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https://github.com/paboyle/Grid.git
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116 lines
3.3 KiB
C++
116 lines
3.3 KiB
C++
#ifndef GRID_MATH_TA_H
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#define GRID_MATH_TA_H
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namespace Grid {
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///////////////////////////////////////////////
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// Ta function for scalar, vector, matrix
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///////////////////////////////////////////////
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inline ComplexF Ta( const ComplexF &arg){ return arg;}
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inline ComplexD Ta( const ComplexD &arg){ return arg;}
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inline RealF Ta( const RealF &arg){ return arg;}
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inline RealD Ta( const RealD &arg){ return arg;}
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template<class vtype> inline iScalar<vtype> Ta(const iScalar<vtype>&r)
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{
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iScalar<vtype> ret;
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ret._internal = Ta(r._internal);
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return ret;
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}
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template<class vtype,int N> inline iVector<vtype,N> Ta(const iVector<vtype,N>&r)
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{
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iVector<vtype,N> ret;
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for(int i=0;i<N;i++){
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ret._internal[i] = Ta(r._internal[i]);
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}
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return ret;
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}
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template<class vtype,int N> inline iMatrix<vtype,N> Ta(const iMatrix<vtype,N> &arg)
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{
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iMatrix<vtype,N> ret(arg);
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double factor = (1/(double)N);
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ret = (ret - adj(arg))*0.5;
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ret -= trace(ret)*factor;
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return ret;
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}
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///////////////////////////////////////////////
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// ProjectOnGroup function for scalar, vector, matrix
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///////////////////////////////////////////////
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template<class vtype> inline iScalar<vtype> ProjectOnGroup(const iScalar<vtype>&r)
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{
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iScalar<vtype> ret;
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ret._internal = ProjectOnGroup(r._internal);
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return ret;
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}
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template<class vtype,int N> inline iVector<vtype,N> ProjectOnGroup(const iVector<vtype,N>&r)
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{
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iVector<vtype,N> ret;
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for(int i=0;i<N;i++){
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ret._internal[i] = ProjectOnGroup(r._internal[i]);
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}
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return ret;
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}
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template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
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inline iMatrix<vtype,N> ProjectOnGroup(const iMatrix<vtype,N> &arg)
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{
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// need a check for the group type?
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iMatrix<vtype,N> ret(arg);
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double nrm;
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for(int c1=0;c1<N;c1++){
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nrm = 0.0;
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for(int c2=0;c2<N;c2++)
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nrm = real(innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]));
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nrm = 1.0/sqrt(nrm);
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for(int c2=0;c2<N;c2++)
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ret._internal[c1][c2]*= nrm;
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for (int b=c1+1; b<N; ++b){
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decltype(ret._internal[b][b]*ret._internal[b][b]) pr = 0.0;
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for(int c=0; c<N; ++c)
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pr += ret._internal[c1][c]*ret._internal[b][c];
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for(int c=0; c<N; ++c){
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ret._internal[b][c] -= pr * ret._internal[c1][c];
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}
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}
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}
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return ret;
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}
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///////////////////////////////////////////////
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// Exponentiate function for scalar, vector, matrix
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///////////////////////////////////////////////
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template<class vtype> inline iScalar<vtype> Exponentiate(const iScalar<vtype>&r, double alpha, int Nexp)
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{
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iScalar<vtype> ret;
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ret._internal = Exponentiate(r._internal, alpha, Nexp);
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return ret;
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}
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template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
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inline iMatrix<vtype,N> Exponentiate(const iMatrix<vtype,N> &arg, double alpha, int Nexp)
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{
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iMatrix<vtype,N> unit(1.0);
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iMatrix<vtype,N> temp(unit);
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for(int i=Nexp; i>=1;--i){
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temp *= alpha/double(i);
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temp = unit + temp*arg;
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}
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return ProjectOnGroup(temp);
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}
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}
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#endif
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