portelli/Grid
1
0
Fork 0
mirror of https://github.com/paboyle/Grid.git synced 2025-06-20 16:56:55 +01:00
Code Releases Activity
Files
a09aa352a9cf5e5c18546a3fc99dcaa6afc54584
Grid/Grid/tensors/Tensor_Ta.h

270 lines
8.1 KiB
C++
Raw Blame History

/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./lib/tensors/Tensor_Ta.h
Copyright (C) 2015
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: neo <cossu@post.kek.jp>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
See the full license in the file "LICENSE" in the top level distribution directory
*************************************************************************************/
/* END LEGAL */
#ifndef GRID_MATH_TA_H
#define GRID_MATH_TA_H
NAMESPACE_BEGIN(Grid);
///////////////////////////////////////////////
// Ta function for scalar, vector, matrix
///////////////////////////////////////////////
/*
accelerator_inline ComplexF Ta( const ComplexF &arg){ return arg;}
accelerator_inline ComplexD Ta( const ComplexD &arg){ return arg;}
accelerator_inline RealF Ta( const RealF &arg){ return arg;}
accelerator_inline RealD Ta( const RealD &arg){ return arg;}
*/
template<class vtype> accelerator_inline iScalar<vtype> Ta(const iScalar<vtype>&r)
{
iScalar<vtype> ret;
ret._internal = Ta(r._internal);
return ret;
}
template<class vtype,int N> accelerator_inline iVector<vtype,N> Ta(const iVector<vtype,N>&r)
{
iVector<vtype,N> ret;
for(int i=0;i<N;i++){
ret._internal[i] = Ta(r._internal[i]);
}
return ret;
}
template<class vtype,int N> accelerator_inline iMatrix<vtype,N> Ta(const iMatrix<vtype,N> &arg)
{
iMatrix<vtype,N> ret;
double factor = (1.0/(double)N);
ret= (arg - adj(arg))*0.5;
ret=ret - (trace(ret)*factor);
return ret;
}
template<class vtype> accelerator_inline iScalar<vtype> SpTa(const iScalar<vtype>&r)
{
iScalar<vtype> ret;
ret._internal = SpTa(r._internal);
return ret;
}
template<class vtype,int N> accelerator_inline iVector<vtype,N> SpTa(const iVector<vtype,N>&r)
{
iVector<vtype,N> ret;
for(int i=0;i<N;i++){
ret._internal[i] = SpTa(r._internal[i]);
}
return ret;
}
template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
accelerator_inline iMatrix<vtype,N> SpTa(const iMatrix<vtype,N> &arg)
{
// Generalises Ta to Sp2n
// Applies the following projections
// P_{antihermitian} P_{antihermitian-Sp-algebra} P_{traceless}
// where the ordering matters
// P_{traceless} subtracts the trace
// P_{antihermitian-Sp-algebra} provides the block structure of the algebra based on U = exp(T) i.e. anti-hermitian generators
// P_{antihermitian} does in-adj(in) / 2
iMatrix<vtype,N> ret(arg);
double factor = (1.0/(double)N);
vtype nrm;
nrm = 0.5;
ret = arg - (trace(arg)*factor);
for(int c1=0;c1<N/2;c1++)
{
for(int c2=0;c2<N/2;c2++)
{
ret._internal[c1][c2] = nrm*(conjugate(ret._internal[c1+N/2][c2+N/2]) + ret._internal[c1][c2]); // new[up-left] = old[up-left]+old*[down-right]
ret._internal[c1][c2+N/2] = nrm*(ret._internal[c1][c2+N/2] - conjugate(ret._internal[c1+N/2][c2])); // new[up-right] = old[up-right]-old*[down-left]
}
for(int c2=N/2;c2<N;c2++)
{
ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]); // reconstructs lower blocks
ret._internal[c1+N/2][c2] = conjugate(ret._internal[c1][c2-N/2]); // from upper blocks
}
}
ret = (ret - adj(ret))*0.5;
return ret;
}
///////////////////////////////////////////////
// ProjectOnGroup function for scalar, vector, matrix
// Projects on orthogonal, unitary group
///////////////////////////////////////////////
template<class vtype> accelerator_inline iScalar<vtype> ProjectOnGroup(const iScalar<vtype>&r)
{
iScalar<vtype> ret;
ret._internal = ProjectOnGroup(r._internal);
return ret;
}
template<class vtype,int N> accelerator_inline iVector<vtype,N> ProjectOnGroup(const iVector<vtype,N>&r)
{
iVector<vtype,N> ret;
for(int i=0;i<N;i++){
ret._internal[i] = ProjectOnGroup(r._internal[i]);
}
return ret;
}
template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
accelerator_inline iMatrix<vtype,N> ProjectOnGroup(const iMatrix<vtype,N> &arg)
{
typedef typename iMatrix<vtype,N>::scalar_type scalar;
// need a check for the group type?
iMatrix<vtype,N> ret(arg);
vtype nrm;
vtype inner;
scalar one(1.0);
for(int c1=0;c1<N;c1++){
// Normalises row c1
zeroit(inner);
for(int c2=0;c2<N;c2++)
inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
nrm = sqrt(inner);
nrm = one/nrm;
for(int c2=0;c2<N;c2++)
ret._internal[c1][c2]*= nrm;
// Remove c1 from rows c1+1...N-1
for (int b=c1+1; b<N; ++b){
decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
zeroit(pr);
for(int c=0; c<N; ++c)
pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];
for(int c=0; c<N; ++c){
ret._internal[b][c] -= pr * ret._internal[c1][c];
}
}
}
// Normalise last row
{
int c1 = N-1;
zeroit(inner);
for(int c2=0;c2<N;c2++)
inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
nrm = sqrt(inner);
nrm = one/nrm;
for(int c2=0;c2<N;c2++)
ret._internal[c1][c2]*= nrm;
}
// assuming the determinant is ok
return ret;
}
// re-do for sp2n
// Ta cannot be defined here for Sp2n because I need the generators from the Sp class
// It is defined in gauge impl types
template<class vtype> accelerator_inline iScalar<vtype> ProjectOnSpGroup(const iScalar<vtype>&r)
{
iScalar<vtype> ret;
ret._internal = ProjectOnSpGroup(r._internal);
return ret;
}
template<class vtype,int N> accelerator_inline iVector<vtype,N> ProjectOnSpGroup(const iVector<vtype,N>&r)
{
iVector<vtype,N> ret;
for(int i=0;i<N;i++){
ret._internal[i] = ProjectOnSpGroup(r._internal[i]);
}
return ret;
}
// int N is 2n in Sp(2n)
template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg)
{
// need a check for the group type?
iMatrix<vtype,N> ret(arg);
vtype nrm;
vtype inner;
for(int c1=0;c1<N/2;c1++)
{
for (int b=0; b<c1; b++) // remove the b-rows from U_c1
{
decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
decltype(ret._internal[b][b]*ret._internal[b][b]) prn;
zeroit(pr);
zeroit(prn);
for(int c=0; c<N; c++)
{
pr += conjugate(ret._internal[c1][c])*ret._internal[b][c]; // <U_c1 | U_b >
prn += conjugate(ret._internal[c1][c])*ret._internal[b+N/2][c]; // <U_c1 | U_{b+N} >
}
for(int c=0; c<N; c++)
{
ret._internal[c1][c] -= (conjugate(pr) * ret._internal[b][c] + conjugate(prn) * ret._internal[b+N/2][c] ); // U_c1 -= ( <U_c1 | U_b > U_b + <U_c1 | U_{b+N} > U_{b+N} )
}
}
zeroit(inner);
for(int c2=0;c2<N;c2++)
{
inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
}
nrm = sqrt(inner);
nrm = 1.0/nrm;
for(int c2=0;c2<N;c2++)
{
ret._internal[c1][c2]*= nrm;
}
for(int c2=0;c2<N/2;c2++)
{
ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]); // down right in the new matrix = (up-left)* of the old matrix
}
for(int c2=N/2;c2<N;c2++)
{
ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);; // down left in the new matrix = -(up-right)* of the old
}
}
return ret;
}
NAMESPACE_END(Grid);
#endif
View Git Blame Copy Permalink