
RealD cn = norm2(src);
|
||||
std::cout<<"CGMultiShift: shift["<<s<<"] true residual "<<std::sqrt(rn/cn)<<std::endl;
|
||||
}
|
||||
return;
|
||||
}
|
||||
}
|
||||
// ugly hack
|
||||
std::cout<<"CG multi shift did not converge"<<std::endl;
|
||||
assert(0);
|
||||
}
|
||||
|
||||
};
|
||||
}
|
||||
#endif
|
||||
Reference in New Issue
Block a user