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Attempt with SFINAE (failed)
This commit is contained in:
Julian Lenz
parent
54c8025aad
commit
7c2ad4f8c8
@ -33,12 +33,19 @@ directory
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#define QCD_UTIL_SUN_H
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#define ONLY_IF_SU \
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typename dummy_name = group_name, \
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typename = std::enable_if_t<is_su<dummy_name>::value>
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typename \
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typename std::enable_if_t<is_su<group_name>::value, dummy_name> ,\
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dummy_name = group_name,
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#define ONLY_IF_Sp \
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typename \
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typename std::enable_if_t<is_sp<group_name>::value, dummy_name> ,\
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dummy_name =group_name,
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NAMESPACE_BEGIN(Grid);
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namespace GroupName {
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class SU {};
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class Sp {};
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} // namespace GroupName
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template <typename group_name>
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@ -51,18 +58,44 @@ struct is_su<GroupName::SU> {
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static const bool value = true;
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};
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template <typename group_name>
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struct is_sp {
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static const bool value = false;
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};
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template <>
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struct is_sp<GroupName::Sp> {
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static const bool value = true;
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};
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template<typename group_name>
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constexpr int compute_adjoint_dimension(int ncolour);
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template<>
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constexpr int compute_adjoint_dimension<GroupName::SU>(int ncolour) { return ncolour * ncolour - 1;}
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template<>
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constexpr int compute_adjoint_dimension<GroupName::Sp>(int ncolour) { return ncolour/2*(ncolour+1);}
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template <int ncolour, class group_name = GroupName::SU>
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class GaugeGroup;
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template <int ncolour>
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using SU = GaugeGroup<ncolour, GroupName::SU>;
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template <int ncolour>
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using Sp = GaugeGroup<ncolour, GroupName::Sp>;
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template <int ncolour, class group_name>
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class GaugeGroup {
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public:
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static const int Dimension = ncolour;
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static const int AdjointDimension = ncolour * ncolour - 1;
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static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
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static const int AdjointDimension = compute_adjoint_dimension<group_name>(ncolour);
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static const int AlgebraDimension = compute_adjoint_dimension<group_name>(ncolour);
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// Don't know how to only enable this for Sp:
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static const int nsp = ncolour/2;
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template <typename vtype>
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using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
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@ -115,6 +148,7 @@ class GaugeGroup {
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typedef Lattice<vSU2MatrixD> LatticeSU2MatrixD;
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#include "Grid/qcd/utils/SUn_impl.h"
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#include "Grid/qcd/utils/Sp2n_impl.h"
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static void printGenerators(void) {
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for (int gen = 0; gen < AdjointDimension; gen++) {
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@ -6,6 +6,8 @@
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//
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// around it.
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template<ONLY_IF_SU>
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static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
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template <typename vtype, ONLY_IF_SU>
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using iSUnMatrix = iGroupMatrix<vtype>;
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template <typename vtype, ONLY_IF_SU>
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File diff suppressed because it is too large
Load Diff
245
Grid/qcd/utils/Sp2n_impl.h
Normal file
245
Grid/qcd/utils/Sp2n_impl.h
Normal file
@ -0,0 +1,245 @@
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template<ONLY_IF_Sp>
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static int su2subgroups(void) { return (nsp * (nsp - 1)) / 2; }
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template <typename vtype, ONLY_IF_Sp>
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using iSp2nMatrix = iGroupMatrix<vtype>;
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template <typename vtype, ONLY_IF_Sp>
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using iSp2nAlgebraVector = iAlgebraVector<vtype>;
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// Sp(2N) has N(2N+1) = 2N^2+N generators
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//
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// normalise the generators such that
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// Trace ( Ta Tb) = 1/2 delta_ab
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//
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// N generators in the cartan, 2N^2 off
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// off diagonal:
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// there are 6 types named a,b,c,d and w,z
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// abcd are N(N-1)/2 each while wz are N each
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template <class cplx, ONLY_IF_Sp>
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static void generator(int lieIndex, iSp2nMatrix<cplx> &ta) {
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// map lie index into type of generators: diagonal, abcd type, wz type
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int diagIndex;
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int aIndex, bIndex, cIndex, dIndex;
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int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
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int mod = nsp * (nsp-1) * 0.5;
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int offdiag = 2*nsp*nsp; // number of generators not in the cartan subalgebra
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int wmod = 4*mod;
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int zmod = wmod+nsp;
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if (lieIndex >= offdiag) {
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diagIndex = lieIndex - offdiag; // 0, ... ,N-1
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//std::cout << GridLogMessage << "diag type " << std::endl;
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generatorDiagtype(diagIndex, ta);
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return;
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}
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if ( (lieIndex >= wmod) && (lieIndex < zmod) ) {
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//std::cout << GridLogMessage << "w type " << std::endl;
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wIndex = lieIndex- wmod; // 0, ... ,N-1
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generatorWtype(wIndex,ta);
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return;
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}
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if ( (lieIndex >= zmod) && (lieIndex < offdiag) ) {
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//std::cout << GridLogMessage << "z type " << std::endl;
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//std::cout << GridLogMessage << "lie index " << lieIndex << std::endl;
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//std::cout << GridLogMessage << "z mod " << zmod << std::endl;
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zIndex = lieIndex - zmod; // 0, ... ,N-1
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generatorZtype(zIndex,ta);
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return;
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}
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if (lieIndex < mod) { // atype 0, ... , N(N-1)/2=mod
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//std::cout << GridLogMessage << "a type " << std::endl;
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aIndex = lieIndex;
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//std::cout << GridLogMessage << "a indx " << aIndex << std::endl;
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generatorAtype(aIndex, ta);
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return;
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}
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if ( (lieIndex >= mod) && lieIndex < 2*mod) { // btype mod, ... , 2mod-1
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//std::cout << GridLogMessage << "b type " << std::endl;
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bIndex = lieIndex - mod;
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generatorBtype(bIndex, ta);
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return;
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}
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if ( (lieIndex >= 2*mod) && lieIndex < 3*mod) { // ctype 2mod, ... , 3mod-1
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//std::cout << GridLogMessage << "c type " << std::endl;
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cIndex = lieIndex - 2*mod;
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generatorCtype(cIndex, ta);
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return;
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}
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if ( (lieIndex >= 3*mod) && lieIndex < wmod) { // ctype 3mod, ... , 4mod-1 = wmod-1
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//std::cout << GridLogMessage << "d type " << std::endl;
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dIndex = lieIndex - 3*mod;
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generatorDtype(dIndex, ta);
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return;
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}
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} //end of generator
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template <class cplx, ONLY_IF_Sp>
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static void generatorDiagtype(int diagIndex, iSp2nMatrix<cplx> &ta) {
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// ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
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ta = Zero();
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RealD nrm = 1.0 / 2;
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ta()()(diagIndex,diagIndex) = nrm;
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ta()()(diagIndex+nsp,diagIndex+nsp) = -nrm;
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}
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template <class cplx, ONLY_IF_Sp>
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static void generatorAtype(int aIndex, iSp2nMatrix<cplx> &ta) {
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// ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
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// with i<j and i=0,...,N-2
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// follows that j=i+1, ... , N
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int i1, i2;
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ta = Zero();
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RealD nrm = 1 / (2 * std::sqrt(2) );
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su2SubGroupIndex(i1, i2, aIndex);
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ta()()(i1,i2) = 1;
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ta()()(i2,i1) = 1;
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ta()()(i1+nsp,i2+nsp) = -1;
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ta()()(i2+nsp,i1+nsp) = -1;
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ta = ta * nrm;
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}
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template <class cplx, ONLY_IF_Sp>
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static void generatorBtype(int bIndex, iSp2nMatrix<cplx> &ta) {
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// ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
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// with i<j and i=0,...,N-2
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// follows that j=i+1, ... , N-1
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int i1, i2;
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ta = Zero();
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cplx i(0.0, 1.0);
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RealD nrm = 1 / (2 * std::sqrt(2));
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su2SubGroupIndex(i1, i2, bIndex);
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ta()()(i1,i2) = i;
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ta()()(i2,i1) = -i;
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ta()()(i1+nsp,i2+nsp) = i;
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ta()()(i2+nsp,i1+nsp) = -i;
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ta = ta * nrm;
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}
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template <class cplx, ONLY_IF_Sp>
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static void generatorCtype(int cIndex, iSp2nMatrix<cplx> &ta) {
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// ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
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int i1, i2;
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ta = Zero();
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RealD nrm = 1 / (2 * std::sqrt(2) );
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su2SubGroupIndex(i1, i2, cIndex);
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ta()()(i1,i2+nsp) = 1;
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ta()()(i2,i1+nsp) = 1;
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ta()()(i1+nsp,i2) = 1;
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ta()()(i2+nsp,i1) = 1;
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ta = ta * nrm;
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}
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template <class cplx, ONLY_IF_Sp>
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static void generatorDtype(int dIndex, iSp2nMatrix<cplx> &ta) {
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// ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i / 2 sqrt(2)
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int i1, i2;
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ta = Zero();
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cplx i(0.0, 1.0);
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RealD nrm = 1 / (2 * std::sqrt(2) );
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su2SubGroupIndex(i1, i2, dIndex);
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ta()()(i1,i2+nsp) = i;
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ta()()(i2,i1+nsp) = i;
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ta()()(i1+nsp,i2) = -i;
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ta()()(i2+nsp,i1) = -i;
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ta = ta * nrm;
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}
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template <class cplx, ONLY_IF_Sp>
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static void generatorWtype(int wIndex, iSp2nMatrix<cplx> &ta) {
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// ta(i,i+N) = ta(i+N,i) = 1/2
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ta = Zero();
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RealD nrm = 1.0 / 2; //check
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ta()()(wIndex,wIndex+nsp) = 1;
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ta()()(wIndex+nsp,wIndex) = 1;
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ta = ta * nrm;
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}
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template <class cplx, ONLY_IF_Sp>
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static void generatorZtype(int zIndex, iSp2nMatrix<cplx> &ta) {
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// ta(i,i+N) = - ta(i+N,i) = i/2
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ta = Zero();
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RealD nrm = 1.0 / 2; //check
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cplx i(0.0, 1.0);
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ta()()(zIndex,zIndex+nsp) = i;
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ta()()(zIndex+nsp,zIndex) = -i;
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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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template<ONLY_IF_Sp>
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static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
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assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
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int spare = su2_index;
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for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
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spare = spare - (nsp - 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<ONLY_IF_Sp>
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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 << GridLogMessage << "Fundamental - Checking trace ta tb is 0.5 delta_ab " << std::endl;
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for (int a = 0; a < AlgebraDimension; a++) {
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for (int b = 0; b < AlgebraDimension; 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 << GridLogMessage << "(" << a << "," << b << ") = " << tr
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<< std::endl;
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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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}
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std::cout << GridLogMessage << std::endl;
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std::cout << GridLogMessage << "Fundamental - Checking if hermitian" << std::endl;
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for (int a = 0; a < AlgebraDimension; a++) {
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generator(a,ta);
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std::cout << GridLogMessage << a << std::endl;
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assert(norm2(ta - adj(ta)) < 1.0e-6);
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}
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std::cout << GridLogMessage << std::endl;
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std::cout << GridLogMessage << "Fundamental - Checking if traceless" << std::endl;
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for (int a = 0; a < AlgebraDimension; a++) {
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generator(a, ta);
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Complex tr = TensorRemove(trace(ta));
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std::cout << GridLogMessage << a << std::endl;
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assert(abs(tr) < 1.0e-6);
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}
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}
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