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Grid/tests/core/Test_gamma.cc

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/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./tests/Test_gamma.cc
Copyright (C) 2015-2017
Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: Antonin Portelli <antonin.portelli@ed.ac.uk>
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 */
#include <Grid/Grid.h>
using namespace Grid;
static constexpr double tolerance = 1.0e-6;
static std::array<SpinMatrix, Gamma::nGamma> testAlgebra;
void print(const SpinMatrix &g)
{
for(int i = 0; i < Ns; i++)
{
std::cout << GridLogMessage << "(";
for(int j=0;j<Ns;j++){
if ( abs(g()(i,j)()) == 0 ) {
std::cout<< " 0";
} else if ( abs(g()(i,j)() - Complex(0,1)) == 0){
std::cout<< " i";
} else if ( abs(g()(i,j)() + Complex(0,1)) == 0){
std::cout<< "-i";
} else if ( abs(g()(i,j)() - Complex(1,0)) == 0){
std::cout<< " 1";
} else if ( abs(g()(i,j)() + Complex(1,0)) == 0){
std::cout<< "-1";
}
std::cout<<((j == Ns-1) ? ")" : "," );
}
std::cout << std::endl;
}
std::cout << GridLogMessage << std::endl;
}
void createTestAlgebra(void)
{
std::array<SpinMatrix, 4> testg;
SpinMatrix testg5;
const Complex I(0., 1.), mI(0., -1.);
testg[0] = Zero();
testg[0]()(0, 3) = I;
testg[0]()(1, 2) = I;
testg[0]()(2, 1) = mI;
testg[0]()(3, 0) = mI;
std::cout << GridLogMessage << "test GammaX= " << std::endl;
print(testg[0]);
testg[1] = Zero();
testg[1]()(0, 3) = -1.;
testg[1]()(1, 2) = 1.;
testg[1]()(2, 1) = 1.;
testg[1]()(3, 0) = -1.;
std::cout << GridLogMessage << "test GammaY= " << std::endl;
print(testg[1]);
testg[2] = Zero();
testg[2]()(0, 2) = I;
testg[2]()(1, 3) = mI;
testg[2]()(2, 0) = mI;
testg[2]()(3, 1) = I;
std::cout << GridLogMessage << "test GammaZ= " << std::endl;
print(testg[2]);
testg[3] = Zero();
testg[3]()(0, 2) = 1.;
testg[3]()(1, 3) = 1.;
testg[3]()(2, 0) = 1.;
testg[3]()(3, 1) = 1.;
std::cout << GridLogMessage << "test GammaT= " << std::endl;
print(testg[3]);
testg5 = testg[0]*testg[1]*testg[2]*testg[3];
#define DEFINE_TEST_G(g, exp)\
testAlgebra[Gamma::Algebra::g] = exp;\
testAlgebra[Gamma::Algebra::Minus##g] = -exp;\
DEFINE_TEST_G(Identity , 1.);
DEFINE_TEST_G(Gamma5 , testg5);
DEFINE_TEST_G(GammaX , testg[0]);
DEFINE_TEST_G(GammaY , testg[1]);
DEFINE_TEST_G(GammaZ , testg[2]);
DEFINE_TEST_G(GammaT , testg[3]);
DEFINE_TEST_G(GammaXGamma5, testg[0]*testg5);
DEFINE_TEST_G(GammaYGamma5, testg[1]*testg5);
DEFINE_TEST_G(GammaZGamma5, testg[2]*testg5);
DEFINE_TEST_G(GammaTGamma5, testg[3]*testg5);
DEFINE_TEST_G(SigmaXY , .5*(testg[0]*testg[1] - testg[1]*testg[0]));
DEFINE_TEST_G(SigmaXZ , .5*(testg[0]*testg[2] - testg[2]*testg[0]));
DEFINE_TEST_G(SigmaXT , .5*(testg[0]*testg[3] - testg[3]*testg[0]));
DEFINE_TEST_G(SigmaYZ , .5*(testg[1]*testg[2] - testg[2]*testg[1]));
DEFINE_TEST_G(SigmaYT , .5*(testg[1]*testg[3] - testg[3]*testg[1]));
DEFINE_TEST_G(SigmaZT , .5*(testg[2]*testg[3] - testg[3]*testg[2]));
#undef DEFINE_TEST_G
}
template <typename Expr>
void test(const Expr &a, const Expr &b)
{
if (norm2(a - b) < tolerance)
{
std::cout << "[OK] ";
}
else
{
std::cout << "[fail]" << std::endl;
std::cout << GridLogError << "a= " << a << std::endl;
std::cout << GridLogError << "is different (tolerance= " << tolerance << ") from " << std::endl;
std::cout << GridLogError << "b= " << b << std::endl;
exit(EXIT_FAILURE);
}
}
void checkGamma(const Gamma::Algebra a, GridSerialRNG &rng)
{
SpinVector v;
SpinMatrix m, &testg = testAlgebra[a];
Gamma g(a);
random(rng, v);
random(rng, m);
std::cout << GridLogMessage << "Checking " << Gamma::name[a] << ": ";
std::cout << "vecmul ";
test(g*v, testg*v);
std::cout << "matlmul ";
test(g*m, testg*m);
std::cout << "matrmul ";
test(m*g, m*testg);
std::cout << std::endl;
}
void checkProd(const Gamma::Algebra a, const Gamma::Algebra b)
{
SpinMatrix gm, testg = testAlgebra[a]*testAlgebra[b];
Gamma g = Gamma(a)*Gamma(b);
std::cout << GridLogMessage << "Checking " << Gamma::name[a] << " * "
<< Gamma::name[b] << ": ";
gm = 1.0;
gm = g*gm;
test(gm, testg);
std::cout << "(= " << Gamma::name[g.g] << ")" << std::endl;
}
void checkAdj(const Gamma::Algebra a)
{
SpinMatrix gm, testg = adj(testAlgebra[a]);
Gamma g(adj(Gamma(a)));
std::cout << GridLogMessage << "Checking adj(" << Gamma::name[a] << "): ";
gm = 1.0;
gm = g*gm;
test(gm, testg);
std::cout << "(= " << Gamma::name[g.g] << ")" << std::endl;
}
void checkProject(GridSerialRNG &rng)
{
SpinVector rv, recon;
HalfSpinVector hsm;
random(rng, rv);
#define CHECK_PROJ(dir, gamma)\
std::cout << GridLogMessage << "Checking " << #dir << " projector: ";\
spProj##dir(hsm,rv);\
spRecon##dir(recon,hsm);\
test(recon, rv + Gamma(Gamma::Algebra::gamma)*rv);\
std::cout << std::endl;
CHECK_PROJ(Xp, GammaX);
CHECK_PROJ(Yp, GammaY);
CHECK_PROJ(Zp, GammaZ);
CHECK_PROJ(Tp, GammaT);
CHECK_PROJ(5p, Gamma5);
CHECK_PROJ(Xm, MinusGammaX);
CHECK_PROJ(Ym, MinusGammaY);
CHECK_PROJ(Zm, MinusGammaZ);
CHECK_PROJ(Tm, MinusGammaT);
CHECK_PROJ(5m, MinusGamma5);
#undef CHECK_PROJ
}
void checkGammaL(const Gamma::Algebra a, GridSerialRNG &rng)
{
SpinVector v;
SpinMatrix m, &testg = testAlgebra[a], pl;
GammaL gl(a);
random(rng, v);
random(rng, m);
pl = testAlgebra[Gamma::Algebra::Identity]
- testAlgebra[Gamma::Algebra::Gamma5];
std::cout << GridLogMessage << "Checking left-projected " << Gamma::name[a] << ": ";
std::cout << "vecmul ";
test(gl*v, testg*pl*v);
std::cout << "matlmul ";
test(gl*m, testg*pl*m);
std::cout << "matrmul ";
test(m*gl, m*testg*pl);
std::cout << std::endl;
}
int main(int argc, char *argv[])
{
Grid_init(&argc,&argv);
Coordinate latt_size = GridDefaultLatt();
Coordinate simd_layout = GridDefaultSimd(4,vComplex::Nsimd());
Coordinate mpi_layout = GridDefaultMpi();
GridCartesian Grid(latt_size,simd_layout,mpi_layout);
GridSerialRNG sRNG;
sRNG.SeedFixedIntegers(std::vector<int>({45,12,81,9}));
std::cout << GridLogMessage << "======== Test algebra" << std::endl;
createTestAlgebra();
std::cout << GridLogMessage << "======== Multiplication operators check" << std::endl;
for (int i = 0; i < Gamma::nGamma; ++i)
{
checkGamma(i, sRNG);
}
std::cout << GridLogMessage << std::endl;
std::cout << GridLogMessage << "======== Algebra multiplication table check" << std::endl;
for (int i = 0; i < Gamma::nGamma; ++i)
for (int j = 0; j < Gamma::nGamma; ++j)
{
checkProd(i, j);
}
std::cout << GridLogMessage << std::endl;
std::cout << GridLogMessage << "======== Adjoints check" << std::endl;
for (int i = 0; i < Gamma::nGamma; ++i)
{
checkAdj(i);
}
std::cout << GridLogMessage << std::endl;
std::cout << GridLogMessage << "======== Spin projectors check" << std::endl;
checkProject(sRNG);
std::cout << GridLogMessage << std::endl;
std::cout << GridLogMessage << "======== Gamma-left matrices check" << std::endl;
for (int i = 0; i < Gamma::nGamma; ++i)
{
checkGammaL(i, sRNG);
}
Grid_finalize();
return EXIT_SUCCESS;
}
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