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Q_phi2_imp.c
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Q_phi2_imp.c
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/*********************************************
* Q_phi2.c
*
* Wed Nov 18 09:26:06 CET 2009
*
* PURPOSE:
* - function to recursively calculate
* xi = (H^deg phi)(x) for point source phi
* TODO:
* - improve Hopping_iter
* (1) at (sigma_n, mu_n) check, if (sigma_(n+1), mu_(n+1)) = (-sigma_n, mu_n),
* if so, skip multiplication
* (2) avoid calculation of forward loops, take complex conjugate of backward loops
* (3) reduce loops before starting Hopping_iter
* DONE:
* - tested HPE matrix calculation _fv_eq_hpem_ti_fv
* against the stepwise calculation
* CHANGES:
*********************************************/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#ifdef MPI
# include <mpi.h>
#endif
#include "cvc_complex.h"
#include "global.h"
#include "cvc_linalg.h"
#include "cvc_geometry.h"
#include "cvc_utils.h"
#include "Q_phi.h"
/****************************************************************************
* void Hopping_rec(double *xi, double *phi, int xd, int xs, int l, int deg, int *steps)
*
* xi destination (target spinor field at destination point)
* phi source (source spinor field at source location)
* xd destination lattice site
* xs source lattice site
* l level (current exponent of H)
* deg degree (final exponent of H)
****************************************************************************/
void Hopping_rec(double *xi, double *phi, int xd, int xs, int l, int deg, int *steps) {
int steps_new[4];
double SU3_1[18];
double spinor1[24], spinor2[24];
double norminv = 1. / (1. + 4. * g_kappa*g_kappa * g_mu*g_mu);
double *xi_, *U_;
if(l<deg) {
/**************************************
* call Hopping_rec with for two sites
* at next level l+1
**************************************/
_fv_eq_zero(xi);
/* Negative t-direction. */
if( abs(steps[0]-1)+abs(steps[1])+abs(steps[2])+abs(steps[3]) <= (deg-l) ) {
steps_new[0] = steps[0]-1; steps_new[1] = steps[1];
steps_new[2] = steps[2]; steps_new[3] = steps[3];
Hopping_rec(spinor1, phi, g_idn[xd][0], xs, l+1, deg, steps_new);
_fv_eq_gamma_ti_fv(spinor2, 0, spinor1);
_fv_pl_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(g_idn[xd][0], 0);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[0]);
_fv_eq_cm_dag_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Positive t-direction. */
if( abs(steps[0]+1)+abs(steps[1])+abs(steps[2])+abs(steps[3]) <= (deg-l) ) {
steps_new[0] = steps[0]+1; steps_new[1] = steps[1];
steps_new[2] = steps[2]; steps_new[3] = steps[3];
Hopping_rec(spinor1, phi, g_iup[xd][0], xs, l+1, deg, steps_new);
_fv_eq_gamma_ti_fv(spinor2, 0, spinor1);
_fv_mi_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(xd, 0);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[0]);
_fv_eq_cm_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Negative x-direction. */
if( abs(steps[0])+abs(steps[1]-1)+abs(steps[2])+abs(steps[3]) <= (deg-l) ) {
steps_new[0] = steps[0]; steps_new[1] = steps[1]-1;
steps_new[2] = steps[2]; steps_new[3] = steps[3];
Hopping_rec(spinor1, phi, g_idn[xd][1], xs, l+1, deg, steps_new);
_fv_eq_gamma_ti_fv(spinor2, 1, spinor1);
_fv_pl_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(g_idn[xd][1], 1);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[1]);
_fv_eq_cm_dag_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Positive x-direction. */
if( abs(steps[0])+abs(steps[1]+1)+abs(steps[2])+abs(steps[3]) <= (deg-l) ) {
steps_new[0] = steps[0]; steps_new[1] = steps[1]+1;
steps_new[2] = steps[2]; steps_new[3] = steps[3];
Hopping_rec(spinor1, phi, g_iup[xd][1], xs, l+1, deg, steps_new);
_fv_eq_gamma_ti_fv(spinor2, 1, spinor1);
_fv_mi_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(xd, 1);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[1]);
_fv_eq_cm_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Negative y-direction. */
if( abs(steps[0])+abs(steps[1])+abs(steps[2]-1)+abs(steps[3]) <= (deg-l) ) {
steps_new[0] = steps[0]; steps_new[1] = steps[1];
steps_new[2] = steps[2]-1; steps_new[3] = steps[3];
Hopping_rec(spinor1, phi, g_idn[xd][2], xs, l+1, deg, steps_new);
_fv_eq_gamma_ti_fv(spinor2, 2, spinor1);
_fv_pl_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(g_idn[xd][2], 2);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[2]);
_fv_eq_cm_dag_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Positive y-direction. */
if( abs(steps[0])+abs(steps[1])+abs(steps[2]+1)+abs(steps[3]) <= (deg-l) ) {
steps_new[0] = steps[0]; steps_new[1] = steps[1];
steps_new[2] = steps[2]+1; steps_new[3] = steps[3];
Hopping_rec(spinor1, phi, g_iup[xd][2], xs, l+1, deg, steps_new);
_fv_eq_gamma_ti_fv(spinor2, 2, spinor1);
_fv_mi_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(xd, 2);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[2]);
_fv_eq_cm_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Negative z-direction. */
if( abs(steps[0])+abs(steps[1])+abs(steps[2])+abs(steps[3]-1) <= (deg-l) ) {
steps_new[0] = steps[0]; steps_new[1] = steps[1];
steps_new[2] = steps[2]; steps_new[3] = steps[3]-1;
Hopping_rec(spinor1, phi, g_idn[xd][3], xs, l+1, deg, steps_new);
_fv_eq_gamma_ti_fv(spinor2, 3, spinor1);
_fv_pl_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(g_idn[xd][3], 3);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[3]);
_fv_eq_cm_dag_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Positive z-direction. */
if( abs(steps[0])+abs(steps[1])+abs(steps[2])+abs(steps[3]+1) <= (deg-l) ) {
steps_new[0] = steps[0]; steps_new[1] = steps[1];
steps_new[2] = steps[2]; steps_new[3] = steps[3]+1;
Hopping_rec(spinor1, phi, g_iup[xd][3], xs, l+1, deg, steps_new);
_fv_eq_gamma_ti_fv(spinor2, 3, spinor1);
_fv_mi_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(xd, 3);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[3]);
_fv_eq_cm_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Multiplication with -kappa (hopping parameter repr.) */
_fv_ti_eq_re(xi, -g_kappa);
/* apply Inverse of 1+i gamma5 mu */
_fv_eq_gamma_ti_fv(spinor1, 5, xi);
_fv_eq_fv_ti_im(spinor2, spinor1, -2.*g_kappa*g_mu);
_fv_eq_fv_pl_fv(spinor1, xi, spinor2);
_fv_eq_fv_ti_re(xi, spinor1, norminv);
} /* of if l<deg ... */
if(l==deg) {
/**************************************
* apply the Hopping matrix to the
* source field
**************************************/
_fv_eq_zero(xi);
/* Negative t-direction. */
if(g_idn[xd][0] == xs) {
_fv_eq_gamma_ti_fv(spinor1, 5, phi);
_fv_eq_fv_ti_im(spinor2, spinor1, -2.*g_kappa*g_mu);
_fv_pl_eq_fv(spinor2, phi);
_fv_eq_fv_ti_re(spinor1, spinor2, norminv);
_fv_eq_gamma_ti_fv(spinor2, 0, spinor1);
_fv_pl_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(g_idn[xd][0], 0);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[0]);
_fv_eq_cm_dag_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Positive t-direction. */
if(g_iup[xd][0] == xs) {
_fv_eq_gamma_ti_fv(spinor1, 5, phi);
_fv_eq_fv_ti_im(spinor2, spinor1, -2.*g_kappa*g_mu);
_fv_pl_eq_fv(spinor2, phi);
_fv_eq_fv_ti_re(spinor1, spinor2, norminv);
_fv_eq_gamma_ti_fv(spinor2, 0, spinor1);
_fv_mi_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(xd, 0);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[0]);
_fv_eq_cm_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Negative x-direction. */
if(g_idn[xd][1] == xs) {
_fv_eq_gamma_ti_fv(spinor1, 5, phi);
_fv_eq_fv_ti_im(spinor2, spinor1, -2.*g_kappa*g_mu);
_fv_pl_eq_fv(spinor2, phi);
_fv_eq_fv_ti_re(spinor1, spinor2, norminv);
_fv_eq_gamma_ti_fv(spinor2, 1, spinor1);
_fv_pl_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(g_idn[xd][1], 1);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[1]);
_fv_eq_cm_dag_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Positive x-direction. */
if(g_iup[xd][1] == xs) {
_fv_eq_gamma_ti_fv(spinor1, 5, phi);
_fv_eq_fv_ti_im(spinor2, spinor1, -2.*g_kappa*g_mu);
_fv_pl_eq_fv(spinor2, phi);
_fv_eq_fv_ti_re(spinor1, spinor2, norminv);
_fv_eq_gamma_ti_fv(spinor2, 1, spinor1);
_fv_mi_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(xd, 1);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[1]);
_fv_eq_cm_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Negative y-direction. */
if(g_idn[xd][2] == xs) {
_fv_eq_gamma_ti_fv(spinor1, 5, phi);
_fv_eq_fv_ti_im(spinor2, spinor1, -2.*g_kappa*g_mu);
_fv_pl_eq_fv(spinor2, phi);
_fv_eq_fv_ti_re(spinor1, spinor2, norminv);
_fv_eq_gamma_ti_fv(spinor2, 2, spinor1);
_fv_pl_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(g_idn[xd][2], 2);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[2]);
_fv_eq_cm_dag_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Positive y-direction. */
if(g_iup[xd][2] == xs) {
_fv_eq_gamma_ti_fv(spinor1, 5, phi);
_fv_eq_fv_ti_im(spinor2, spinor1, -2.*g_kappa*g_mu);
_fv_pl_eq_fv(spinor2, phi);
_fv_eq_fv_ti_re(spinor1, spinor2, norminv);
_fv_eq_gamma_ti_fv(spinor2, 2, spinor1);
_fv_mi_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(xd, 2);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[2]);
_fv_eq_cm_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Negative z-direction. */
if(g_idn[xd][3] == xs) {
_fv_eq_gamma_ti_fv(spinor1, 5, phi);
_fv_eq_fv_ti_im(spinor2, spinor1, -2.*g_kappa*g_mu);
_fv_pl_eq_fv(spinor2, phi);
_fv_eq_fv_ti_re(spinor1, spinor2, norminv);
_fv_eq_gamma_ti_fv(spinor2, 3, spinor1);
_fv_pl_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(g_idn[xd][3], 3);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[3]);
_fv_eq_cm_dag_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Positive z-direction. */
if(g_iup[xd][3] == xs) {
_fv_eq_gamma_ti_fv(spinor1, 5, phi);
_fv_eq_fv_ti_im(spinor2, spinor1, -2.*g_kappa*g_mu);
_fv_pl_eq_fv(spinor2, phi);
_fv_eq_fv_ti_re(spinor1, spinor2, norminv);
_fv_eq_gamma_ti_fv(spinor2, 3, spinor1);
_fv_mi_eq_fv(spinor1, spinor2);
U_ = g_gauge_field + _GGI(xd, 3);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[3]);
_fv_eq_cm_ti_fv(spinor2, SU3_1, spinor1);
_fv_pl_eq_fv(xi, spinor2);
}
/* Multiplication with -kappa (hopping parameter repr.) */
_fv_ti_eq_re(xi, -g_kappa);
/* apply Inverse of 1+i gamma5 mu */
_fv_eq_gamma_ti_fv(spinor1, 5, xi);
_fv_eq_fv_ti_im(spinor2, spinor1, -2.*g_kappa*g_mu);
_fv_eq_fv_pl_fv(spinor1, xi, spinor2);
_fv_eq_fv_ti_re(xi, spinor1, norminv);
} /* of l==deg */
}
/****************************************************************************
* void init_trace_coeff()
*
****************************************************************************/
void init_trace_coeff(double **tcf, double **tcb, int ***loop_tab, int deg, int *N) {
int l, l1, mu, steps[4], steps2[4], count, isign, sid, nloop, ix;
int *loop, Nloop_max, end_flag;
int **lpath, dist;
double spinor1[24], spinor2[24], *sp1, *sp2, *sp3;
double mutilde = 2.*g_kappa*g_mu;
double norminv = 1. / (1. + mutilde*mutilde);
double sigma;
double kappatodeg=1;
loop = (int*)malloc(deg*sizeof(int));
Nloop_max=8; for(l=2; l<=deg; l++) Nloop_max*=8;
if(g_cart_id==0) fprintf(stdout, "deg=%d, Nloop_max=%d\n", deg, Nloop_max);
lpath = (int**)malloc(Nloop_max*sizeof(int*));
for(l=1; l<=deg; l++) kappatodeg *= -g_kappa; kappatodeg*=g_kappa;
fprintf(stdout, "kappatodeg = %25.16e\n", kappatodeg);
/********************************************************
* (1) count the loops
********************************************************/
nloop = 0;
for(l=0; l<deg; l++) loop[l]=0;
for(ix=0; ix<Nloop_max; ix++) {
steps[0]=0; steps[1]=0; steps[2]=0; steps[3]=0;
steps[0]++;
for(l=0; l<deg; l++) {
if(loop[l]<4) {
steps[loop[l]]++;
} else {
steps[loop[l]-4]--;
}
dist = abs(steps[0]) + abs(steps[1]) + abs(steps[2]) + abs(steps[3]);
/* fprintf(stdout, "ix=%5d; l=%1d; steps= %1d, %1d, %1d, %1d; loop= %1d, %1d, %1d; dist=%d\n", \
ix, l, steps[0], steps[1], steps[2], steps[3], loop[0], loop[1], loop[2], dist);
*/
if(abs(steps[0]) + abs(steps[1]) + abs(steps[2]) + abs(steps[3]) < deg-l ) {
if(l==deg-1) {
nloop++;
/* fprintf(stdout, "found loop number %d\n", nloop); */
lpath[nloop-1] = (int*)malloc(deg*sizeof(int));
for(l1=0; l1<deg; l1++) lpath[nloop-1][l1] = loop[l1];
}
} else {
/* fprintf(stdout, "dist too large ...\n"); */
/*
l1 = l;
while( l1>=0 && (loop[l1]+1)%8==0 ) l1--;
l=l1;
fprintf(stdout, "\tnew l = %d\n", l);
loop[l] = (loop[l]+1)%8;
for(l1=l+1; l1<deg; l1++) loop[l1]=0;
fprintf(stdout, "\tnew loop = %1d, %1d, %1d\n", loop[0], loop[1], loop[2]);
l--;
*/
break;
}
}
/*
end_flag=1;
for(l=0; l<deg; l++) end_flag *= (loop[l]==7);
fprintf(stdout, "\tix=%d; end_flag=%d\n", ix, end_flag);
if(end_flag==1) break;
*/
l1=deg-1;
while( l1>=0 && (loop[l1]=(loop[l1]+1)%8)==0 ) l1--;
/* fprintf(stdout, "\tnew loop = %1d, %1d, %1d\n", loop[0], loop[1], loop[2]); */
} /* of ix */
/*
if(g_cart_id==0) {
fprintf(stdout, "nloop = %d\n", nloop);
fprintf(stdout, "\nlpath table: \n");
for(l=0; l<nloop; l++) {
fprintf(stdout, "%3d: ", l);
for(l1=0; l1<deg-1; l1++) {
if(lpath[l][l1]<4) {
fprintf(stdout, "\t+%1d", lpath[l][l1]);
} else {
fprintf(stdout, "\t-%1d", lpath[l][l1]-4);
}
}
if(lpath[l][deg-1]<4) {
fprintf(stdout, "\t+%1d\n", lpath[l][deg-1]);
} else {
fprintf(stdout, "\t-%1d\n", lpath[l][deg-1]-4);
}
}
}
*/
/***************************************************
* copy lpath to loop_tab
***************************************************/
*loop_tab = (int**)malloc(nloop * sizeof(int*));
(*loop_tab)[0] = (int* )malloc(nloop * deg * sizeof(int));
for(l=1; l<nloop; l++) (*loop_tab)[l] = (*loop_tab)[l-1] + deg;
for(l=0; l<nloop; l++) memcpy((void*)(*loop_tab)[l], (void*)lpath[l], deg*sizeof(int));
/***************************************************
* print lpath to stdout
***************************************************/
if(g_cart_id==0) {
fprintf(stdout, "nloop = %d\n", nloop);
fprintf(stdout, "\nloop_tab: \n");
for(l=0; l<nloop; l++) {
fprintf(stdout, "%3d: ", l);
for(l1=0; l1<deg-1; l1++) {
if( (*loop_tab)[l][l1]<4) {
fprintf(stdout, "\t+%1d", (*loop_tab)[l][l1]);
} else {
fprintf(stdout, "\t-%1d", (*loop_tab)[l][l1]-4);
}
}
if( (*loop_tab)[l][deg-1]<4) {
fprintf(stdout, "\t+%1d\n", (*loop_tab)[l][deg-1]);
} else {
fprintf(stdout, "\t-%1d\n", (*loop_tab)[l][deg-1]-4);
}
}
}
*N = nloop;
free(loop);
for(l=0; l<nloop; l++) free(lpath[l]);
free(lpath);
/********************************************************
* (2) tcf/b
* _ATTENTION_ isign gives the direction on the lattice,
* i.e. +/-1 means 1 -/+ gamma_mu
* - tcf/b have real and imaginary part
********************************************************/
*tcf = (double*)malloc(2*nloop*sizeof(double));
*tcb = (double*)malloc(2*nloop*sizeof(double));
for(l=0; l<nloop; l++) {
(*tcb)[2*l ] = 0.; (*tcb)[2*l+1] = 0.;
(*tcf)[2*l ] = 0.; (*tcf)[2*l+1] = 0.;
for(sid=0; sid<4; sid++) {
_fv_eq_zero(spinor1);
spinor1[6*sid] = 1.;
sp2 = spinor1; sp1 = spinor2;
for(l1=0; l1<deg; l1++) {
sp3=sp1; sp1=sp2; sp2=sp3;
mu = ((*loop_tab)[l][l1]) % 4;
sigma = - ( 2. * (int)(((*loop_tab)[l][l1]) / 4) - 1. );
_fv_eq_hpem_ti_fv(sp2, sp1, mu, sigma, mutilde, norminv);
}
_fv_eq_hpem_ti_fv(sp1, sp2, 0, +1., mutilde, norminv);
(*tcb)[2*l ] += sp1[6*sid ];
(*tcb)[2*l+1] += sp1[6*sid+1];
_fv_eq_zero(spinor1);
spinor1[6*sid] = 1.;
sp2 = spinor1; sp1 = spinor2;
for(l1=deg-1; l1>=0; l1--) {
sp3=sp1; sp1=sp2; sp2=sp3;
mu = ((*loop_tab)[l][l1]) % 4;
sigma = ( 2. * (int)(((*loop_tab)[l][l1]) / 4) - 1. );
_fv_eq_hpem_ti_fv(sp2, sp1, mu, sigma, mutilde, norminv);
}
_fv_eq_hpem_ti_fv(sp1, sp2, 0, -1., mutilde, norminv);
(*tcf)[2*l ] += sp1[6*sid ];
(*tcf)[2*l+1] += sp1[6*sid+1];
}
(*tcf)[2*l ] *= kappatodeg;
(*tcf)[2*l+1] *= kappatodeg;
(*tcb)[2*l ] *= -kappatodeg;
(*tcb)[2*l+1] *= -kappatodeg;
}
for(l=0; l<nloop; l++) fprintf(stdout, "%4d%25.16e%25.16e%25.16e%25.16e\n", l,
(*tcf)[2*l], (*tcf)[2*l+1], (*tcb)[2*l], (*tcb)[2*l+1]);
}
/****************************************************************************
* void Hopping_iter()
*
****************************************************************************/
void Hopping_iter(double *truf, double *trub, double *tcf, double *tcb, int xd,
int mu, int deg, int nloop, int **loop_tab) {
int l, l1, steps[4], mu1, isign, count, perm[4];
double U1_[18], U2_[18], *u1, *u2, *u3;
int sigma, xs, xnew, xold;
complex w;
for(l=0; l<4; l++) perm[l] = (l+mu)%4;
/* fprintf(stdout, "perm = %2d, %2d, %2d, %2d\n", perm[0], perm[1], perm[2], perm[3]); */
xs = g_iup[xd][mu];
/* fprintf(stdout, "xs = %d\n", xs); */
for(l=0; l<nloop; l++) {
/* fprintf(stdout, "\nbackward loops:\n"); */
_cm_eq_id(U1_);
u2=U1_; u1=U2_;
xnew=xs;
/* fprintf(stdout, "before: xnew = %5d\n", xnew); */
for(l1=0; l1<deg; l1++) {
if(l1<deg-1) {
if( abs(loop_tab[l][l1]-loop_tab[l][l1+1]) == 4 ) {
/* fprintf(stdout, "skipping l1-pair %d, %d for loop %d\n", l1, l1+1, l); */
if(l1==deg-2) {
_cm_eq_cm_dag_ti_cm(u1, g_gauge_field+_GGI(xd, mu), u2);
}
l1++;
continue;
}
} else if(l1==deg-1) {
if( loop_tab[l][l1]>3 && perm[loop_tab[l][l1]%4]==mu ) {
/* fprintf(stdout, "skipping last l1=%d for loop %d\n", l1, l); */
u3=u1; u1=u2; u2=u3;
continue;
}
}
u3=u1; u1=u2; u2=u3;
mu1 = perm[loop_tab[l][l1]%4];
sigma = -(2*(loop_tab[l][l1]/4) - 1);
if(sigma==+1) {
xold=xnew;
xnew = g_iup[xold][mu1];
/* fprintf(stdout, "l=%3d, l1=%3d, step=%2d, sigma=%2d; xnew = %5d; applying U_%1d(%4d)^+\n", l, l1, perm[loop_tab[l][l1]%4], sigma, xnew, mu1, xold);
*/
_cm_eq_cm_dag_ti_cm(u2, g_gauge_field+_GGI(xold, mu1), u1);
} else {
xold=xnew;
xnew = g_idn[xold][mu1];
/* fprintf(stdout, "l=%3d, l1=%3d, step=%2d, sigma=%2d; xnew = %5d, applying U_%1d(%4d)\n", l, l1, perm[loop_tab[l][l1]%4], sigma, xnew, mu1, xnew);
*/
_cm_eq_cm_ti_cm(u2, g_gauge_field+_GGI(xnew, mu1), u1);
}
if(l1==deg-1) {
_cm_eq_cm_dag_ti_cm(u1, g_gauge_field+_GGI(xd, mu), u2);
}
}
/* fprintf(stdout, "current w = %25.16e +i %25.16e\n", w.re, w.im); */
_co_eq_tr_cm(&w, u1);
_co_pl_eq_co_ti_co((complex*)trub, (complex*)(tcb+2*l), &w);
w.im = -w.im;
_co_pl_eq_co_ti_co((complex*)truf, (complex*)(tcf+2*l), &w);
/* fprintf(stdout, "\nforward loops:\n"); */
/*
_cm_eq_id(U1_);
u2=U1_; u1=U2_;
xnew=xd;
for(l1=deg-1; l1>=0; l1--) {
u3=u1; u1=u2; u2=u3;
mu1 = perm[loop_tab[l][l1]%4];
sigma = -(2*(loop_tab[l][l1]/4) - 1);
if(sigma==-1) {
xold=xnew;
xnew = g_iup[xold][mu1];
_cm_eq_cm_dag_ti_cm(u2, g_gauge_field+_GGI(xold, mu1), u1);
} else {
xold=xnew;
xnew = g_idn[xold][mu1];
_cm_eq_cm_ti_cm(u2, g_gauge_field+_GGI(xnew, mu1), u1);
}
}
_cm_eq_cm_ti_cm(u1, g_gauge_field+_GGI(xd, mu), u2);
_co_eq_tr_cm(&w, u1);
_co_pl_eq_co_ti_co((complex*)truf, (complex*)(tcf+2*l), &w);
*/
}
/* fprintf(stdout, "%6d%3d%25.16e%25.16e%25.16e%25.16e\n", xd, mu, truf[0], truf[1], trub[0], trub[1]); */
}
/*********************************************
* functions for testing
*********************************************/
void test_hpem(void) {
int sid, mu, i, j;
double spinor1[24], spinor2[24], spinor3[24], spinor4[24];
double mutilde = 2.*g_kappa*g_mu;
/* double mutilde = 0.; */
double norminv = 1. / (1. + mutilde*mutilde);
/* double norminv = 1.; */
int sigma, count=-1;
for(sigma=-1; sigma<2; sigma+=2) {
for(mu=0; mu<4; mu++) {
for(sid=0; sid<24; sid++) {
_fv_eq_zero(spinor1);
spinor1[sid] = 1.;
/* 1st way */
_fv_eq_gamma_ti_fv(spinor2, 5, spinor1);
_fv_eq_fv_ti_im(spinor3, spinor2, -mutilde);
_fv_eq_fv_pl_fv(spinor2, spinor1, spinor3);
_fv_ti_eq_re(spinor2, norminv);
_fv_eq_gamma_ti_fv(spinor3, mu, spinor2);
if(sigma==-1) {
_fv_mi_eq_fv(spinor2, spinor3);
} else {
_fv_pl_eq_fv(spinor2, spinor3);
}
/* 2nd way */
_fv_eq_hpem_ti_fv(spinor4, spinor1, mu, sigma, mutilde, norminv);
fprintf(stdout, "#----------------------------------------------------------------\n");
for(i=0; i<12; i++) fprintf(stdout, "%5d%3d%2d%3d\t%25.16e%25.16e%25.16e%25.16e\n", \
++count, sigma, mu, sid, spinor2[2*i], spinor2[2*i+1], spinor4[2*i], spinor4[2*i+1]);
}
}
}
}
void test_cm_eq_cm_dag_ti_cm(void) {
int i, j;
double U1[18], U2[18], U3[18];
_cm_eq_cm_dag_ti_cm(U1, g_gauge_field+_GGI(50,3), g_gauge_field+_GGI(30,2));
_cm_eq_cm_dag(U2, g_gauge_field+_GGI(50,3))
_cm_eq_cm_ti_cm(U3, U2, g_gauge_field+_GGI(30,2));
for(i=0; i<9; i++) {
fprintf(stdout, "i=%d; %25.16e%25.16e%25.16e%25.16e\n", i, U1[2*i], U1[2*i+1], U3[2*i], U3[2*i+1]);
}
_cm_eq_cm_dag_ti_cm(U1, g_gauge_field+_GGI(50,3), g_gauge_field+_GGI(50,3));
for(i=0; i<9; i++) {
fprintf(stdout, "i=%d; %25.16e%25.16e\n", i, U1[2*i], U1[2*i+1]);
}
}