Added support for FFT accelerated updates

lib/qcd/action/scalar/ScalarImpl.h

@@ -89,6 +89,10 @@ class ScalarImplTypes {
 
   };
 
+
+  #define USE_FFT_ACCELERATION
+
+
   template <class S, unsigned int N>
   class ScalarAdjMatrixImplTypes {
   public:
@@ -109,18 +113,113 @@ class ScalarImplTypes {
     typedef Field                FermionField;
     typedef Field                PropagatorField;
 
+
+    static void MomentaSquare(ComplexField& out){
+      GridBase           *grid = out._grid;
+      const std::vector<int>   &l    = grid->FullDimensions();
+      ComplexField              kmu(grid);
+      
+      for(int mu = 0; mu < grid->Nd(); mu++)
+      {
+        Real twoPiL = M_PI*2.0/l[mu];
+        LatticeCoordinate(kmu,mu);
+        kmu = 2.0*sin(0.5*twoPiL*kmu);
+        out += kmu*kmu;
+      }
+    }
+
+    static void MomentumSpacePropagator(ComplexField &out, RealD m)
+    {
+      GridBase           *grid = out._grid;
+      ComplexField one(grid); one = Complex(1.0,0.0);
+      out = m*m;
+      MomentaSquare(out);
+      out = one/out;
+    }
+
+
     static inline void generate_momenta(Field& P, GridParallelRNG& pRNG) {
+      #ifndef USE_FFT_ACCELERATION
       Group::GaussianFundamentalLieAlgebraMatrix(pRNG, P);
+      #else
+      
+      Field Ptmp(P._grid), Pp(P._grid);
+      Group::GaussianFundamentalLieAlgebraMatrix(pRNG, Ptmp);
+      // if we change the mass I need a renormalization here
+      // transform and multiply by (M*M+p*p)^-1
+      GridCartesian *Grid = dynamic_cast<GridCartesian*>(P._grid);
+      FFT theFFT(Grid);
+      ComplexField p2(Grid);
+      RealD M = 1.0;
+      p2= zero;
+
+      theFFT.FFT_all_dim(Pp,Ptmp,FFT::forward);
+      MomentaSquare(p2);
+      p2 += M*M;
+      p2 = sqrt(p2);
+      Pp *= p2;
+      theFFT.FFT_all_dim(P,Pp,FFT::backward);
+      
+      #endif //USE_FFT_ACCELERATION
     }
 
     static inline Field projectForce(Field& P) {return P;}
 
     static inline void update_field(Field& P, Field& U, double ep) {
+      #ifndef USE_FFT_ACCELERATION
       U += P*ep;
+      #else
+      // Here we can eventually add the Fourier acceleration
+      // FFT transform P(x) -> P(p)
+      // divide by (M^2+p^2)  M external parameter (how to pass?)
+      // P'(p) = P(p)/(M^2+p^2)
+      // Transform back -> P'(x)
+      // U += P'(x)*ep
+      
+      // the dynamic cast is safe
+      GridCartesian *Grid = dynamic_cast<GridCartesian*>(U._grid);
+      FFT theFFT(Grid);
+      Field Pp(Grid), Pnew(Grid);
+      std::vector<int> full_dim = Grid->FullDimensions();
+
+      theFFT.FFT_all_dim(Pp,P,FFT::forward);
+      RealD M = 1.0;  
+      static bool first_call = true;
+      static ComplexField p2(Grid);
+      if (first_call){
+      MomentumSpacePropagator(p2,M);
+      first_call = false;
+      }
+      Pp *= p2;
+      theFFT.FFT_all_dim(Pnew,Pp,FFT::backward);     
+      U += Pnew * ep;
+      
+      #endif //USE_FFT_ACCELERATION
     }
 
-    static inline RealD FieldSquareNorm(Field& U) {
+    static inline RealD FieldSquareNorm(Field &U)
+    {
+      #ifndef USE_FFT_ACCELERATION
       return (TensorRemove(sum(trace(U*U))).real());
+      #else
+      // In case of Fourier acceleration we have to:
+      // compute U(p)*U(p)/(M^2+p^2))   Parseval theorem
+      // 1 FFT needed U(x) -> U(p)
+      // M to be passed
+      
+      GridCartesian *Grid = dynamic_cast<GridCartesian *>(U._grid);
+      FFT theFFT(Grid);
+      Field Up(Grid), Utilde(Grid);
+      std::vector<int> full_dim = Grid->FullDimensions();
+      
+      theFFT.FFT_all_dim(Up, U, FFT::forward);
+      RealD M = 1.0;  
+      ComplexField p2(Grid);
+      MomentumSpacePropagator(p2,M);
+      Field Up2 = Up*p2; 
+      // from the definition of the DFT we need to divide by the volume
+      return (-TensorRemove(sum(trace(adj(Up)*Up2))).real()/U._grid->gSites());
+      #endif //USE_FFT_ACCELERATION
     }
 
     static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U) {