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Q_phi.c
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Q_phi.c
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/********************
* Q_phi.c
********************/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#ifdef MPI
# include <mpi.h>
#endif
#ifdef OPENMP
#include <omp.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"
/********************
Q_phi_tbc
- computes xi = Q phi, where Q is the tm Dirac operator with twisted boundary conditions.
- should be compatible with Carsten's implementation of the Dirac operator
in hmc's invert programme
- Q is written as Q = m_0 + i mu gamma_5 + ...
(not in the hopping parameter representation)
- off-diagonal part as:
-1/2 sum over mu [ (1 - gamma_mu) U_mu(x) phi(x+mu) +
(1 + gamma_mu) U_mu(x-mu)^+ phi(x-mu) ]
- diagonal part as: 1 / (2 kappa) phi(x) + i mu gamma_5 \phi(x)
*/
#ifndef OPENMP
void Q_phi_tbc(double *xi, double *phi) {
int it, ix, iy, iz;
int index_s;
double SU3_1[18];
double spinor1[24], spinor2[24];
double *xi_, *phi_, *U_;
double _1_2_kappa = 0.5 / g_kappa;
for(it = 0; it < T; it++) {
for(ix = 0; ix < LX; ix++) {
for(iy = 0; iy < LY; iy++) {
for(iz = 0; iz < LZ; iz++) {
index_s = g_ipt[it][ix][iy][iz];
xi_ = xi + _GSI(index_s);
_fv_eq_zero(xi_);
/* Negative t-direction. */
phi_ = phi + _GSI(g_idn[index_s][0]);
_fv_eq_gamma_ti_fv(spinor1, 0, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][0]);
_fv_eq_gamma_ti_fv(spinor1, 0, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][1]);
_fv_eq_gamma_ti_fv(spinor1, 1, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][1]);
_fv_eq_gamma_ti_fv(spinor1, 1, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][2]);
_fv_eq_gamma_ti_fv(spinor1, 2, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][2]);
_fv_eq_gamma_ti_fv(spinor1, 2, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][3]);
_fv_eq_gamma_ti_fv(spinor1, 3, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][3]);
_fv_eq_gamma_ti_fv(spinor1, 3, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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 -1/2. */
_fv_ti_eq_re(xi_, -0.5);
/* Diagonal elements. */
phi_ = phi + _GSI(index_s);
_fv_eq_fv_ti_re(spinor1, phi_, _1_2_kappa);
_fv_pl_eq_fv(xi_, spinor1);
_fv_eq_gamma_ti_fv(spinor1, 5, phi_);
_fv_eq_fv_ti_im(spinor2, spinor1, g_mu);
_fv_pl_eq_fv(xi_, spinor2);
}
}
}
}
/****************************************
* call xchange_field in calling process
*
#ifdef MPI
xchange_field(xi);
#endif
*
****************************************/
}
#else
void Q_phi_tbc(double *xi, double *phi) {
int ix;
int index_s;
double *xi_, *phi_, *U_;
double _1_2_kappa = 0.5 / g_kappa;
// #pragma omp parallel for private(ix,index_s,phi_,xi_,spinor1,spinor2,U_,SU3_1) shared(phi,xi,T,_1_2_kappa,g_gauge_field,g_iup,g_idn, co_phase_up)
#pragma omp parallel private(ix,index_s,phi_,xi_,U_) shared(phi,xi,_1_2_kappa,g_gauge_field,g_iup,g_idn, co_phase_up, VOLUME)
{
double SU3_1[18];
double spinor1[24], spinor2[24];
int threadid = omp_get_thread_num();
int num_threads = omp_get_num_threads();
for(ix = threadid; ix < VOLUME; ix+=num_threads)
// for(ix = 0; ix < g_num_threads; ix++)
{
#if 0
// TEST
index_s = omp_get_thread_num();
fprintf(stdout, "# [Q_phi_tbc] thread%.4d number of threads = %d\n", index_s, omp_get_num_threads());
fprintf(stdout, "# [Q_phi_tbc] thread%.4d address of spinor1 = %lu\n", index_s, spinor1);
fprintf(stdout, "# [Q_phi_tbc] thread%.4d address of spinor2 = %lu\n", index_s, spinor2);
// TEST
fprintf(stdout, "# [Q_phi_tbc] thread%.4d ix = %d\n", threadid, ix);
#endif
index_s = ix;
xi_ = xi + _GSI(index_s);
_fv_eq_zero(xi_);
/* Negative t-direction. */
phi_ = phi + _GSI(g_idn[index_s][0]);
_fv_eq_gamma_ti_fv(spinor1, 0, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][0]);
_fv_eq_gamma_ti_fv(spinor1, 0, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][1]);
_fv_eq_gamma_ti_fv(spinor1, 1, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][1]);
_fv_eq_gamma_ti_fv(spinor1, 1, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][2]);
_fv_eq_gamma_ti_fv(spinor1, 2, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][2]);
_fv_eq_gamma_ti_fv(spinor1, 2, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][3]);
_fv_eq_gamma_ti_fv(spinor1, 3, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][3]);
_fv_eq_gamma_ti_fv(spinor1, 3, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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 -1/2. */
_fv_ti_eq_re(xi_, -0.5);
/* Diagonal elements. */
phi_ = phi + _GSI(index_s);
_fv_eq_fv_ti_re(spinor1, phi_, _1_2_kappa);
_fv_pl_eq_fv(xi_, spinor1);
_fv_eq_gamma_ti_fv(spinor1, 5, phi_);
_fv_eq_fv_ti_im(spinor2, spinor1, g_mu);
_fv_pl_eq_fv(xi_, spinor2);
}
} // end of parallel region
}
#endif // of ifndef OPENMP
#ifndef OPENMP
void g5_phi(double *phi) {
double spinor1[24];
int ix;
double *phi_;
for(ix = 0; ix < VOLUME; ix++)
{
phi_ = phi + _GSI(ix);
_fv_eq_gamma_ti_fv(spinor1, 5, phi_);
_fv_eq_fv(phi_, spinor1);
}
} // end of g5_phi
#else
void g5_phi(double *phi) {
#pragma omp parallel shared(phi, VOLUME)
{
double spinor1[24];
int threadid = omp_get_thread_num();
int num_threads = omp_get_num_threads();
int ix;
double *phi_;
// TEST
// fprintf(stdout, "# [g5_phi] thread%.4d number of threads %d\n", threadid, num_threads);
for(ix = threadid; ix < VOLUME; ix+=num_threads)
{
phi_ = phi + _GSI(ix);
_fv_eq_gamma_ti_fv(spinor1, 5, phi_);
_fv_eq_fv(phi_, spinor1);
}
} // end of parallel region
} // end of g5_phi
#endif
/**********************************************************************
* Hopping
* - computes xi = H phi, where H is the Dirac Wilson hopping matrix
* - off-diagonal part as:
* - kappa sum over mu [ (1 - gamma_mu) U_mu(x) phi(x+mu) +
* (1 + gamma_mu) U_mu(x-mu)^+ phi(x-mu) ]
* - in the hopping parameter representation
* - _NO_ field exchange in Hopping
**********************************************************************/
void Hopping(double *xi, double *phi) {
int it, ix, iy, iz;
double SU3_1[18];
double spinor1[24], spinor2[24];
int index_s;
double *xi_, *phi_, *U_;
for(it = 0; it < T; it++) {
for(ix = 0; ix < LX; ix++) {
for(iy = 0; iy < LY; iy++) {
for(iz = 0; iz < LZ; iz++) {
index_s = g_ipt[it][ix][iy][iz];
xi_ = xi + _GSI(index_s);
_fv_eq_zero(xi_);
/* Negative t-direction. */
phi_ = phi + _GSI(g_idn[index_s][0]);
_fv_eq_gamma_ti_fv(spinor1, 0, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][0]);
_fv_eq_gamma_ti_fv(spinor1, 0, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][1]);
_fv_eq_gamma_ti_fv(spinor1, 1, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][1]);
_fv_eq_gamma_ti_fv(spinor1, 1, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][2]);
_fv_eq_gamma_ti_fv(spinor1, 2, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][2]);
_fv_eq_gamma_ti_fv(spinor1, 2, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][3]);
_fv_eq_gamma_ti_fv(spinor1, 3, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][3]);
_fv_eq_gamma_ti_fv(spinor1, 3, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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);
}
}
}
}
}
/*****************************************************
* gamma5_BH4_gamma5
* - calculates xi = gamma5 (B^+ H)^4 gamma5 phi
* - _NOTE_ : B^+H is indep. of repr.
*****************************************************/
void gamma5_BdagH4_gamma5 (double *xi, double *phi, double *work) {
int ix, i;
double spinor1[24];
double _2kappamu = 2 * g_kappa * g_mu;
/* multiply original source (phi) with gamma_5, save in xi */
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_gamma_ti_fv(&xi[_GSI(ix)], 5, &phi[_GSI(ix)]);
}
/* apply B^+ H four times
* status: source = xi from last step, dest = work
*/
for(i=0; i<2; i++) {
/* apply the hopping matrix */
xchange_field(xi);
Hopping(work, xi);
/* apply B^+ */
mul_one_pm_imu_inv(work, -1., VOLUME);
/* apply the hopping matrix */
xchange_field(work);
Hopping(xi, work);
/* apply B^+ */
mul_one_pm_imu_inv(xi, -1., VOLUME);
}
/* final step: multiply with gamma_5 and */
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_gamma_ti_fv(spinor1, 5, &xi[_GSI(ix)]);
_fv_eq_fv(&xi[_GSI(ix)], spinor1);
}
}
/***********************************
* mul_one_pm_imu_inv
*
***********************************/
void mul_one_pm_imu_inv (double *phi, double sign, int V) {
int ix;
double spinor1[24], spinor2[24];
double _2kappamu = 2. * g_kappa * g_mu;
double norminv = 1. / (1. + _2kappamu*_2kappamu);
for(ix=0; ix<V; ix++) {
_fv_eq_gamma_ti_fv(spinor1, 5, &phi[_GSI(ix)]);
_fv_eq_fv_ti_im(spinor2, spinor1, -sign*_2kappamu);
_fv_eq_fv_pl_fv(spinor1, &phi[_GSI(ix)], spinor2);
_fv_eq_fv_ti_re(&phi[_GSI(ix)], spinor1, norminv);
}
}
/*****************************************************
* BH3
* - calculates xi = (B^+ H)^3 phi
* - B = A^{-1}, A = 1 + i gamma_5 \tilde{\mu}
* - _NOTE_ : BH is indep. of repr.
*****************************************************/
void BH3 (double *xi, double *phi) {
/*************************************************
* apply B H three times
*************************************************/
/* 1st application of the hopping matrix */
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
/* 2nd application of the hopping matrix */
Hopping(phi, xi);
mul_one_pm_imu_inv(phi, +1., VOLUME);
xchange_field(phi);
/* 3rd application of the hopping matrix */
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
}
/*****************************************************
* BH5
* - calculates xi = (B H)^5 phi
* - B = A^{-1}, A = 1 + i gamma_5 \tilde{\mu}
* - _NOTE_ : BH is indep. of repr.
*****************************************************/
void BH5 (double *xi, double *phi) {
/*************************************************
* apply B H three times
*************************************************/
/* 1st application of the hopping matrix */
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
/* 2nd application of the hopping matrix */
Hopping(phi, xi);
mul_one_pm_imu_inv(phi, +1., VOLUME);
xchange_field(phi);
/* 3rd application of the hopping matrix */
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
/* 4th application of the hopping matrix */
Hopping(phi, xi);
mul_one_pm_imu_inv(phi, +1., VOLUME);
xchange_field(phi);
/* 5th application of the hopping matrix */
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
}
/*****************************************************
* BH
* - calculates xi = (B H) phi
* - B = A^{-1}, A = 1 + i gamma_5 \tilde{\mu}
* - _NOTE_ : BH is indep. of repr.
*****************************************************/
void BH (double *xi, double *phi) {
/*************************************************
* apply B H
*************************************************/
/* application of the hopping matrix */
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
}
/*****************************************************
* BH2
* - calculates phi = (B H)^2 phi via xi
* - B = A^{-1}, A = 1 + i gamma_5 \tilde{\mu}
* - _NOTE_ : BH is indep. of repr.
*****************************************************/
void BH2 (double *xi, double *phi) {
/*************************************************
* apply B H
*************************************************/
/* application of the hopping matrix */
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
Hopping(phi, xi);
mul_one_pm_imu_inv(phi, +1., VOLUME);
xchange_field(phi);
}
/*****************************************************
* BH7
* - calculates xi = (B H)^7 phi
* - B = A^{-1}, A = 1 + i gamma_5 \tilde{\mu}
* - _NOTE_ : BH is indep. of repr.
*****************************************************/
void BH7 (double *xi, double *phi) {
/*************************************************
* apply B H sevev times
*************************************************/
/* 1st application of the hopping matrix */
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
/* 2nd application of the hopping matrix */
Hopping(phi, xi);
mul_one_pm_imu_inv(phi, +1., VOLUME);
xchange_field(phi);
/* 3rd application of the hopping matrix */
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
/* 4th application of the hopping matrix */
Hopping(phi, xi);
mul_one_pm_imu_inv(phi, +1., VOLUME);
xchange_field(phi);
/* 5th application of the hopping matrix */
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
/* 6th application of the hopping matrix */
Hopping(phi, xi);
mul_one_pm_imu_inv(phi, +1., VOLUME);
xchange_field(phi);
/* 7th application of the hopping matrix */
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
}
/*****************************************************
* BHn
* - calculates xi = (B H)^n phi
* - B = A^{-1}, A = 1 + i gamma_5 \tilde{\mu}
* - _NOTE_ : BH is indep. of repr.
*****************************************************/
void BHn (double *xi, double *phi, int n) {
int m, r, i;
/*************************************************
* apply B H n times
*************************************************/
m = n / 2;
r = n % 2;
for(i=0; i<m; i++) {
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
Hopping(phi, xi);
mul_one_pm_imu_inv(phi, +1., VOLUME);
xchange_field(phi);
}
if(r==1) {
Hopping(xi, phi);
mul_one_pm_imu_inv(xi, +1., VOLUME);
xchange_field(xi);
} else {
memcpy((void*)xi, (void*)phi, 24*VOLUMEPLUSRAND*sizeof(double));
}
}
/**************************************************************************************
* Qf5
* - computes xi = gamma_5 Q_f phi
* where Q_f is the tm Dirac operator with twisted boundary conditions.
**************************************************************************************/
#ifndef OPENMP
void Qf5(double *xi, double *phi, double mutm) {
int it, ix, iy, iz;
int index_s;
double SU3_1[18];
double spinor1[24], spinor2[24], spinor3[24];
double *xi_, *phi_, *U_;
double _1_2_kappa = 0.5 / g_kappa;
for(it = 0; it < T; it++) {
for(ix = 0; ix < LX; ix++) {
for(iy = 0; iy < LY; iy++) {
for(iz = 0; iz < LZ; iz++) {
index_s = g_ipt[it][ix][iy][iz];
xi_ = spinor3;
_fv_eq_zero(xi_);
/* Negative t-direction. */
phi_ = phi + _GSI(g_idn[index_s][0]);
_fv_eq_gamma_ti_fv(spinor1, 0, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][0]);
_fv_eq_gamma_ti_fv(spinor1, 0, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][1]);
_fv_eq_gamma_ti_fv(spinor1, 1, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][1]);
_fv_eq_gamma_ti_fv(spinor1, 1, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][2]);
_fv_eq_gamma_ti_fv(spinor1, 2, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][2]);
_fv_eq_gamma_ti_fv(spinor1, 2, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][3]);
_fv_eq_gamma_ti_fv(spinor1, 3, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][3]);
_fv_eq_gamma_ti_fv(spinor1, 3, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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 -1/2. */
_fv_ti_eq_re(xi_, -0.5);
/* Diagonal elements. */
phi_ = phi + _GSI(index_s);
_fv_eq_fv_ti_re(spinor1, phi_, _1_2_kappa);
_fv_pl_eq_fv(xi_, spinor1);
_fv_eq_gamma_ti_fv(spinor1, 5, phi_);
_fv_eq_fv_ti_im(spinor2, spinor1, mutm);
_fv_pl_eq_fv(xi_, spinor2);
_fv_eq_gamma_ti_fv(xi+_GSI(index_s), 5, xi_);
}
}
}
}
}
#else
void Qf5(double *xi, double *phi, double mutm) {
int ix;
int index_s;
double SU3_1[18];
double spinor1[24], spinor2[24], spinor3[24];
double *xi_, *phi_, *U_;
double _1_2_kappa = 0.5 / g_kappa;
#pragma omp parallel for private(ix,index_s,phi_,xi_,spinor1,spinor2,U_,SU3_1) shared(phi,xi,T,_1_2_kappa,g_gauge_field,g_iup,g_idn, co_phase_up)
for(ix = 0; ix < VOLUME; ix++) {
index_s = ix;
xi_ = spinor3;
_fv_eq_zero(xi_);
/* Negative t-direction. */
phi_ = phi + _GSI(g_idn[index_s][0]);
_fv_eq_gamma_ti_fv(spinor1, 0, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][0]);
_fv_eq_gamma_ti_fv(spinor1, 0, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 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. */
phi_ = phi + _GSI(g_idn[index_s][1]);
_fv_eq_gamma_ti_fv(spinor1, 1, phi_);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(g_idn[index_s][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. */
phi_ = phi + _GSI(g_iup[index_s][1]);
_fv_eq_gamma_ti_fv(spinor1, 1, phi_);
_fv_mi(spinor1);
_fv_pl_eq_fv(spinor1, phi_);
U_ = g_gauge_field + _GGI(index_s, 1);
_cm_eq_cm_ti_co(SU3_1, U_, &co_phase_up[1]);
_fv_eq_cm_ti_fv(spinor2, SU3_1, spinor1);