// Build a SU(3)-matrix from a random complex matrix and a back-projection
static Eigen::Matrix3cd construct_random_su3() {
std::vector<std::complex<double>> random(9);
// 9 complex random numbers
for (auto &c : random)
c = std::complex<double>((double(rand()) / RAND_MAX) - 0.5,
(double(rand()) / RAND_MAX) - 0.5);
Eigen::Matrix3cd y =
Eigen::Matrix<std::complex<double>, 3, 3, Eigen::RowMajor>(random.data());
y = proj_to_su3_imp(y);
check_su3(y);
return y;
}
/*----------------------------------------------------------------------*/
float ck_unitarity(su3_matrix *work,int x, int y, int z, int t)
{
register int dir;
register su3_matrix *mat;
static int errcount = 0;
int ii,jj;
float deviation,max_deviation;
union {
float fval;
int ival;
} ifval;
float check_su3(su3_matrix *c);
mat = work;
max_deviation=0;
for(dir = 0; dir < 3; dir++)
{
deviation = check_su3(&work[dir]);
if (deviation>TOLERANCE){
printf("Unitarity problem on node %d, site (%d,%d,%d,%d) dir %d, deviation=%f\n",
mynode(),x,y,z,t,dir,deviation);
printf("SU3 matrix:\n");
for(ii=0;ii<=2;ii++){
for(jj=0;jj<=2;jj++){
printf("%f ",(*mat).e[ii][jj].real);
printf("%f ",(*mat).e[ii][jj].imag);
}
printf("\n");
}
printf("repeat in hex:\n");
for(ii=0;ii<=2;ii++){
for(jj=0;jj<=2;jj++){
ifval.fval = (*mat).e[ii][jj].real;
printf("%08x ", ifval.ival);
ifval.fval = (*mat).e[ii][jj].imag;
printf("%08x ", ifval.ival);
}
printf("\n");
}
printf(" \n \n");
if(errcount++ >= MAXERRCOUNT)
{
fflush(stdout); terminate(1);
}
}
if(max_deviation<deviation) max_deviation=deviation;
}
return max_deviation;
}
Real check_unitarity() {
register int i,dir;
int ii,jj;
register site *s;
register su3_matrix *mat;
Real deviation,max_deviation;
double av_deviation;
union {
Real fval;
int ival;
} ifval;
max_deviation=av_deviation=0;
FORALLSITES(i,s){
#ifdef SCHROED_FUN
for(dir=XUP; dir<=TUP; dir++ ) if(dir==TUP || s->t>0){
#else
for(dir=XUP; dir<=TUP; dir++ ){
#endif
mat = (su3_matrix *)&(s->link[dir]);
deviation=check_su3( mat );
if (deviation>TOLERANCE){
printf("Unitarity problem on node %d, site %d, dir %d, deviation=%f\n",
mynode(),i,dir,deviation);
printf("SU3 matrix:\n");
for(ii=0;ii<=2;ii++){
for(jj=0;jj<=2;jj++){
printf("%f ",(*mat).e[ii][jj].real);
printf("%f ",(*mat).e[ii][jj].imag);
}
printf("\n");
}
printf("repeat in hex:\n");
for(ii=0;ii<=2;ii++){
for(jj=0;jj<=2;jj++){
ifval.fval = (*mat).e[ii][jj].real;
printf("%08x ", ifval.ival);
ifval.fval = (*mat).e[ii][jj].imag;
printf("%08x ", ifval.ival);
}
printf("\n");
}
printf(" \n \n");
fflush(stdout); terminate(1);
}
if(max_deviation<deviation) max_deviation=deviation;
av_deviation += deviation*deviation;
}
}
av_deviation = sqrt(av_deviation/(4*i));
#ifdef UNIDEBUG
printf("Deviation from unitarity on node %d: max %g, avrg %g\n",
mynode(), max_deviation, av_deviation);
#endif
if(max_deviation> TOLERANCE)
printf("Unitarity problem on node %d, maximum deviation=%f\n",
mynode(),max_deviation);
return max_deviation;
} /*check_unitarity() */
Real check_su3(su3_matrix *c) {
register Real ar, ai, ari, max;
register int i;
/* first normalize row */
for(i=0 , max=0.; i<3; ++i) {
ar = (*c).e[i][0].real * (*c).e[i][0].real + /* sum of squares of row */
(*c).e[i][0].imag * (*c).e[i][0].imag +
(*c).e[i][1].real * (*c).e[i][1].real +
(*c).e[i][1].imag * (*c).e[i][1].imag +
(*c).e[i][2].real * (*c).e[i][2].real +
(*c).e[i][2].imag * (*c).e[i][2].imag;
ar = fabs( sqrt((double)ar) - 1.);
if(max<ar) max=ar;
}
#ifdef STRONG
/* Test orthogonality of row 0 and row 1 */
ar = (*c).e[0][0].real * (*c).e[1][0].real + /* real part of 0 dot 1 */
(*c).e[0][0].imag * (*c).e[1][0].imag +
(*c).e[0][1].real * (*c).e[1][1].real +
(*c).e[0][1].imag * (*c).e[1][1].imag +
(*c).e[0][2].real * (*c).e[1][2].real +
(*c).e[0][2].imag * (*c).e[1][2].imag;
ai = (*c).e[0][0].real * (*c).e[1][0].imag - /* imag part of 0 dot 1 */
(*c).e[0][0].imag * (*c).e[1][0].real +
(*c).e[0][1].real * (*c).e[1][1].imag -
(*c).e[0][1].imag * (*c).e[1][1].real +
(*c).e[0][2].real * (*c).e[1][2].imag -
(*c).e[0][2].imag * (*c).e[1][2].real;
ari = sqrt((double)(ar*ar + ai*ai));
if(max<ari) max=ari;
/* Test orthogonality of row 0 and row 2 */
ar = (*c).e[0][0].real * (*c).e[2][0].real + /* real part of 0 dot 1 */
(*c).e[0][0].imag * (*c).e[2][0].imag +
(*c).e[0][1].real * (*c).e[2][1].real +
(*c).e[0][1].imag * (*c).e[2][1].imag +
(*c).e[0][2].real * (*c).e[2][2].real +
(*c).e[0][2].imag * (*c).e[2][2].imag;
ai = (*c).e[0][0].real * (*c).e[2][0].imag - /* imag part of 0 dot 1 */
(*c).e[0][0].imag * (*c).e[2][0].real +
(*c).e[0][1].real * (*c).e[2][1].imag -
(*c).e[0][1].imag * (*c).e[2][1].real +
(*c).e[0][2].real * (*c).e[2][2].imag -
(*c).e[0][2].imag * (*c).e[2][2].real;
ari = sqrt((double)(ar*ar + ai*ai));
if(max<ari) max=ari;
/* Test orthogonality of row 1 and row 2 */
ar = (*c).e[1][0].real * (*c).e[2][0].real + /* real part of 0 dot 1 */
(*c).e[1][0].imag * (*c).e[2][0].imag +
(*c).e[1][1].real * (*c).e[2][1].real +
(*c).e[1][1].imag * (*c).e[2][1].imag +
(*c).e[1][2].real * (*c).e[2][2].real +
(*c).e[1][2].imag * (*c).e[2][2].imag;
ai = (*c).e[1][0].real * (*c).e[2][0].imag - /* imag part of 0 dot 1 */
(*c).e[1][0].imag * (*c).e[2][0].real +
(*c).e[1][1].real * (*c).e[2][1].imag -
(*c).e[1][1].imag * (*c).e[2][1].real +
(*c).e[1][2].real * (*c).e[2][2].imag -
(*c).e[1][2].imag * (*c).e[2][2].real;
ari = sqrt((double)(ar*ar + ai*ai));
if(max<ari) max=ari;
#endif /*STRONG*/
return(max);
} /* check_su3 */