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209 lines
6.3 KiB
C++
209 lines
6.3 KiB
C++
/*************************************************************************************
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Grid physics library, www.github.com/paboyle/Grid
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Source file: ./lib/qcd/action/scalar/CovariantLaplacian.h
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Copyright (C) 2016
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Author: Guido Cossu <guido.cossu@ed.ac.uk>
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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 COVARIANT_LAPLACIAN_H
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#define COVARIANT_LAPLACIAN_H
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namespace Grid {
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namespace QCD {
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struct LaplacianParams : Serializable {
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GRID_SERIALIZABLE_CLASS_MEMBERS(LaplacianParams,
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RealD, lo,
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RealD, hi,
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int, MaxIter,
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RealD, tolerance,
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int, degree,
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int, precision);
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// constructor
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LaplacianParams(RealD lo = 0.0,
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RealD hi = 1.0,
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int maxit = 1000,
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RealD tol = 1.0e-8,
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int degree = 10,
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int precision = 64)
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: lo(lo),
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hi(hi),
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MaxIter(maxit),
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tolerance(tol),
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degree(degree),
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precision(precision){};
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};
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////////////////////////////////////////////////////////////
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// Laplacian operator L on adjoint fields
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//
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// phi: adjoint field
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// L: D_mu^dag D_mu
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//
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// L phi(x) = Sum_mu [ U_mu(x)phi(x+mu)U_mu(x)^dag +
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// U_mu(x-mu)^dag phi(x-mu)U_mu(x-mu)
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// -2phi(x)]
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//
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// Operator designed to be encapsulated by
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// an HermitianLinearOperator<.. , ..>
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////////////////////////////////////////////////////////////
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template <class Impl>
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class LaplacianAdjointField: public Metric<typename Impl::Field> {
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OperatorFunction<typename Impl::Field> &Solver;
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LaplacianParams param;
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MultiShiftFunction PowerNegHalf;
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public:
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INHERIT_GIMPL_TYPES(Impl);
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LaplacianAdjointField(GridBase* grid, OperatorFunction<GaugeField>& S, LaplacianParams& p, const RealD k = 1.0)
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: U(Nd, grid), Solver(S), param(p), kappa(k){
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AlgRemez remez(param.lo,param.hi,param.precision);
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std::cout<<GridLogMessage << "Generating degree "<<param.degree<<" for x^(1/2)"<<std::endl;
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remez.generateApprox(param.degree,1,2);
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PowerNegHalf.Init(remez,param.tolerance,true);
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};
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void ImportGauge(const GaugeField& _U) {
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for (int mu = 0; mu < Nd; mu++) {
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U[mu] = PeekIndex<LorentzIndex>(_U, mu);
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}
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}
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void M(const GaugeField& in, GaugeField& out) {
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GaugeLinkField tmp(in._grid);
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GaugeLinkField tmp2(in._grid);
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GaugeLinkField sum(in._grid);
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for (int nu = 0; nu < Nd; nu++) {
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sum = zero;
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GaugeLinkField in_nu = PeekIndex<LorentzIndex>(in, nu);
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GaugeLinkField out_nu(out._grid);
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for (int mu = 0; mu < Nd; mu++) {
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tmp = U[mu] * Cshift(in_nu, mu, +1) * adj(U[mu]);
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tmp2 = adj(U[mu]) * in_nu * U[mu];
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sum += tmp + Cshift(tmp2, mu, -1) - 2.0 * in_nu;
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}
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out_nu = (1.0 - kappa) * in_nu - kappa / (double(4 * Nd)) * sum;
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PokeIndex<LorentzIndex>(out, out_nu, nu);
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}
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}
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void MDeriv(const GaugeField& in, GaugeField& der, bool dag) {
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RealD factor = -kappa / (double(4 * Nd));
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for (int mu = 0; mu < Nd; mu++) {
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GaugeLinkField in_mu = PeekIndex<LorentzIndex>(in, mu);
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GaugeLinkField der_mu(der._grid);
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if (!dag)
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der_mu =
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factor * Cshift(in_mu, mu, +1) * adj(U[mu]) + adj(U[mu]) * in_mu;
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else
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der_mu = factor * U[mu] * Cshift(in_mu, mu, +1) + in_mu * U[mu];
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}
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}
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void Minv(const GaugeField& in, GaugeField& inverted){
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HermitianLinearOperator<LaplacianAdjointField<Impl>,GaugeField> HermOp(*this);
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Solver(HermOp, in, inverted);
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}
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void MInvSquareRoot(GaugeField& P){
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// Takes a gaussian gauge field and multiplies by the metric
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// need the rational approximation for the square root
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GaugeField Gp(P._grid);
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HermitianLinearOperator<LaplacianAdjointField<Impl>,GaugeField> HermOp(*this);
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ConjugateGradientMultiShift<GaugeField> msCG(param.MaxIter,PowerNegHalf);
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msCG(HermOp,P,Gp);
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P = Gp; // now P has the correct distribution
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}
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private:
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RealD kappa;
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std::vector<GaugeLinkField> U;
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};
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// This is just for debuggin purposes
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// not meant to be used by the final users
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template <class Impl>
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class LaplacianAlgebraField {
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public:
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INHERIT_GIMPL_TYPES(Impl);
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typedef SU<Nc>::LatticeAlgebraVector AVector;
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LaplacianAlgebraField(GridBase* grid, const RealD k) :
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U(Nd, grid), kappa(k){};
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void ImportGauge(const GaugeField& _U) {
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for (int mu = 0; mu < Nd; mu++) {
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U[mu] = PeekIndex<LorentzIndex>(_U, mu);
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}
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}
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void Mdiag(const AVector& in, AVector& out) { assert(0); }
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void Mdir(const AVector& in, AVector& out, int dir, int disp) { assert(0); }
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// Operator with algebra vector inputs and outputs
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void M(const AVector& in, AVector& out) {
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GaugeLinkField tmp(in._grid);
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GaugeLinkField tmp2(in._grid);
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GaugeLinkField sum(in._grid);
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GaugeLinkField out_mat(in._grid);
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GaugeLinkField in_mat(in._grid);
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// Reconstruct matrix
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SU<Nc>::FundamentalLieAlgebraMatrix(in, in_mat);
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sum = zero;
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for (int mu = 0; mu < Nd; mu++) {
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tmp = U[mu] * Cshift(in_mat, mu, +1) * adj(U[mu]);
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tmp2 = adj(U[mu]) * in_mat * U[mu];
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sum += tmp + Cshift(tmp2, mu, -1) - 2.0 * in_mat;
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}
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out_mat = (1.0 - kappa) * in_mat - kappa / (double(4 * Nd)) * sum;
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// Project
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SU<Nc>::projectOnAlgebra(out, out_mat);
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}
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private:
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RealD kappa;
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std::vector<GaugeLinkField> U;
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};
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}
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}
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#endif
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