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Merge pull request #405 from giltirn/feature/dirichlet-gparity-stage
Import round 3
This commit is contained in:
Peter Boyle
GitHub
commit
9a9f4a111f
@ -855,7 +855,7 @@ void ExtractSliceLocal(Lattice<vobj> &lowDim,const Lattice<vobj> & higherDim,int
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template<class vobj>
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void Replicate(Lattice<vobj> &coarse,Lattice<vobj> & fine)
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void Replicate(const Lattice<vobj> &coarse,Lattice<vobj> & fine)
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{
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typedef typename vobj::scalar_object sobj;
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@ -69,6 +69,11 @@ public:
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return PeriodicBC::ShiftStaple(Link,mu);
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}
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//Same as Cshift for periodic BCs
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static inline GaugeLinkField CshiftLink(const GaugeLinkField &Link, int mu, int shift){
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return PeriodicBC::CshiftLink(Link,mu,shift);
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}
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static inline bool isPeriodicGaugeField(void) { return true; }
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};
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@ -110,6 +115,11 @@ public:
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return PeriodicBC::CovShiftBackward(Link, mu, field);
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}
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//If mu is a conjugate BC direction
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//Out(x) = U^dag_\mu(x-mu) | x_\mu != 0
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// = U^T_\mu(L-1) | x_\mu == 0
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//else
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//Out(x) = U^dag_\mu(x-mu mod L)
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static inline GaugeLinkField
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CovShiftIdentityBackward(const GaugeLinkField &Link, int mu)
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{
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@ -129,6 +139,13 @@ public:
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return PeriodicBC::CovShiftIdentityForward(Link,mu);
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}
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//If mu is a conjugate BC direction
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//Out(x) = S_\mu(x+mu) | x_\mu != L-1
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// = S*_\mu(x+mu) | x_\mu == L-1
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//else
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//Out(x) = S_\mu(x+mu mod L)
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//Note: While this is used for Staples it is also applicable for shifting gauge links or gauge transformation matrices
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static inline GaugeLinkField ShiftStaple(const GaugeLinkField &Link, int mu)
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{
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assert(_conjDirs.size() == Nd);
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@ -138,6 +155,27 @@ public:
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return PeriodicBC::ShiftStaple(Link,mu);
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}
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//Boundary-aware C-shift of gauge links / gauge transformation matrices
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//For conjugate BC direction
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//shift = 1
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//Out(x) = U_\mu(x+\hat\mu) | x_\mu != L-1
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// = U*_\mu(0) | x_\mu == L-1
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//shift = -1
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//Out(x) = U_\mu(x-mu) | x_\mu != 0
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// = U*_\mu(L-1) | x_\mu == 0
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//else
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//shift = 1
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//Out(x) = U_\mu(x+\hat\mu mod L)
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//shift = -1
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//Out(x) = U_\mu(x-\hat\mu mod L)
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static inline GaugeLinkField CshiftLink(const GaugeLinkField &Link, int mu, int shift){
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assert(_conjDirs.size() == Nd);
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if(_conjDirs[mu])
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return ConjugateBC::CshiftLink(Link,mu,shift);
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else
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return PeriodicBC::CshiftLink(Link,mu,shift);
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}
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static inline void setDirections(std::vector<int> &conjDirs) { _conjDirs=conjDirs; }
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static inline std::vector<int> getDirections(void) { return _conjDirs; }
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static inline bool isPeriodicGaugeField(void) { return false; }
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@ -88,6 +88,12 @@ namespace PeriodicBC {
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return CovShiftBackward(Link,mu,arg);
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}
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//Boundary-aware C-shift of gauge links / gauge transformation matrices
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template<class gauge> Lattice<gauge>
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CshiftLink(const Lattice<gauge> &Link, int mu, int shift)
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{
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return Cshift(Link, mu, shift);
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}
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}
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@ -158,6 +164,9 @@ namespace ConjugateBC {
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// std::cout<<"Gparity::CovCshiftBackward mu="<<mu<<std::endl;
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return Cshift(tmp,mu,-1);// moves towards positive mu
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}
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//Out(x) = U^dag_\mu(x-mu) | x_\mu != 0
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// = U^T_\mu(L-1) | x_\mu == 0
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template<class gauge> Lattice<gauge>
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CovShiftIdentityBackward(const Lattice<gauge> &Link, int mu) {
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GridBase *grid = Link.Grid();
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@ -176,6 +185,9 @@ namespace ConjugateBC {
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return Link;
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}
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//Out(x) = S_\mu(x+\hat\mu) | x_\mu != L-1
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// = S*_\mu(0) | x_\mu == L-1
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//Note: While this is used for Staples it is also applicable for shifting gauge links or gauge transformation matrices
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template<class gauge> Lattice<gauge>
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ShiftStaple(const Lattice<gauge> &Link, int mu)
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{
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@ -208,6 +220,35 @@ namespace ConjugateBC {
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return CovShiftBackward(Link,mu,arg);
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}
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//Boundary-aware C-shift of gauge links / gauge transformation matrices
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//shift = 1
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//Out(x) = U_\mu(x+\hat\mu) | x_\mu != L-1
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// = U*_\mu(0) | x_\mu == L-1
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//shift = -1
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//Out(x) = U_\mu(x-mu) | x_\mu != 0
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// = U*_\mu(L-1) | x_\mu == 0
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template<class gauge> Lattice<gauge>
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CshiftLink(const Lattice<gauge> &Link, int mu, int shift)
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{
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GridBase *grid = Link.Grid();
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int Lmu = grid->GlobalDimensions()[mu] - 1;
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Lattice<iScalar<vInteger>> coor(grid);
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LatticeCoordinate(coor, mu);
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Lattice<gauge> tmp(grid);
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if(shift == 1){
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tmp = Cshift(Link, mu, 1);
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tmp = where(coor == Lmu, conjugate(tmp), tmp);
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return tmp;
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}else if(shift == -1){
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tmp = Link;
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tmp = where(coor == Lmu, conjugate(tmp), tmp);
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return Cshift(tmp, mu, -1);
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}else assert(0 && "Invalid shift value");
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return tmp; //shuts up the compiler fussing about the return type
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}
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}
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@ -40,27 +40,46 @@ public:
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typedef typename Gimpl::GaugeLinkField GaugeMat;
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typedef typename Gimpl::GaugeField GaugeLorentz;
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static void GaugeLinkToLieAlgebraField(const std::vector<GaugeMat> &U,std::vector<GaugeMat> &A) {
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for(int mu=0;mu<Nd;mu++){
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Complex cmi(0.0,-1.0);
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A[mu] = Ta(U[mu]) * cmi;
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}
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//A_\mu(x) = -i Ta(U_\mu(x) ) where Ta(U) = 1/2( U - U^dag ) - 1/2N tr(U - U^dag) is the traceless antihermitian part. This is an O(A^3) approximation to the logarithm of U
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static void GaugeLinkToLieAlgebraField(const GaugeMat &U, GaugeMat &A) {
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Complex cmi(0.0,-1.0);
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A = Ta(U) * cmi;
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}
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static void DmuAmu(const std::vector<GaugeMat> &A,GaugeMat &dmuAmu,int orthog) {
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//The derivative of the Lie algebra field
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static void DmuAmu(const std::vector<GaugeMat> &U, GaugeMat &dmuAmu,int orthog) {
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GridBase* grid = U[0].Grid();
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GaugeMat Ax(grid);
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GaugeMat Axm1(grid);
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GaugeMat Utmp(grid);
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dmuAmu=Zero();
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for(int mu=0;mu<Nd;mu++){
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if ( mu != orthog ) {
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dmuAmu = dmuAmu + A[mu] - Cshift(A[mu],mu,-1);
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//Rather than define functionality to work out how the BCs apply to A_\mu we simply use the BC-aware Cshift to the gauge links and compute A_\mu(x) and A_\mu(x-1) separately
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//Ax = A_\mu(x)
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GaugeLinkToLieAlgebraField(U[mu], Ax);
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//Axm1 = A_\mu(x_\mu-1)
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Utmp = Gimpl::CshiftLink(U[mu], mu, -1);
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GaugeLinkToLieAlgebraField(Utmp, Axm1);
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//Derivative
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dmuAmu = dmuAmu + Ax - Axm1;
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}
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}
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}
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static void SteepestDescentGaugeFix(GaugeLorentz &Umu,Real & alpha,int maxiter,Real Omega_tol, Real Phi_tol,bool Fourier=false,int orthog=-1) {
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//Fix the gauge field Umu
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//0 < alpha < 1 is related to the step size, cf https://arxiv.org/pdf/1405.5812.pdf
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static void SteepestDescentGaugeFix(GaugeLorentz &Umu, Real alpha,int maxiter,Real Omega_tol, Real Phi_tol,bool Fourier=false,int orthog=-1) {
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GridBase *grid = Umu.Grid();
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GaugeMat xform(grid);
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SteepestDescentGaugeFix(Umu,xform,alpha,maxiter,Omega_tol,Phi_tol,Fourier,orthog);
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}
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static void SteepestDescentGaugeFix(GaugeLorentz &Umu,GaugeMat &xform,Real & alpha,int maxiter,Real Omega_tol, Real Phi_tol,bool Fourier=false,int orthog=-1) {
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//Fix the gauge field Umu and also return the gauge transformation from the original gauge field, xform
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static void SteepestDescentGaugeFix(GaugeLorentz &Umu,GaugeMat &xform, Real alpha,int maxiter,Real Omega_tol, Real Phi_tol,bool Fourier=false,int orthog=-1) {
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GridBase *grid = Umu.Grid();
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@ -122,27 +141,24 @@ public:
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}
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}
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assert(0 && "Gauge fixing did not converge within the specified number of iterations");
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};
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static Real SteepestDescentStep(std::vector<GaugeMat> &U,GaugeMat &xform,Real & alpha, GaugeMat & dmuAmu,int orthog) {
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static Real SteepestDescentStep(std::vector<GaugeMat> &U,GaugeMat &xform, Real alpha, GaugeMat & dmuAmu,int orthog) {
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GridBase *grid = U[0].Grid();
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std::vector<GaugeMat> A(Nd,grid);
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GaugeMat g(grid);
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GaugeLinkToLieAlgebraField(U,A);
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ExpiAlphaDmuAmu(A,g,alpha,dmuAmu,orthog);
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ExpiAlphaDmuAmu(U,g,alpha,dmuAmu,orthog);
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Real vol = grid->gSites();
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Real trG = TensorRemove(sum(trace(g))).real()/vol/Nc;
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xform = g*xform ;
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SU<Nc>::GaugeTransform(U,g);
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SU<Nc>::GaugeTransform<Gimpl>(U,g);
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return trG;
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}
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static Real FourierAccelSteepestDescentStep(std::vector<GaugeMat> &U,GaugeMat &xform,Real & alpha, GaugeMat & dmuAmu,int orthog) {
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static Real FourierAccelSteepestDescentStep(std::vector<GaugeMat> &U,GaugeMat &xform, Real alpha, GaugeMat & dmuAmu,int orthog) {
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GridBase *grid = U[0].Grid();
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@ -157,11 +173,7 @@ public:
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GaugeMat g(grid);
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GaugeMat dmuAmu_p(grid);
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std::vector<GaugeMat> A(Nd,grid);
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GaugeLinkToLieAlgebraField(U,A);
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DmuAmu(A,dmuAmu,orthog);
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DmuAmu(U,dmuAmu,orthog);
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std::vector<int> mask(Nd,1);
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for(int mu=0;mu<Nd;mu++) if (mu==orthog) mask[mu]=0;
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@ -205,16 +217,16 @@ public:
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Real trG = TensorRemove(sum(trace(g))).real()/vol/Nc;
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xform = g*xform ;
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SU<Nc>::GaugeTransform(U,g);
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SU<Nc>::GaugeTransform<Gimpl>(U,g);
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return trG;
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}
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static void ExpiAlphaDmuAmu(const std::vector<GaugeMat> &A,GaugeMat &g,Real & alpha, GaugeMat &dmuAmu,int orthog) {
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static void ExpiAlphaDmuAmu(const std::vector<GaugeMat> &U,GaugeMat &g, Real alpha, GaugeMat &dmuAmu,int orthog) {
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GridBase *grid = g.Grid();
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Complex cialpha(0.0,-alpha);
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GaugeMat ciadmam(grid);
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DmuAmu(A,dmuAmu,orthog);
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DmuAmu(U,dmuAmu,orthog);
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ciadmam = dmuAmu*cialpha;
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SU<Nc>::taExp(ciadmam,g);
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}
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@ -694,32 +694,32 @@ public:
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* Adjoint rep gauge xform
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*/
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template<typename GaugeField,typename GaugeMat>
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static void GaugeTransform( GaugeField &Umu, GaugeMat &g){
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template<typename Gimpl>
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static void GaugeTransform(typename Gimpl::GaugeField &Umu, typename Gimpl::GaugeLinkField &g){
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GridBase *grid = Umu.Grid();
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conformable(grid,g.Grid());
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GaugeMat U(grid);
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GaugeMat ag(grid); ag = adj(g);
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typename Gimpl::GaugeLinkField U(grid);
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typename Gimpl::GaugeLinkField ag(grid); ag = adj(g);
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for(int mu=0;mu<Nd;mu++){
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U= PeekIndex<LorentzIndex>(Umu,mu);
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U = g*U*Cshift(ag, mu, 1);
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U = g*U*Gimpl::CshiftLink(ag, mu, 1); //BC-aware
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PokeIndex<LorentzIndex>(Umu,U,mu);
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}
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}
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template<typename GaugeMat>
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static void GaugeTransform( std::vector<GaugeMat> &U, GaugeMat &g){
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template<typename Gimpl>
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static void GaugeTransform( std::vector<typename Gimpl::GaugeLinkField> &U, typename Gimpl::GaugeLinkField &g){
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GridBase *grid = g.Grid();
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GaugeMat ag(grid); ag = adj(g);
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typename Gimpl::GaugeLinkField ag(grid); ag = adj(g);
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for(int mu=0;mu<Nd;mu++){
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U[mu] = g*U[mu]*Cshift(ag, mu, 1);
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U[mu] = g*U[mu]*Gimpl::CshiftLink(ag, mu, 1); //BC-aware
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}
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}
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template<typename GaugeField,typename GaugeMat>
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static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu, GaugeMat &g){
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template<typename Gimpl>
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static void RandomGaugeTransform(GridParallelRNG &pRNG, typename Gimpl::GaugeField &Umu, typename Gimpl::GaugeLinkField &g){
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LieRandomize(pRNG,g,1.0);
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GaugeTransform(Umu,g);
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GaugeTransform<Gimpl>(Umu,g);
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}
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// Projects the algebra components a lattice matrix (of dimension ncol*ncol -1 )
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@ -125,6 +125,56 @@ public:
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return sumplaq / vol / faces / Nc; // Nd , Nc dependent... FIXME
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}
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//////////////////////////////////////////////////
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// sum over all spatial planes of plaquette
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//////////////////////////////////////////////////
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static void siteSpatialPlaquette(ComplexField &Plaq,
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const std::vector<GaugeMat> &U) {
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ComplexField sitePlaq(U[0].Grid());
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Plaq = Zero();
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for (int mu = 1; mu < Nd-1; mu++) {
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for (int nu = 0; nu < mu; nu++) {
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traceDirPlaquette(sitePlaq, U, mu, nu);
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Plaq = Plaq + sitePlaq;
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}
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}
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}
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////////////////////////////////////
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// sum over all x,y,z and over all spatial planes of plaquette
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//////////////////////////////////////////////////
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static std::vector<RealD> timesliceSumSpatialPlaquette(const GaugeLorentz &Umu) {
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std::vector<GaugeMat> U(Nd, Umu.Grid());
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// inefficient here
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for (int mu = 0; mu < Nd; mu++) {
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U[mu] = PeekIndex<LorentzIndex>(Umu, mu);
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}
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ComplexField Plaq(Umu.Grid());
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siteSpatialPlaquette(Plaq, U);
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typedef typename ComplexField::scalar_object sobj;
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std::vector<sobj> Tq;
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sliceSum(Plaq, Tq, Nd-1);
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std::vector<Real> out(Tq.size());
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for(int t=0;t<Tq.size();t++) out[t] = TensorRemove(Tq[t]).real();
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return out;
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}
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//////////////////////////////////////////////////
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// average over all x,y,z and over all spatial planes of plaquette
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//////////////////////////////////////////////////
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static std::vector<RealD> timesliceAvgSpatialPlaquette(const GaugeLorentz &Umu) {
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std::vector<RealD> sumplaq = timesliceSumSpatialPlaquette(Umu);
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int Lt = Umu.Grid()->FullDimensions()[Nd-1];
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assert(sumplaq.size() == Lt);
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double vol = Umu.Grid()->gSites() / Lt;
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double faces = (1.0 * (Nd - 1)* (Nd - 2)) / 2.0;
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for(int t=0;t<Lt;t++)
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sumplaq[t] = sumplaq[t] / vol / faces / Nc; // Nd , Nc dependent... FIXME
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return sumplaq;
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}
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//////////////////////////////////////////////////
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// average over all x,y,z the temporal loop
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@ -363,11 +413,11 @@ public:
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GaugeMat u = PeekIndex<LorentzIndex>(Umu, mu); // some redundant copies
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GaugeMat vu = v*u;
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//FS = 0.25*Ta(u*v + Cshift(vu, mu, -1));
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FS = (u*v + Cshift(vu, mu, -1));
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FS = (u*v + Gimpl::CshiftLink(vu, mu, -1));
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FS = 0.125*(FS - adj(FS));
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}
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static Real TopologicalCharge(GaugeLorentz &U){
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static Real TopologicalCharge(const GaugeLorentz &U){
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// 4d topological charge
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assert(Nd==4);
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// Bx = -iF(y,z), By = -iF(z,y), Bz = -iF(x,y)
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@ -390,6 +440,203 @@ public:
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}
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//Clover-leaf Wilson loop combination for arbitrary mu-extent M and nu extent N, mu >= nu
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//cf https://arxiv.org/pdf/hep-lat/9701012.pdf Eq 7 for 1x2 Wilson loop
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//Clockwise ordering
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static void CloverleafMxN(GaugeMat &FS, const GaugeMat &Umu, const GaugeMat &Unu, int mu, int nu, int M, int N){
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#define Fmu(A) Gimpl::CovShiftForward(Umu, mu, A)
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#define Bmu(A) Gimpl::CovShiftBackward(Umu, mu, A)
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#define Fnu(A) Gimpl::CovShiftForward(Unu, nu, A)
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#define Bnu(A) Gimpl::CovShiftBackward(Unu, nu, A)
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||||
#define FmuI Gimpl::CovShiftIdentityForward(Umu, mu)
|
||||
#define BmuI Gimpl::CovShiftIdentityBackward(Umu, mu)
|
||||
#define FnuI Gimpl::CovShiftIdentityForward(Unu, nu)
|
||||
#define BnuI Gimpl::CovShiftIdentityBackward(Unu, nu)
|
||||
|
||||
//Upper right loop
|
||||
GaugeMat tmp = BmuI;
|
||||
for(int i=1;i<M;i++)
|
||||
tmp = Bmu(tmp);
|
||||
for(int j=0;j<N;j++)
|
||||
tmp = Bnu(tmp);
|
||||
for(int i=0;i<M;i++)
|
||||
tmp = Fmu(tmp);
|
||||
for(int j=0;j<N;j++)
|
||||
tmp = Fnu(tmp);
|
||||
|
||||
FS = tmp;
|
||||
|
||||
//Upper left loop
|
||||
tmp = BnuI;
|
||||
for(int j=1;j<N;j++)
|
||||
tmp = Bnu(tmp);
|
||||
for(int i=0;i<M;i++)
|
||||
tmp = Fmu(tmp);
|
||||
for(int j=0;j<N;j++)
|
||||
tmp = Fnu(tmp);
|
||||
for(int i=0;i<M;i++)
|
||||
tmp = Bmu(tmp);
|
||||
|
||||
FS = FS + tmp;
|
||||
|
||||
//Lower right loop
|
||||
tmp = FnuI;
|
||||
for(int j=1;j<N;j++)
|
||||
tmp = Fnu(tmp);
|
||||
for(int i=0;i<M;i++)
|
||||
tmp = Bmu(tmp);
|
||||
for(int j=0;j<N;j++)
|
||||
tmp = Bnu(tmp);
|
||||
for(int i=0;i<M;i++)
|
||||
tmp = Fmu(tmp);
|
||||
|
||||
FS = FS + tmp;
|
||||
|
||||
//Lower left loop
|
||||
tmp = FmuI;
|
||||
for(int i=1;i<M;i++)
|
||||
tmp = Fmu(tmp);
|
||||
for(int j=0;j<N;j++)
|
||||
tmp = Fnu(tmp);
|
||||
for(int i=0;i<M;i++)
|
||||
tmp = Bmu(tmp);
|
||||
for(int j=0;j<N;j++)
|
||||
tmp = Bnu(tmp);
|
||||
|
||||
FS = FS + tmp;
|
||||
|
||||
#undef Fmu
|
||||
#undef Bmu
|
||||
#undef Fnu
|
||||
#undef Bnu
|
||||
#undef FmuI
|
||||
#undef BmuI
|
||||
#undef FnuI
|
||||
#undef BnuI
|
||||
}
|
||||
|
||||
//Field strength from MxN Wilson loop
|
||||
//Note F_numu = - F_munu
|
||||
static void FieldStrengthMxN(GaugeMat &FS, const GaugeLorentz &U, int mu, int nu, int M, int N){
|
||||
GaugeMat Umu = PeekIndex<LorentzIndex>(U, mu);
|
||||
GaugeMat Unu = PeekIndex<LorentzIndex>(U, nu);
|
||||
if(M == N){
|
||||
GaugeMat F(Umu.Grid());
|
||||
CloverleafMxN(F, Umu, Unu, mu, nu, M, N);
|
||||
FS = 0.125 * ( F - adj(F) );
|
||||
}else{
|
||||
//Average over both orientations
|
||||
GaugeMat horizontal(Umu.Grid()), vertical(Umu.Grid());
|
||||
CloverleafMxN(horizontal, Umu, Unu, mu, nu, M, N);
|
||||
CloverleafMxN(vertical, Umu, Unu, mu, nu, N, M);
|
||||
FS = 0.0625 * ( horizontal - adj(horizontal) + vertical - adj(vertical) );
|
||||
}
|
||||
}
|
||||
|
||||
//Topological charge contribution from MxN Wilson loops
|
||||
//cf https://arxiv.org/pdf/hep-lat/9701012.pdf Eq 6
|
||||
//output is the charge by timeslice: sum over timeslices to obtain the total
|
||||
static std::vector<Real> TimesliceTopologicalChargeMxN(const GaugeLorentz &U, int M, int N){
|
||||
assert(Nd == 4);
|
||||
std::vector<std::vector<GaugeMat*> > F(Nd,std::vector<GaugeMat*>(Nd,nullptr));
|
||||
//Note F_numu = - F_munu
|
||||
//hence we only need to loop over mu,nu,rho,sigma that aren't related by permuting mu,nu or rho,sigma
|
||||
//Use nu > mu
|
||||
for(int mu=0;mu<Nd-1;mu++){
|
||||
for(int nu=mu+1; nu<Nd; nu++){
|
||||
F[mu][nu] = new GaugeMat(U.Grid());
|
||||
FieldStrengthMxN(*F[mu][nu], U, mu, nu, M, N);
|
||||
}
|
||||
}
|
||||
Real coeff = -1./(32 * M_PI*M_PI * M*M * N*N); //overall sign to match CPS and Grid conventions, possibly related to time direction = 3 vs 0
|
||||
|
||||
static const int combs[3][4] = { {0,1,2,3}, {0,2,1,3}, {0,3,1,2} };
|
||||
static const int signs[3] = { 1, -1, 1 }; //epsilon_{mu nu rho sigma}
|
||||
|
||||
ComplexField fsum(U.Grid());
|
||||
fsum = Zero();
|
||||
for(int c=0;c<3;c++){
|
||||
int mu = combs[c][0], nu = combs[c][1], rho = combs[c][2], sigma = combs[c][3];
|
||||
int eps = signs[c];
|
||||
fsum = fsum + (8. * coeff * eps) * trace( (*F[mu][nu]) * (*F[rho][sigma]) );
|
||||
}
|
||||
|
||||
for(int mu=0;mu<Nd-1;mu++)
|
||||
for(int nu=mu+1; nu<Nd; nu++)
|
||||
delete F[mu][nu];
|
||||
|
||||
typedef typename ComplexField::scalar_object sobj;
|
||||
std::vector<sobj> Tq;
|
||||
sliceSum(fsum, Tq, Nd-1);
|
||||
|
||||
std::vector<Real> out(Tq.size());
|
||||
for(int t=0;t<Tq.size();t++) out[t] = TensorRemove(Tq[t]).real();
|
||||
return out;
|
||||
}
|
||||
static Real TopologicalChargeMxN(const GaugeLorentz &U, int M, int N){
|
||||
std::vector<Real> Tq = TimesliceTopologicalChargeMxN(U,M,N);
|
||||
Real out(0);
|
||||
for(int t=0;t<Tq.size();t++) out += Tq[t];
|
||||
return out;
|
||||
}
|
||||
|
||||
//Generate the contributions to the 5Li topological charge from Wilson loops of the following sizes
|
||||
//Use coefficients from hep-lat/9701012
|
||||
//1x1 : c1=(19.-55.*c5)/9.
|
||||
//2x2 : c2=(1-64.*c5)/9.
|
||||
//1x2 : c3=(-64.+640.*c5)/45.
|
||||
//1x3 : c4=1./5.-2.*c5
|
||||
//3x3 : c5=1./20.
|
||||
//Output array outer index contains the loops in the above order
|
||||
//Inner index is the time coordinate
|
||||
static std::vector<std::vector<Real> > TimesliceTopologicalCharge5LiContributions(const GaugeLorentz &U){
|
||||
static const int exts[5][2] = { {1,1}, {2,2}, {1,2}, {1,3}, {3,3} };
|
||||
std::vector<std::vector<Real> > out(5);
|
||||
for(int i=0;i<5;i++){
|
||||
out[i] = TimesliceTopologicalChargeMxN(U,exts[i][0],exts[i][1]);
|
||||
}
|
||||
return out;
|
||||
}
|
||||
|
||||
static std::vector<Real> TopologicalCharge5LiContributions(const GaugeLorentz &U){
|
||||
static const int exts[5][2] = { {1,1}, {2,2}, {1,2}, {1,3}, {3,3} };
|
||||
std::vector<Real> out(5);
|
||||
std::cout << GridLogMessage << "Computing topological charge" << std::endl;
|
||||
for(int i=0;i<5;i++){
|
||||
out[i] = TopologicalChargeMxN(U,exts[i][0],exts[i][1]);
|
||||
std::cout << GridLogMessage << exts[i][0] << "x" << exts[i][1] << " Wilson loop contribution " << out[i] << std::endl;
|
||||
}
|
||||
return out;
|
||||
}
|
||||
|
||||
//Compute the 5Li topological charge
|
||||
static std::vector<Real> TimesliceTopologicalCharge5Li(const GaugeLorentz &U){
|
||||
std::vector<std::vector<Real> > loops = TimesliceTopologicalCharge5LiContributions(U);
|
||||
|
||||
double c5=1./20.;
|
||||
double c4=1./5.-2.*c5;
|
||||
double c3=(-64.+640.*c5)/45.;
|
||||
double c2=(1-64.*c5)/9.;
|
||||
double c1=(19.-55.*c5)/9.;
|
||||
|
||||
int Lt = loops[0].size();
|
||||
std::vector<Real> out(Lt,0.);
|
||||
for(int t=0;t<Lt;t++)
|
||||
out[t] += c1*loops[0][t] + c2*loops[1][t] + c3*loops[2][t] + c4*loops[3][t] + c5*loops[4][t];
|
||||
return out;
|
||||
}
|
||||
|
||||
static Real TopologicalCharge5Li(const GaugeLorentz &U){
|
||||
std::vector<Real> Qt = TimesliceTopologicalCharge5Li(U);
|
||||
Real Q = 0.;
|
||||
for(int t=0;t<Qt.size();t++) Q += Qt[t];
|
||||
std::cout << GridLogMessage << "5Li Topological charge: " << Q << std::endl;
|
||||
return Q;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
//////////////////////////////////////////////////////
|
||||
// Similar to above for rectangle is required
|
||||
//////////////////////////////////////////////////////
|
||||
|
||||
@ -324,7 +324,7 @@ int main(int argc, char ** argv)
|
||||
|
||||
U_GT = U;
|
||||
// Make a random xform to teh gauge field
|
||||
SU<Nc>::RandomGaugeTransform(RNG,U_GT,g); // Unit gauge
|
||||
SU<Nc>::RandomGaugeTransform<PeriodicGimplR>(RNG,U_GT,g); // Unit gauge
|
||||
|
||||
Field in_GT(&Grid);
|
||||
Field out_GT(&Grid);
|
||||
|
||||
@ -29,14 +29,10 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
|
||||
#include <Grid/Grid.h>
|
||||
|
||||
using namespace Grid;
|
||||
;
|
||||
|
||||
int main (int argc, char ** argv)
|
||||
{
|
||||
template<typename Gimpl>
|
||||
void run(double alpha, bool do_fft_gfix){
|
||||
std::vector<int> seeds({1,2,3,4});
|
||||
|
||||
Grid_init(&argc,&argv);
|
||||
|
||||
int threads = GridThread::GetThreads();
|
||||
|
||||
Coordinate latt_size = GridDefaultLatt();
|
||||
@ -55,10 +51,7 @@ int main (int argc, char ** argv)
|
||||
FFT theFFT(&GRID);
|
||||
|
||||
std::cout<<GridLogMessage << "Grid is setup to use "<<threads<<" threads"<<std::endl;
|
||||
|
||||
std::cout<< "*****************************************************************" <<std::endl;
|
||||
std::cout<< "* Testing we can gauge fix steep descent a RGT of Unit gauge *" <<std::endl;
|
||||
std::cout<< "*****************************************************************" <<std::endl;
|
||||
std::cout<<GridLogMessage << "Using alpha=" << alpha << std::endl;
|
||||
|
||||
// int coulomb_dir = -1;
|
||||
int coulomb_dir = Nd-1;
|
||||
@ -72,81 +65,167 @@ int main (int argc, char ** argv)
|
||||
LatticeColourMatrix xform1(&GRID); // Gauge xform
|
||||
LatticeColourMatrix xform2(&GRID); // Gauge xform
|
||||
LatticeColourMatrix xform3(&GRID); // Gauge xform
|
||||
|
||||
//#########################################################################################
|
||||
|
||||
std::cout<< "*********************************************************************************************************" <<std::endl;
|
||||
std::cout<< "* Testing steepest descent fixing to Landau gauge with randomly transformed unit gauge configuration *" <<std::endl;
|
||||
std::cout<< "*********************************************************************************************************" <<std::endl;
|
||||
|
||||
SU<Nc>::ColdConfiguration(pRNG,Umu); // Unit gauge
|
||||
Uorg=Umu;
|
||||
|
||||
Real init_plaq=WilsonLoops<Gimpl>::avgPlaquette(Umu);
|
||||
std::cout << " Initial plaquette "<< init_plaq << std::endl;
|
||||
|
||||
//Apply a random gauge transformation to the unit gauge config
|
||||
Urnd=Umu;
|
||||
SU<Nc>::RandomGaugeTransform<Gimpl>(pRNG,Urnd,g);
|
||||
|
||||
SU<Nc>::RandomGaugeTransform(pRNG,Urnd,g); // Unit gauge
|
||||
|
||||
Real plaq=WilsonLoops<PeriodicGimplR>::avgPlaquette(Umu);
|
||||
std::cout << " Initial plaquette "<<plaq << std::endl;
|
||||
|
||||
Real alpha=0.1;
|
||||
|
||||
//Gauge fix the randomly transformed field
|
||||
Umu = Urnd;
|
||||
FourierAcceleratedGaugeFixer<PeriodicGimplR>::SteepestDescentGaugeFix(Umu,xform1,alpha,10000,1.0e-12, 1.0e-12,false);
|
||||
FourierAcceleratedGaugeFixer<Gimpl>::SteepestDescentGaugeFix(Umu,xform1,alpha,10000,1.0e-12, 1.0e-12,false);
|
||||
|
||||
// Check the gauge xform matrices
|
||||
Utmp=Urnd;
|
||||
SU<Nc>::GaugeTransform(Utmp,xform1);
|
||||
SU<Nc>::GaugeTransform<Gimpl>(Utmp,xform1);
|
||||
Utmp = Utmp - Umu;
|
||||
std::cout << " Norm Difference of xformed gauge "<< norm2(Utmp) << std::endl;
|
||||
std::cout << " Check the output gauge transformation matrices applied to the original field produce the xformed field "<< norm2(Utmp) << " (expect 0)" << std::endl;
|
||||
|
||||
|
||||
plaq=WilsonLoops<PeriodicGimplR>::avgPlaquette(Umu);
|
||||
std::cout << " Final plaquette "<<plaq << std::endl;
|
||||
Real plaq=WilsonLoops<Gimpl>::avgPlaquette(Umu);
|
||||
std::cout << " Final plaquette "<<plaq << " diff " << plaq - init_plaq << " (expect 0)" << std::endl;
|
||||
|
||||
Uorg = Uorg - Umu;
|
||||
std::cout << " Norm Difference "<< norm2(Uorg) << std::endl;
|
||||
std::cout << " Norm "<< norm2(Umu) << std::endl;
|
||||
std::cout << " Norm difference between a unit gauge configuration and the gauge fixed configuration "<< norm2(Uorg) << " (expect 0)" << std::endl;
|
||||
std::cout << " Norm of gauge fixed configuration "<< norm2(Umu) << std::endl;
|
||||
|
||||
//#########################################################################################
|
||||
if(do_fft_gfix){
|
||||
std::cout<< "*************************************************************************************" <<std::endl;
|
||||
std::cout<< "* Testing Fourier accelerated fixing to Landau gauge with unit gauge configuration *" <<std::endl;
|
||||
std::cout<< "*************************************************************************************" <<std::endl;
|
||||
Umu=Urnd;
|
||||
FourierAcceleratedGaugeFixer<Gimpl>::SteepestDescentGaugeFix(Umu,xform2,alpha,10000,1.0e-12, 1.0e-12,true);
|
||||
|
||||
Utmp=Urnd;
|
||||
SU<Nc>::GaugeTransform<Gimpl>(Utmp,xform2);
|
||||
Utmp = Utmp - Umu;
|
||||
std::cout << " Check the output gauge transformation matrices applied to the original field produce the xformed field "<< norm2(Utmp) << " (expect 0)" << std::endl;
|
||||
|
||||
|
||||
std::cout<< "*****************************************************************" <<std::endl;
|
||||
std::cout<< "* Testing Fourier accelerated fixing *" <<std::endl;
|
||||
std::cout<< "*****************************************************************" <<std::endl;
|
||||
Umu=Urnd;
|
||||
FourierAcceleratedGaugeFixer<PeriodicGimplR>::SteepestDescentGaugeFix(Umu,xform2,alpha,10000,1.0e-12, 1.0e-12,true);
|
||||
plaq=WilsonLoops<Gimpl>::avgPlaquette(Umu);
|
||||
std::cout << " Final plaquette "<<plaq << " diff " << plaq - init_plaq << " (expect 0)" << std::endl;
|
||||
}
|
||||
//#########################################################################################
|
||||
|
||||
Utmp=Urnd;
|
||||
SU<Nc>::GaugeTransform(Utmp,xform2);
|
||||
Utmp = Utmp - Umu;
|
||||
std::cout << " Norm Difference of xformed gauge "<< norm2(Utmp) << std::endl;
|
||||
std::cout<< "******************************************************************************************" <<std::endl;
|
||||
std::cout<< "* Testing steepest descent fixing to Landau gauge with random configuration **" <<std::endl;
|
||||
std::cout<< "******************************************************************************************" <<std::endl;
|
||||
|
||||
SU<Nc>::HotConfiguration(pRNG,Umu);
|
||||
|
||||
plaq=WilsonLoops<PeriodicGimplR>::avgPlaquette(Umu);
|
||||
std::cout << " Final plaquette "<<plaq << std::endl;
|
||||
init_plaq=WilsonLoops<Gimpl>::avgPlaquette(Umu);
|
||||
std::cout << " Initial plaquette "<< init_plaq << std::endl;
|
||||
|
||||
std::cout<< "*****************************************************************" <<std::endl;
|
||||
std::cout<< "* Testing non-unit configuration *" <<std::endl;
|
||||
std::cout<< "*****************************************************************" <<std::endl;
|
||||
FourierAcceleratedGaugeFixer<Gimpl>::SteepestDescentGaugeFix(Umu,alpha,10000,1.0e-12, 1.0e-12,false);
|
||||
|
||||
SU<Nc>::HotConfiguration(pRNG,Umu); // Unit gauge
|
||||
plaq=WilsonLoops<Gimpl>::avgPlaquette(Umu);
|
||||
std::cout << " Final plaquette "<<plaq << " diff " << plaq - init_plaq << " (expect 0)" << std::endl;
|
||||
|
||||
plaq=WilsonLoops<PeriodicGimplR>::avgPlaquette(Umu);
|
||||
std::cout << " Initial plaquette "<<plaq << std::endl;
|
||||
//#########################################################################################
|
||||
if(do_fft_gfix){
|
||||
std::cout<< "******************************************************************************************" <<std::endl;
|
||||
std::cout<< "* Testing Fourier accelerated fixing to Landau gauge with random configuration **" <<std::endl;
|
||||
std::cout<< "******************************************************************************************" <<std::endl;
|
||||
|
||||
FourierAcceleratedGaugeFixer<PeriodicGimplR>::SteepestDescentGaugeFix(Umu,alpha,10000,1.0e-12, 1.0e-12,true);
|
||||
SU<Nc>::HotConfiguration(pRNG,Umu);
|
||||
|
||||
plaq=WilsonLoops<PeriodicGimplR>::avgPlaquette(Umu);
|
||||
std::cout << " Final plaquette "<<plaq << std::endl;
|
||||
init_plaq=WilsonLoops<Gimpl>::avgPlaquette(Umu);
|
||||
std::cout << " Initial plaquette "<< init_plaq << std::endl;
|
||||
|
||||
std::cout<< "*****************************************************************" <<std::endl;
|
||||
std::cout<< "* Testing Fourier accelerated fixing to coulomb gauge *" <<std::endl;
|
||||
std::cout<< "*****************************************************************" <<std::endl;
|
||||
FourierAcceleratedGaugeFixer<Gimpl>::SteepestDescentGaugeFix(Umu,alpha,10000,1.0e-12, 1.0e-12,true);
|
||||
|
||||
plaq=WilsonLoops<Gimpl>::avgPlaquette(Umu);
|
||||
std::cout << " Final plaquette "<<plaq << " diff " << plaq - init_plaq << " (expect 0)" << std::endl;
|
||||
}
|
||||
//#########################################################################################
|
||||
|
||||
std::cout<< "*******************************************************************************************" <<std::endl;
|
||||
std::cout<< "* Testing steepest descent fixing to coulomb gauge with random configuration *" <<std::endl;
|
||||
std::cout<< "*******************************************************************************************" <<std::endl;
|
||||
|
||||
Umu=Urnd;
|
||||
SU<Nc>::HotConfiguration(pRNG,Umu); // Unit gauge
|
||||
SU<Nc>::HotConfiguration(pRNG,Umu);
|
||||
|
||||
plaq=WilsonLoops<PeriodicGimplR>::avgPlaquette(Umu);
|
||||
std::cout << " Initial plaquette "<<plaq << std::endl;
|
||||
init_plaq=WilsonLoops<Gimpl>::avgPlaquette(Umu);
|
||||
std::cout << " Initial plaquette "<< init_plaq << std::endl;
|
||||
|
||||
FourierAcceleratedGaugeFixer<PeriodicGimplR>::SteepestDescentGaugeFix(Umu,xform3,alpha,10000,1.0e-12, 1.0e-12,true,coulomb_dir);
|
||||
FourierAcceleratedGaugeFixer<Gimpl>::SteepestDescentGaugeFix(Umu,xform3,alpha,10000,1.0e-12, 1.0e-12,false,coulomb_dir);
|
||||
|
||||
std::cout << Umu<<std::endl;
|
||||
plaq=WilsonLoops<Gimpl>::avgPlaquette(Umu);
|
||||
std::cout << " Final plaquette "<<plaq << " diff " << plaq - init_plaq << " (expect 0)" << std::endl;
|
||||
|
||||
plaq=WilsonLoops<PeriodicGimplR>::avgPlaquette(Umu);
|
||||
std::cout << " Final plaquette "<<plaq << std::endl;
|
||||
|
||||
//#########################################################################################
|
||||
if(do_fft_gfix){
|
||||
std::cout<< "*******************************************************************************************" <<std::endl;
|
||||
std::cout<< "* Testing Fourier accelerated fixing to coulomb gauge with random configuration *" <<std::endl;
|
||||
std::cout<< "*******************************************************************************************" <<std::endl;
|
||||
|
||||
Umu=Urnd;
|
||||
SU<Nc>::HotConfiguration(pRNG,Umu);
|
||||
|
||||
init_plaq=WilsonLoops<Gimpl>::avgPlaquette(Umu);
|
||||
std::cout << " Initial plaquette "<< init_plaq << std::endl;
|
||||
|
||||
FourierAcceleratedGaugeFixer<Gimpl>::SteepestDescentGaugeFix(Umu,xform3,alpha,10000,1.0e-12, 1.0e-12,true,coulomb_dir);
|
||||
|
||||
plaq=WilsonLoops<Gimpl>::avgPlaquette(Umu);
|
||||
std::cout << " Final plaquette "<<plaq << " diff " << plaq - init_plaq << " (expect 0)" << std::endl;
|
||||
}
|
||||
}
|
||||
|
||||
int main (int argc, char ** argv)
|
||||
{
|
||||
Grid_init(&argc,&argv);
|
||||
|
||||
double alpha=0.1; //step size
|
||||
std::string gimpl = "periodic";
|
||||
bool do_fft_gfix = true; //test fourier transformed gfix as well as steepest descent
|
||||
for(int i=1;i<argc;i++){
|
||||
std::string sarg(argv[i]);
|
||||
if(sarg == "--gimpl"){
|
||||
assert(i<argc-1 && "--gimpl option requires an argument");
|
||||
gimpl = argv[i+1];
|
||||
if(gimpl != "periodic" && gimpl != "conjugate")
|
||||
assert(0 && "Invalid gimpl");
|
||||
if(gimpl == "conjugate")
|
||||
alpha = 0.025; //default alpha too large for CCBC
|
||||
}else if(sarg == "--no-fft-gfix"){
|
||||
std::cout << "Not doing the Fourier accelerated gauge fixing tests" << std::endl;
|
||||
do_fft_gfix = false;
|
||||
}else if(sarg == "--alpha"){
|
||||
assert(i<argc-1 && "--alpha option requires an argument");
|
||||
std::istringstream ss(argv[i+1]); ss >> alpha;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
if(gimpl == "periodic"){
|
||||
std::cout << GridLogMessage << "Using periodic boundary condition" << std::endl;
|
||||
run<PeriodicGimplR>(alpha, do_fft_gfix);
|
||||
}else{
|
||||
std::vector<int> conjdirs = {1,1,0,0}; //test with 2 conjugate dirs and 2 not
|
||||
std::cout << GridLogMessage << "Using complex conjugate boundary conditions in dimensions ";
|
||||
for(int i=0;i<Nd;i++)
|
||||
if(conjdirs[i])
|
||||
std::cout << i << " ";
|
||||
std::cout << std::endl;
|
||||
|
||||
ConjugateGimplR::setDirections(conjdirs);
|
||||
run<ConjugateGimplR>(alpha, do_fft_gfix);
|
||||
}
|
||||
|
||||
Grid_finalize();
|
||||
}
|
||||
|
||||
@ -228,6 +228,59 @@ void checkGammaL(const Gamma::Algebra a, GridSerialRNG &rng)
|
||||
std::cout << std::endl;
|
||||
}
|
||||
|
||||
void checkChargeConjMatrix(){
|
||||
//Check the properties of the charge conjugation matrix
|
||||
//In the Grid basis C = -\gamma^2 \gamma^4
|
||||
SpinMatrix C = testAlgebra[Gamma::Algebra::MinusGammaY] * testAlgebra[Gamma::Algebra::GammaT];
|
||||
SpinMatrix mC = -C;
|
||||
SpinMatrix one = testAlgebra[Gamma::Algebra::Identity];
|
||||
|
||||
std::cout << "Testing properties of charge conjugation matrix C = -\\gamma^2 \\gamma^4 (in Grid's basis)" << std::endl;
|
||||
|
||||
//C^T = -C
|
||||
SpinMatrix Ct = transpose(C);
|
||||
std::cout << GridLogMessage << "C^T=-C ";
|
||||
test(Ct, mC);
|
||||
std::cout << std::endl;
|
||||
|
||||
//C^\dagger = -C
|
||||
SpinMatrix Cdag = adj(C);
|
||||
std::cout << GridLogMessage << "C^dag=-C ";
|
||||
test(Cdag, mC);
|
||||
std::cout << std::endl;
|
||||
|
||||
//C^* = C
|
||||
SpinMatrix Cstar = conjugate(C);
|
||||
std::cout << GridLogMessage << "C^*=C ";
|
||||
test(Cstar, C);
|
||||
std::cout << std::endl;
|
||||
|
||||
//C^{-1} = -C
|
||||
SpinMatrix CinvC = mC * C;
|
||||
std::cout << GridLogMessage << "C^{-1}=-C ";
|
||||
test(CinvC, one);
|
||||
std::cout << std::endl;
|
||||
|
||||
// C^{-1} \gamma^\mu C = -[\gamma^\mu]^T
|
||||
Gamma::Algebra gmu_a[4] = { Gamma::Algebra::GammaX, Gamma::Algebra::GammaY, Gamma::Algebra::GammaZ, Gamma::Algebra::GammaT };
|
||||
for(int mu=0;mu<4;mu++){
|
||||
SpinMatrix gmu = testAlgebra[gmu_a[mu]];
|
||||
SpinMatrix Cinv_gmu_C = mC * gmu * C;
|
||||
SpinMatrix mgmu_T = -transpose(gmu);
|
||||
std::cout << GridLogMessage << "C^{-1} \\gamma^" << mu << " C = -[\\gamma^" << mu << "]^T ";
|
||||
test(Cinv_gmu_C, mgmu_T);
|
||||
std::cout << std::endl;
|
||||
}
|
||||
|
||||
//[C, \gamma^5] = 0
|
||||
SpinMatrix Cg5 = C * testAlgebra[Gamma::Algebra::Gamma5];
|
||||
SpinMatrix g5C = testAlgebra[Gamma::Algebra::Gamma5] * C;
|
||||
std::cout << GridLogMessage << "C \\gamma^5 = \\gamma^5 C";
|
||||
test(Cg5, g5C);
|
||||
std::cout << std::endl;
|
||||
}
|
||||
|
||||
|
||||
int main(int argc, char *argv[])
|
||||
{
|
||||
Grid_init(&argc,&argv);
|
||||
@ -270,6 +323,13 @@ int main(int argc, char *argv[])
|
||||
{
|
||||
checkGammaL(i, sRNG);
|
||||
}
|
||||
|
||||
std::cout << GridLogMessage << "======== Charge conjugation matrix check" << std::endl;
|
||||
checkChargeConjMatrix();
|
||||
std::cout << GridLogMessage << std::endl;
|
||||
|
||||
|
||||
|
||||
|
||||
Grid_finalize();
|
||||
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user