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Merge branch 'master' of https://github.com/paboyle/Grid
This commit is contained in:
Peter Boyle
commit
308d53858b
414
lib/qcd/utils/SUn.h
Normal file
414
lib/qcd/utils/SUn.h
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@ -0,0 +1,414 @@
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#ifndef QCD_UTIL_SUN_H
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#define QCD_UTIL_SUN_H
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namespace Grid {
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namespace QCD {
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template<int ncolour>
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class SU {
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public:
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static int generators(void) { return ncolour*ncolour-1; }
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static int su2subgroups(void) { return (ncolour*(ncolour-1))/2; }
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template<typename vtype> using iSUnMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > > ;
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//////////////////////////////////////////////////////////////////////////////////////////////////
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// Types can be accessed as SU<2>::Matrix , SU<2>::vSUnMatrix, SU<2>::LatticeMatrix etc...
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//////////////////////////////////////////////////////////////////////////////////////////////////
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typedef iSUnMatrix<Complex> Matrix;
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typedef iSUnMatrix<ComplexF> MatrixF;
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typedef iSUnMatrix<ComplexD> MatrixD;
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typedef iSUnMatrix<vComplex> vMatrix;
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typedef iSUnMatrix<vComplexF> vMatrixF;
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typedef iSUnMatrix<vComplexD> vMatrixD;
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typedef Lattice<vMatrix> LatticeMatrix;
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typedef Lattice<vMatrixF> LatticeMatrixF;
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typedef Lattice<vMatrixD> LatticeMatrixD;
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////////////////////////////////////////////////////////////////////////
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// There are N^2-1 generators for SU(N).
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//
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// We take a traceless hermitian generator basis as follows
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//
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// * Normalisation: trace ta tb = 1/2 delta_ab
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//
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// * Off diagonal
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// - pairs of rows i1,i2 behaving like pauli matrices signma_x, sigma_y
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//
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// - there are (Nc-1-i1) slots for i2 on each row [ x 0 x ]
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// direct count off each row
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//
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// - Sum of all pairs is Nc(Nc-1)/2: proof arithmetic series
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//
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// (Nc-1) + (Nc-2)+... 1 ==> Nc*(Nc-1)/2
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// 1+ 2+ + + Nc-1
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//
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// - There are 2 x Nc (Nc-1)/ 2 of these = Nc^2 - Nc
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//
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// - We enumerate the row-col pairs.
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// - for each row col pair there is a (sigma_x) and a (sigma_y) like generator
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//
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//
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// t^a_ij = { in 0.. Nc(Nc-1)/2 -1} => delta_{i,i1} delta_{j,i2} + delta_{i,i1} delta_{j,i2}
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// 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}
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//
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// * Diagonal; must be traceless and normalised
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// - Sequence is
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// N (1,-1,0,0...)
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// N (1, 1,-2,0...)
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// N (1, 1, 1,-3,0...)
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// N (1, 1, 1, 1,-4,0...)
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//
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// where 1/2 = N^2 (1+.. m^2)etc.... for the m-th diagonal generator
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// NB this gives the famous SU3 result for su2 index 8
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//
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// N= sqrt(1/2 . 1/6 ) = 1/2 . 1/sqrt(3)
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//
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// ( 1 )
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// ( 1 ) / sqrt(3) /2 = 1/2 lambda_8
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// ( -2)
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////////////////////////////////////////////////////////////////////////
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template<class cplx>
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static void generator(int lieIndex,iSUnMatrix<cplx> &ta){
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// map lie index to which type of generator
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int diagIndex;
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int su2Index;
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int sigxy;
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int NNm1 = ncolour*(ncolour-1);
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if ( lieIndex>= NNm1 ) {
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diagIndex = lieIndex -NNm1;
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generatorDiagonal(diagIndex,ta);
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return;
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}
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sigxy = lieIndex&0x1;
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su2Index= lieIndex>>1;
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if ( sigxy ) generatorSigmaY(su2Index,ta);
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else generatorSigmaX(su2Index,ta);
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}
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template<class cplx>
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static void generatorSigmaX(int su2Index,iSUnMatrix<cplx> &ta){
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ta=zero;
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int i1,i2;
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su2SubGroupIndex(i1,i2,su2Index);
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ta()()(i1,i2)=1.0;
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ta()()(i2,i1)=1.0;
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ta= ta *0.5;
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}
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template<class cplx>
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static void generatorSigmaY(int su2Index,iSUnMatrix<cplx> &ta){
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ta=zero;
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cplx i(0.0,1.0);
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int i1,i2;
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su2SubGroupIndex(i1,i2,su2Index);
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ta()()(i1,i2)=-i;
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ta()()(i2,i1)= i;
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ta= ta *0.5;
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}
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template<class cplx>
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static void generatorDiagonal(int diagIndex,iSUnMatrix<cplx> &ta){
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ta=zero;
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int trsq=0;
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int last=diagIndex+1;
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for(int i=0;i<=diagIndex;i++){
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ta()()(i,i) = 1.0;
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trsq++;
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}
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ta()()(last,last) = -last;
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trsq+=last*last;
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RealD nrm = 1.0/std::sqrt(2.0*trsq);
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ta = ta *nrm;
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}
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////////////////////////////////////////////////////////////////////////
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// Map a su2 subgroup number to the pair of rows that are non zero
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////////////////////////////////////////////////////////////////////////
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static void su2SubGroupIndex(int &i1,int &i2,int su2_index){
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assert( (su2_index>=0) && (su2_index< (ncolour*(ncolour-1))/2) );
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int spare=su2_index;
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for(i1=0;spare >= (ncolour-1-i1);i1++ ){
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spare = spare - (ncolour-1-i1); // remove the Nc-1-i1 terms
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}
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i2=i1+1+spare;
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}
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template<class vreal,class vcplx>
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static void su2Extract(std::vector<Lattice<iSinglet <vreal> > > &r,
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const Lattice<iSUnMatrix<vcplx> > &source,
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int su2_index)
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{
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GridBase *grid(source._grid);
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assert(r.size() == 4); // store in 4 real parts
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for(int i=0;i<4;i++){
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conformable(r[i],source);
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}
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int i1,i2;
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su2SubGroupIndex(i1,i2,su2_index);
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/* Compute the b(k) of A_SU(2) = b0 + i sum_k bk sigma_k */
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// r[0] = toReal(real(peekColour(source,i1,i1)) + real(peekColour(source,i2,i2)));
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// r[1] = toReal(imag(peekColour(source,i1,i2)) + imag(peekColour(source,i2,i1)));
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// r[2] = toReal(real(peekColour(source,i1,i2)) - real(peekColour(source,i2,i1)));
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// r[3] = toReal(imag(peekColour(source,i1,i1)) - imag(peekColour(source,i2,i2)));
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r[0] = toReal(real(peekColour(source,i1,i1)) + real(peekColour(source,i2,i2)));
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r[1] = toReal(imag(peekColour(source,i1,i2)) + imag(peekColour(source,i2,i1)));
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r[2] = toReal(real(peekColour(source,i1,i2)) - real(peekColour(source,i2,i1)));
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r[3] = toReal(imag(peekColour(source,i1,i1)) - imag(peekColour(source,i2,i2)));
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}
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template<class vreal,class vcplx>
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static void su2Insert(const std::vector<Lattice<iSinglet<vreal> > > &r,
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Lattice<iSUnMatrix<vcplx> > &dest,
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int su2_index)
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{
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typedef typename Lattice<iSUnMatrix<vcplx> >::scalar_type cplx;
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typedef Lattice<iSinglet<vcplx> > Lcomplex;
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GridBase * grid = dest._grid;
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assert(r.size() == 4); // store in 4 real parts
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Lcomplex tmp(grid);
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std::vector<Lcomplex > cr(4,grid);
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for(int i=0;i<r.size();i++){
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conformable(r[i],dest);
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cr[i]=toComplex(r[i]);
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}
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int i1,i2;
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su2SubGroupIndex(i1,i2,su2_index);
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cplx one (1.0,0.0);
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cplx cplx_i(0.0,1.0);
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tmp = cr[0]*one+ cr[3]*cplx_i; pokeColour(dest,tmp,i1,i2);
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tmp = cr[2]*one+ cr[1]*cplx_i; pokeColour(dest,tmp,i1,i2);
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tmp = -cr[2]*one+ cr[1]*cplx_i; pokeColour(dest,tmp,i2,i1);
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tmp = cr[0]*one- cr[3]*cplx_i; pokeColour(dest,tmp,i2,i2);
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}
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static void SubGroupHeatBath( GridSerialRNG &sRNG,
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GridParallelRNG &pRNG,
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RealD beta,
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LatticeMatrix &link,
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const LatticeMatrix &staple,
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int su2_subgroup,
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int nheatbath,
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int& ntrials,
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int& nfails,
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LatticeInteger &wheremask)
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{
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GridBase *grid = link._grid;
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LatticeMatrix V(grid);
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V = link*staple;
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std::vector<LatticeReal> r(4,grid);
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std::vector<LatticeReal> a(4,grid);
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su2Extract(r,V,su2_subgroup); // HERE
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LatticeReal r_l(grid);
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r_l = r[0]*r[0]+r[1]*r[1]+r[2]*r[2]+r[3]*r[3];
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r_l = sqrt(r_l);
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LatticeReal ftmp(grid);
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LatticeReal ftmp1(grid);
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LatticeReal ftmp2(grid);
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LatticeReal one (grid); one = 1.0;
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LatticeReal zz (grid); zz = zero;
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LatticeReal recip(grid); recip = one/r_l;
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Real machine_epsilon= 1.0e-14;
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ftmp = where(r_l>machine_epsilon,recip,one);
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a[0] = where(r_l>machine_epsilon, r[0] * ftmp , one);
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a[1] = where(r_l>machine_epsilon, -(r[1] * ftmp), zz);
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a[2] = where(r_l>machine_epsilon, -(r[2] * ftmp), zz);
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a[3] = where(r_l>machine_epsilon, -(r[3] * ftmp), zz);
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r_l *= beta / ncolour;
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ftmp1 = where(wheremask,one,zz);
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Real num_sites = TensorRemove(sum(ftmp1));
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Integer itrials = (Integer)num_sites;
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ntrials = 0;
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nfails = 0;
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LatticeInteger lupdate(grid);
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LatticeInteger lbtmp(grid);
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LatticeInteger lbtmp2(grid); lbtmp2=zero;
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int n_done = 0;
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int nhb = 0;
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r[0] = a[0];
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lupdate = 1;
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LatticeReal ones (grid); ones = 1.0;
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LatticeReal zeros(grid); zeros=zero;
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const RealD twopi=2.0*M_PI;
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while ( nhb < nheatbath && n_done < num_sites ) {
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ntrials += itrials;
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random(pRNG,r[1]);
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std::cout<<"RANDOM SPARSE FLOAT r[1]"<<std::endl;
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std::cout<<r[1]<<std::endl;
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random(pRNG,r[2]);
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random(pRNG,ftmp);
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r[1] = log(r[1]);
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r[2] = log(r[2]);
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ftmp = ftmp*twopi;
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r[3] = cos(ftmp);
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r[3] = r[3]*r[3];
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r[1] += r[2] * r[3];
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r[2] = r[1] / r_l;
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random(pRNG,ftmp);
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r[1] = ftmp*ftmp;
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{
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LatticeInteger mask_true (grid); mask_true = 1;
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LatticeInteger mask_false(grid); mask_false= 0;
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LatticeReal thresh(grid); thresh = (1.0 + 0.5*r[2]);
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lbtmp = where(r[1] <= thresh,mask_true,mask_false);
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}
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lbtmp2= lbtmp && lupdate;
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r[0] = where(lbtmp2, 1.0+r[2], r[0]);
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ftmp1 = where(lbtmp2,ones,zeros);
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RealD sitesum = sum(ftmp1);
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Integer itmp = sitesum;
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n_done += itmp;
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itrials -= itmp;
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nfails += itrials;
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lbtmp = !lbtmp;
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lupdate = lupdate & lbtmp;
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++nhb;
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}
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// Now create r[1], r[2] and r[3] according to the spherical measure
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// Take absolute value to guard against round-off
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random(pRNG,ftmp1);
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r[2] = 1.0 - 2.0*ftmp1;
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ftmp1 = abs(1.0 - r[0]*r[0]);
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r[3] = -(sqrt(ftmp1) * r[2]);
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// Take absolute value to guard against round-off
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r_l = sqrt(abs(ftmp1 - r[3]*r[3]));
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random(pRNG,ftmp1);
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ftmp1 *= twopi;
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r[1] = r_l * cos(ftmp1);
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r[2] = r_l * sin(ftmp1);
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// Update matrix is B = R * A, with B, R and A given by b_i, r_i and a_i
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std::vector<LatticeReal> b(4,grid);
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b[0] = r[0]*a[0] - r[1]*a[1] - r[2]*a[2] - r[3]*a[3];
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b[1] = r[0]*a[1] + r[1]*a[0] - r[2]*a[3] + r[3]*a[2];
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b[2] = r[0]*a[2] + r[2]*a[0] - r[3]*a[1] + r[1]*a[3];
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b[3] = r[0]*a[3] + r[3]*a[0] - r[1]*a[2] + r[2]*a[1];
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//
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// Now fill an SU(3) matrix V with the SU(2) submatrix su2_index
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// parametrized by a_k in the sigma matrix basis.
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//
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su2Insert(b,V,su2_subgroup);
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// U = V*U
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LatticeMatrix tmp(grid);
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tmp = V * link;
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//mask the assignment back
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link = where(wheremask,tmp,link);
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}
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static void printGenerators(void)
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{
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for(int gen=0;gen<generators();gen++){
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Matrix ta;
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generator(gen,ta);
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std::cout<< "Nc = "<<ncolour<<" t_"<<gen<<std::endl;
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std::cout<<ta<<std::endl;
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}
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}
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static void testGenerators(void){
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Matrix ta;
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Matrix tb;
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std::cout<<"Checking trace ta tb is 0.5 delta_ab"<<std::endl;
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for(int a=0;a<generators();a++){
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for(int b=0;b<generators();b++){
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generator(a,ta);
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generator(b,tb);
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Complex tr =TensorRemove(trace(ta*tb));
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std::cout<<tr<<" ";
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if(a==b) assert(abs(tr-Complex(0.5))<1.0e-6);
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if(a!=b) assert(abs(tr)<1.0e-6);
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}
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std::cout<<std::endl;
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}
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std::cout<<"Checking hermitian"<<std::endl;
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for(int a=0;a<generators();a++){
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generator(a,ta);
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std::cout<<a<<" ";
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assert(norm2(ta-adj(ta))<1.0e-6);
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}
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std::cout<<std::endl;
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std::cout<<"Checking traceless"<<std::endl;
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for(int a=0;a<generators();a++){
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generator(a,ta);
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Complex tr =TensorRemove(trace(ta));
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std::cout<<a<<" ";
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assert(abs(tr)<1.0e-6);
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}
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std::cout<<std::endl;
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}
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// reunitarise??
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static void taProj( const LatticeMatrix &in, LatticeMatrix &out){
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out = Ta(in);
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}
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static void taExp( const LatticeMatrix &x, LatticeMatrix &ex){
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LatticeMatrix xn = x;
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RealD nfac = 1.0;
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ex = 1+x; // 1+x
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// Do a 12th order exponentiation
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for(int i= 2; i <= 12; ++i)
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{
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nfac = nfac/i;
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xn = xn * x; // x2, x3,x4....
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ex += xn*nfac;// x2/2!, x3/3!....
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}
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}
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};
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typedef SU<2> SU2;
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typedef SU<3> SU3;
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typedef SU<4> SU4;
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typedef SU<5> SU5;
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|
||||
}
|
||||
}
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||||
#endif
|
||||
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