Plaq plus rectangle and Iwasaki, Symanzik DBW2.

http://arxiv.org/pdf/hep-lat/0610075.pdf plaq and rect regress plausibly over 100 trajectories
and under HMC with average plaq and rectangle coming out ok.

lib/qcd/action/gauge/PlaqPlusRectangleAction.h

@@ -0,0 +1,98 @@
+#ifndef QCD_PLAQ_PLUS_RECTANGLE_ACTION_H
+#define QCD_PLAQ_PLUS_RECTANGLE_ACTION_H
+
+namespace Grid{
+  namespace QCD{
+    
+    ////////////////////////////////////////////////////////////////////////
+    // PlaqPlusRectangleActoin
+    ////////////////////////////////////////////////////////////////////////
+    template<class GaugeField>
+    class PlaqPlusRectangleAction : public Action<GaugeField> {
+    public:
+
+      typedef LorentzScalar<GaugeField> GaugeLinkField;
+
+    private:
+      RealD c_plaq;
+      RealD c_rect;
+
+    public:
+    PlaqPlusRectangleAction(RealD b,RealD c): c_plaq(b),c_rect(c){};
+      
+      virtual void refresh(const GaugeField &U, GridParallelRNG& pRNG) {}; // noop as no pseudoferms
+      
+      virtual RealD S(const GaugeField &U) {
+	RealD vol = U._grid->gSites();
+
+	RealD plaq = WilsonLoops<GaugeField>::avgPlaquette(U);
+	RealD rect = WilsonLoops<GaugeField>::avgRectangle(U);
+
+	RealD action=c_plaq*(1.0 -plaq)*(Nd*(Nd-1.0))*vol*0.5
+	            +c_rect*(1.0 -rect)*(Nd*(Nd-1.0))*vol;
+
+	return action;
+      };
+
+      virtual void deriv(const GaugeField &U,GaugeField & dSdU) {
+	//extend Ta to include Lorentz indexes
+	RealD factor_p = c_plaq/RealD(Nc)*0.5;
+	RealD factor_r =   c_rect/RealD(Nc)*0.5;
+
+	GaugeLinkField Umu(U._grid);
+	GaugeLinkField dSdU_mu(U._grid);
+	GaugeLinkField staple(U._grid);
+	for (int mu=0; mu < Nd; mu++){
+
+	  Umu = PeekIndex<LorentzIndex>(U,mu);
+
+	  // Staple in direction mu
+	  WilsonLoops<GaugeField>::Staple(staple,U,mu);
+	  dSdU_mu = Ta(Umu*staple)*factor_p;
+	  
+	  WilsonLoops<GaugeField>::RectStaple(staple,U,mu);
+	  dSdU_mu = dSdU_mu + Ta(Umu*staple)*factor_r;
+	  
+	  PokeIndex<LorentzIndex>(dSdU, dSdU_mu, mu);
+
+	}
+      };
+    };
+
+    // Convenience for common physically defined cases.
+    //
+    // RBC c1 parameterisation is not really RBC but don't have good
+    // reference and we are happy to change name if prior use of this plaq coeff
+    // parameterisation is made known to us. 
+    template<class GaugeField>
+    class RBCGaugeAction : public PlaqPlusRectangleAction<GaugeField> {
+    public:
+      RBCGaugeAction(RealD beta,RealD c1) : PlaqPlusRectangleAction<GaugeField>(beta*(1.0-8.0*c1), beta*c1) {
+      };
+    };
+
+    template<class GaugeField>
+    class IwasakiGaugeAction : public RBCGaugeAction<GaugeField> {
+    public:
+      IwasakiGaugeAction(RealD beta) : RBCGaugeAction<GaugeField>(beta,-0.331) {
+      };
+    };
+
+    template<class GaugeField>
+    class SymanzikGaugeAction : public RBCGaugeAction<GaugeField> {
+    public:
+      SymanzikGaugeAction(RealD beta) : RBCGaugeAction<GaugeField>(beta,-1.0/12.0) {
+      };
+    };
+
+    template<class GaugeField>
+    class DBW2GaugeAction : public RBCGaugeAction<GaugeField> {
+    public:
+      DBW2GaugeAction(RealD beta) : RBCGaugeAction<GaugeField>(beta,-1.4067) {
+      };
+    };
+
+  }
+}
+
+#endif