From ae0873bc77222ba48f3f6edc71621a56a43e8551 Mon Sep 17 00:00:00 2001
From: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
Date: Sun, 14 Jun 2015 01:28:54 +0100
Subject: [PATCH] First cut at SUN support for quenched updates

---
 lib/qcd/utils/SUn.h | 414 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 414 insertions(+)
 create mode 100644 lib/qcd/utils/SUn.h

diff --git a/lib/qcd/utils/SUn.h b/lib/qcd/utils/SUn.h
new file mode 100644
index 00000000..3a8b5f4d
--- /dev/null
+++ b/lib/qcd/utils/SUn.h
@@ -0,0 +1,414 @@
+#ifndef QCD_UTIL_SUN_H
+#define QCD_UTIL_SUN_H
+
+
+namespace Grid {
+  namespace QCD {
+
+template<int ncolour>
+class SU {
+public:
+
+  static int generators(void)   { return ncolour*ncolour-1; }
+  static int su2subgroups(void) { return (ncolour*(ncolour-1))/2; }
+
+  template<typename vtype> using iSUnMatrix              = iScalar<iScalar<iMatrix<vtype, ncolour> > > ;
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+  // Types can be accessed as SU<2>::Matrix , SU<2>::vSUnMatrix, SU<2>::LatticeMatrix etc...
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+  typedef iSUnMatrix<Complex>         Matrix;
+  typedef iSUnMatrix<ComplexF>        MatrixF;
+  typedef iSUnMatrix<ComplexD>        MatrixD;
+
+  typedef iSUnMatrix<vComplex>       vMatrix;
+  typedef iSUnMatrix<vComplexF>      vMatrixF;
+  typedef iSUnMatrix<vComplexD>      vMatrixD;
+
+  typedef Lattice<vMatrix>     LatticeMatrix;
+  typedef Lattice<vMatrixF>    LatticeMatrixF;
+  typedef Lattice<vMatrixD>    LatticeMatrixD;
+
+  ////////////////////////////////////////////////////////////////////////
+  // There are N^2-1 generators for SU(N).
+  //
+  // We take a traceless hermitian generator basis as follows
+  //
+  // * Normalisation: trace ta tb = 1/2 delta_ab
+  // 
+  // * Off diagonal
+  //    - pairs of rows i1,i2 behaving like pauli matrices signma_x, sigma_y
+  //     
+  //    - there are (Nc-1-i1) slots for i2 on each row [ x  0  x ]                                   
+  //      direct count off each row                                                                    
+  //
+  //    - Sum of all pairs is Nc(Nc-1)/2: proof arithmetic series
+  //
+  //      (Nc-1) + (Nc-2)+...  1      ==> Nc*(Nc-1)/2 
+  //      1+ 2+          +   + Nc-1                        
+  // 
+  //    - There are 2 x Nc (Nc-1)/ 2 of these = Nc^2 - Nc
+  //
+  //    - We enumerate the row-col pairs.
+  //    - for each row col pair there is a (sigma_x) and a (sigma_y) like generator
+  //
+  //
+  //   t^a_ij = { in 0.. Nc(Nc-1)/2 -1} =>  delta_{i,i1} delta_{j,i2} +  delta_{i,i1} delta_{j,i2}  
+  //   t^a_ij = { in Nc(Nc-1)/2 ... Nc^(Nc-1) -1} =>  i delta_{i,i1} delta_{j,i2} - i delta_{i,i1} delta_{j,i2}  
+  //   
+  // * Diagonal; must be traceless and normalised
+  //   - Sequence is 
+  //   N  (1,-1,0,0...)
+  //   N  (1, 1,-2,0...)
+  //   N  (1, 1, 1,-3,0...)
+  //   N  (1, 1, 1, 1,-4,0...)
+  //
+  //   where 1/2 = N^2 (1+.. m^2)etc.... for the m-th diagonal generator
+  //   NB this gives the famous SU3 result for su2 index 8
+  //
+  //   N= sqrt(1/2 . 1/6 ) = 1/2 . 1/sqrt(3) 
+  //
+  //   ( 1      )
+  //   (    1   ) / sqrt(3) /2  = 1/2 lambda_8
+  //   (      -2)
+  ////////////////////////////////////////////////////////////////////////
+  template<class cplx>
+  static void generator(int lieIndex,iSUnMatrix<cplx> &ta){
+    // map lie index to which type of generator
+    int diagIndex;
+    int su2Index;
+    int sigxy;
+    int NNm1 =  ncolour*(ncolour-1);
+    if ( lieIndex>= NNm1 ) {
+      diagIndex = lieIndex -NNm1;
+      generatorDiagonal(diagIndex,ta);
+      return;
+    }
+    sigxy   = lieIndex&0x1;
+    su2Index= lieIndex>>1;
+    if ( sigxy ) generatorSigmaY(su2Index,ta);
+    else         generatorSigmaX(su2Index,ta);
+  }
+  template<class cplx>
+  static void generatorSigmaX(int su2Index,iSUnMatrix<cplx> &ta){
+    ta=zero;
+    int i1,i2;
+    su2SubGroupIndex(i1,i2,su2Index);
+    ta()()(i1,i2)=1.0;
+    ta()()(i2,i1)=1.0;
+    ta= ta *0.5;
+  }
+  template<class cplx>
+  static void generatorSigmaY(int su2Index,iSUnMatrix<cplx> &ta){
+    ta=zero;
+    cplx i(0.0,1.0);
+    int i1,i2;
+    su2SubGroupIndex(i1,i2,su2Index);
+    ta()()(i1,i2)=-i;
+    ta()()(i2,i1)= i;
+    ta= ta *0.5;
+  }
+  template<class cplx>
+  static void generatorDiagonal(int diagIndex,iSUnMatrix<cplx> &ta){
+    ta=zero;
+    int trsq=0;
+    int last=diagIndex+1;
+    for(int i=0;i<=diagIndex;i++){
+      ta()()(i,i) = 1.0;
+      trsq++;
+    }
+    ta()()(last,last) = -last;
+    trsq+=last*last;
+    RealD nrm = 1.0/std::sqrt(2.0*trsq);
+    ta = ta *nrm;
+  }
+  ////////////////////////////////////////////////////////////////////////
+  // Map a su2 subgroup number to the pair of rows that are non zero
+  ////////////////////////////////////////////////////////////////////////
+  static void su2SubGroupIndex(int &i1,int &i2,int su2_index){
+
+    assert( (su2_index>=0) && (su2_index< (ncolour*(ncolour-1))/2) );
+
+    int spare=su2_index;
+    for(i1=0;spare >= (ncolour-1-i1);i1++ ){
+      spare = spare - (ncolour-1-i1);  // remove the Nc-1-i1 terms  
+    }
+    i2=i1+1+spare;
+  }
+  template<class vreal,class vcplx>
+  static void su2Extract(std::vector<Lattice<iSinglet  <vreal> > > &r,
+			       const Lattice<iSUnMatrix<vcplx> > &source, 
+			 int su2_index)
+  {
+    GridBase *grid(source._grid);
+
+    assert(r.size() == 4); // store in 4 real parts
+    
+    for(int i=0;i<4;i++){
+      conformable(r[i],source);
+    }
+    
+    int i1,i2;    
+    su2SubGroupIndex(i1,i2,su2_index);
+
+    /* Compute the b(k) of A_SU(2) = b0 + i sum_k bk sigma_k */ 
+    
+    //    r[0] = toReal(real(peekColour(source,i1,i1)) + real(peekColour(source,i2,i2)));
+    //    r[1] = toReal(imag(peekColour(source,i1,i2)) + imag(peekColour(source,i2,i1)));
+    //    r[2] = toReal(real(peekColour(source,i1,i2)) - real(peekColour(source,i2,i1)));
+    //    r[3] = toReal(imag(peekColour(source,i1,i1)) - imag(peekColour(source,i2,i2)));
+    r[0] = toReal(real(peekColour(source,i1,i1)) + real(peekColour(source,i2,i2)));
+    r[1] = toReal(imag(peekColour(source,i1,i2)) + imag(peekColour(source,i2,i1)));
+    r[2] = toReal(real(peekColour(source,i1,i2)) - real(peekColour(source,i2,i1)));
+    r[3] = toReal(imag(peekColour(source,i1,i1)) - imag(peekColour(source,i2,i2)));
+    
+  }
+
+  template<class vreal,class vcplx>
+  static void su2Insert(const std::vector<Lattice<iSinglet<vreal> > > &r,
+			Lattice<iSUnMatrix<vcplx> > &dest,
+			int su2_index)
+  {
+    typedef typename Lattice<iSUnMatrix<vcplx> >::scalar_type cplx;
+    typedef Lattice<iSinglet<vcplx> > Lcomplex;
+    GridBase * grid = dest._grid;
+
+    assert(r.size() == 4); // store in 4 real parts
+
+    Lcomplex tmp(grid);
+
+    std::vector<Lcomplex > cr(4,grid);
+    for(int i=0;i<r.size();i++){
+      conformable(r[i],dest);
+      cr[i]=toComplex(r[i]);
+    }
+
+    int i1,i2;
+    su2SubGroupIndex(i1,i2,su2_index);
+
+    cplx one   (1.0,0.0);
+    cplx cplx_i(0.0,1.0);
+
+    tmp =   cr[0]*one+ cr[3]*cplx_i;   pokeColour(dest,tmp,i1,i2); 
+    tmp =   cr[2]*one+ cr[1]*cplx_i;   pokeColour(dest,tmp,i1,i2);
+    tmp =  -cr[2]*one+ cr[1]*cplx_i;   pokeColour(dest,tmp,i2,i1);
+    tmp =   cr[0]*one- cr[3]*cplx_i;   pokeColour(dest,tmp,i2,i2);
+  }
+
+  static void SubGroupHeatBath(      GridSerialRNG       &sRNG,
+				     GridParallelRNG     &pRNG,
+			             RealD beta,
+				     LatticeMatrix &link, 
+			       const LatticeMatrix &staple, 
+				     int su2_subgroup,
+				     int nheatbath,
+				     int& ntrials,
+				     int& nfails,
+				     LatticeInteger &wheremask)
+  {
+    GridBase *grid = link._grid;
+
+    LatticeMatrix V(grid);
+    V = link*staple;
+
+    std::vector<LatticeReal> r(4,grid);
+    std::vector<LatticeReal> a(4,grid);
+    su2Extract(r,V,su2_subgroup); // HERE
+
+    LatticeReal r_l(grid);
+    r_l  = r[0]*r[0]+r[1]*r[1]+r[2]*r[2]+r[3]*r[3];
+    r_l = sqrt(r_l);
+
+    LatticeReal ftmp(grid);
+    LatticeReal ftmp1(grid);
+    LatticeReal ftmp2(grid);
+    LatticeReal one (grid);    one = 1.0;
+    LatticeReal zz  (grid);    zz  = zero;
+    LatticeReal recip(grid);   recip = one/r_l;
+    
+    Real machine_epsilon= 1.0e-14;
+    
+    ftmp = where(r_l>machine_epsilon,recip,one);
+    a[0] = where(r_l>machine_epsilon,   r[0] * ftmp , one);
+    a[1] = where(r_l>machine_epsilon, -(r[1] * ftmp), zz);
+    a[2] = where(r_l>machine_epsilon, -(r[2] * ftmp), zz);
+    a[3] = where(r_l>machine_epsilon, -(r[3] * ftmp), zz);
+
+    r_l *=  beta / ncolour;
+    
+    ftmp1 = where(wheremask,one,zz);
+    Real num_sites = TensorRemove(sum(ftmp1));
+
+    Integer itrials = (Integer)num_sites;
+    ntrials = 0;
+    nfails = 0;
+
+    LatticeInteger lupdate(grid);
+    LatticeInteger lbtmp(grid);
+    LatticeInteger lbtmp2(grid); lbtmp2=zero;
+
+    int n_done = 0;
+    int nhb = 0;
+
+    r[0] = a[0];
+    lupdate = 1;
+
+    LatticeReal ones (grid); ones = 1.0;
+    LatticeReal zeros(grid); zeros=zero;
+
+    const RealD twopi=2.0*M_PI;
+    while ( nhb < nheatbath && n_done < num_sites ) {
+
+       ntrials += itrials;
+
+       random(pRNG,r[1]);
+       std::cout<<"RANDOM SPARSE FLOAT r[1]"<<std::endl;
+       std::cout<<r[1]<<std::endl;
+
+       random(pRNG,r[2]);
+       random(pRNG,ftmp);
+
+       r[1] = log(r[1]);
+       r[2] = log(r[2]);
+
+       ftmp = ftmp*twopi;
+       r[3] = cos(ftmp);
+       r[3] = r[3]*r[3];
+
+       r[1] += r[2] * r[3];
+       r[2]  = r[1] / r_l;
+
+       random(pRNG,ftmp);
+       r[1] = ftmp*ftmp;
+
+       {
+	 LatticeInteger mask_true (grid); mask_true = 1;
+	 LatticeInteger mask_false(grid); mask_false= 0;
+	 LatticeReal    thresh(grid); thresh = (1.0 + 0.5*r[2]);
+	 lbtmp = where(r[1] <= thresh,mask_true,mask_false);
+       }
+       lbtmp2= lbtmp && lupdate;       
+       r[0]  = where(lbtmp2, 1.0+r[2], r[0]);
+
+       ftmp1 = where(lbtmp2,ones,zeros);
+       RealD sitesum = sum(ftmp1);
+       Integer itmp = sitesum;
+
+       n_done += itmp;
+       itrials -= itmp;
+       nfails += itrials;
+       lbtmp   = !lbtmp;
+       lupdate = lupdate & lbtmp;
+       ++nhb;
+    }
+    // Now create r[1], r[2] and r[3] according to the spherical measure 
+    // Take absolute value to guard against round-off 
+    random(pRNG,ftmp1);
+    r[2] = 1.0 - 2.0*ftmp1;
+ 
+    ftmp1 = abs(1.0 - r[0]*r[0]);
+    r[3]   = -(sqrt(ftmp1) * r[2]);
+
+    // Take absolute value to guard against round-off 
+    r_l    = sqrt(abs(ftmp1 - r[3]*r[3]));
+ 
+    random(pRNG,ftmp1);
+    ftmp1 *= twopi;
+    r[1]    = r_l * cos(ftmp1);
+    r[2]    = r_l * sin(ftmp1);
+
+    // Update matrix is B = R * A, with B, R and A given by b_i, r_i and a_i 
+    std::vector<LatticeReal> b(4,grid);
+    b[0] = r[0]*a[0] - r[1]*a[1] - r[2]*a[2] - r[3]*a[3];
+    b[1] = r[0]*a[1] + r[1]*a[0] - r[2]*a[3] + r[3]*a[2];
+    b[2] = r[0]*a[2] + r[2]*a[0] - r[3]*a[1] + r[1]*a[3];
+    b[3] = r[0]*a[3] + r[3]*a[0] - r[1]*a[2] + r[2]*a[1];
+
+     //
+     // Now fill an SU(3) matrix V with the SU(2) submatrix su2_index
+     // parametrized by a_k in the sigma matrix basis.
+     //
+    su2Insert(b,V,su2_subgroup);
+
+    // U = V*U
+    LatticeMatrix tmp(grid);
+    tmp = V * link;
+
+    //mask the assignment back
+    link = where(wheremask,tmp,link);
+
+  }
+
+  static void printGenerators(void)
+  {
+    for(int gen=0;gen<generators();gen++){
+      Matrix ta;
+      generator(gen,ta);
+      std::cout<< "Nc = "<<ncolour<<" t_"<<gen<<std::endl;
+      std::cout<<ta<<std::endl;
+    }
+  }
+
+  static void testGenerators(void){
+    Matrix ta;
+    Matrix tb;
+    std::cout<<"Checking trace ta tb is 0.5 delta_ab"<<std::endl;
+    for(int a=0;a<generators();a++){
+      for(int b=0;b<generators();b++){
+	generator(a,ta);
+	generator(b,tb);
+	Complex tr =TensorRemove(trace(ta*tb)); 
+	std::cout<<tr<<" ";
+	if(a==b) assert(abs(tr-Complex(0.5))<1.0e-6);
+	if(a!=b) assert(abs(tr)<1.0e-6);
+      }
+      std::cout<<std::endl;
+    }
+    std::cout<<"Checking hermitian"<<std::endl;
+    for(int a=0;a<generators();a++){
+      generator(a,ta);
+      std::cout<<a<<" ";
+      assert(norm2(ta-adj(ta))<1.0e-6);
+    }    
+    std::cout<<std::endl;
+
+    std::cout<<"Checking traceless"<<std::endl;
+    for(int a=0;a<generators();a++){
+      generator(a,ta);
+      Complex tr =TensorRemove(trace(ta)); 
+      std::cout<<a<<" ";
+      assert(abs(tr)<1.0e-6);
+    }    
+    std::cout<<std::endl;
+  }
+
+  // reunitarise??
+
+  static void taProj( const LatticeMatrix &in,  LatticeMatrix &out){
+    out = Ta(in);
+  }
+  static void taExp( const LatticeMatrix &x,  LatticeMatrix &ex){ 
+    LatticeMatrix xn   = x;
+
+    RealD nfac = 1.0;
+    ex = 1+x; // 1+x
+
+    // Do a 12th order exponentiation
+    for(int i= 2; i <= 12; ++i)
+    {
+      nfac = nfac/i; 
+      xn   = xn * x; // x2, x3,x4....
+      ex  += xn*nfac;// x2/2!, x3/3!....
+    }
+  }
+
+};
+
+ typedef SU<2> SU2;
+ typedef SU<3> SU3;
+ typedef SU<4> SU4;
+ typedef SU<5> SU5;
+
+  }
+}
+#endif