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invert_Qtm.c
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invert_Qtm.c
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/*********************************************
* invert_Qtm
*
* PURPOSE:
* - solve phi = D_tm xi for given phi with D_tm
* the twisted-mass Dirac operator
* - phi should be properly initialized by
* calling function
*********************************************/
#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <string.h>
#include <math.h>
#ifdef MPI
# include <mpi.h>
#endif
#include "global.h"
#include "cvc_complex.h"
#include "cvc_linalg.h"
#include "mpi_init.h"
#include "Q_phi.h"
#include "cvc_utils.h"
#include "invert_Qtm.h"
namespace cvc {
void spinor_scalar_product_co(complex *w, double *xi, double *phi, int V) {
int ix, iix;
complex p, p2;
#ifdef MPI
complex pall;
#endif
p2.re = 0.;
p2.im = 0.;
iix=0;
for(ix=0; ix<V; ix++) {
_co_eq_fv_dag_ti_fv(&p, xi+iix, phi+iix);
p2.re += p.re;
p2.im += p.im;
iix+=24;
}
//fprintf(stdout, "# [spinor_scalar_product_co] %d local: %e %e\n", g_cart_id, p2.re, p2.im);
#ifdef MPI
pall.re=0.; pall.im=0.;
MPI_Allreduce(&p2, &pall, 2, MPI_DOUBLE, MPI_SUM, g_cart_grid);
w->re = pall.re;
w->im = pall.im;
#else
w->re = p2.re;
w->im = p2.im;
#endif
}
void spinor_scalar_product_re(double *r, double *xi, double *phi, int V) {
int ix, iix;
double w;
complex p;
#ifdef MPI
double wall;
#endif
w = 0.;
iix=0;
for(ix=0; ix<V; ix++) {
_co_eq_fv_dag_ti_fv(&p, xi+iix, phi+iix);
w += p.re;
iix+=24;
}
//fprintf(stdout, "# [spinor_scalar_product_re] %d local: %e\n", g_cart_id, w);
#ifdef MPI
wall = 0.;
MPI_Allreduce(&w, &wall, 1, MPI_DOUBLE, MPI_SUM, g_cart_grid);
*r = wall;
#else
*r = w;
#endif
}
int invert_Qtm(double *xi, double *phi, int kwork) {
int ix, niter, iix;
double *r1_ptr = (double*)NULL;
double *r2_ptr = (double*)NULL;
double *s_ptr = (double*)NULL;
double *t_ptr = (double*)NULL;
double *x_ptr = (double*)NULL;
double *p_ptr = (double*)NULL;
double *p2_ptr = (double*)NULL;
double u, norm, normb;
double spinor1[24], spinor2[24];
complex alpha, beta, omega;
complex w, w2, w3, r0rn;
/*************************
* set the fields
*************************/
r1_ptr = g_spinor_field[kwork];
r2_ptr = g_spinor_field[kwork+1];
s_ptr = g_spinor_field[kwork+2];
t_ptr = g_spinor_field[kwork+3];
p_ptr = g_spinor_field[kwork+4];
p2_ptr = g_spinor_field[kwork+5];
x_ptr = xi;
if( r1_ptr==(double*)NULL || r2_ptr==(double*)NULL || s_ptr==(double*)NULL || t_ptr==(double*)NULL ||
p_ptr==(double*)NULL || x_ptr==(double*)NULL || phi==(double*)NULL ) return(-2);
/*************************
* initialize
*************************/
alpha.re = 0.; alpha.im = 0.;
beta.re = 0.; beta.im = 0.;
omega.re = 0.; omega.im = 0.;
w.re = 0.; w.im = 0.;
w2.re = 0.; w2.im = 0.;
w3.re = 0.; w3.im = 0.;
u = 0.;
/* normb */
spinor_scalar_product_re(&normb, phi, phi, VOLUME);
if(g_cart_id==0) fprintf(stdout, "# norm of r.-h. side: %e\n", normb);
/* p = phi - D xi */
Q_phi_tbc(p_ptr, xi);
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_mi_fv(p_ptr+iix, phi+iix, p_ptr+iix);
iix+=24;
}
xchange_field(p_ptr);
/* check the norm */
spinor_scalar_product_re(&norm, p_ptr, p_ptr, VOLUME);
/* if(g_cart_id==0) fprintf(stdout, "norm = %25.16e\n", norm); */
if(norm<=solver_precision*normb) {
if(g_cart_id==0) fprintf(stdout, "start spinor solves to requested precision\n");
return(0);
}
/* r1 = p = r2 */
memcpy((void*)r1_ptr, (void*)p_ptr, 24*VOLUME*sizeof(double));
memcpy((void*)r2_ptr, (void*)p_ptr, 24*VOLUME*sizeof(double));
/* p2 = D p */
Q_phi_tbc(p2_ptr, p_ptr);
/*************************
* start iteration
*************************/
for(niter=0; niter<=niter_max; niter++) {
spinor_scalar_product_co(&r0rn, r2_ptr, r1_ptr, VOLUME);
spinor_scalar_product_co(&w, r2_ptr, p2_ptr, VOLUME);
_co_eq_co_ti_co_inv(&alpha, &r0rn, &w);
/*
if(g_cart_id==0) fprintf(stdout, "\nr0rn =\t%25.16e +i %25.16e\n"\
"w =\t%25.16e +i %25.16e\nalpha =\t%25.16e +i %25.16e\n", r0rn.re, r0rn.im, w.re, w.im, alpha.re, alpha.im);
*/
/* the new complete s */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, p2_ptr+iix, &alpha);
_fv_eq_fv_mi_fv(s_ptr+iix, r1_ptr+iix, spinor1);
iix+=24;
}
xchange_field(s_ptr);
/* the new t */
Q_phi_tbc(t_ptr, s_ptr);
spinor_scalar_product_co(&w, t_ptr, s_ptr, VOLUME);
spinor_scalar_product_re(&u, t_ptr, t_ptr, VOLUME);
_co_eq_co_ti_re(&omega, &w, 1./u);
/*
if(g_cart_id==0) fprintf(stdout, "i\nw =\t%25.16e +i %25.16e\n"\
"u =\t%25.16e\nomega =\t%25.16e +i %25.16e\n", w.re, w.im, u, omega.re, omega.im);
*/
/* the new r1 */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, t_ptr+iix, &omega);
_fv_eq_fv_mi_fv(r1_ptr+iix, s_ptr+iix, spinor1);
iix+=24;
}
spinor_scalar_product_re(&norm, r1_ptr, r1_ptr, VOLUME);
if(g_cart_id==0) fprintf(stdout, "# [%d] residuum after iteration %d: %25.16e\n", g_cart_id, niter, norm);
if(norm<=solver_precision*normb) break;
/* the new x */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, s_ptr+iix, &omega);
_fv_pl_eq_fv(x_ptr+iix, spinor1);
_fv_eq_fv_ti_co(spinor1, p_ptr+iix, &alpha);
_fv_pl_eq_fv(x_ptr+iix, spinor1);
iix+=24;
}
spinor_scalar_product_co(&w, r2_ptr, r1_ptr, VOLUME);
_co_eq_co_ti_co_inv(&w2, &w, &r0rn);
_co_eq_co_ti_co_inv(&w3, &alpha, &omega);
_co_eq_co_ti_co(&beta, &w2, &w3);
r0rn.re = w.re; r0rn.im = w.im;
/*
if(g_cart_id==0) fprintf(stdout, "\nw =\t%25.16e +i %25.16e\n"\
"w2 =\t%25.16e +i %25.16e\nw3 =\t%25.16e +i %25.16e\nbeta =\t%25.16e +i %25.16e\n", w.re, w.im, w2.re, w2.im, w3.re, w3.im, beta.re, beta.im);
*/
/* the new p */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, p2_ptr+iix, &omega);
_fv_eq_fv_mi_fv(spinor1, p_ptr+iix, spinor1);
_fv_eq_fv_ti_co(spinor2, spinor1, &beta);
_fv_eq_fv_pl_fv(p_ptr+iix, r1_ptr+iix, spinor2);
iix+=24;
}
xchange_field(p_ptr);
/* the new p2 */
Q_phi_tbc(p2_ptr, p_ptr);
}
/*************************
* output
*************************/
if(norm<=solver_precision*normb && niter<=niter_max) {
if(g_cart_id==0) {
fprintf(stdout, "# BiCGStab converged after %d steps with relative residuum %e\n", niter, norm/normb);
}
} else {
if(g_cart_id==0) {
fprintf(stdout, "# No convergence in BiCGStab; after %d steps relative residuum is %e\n", niter, norm/normb);
}
return(-3);
}
/*************************
* check the solution
*************************/
xchange_field(x_ptr);
Q_phi_tbc(p_ptr, x_ptr);
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_mi_eq_fv(p_ptr+iix, phi+iix);
iix+=24;
}
spinor_scalar_product_re(&norm, p_ptr, p_ptr, VOLUME);
if(g_cart_id==0) {
fprintf(stdout, "# true relative squared residuum is %e\n", norm/normb);
}
return(niter);
}
/****************************************************************
* invert_Qtm_her
****************************************************************/
int invert_Qtm_her(double *xi, double *phi, int kwork) {
int ix, niter, iix;
double *r1_ptr = (double*)NULL;
double *r2_ptr = (double*)NULL;
double *s_ptr = (double*)NULL;
double *t_ptr = (double*)NULL;
double *x_ptr = (double*)NULL;
double *p_ptr = (double*)NULL;
double *p2_ptr = (double*)NULL;
double *aux = (double*)NULL;
double u, norm, normb;
double spinor1[24], spinor2[24];
complex alpha, beta, omega;
complex w, w2, w3, r0rn;
/*************************
* set the fields
*************************/
r1_ptr = g_spinor_field[kwork];
r2_ptr = g_spinor_field[kwork+1];
s_ptr = g_spinor_field[kwork+2];
t_ptr = g_spinor_field[kwork+3];
p_ptr = g_spinor_field[kwork+4];
p2_ptr = g_spinor_field[kwork+5];
x_ptr = xi;
aux = g_spinor_field[kwork+6];
if( r1_ptr==(double*)NULL || r2_ptr==(double*)NULL || s_ptr==(double*)NULL || t_ptr==(double*)NULL ||
p_ptr==(double*)NULL || x_ptr==(double*)NULL || phi==(double*)NULL ) return(-2);
/*************************
* initialize
*************************/
alpha.re = 0.; alpha.im = 0.;
beta.re = 0.; beta.im = 0.;
omega.re = 0.; omega.im = 0.;
w.re = 0.; w.im = 0.;
w2.re = 0.; w2.im = 0.;
w3.re = 0.; w3.im = 0.;
u = 0.;
/* normb */
spinor_scalar_product_re(&normb, phi, phi, VOLUME);
if(g_cart_id==0) fprintf(stdout, "# norm of r.-h. side: %e\n", normb);
/* p = gamma5 phi - g5 Du g5 Dd xi */
Qf5(aux, xi, -g_mu);
xchange_field(aux);
Qf5(p_ptr, aux, g_mu);
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_gamma_ti_fv(spinor1, 5, phi+iix);
_fv_eq_fv_mi_fv(p_ptr+iix, spinor1, p_ptr+iix);
iix+=24;
}
xchange_field(p_ptr);
/* check the norm */
spinor_scalar_product_re(&norm, p_ptr, p_ptr, VOLUME);
/* if(g_cart_id==0) fprintf(stdout, "norm = %25.16e\n", norm); */
if(norm<=solver_precision*normb) {
if(g_cart_id==0) fprintf(stdout, "start spinor solves to requested precision\n");
return(0);
}
/* r1 = p = r2 */
memcpy((void*)r1_ptr, (void*)p_ptr, 24*VOLUME*sizeof(double));
memcpy((void*)r2_ptr, (void*)p_ptr, 24*VOLUME*sizeof(double));
/* p2 = D p */
Qf5(aux, p_ptr, -g_mu);
xchange_field(aux);
Qf5(p2_ptr, aux, g_mu);
/*************************
* start iteration
*************************/
for(niter=0; niter<=niter_max; niter++) {
spinor_scalar_product_co(&r0rn, r2_ptr, r1_ptr, VOLUME);
spinor_scalar_product_co(&w, r2_ptr, p2_ptr, VOLUME);
_co_eq_co_ti_co_inv(&alpha, &r0rn, &w);
/*
if(g_cart_id==0) fprintf(stdout, "\nr0rn =\t%25.16e +i %25.16e\n"\
"w =\t%25.16e +i %25.16e\nalpha =\t%25.16e +i %25.16e\n", r0rn.re, r0rn.im, w.re, w.im, alpha.re, alpha.im);
*/
/* the new complete s */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, p2_ptr+iix, &alpha);
_fv_eq_fv_mi_fv(s_ptr+iix, r1_ptr+iix, spinor1);
iix+=24;
}
xchange_field(s_ptr);
/* the new t */
Qf5(aux, s_ptr, -g_mu);
xchange_field(aux);
Qf5(t_ptr, aux, g_mu);
spinor_scalar_product_co(&w, t_ptr, s_ptr, VOLUME);
spinor_scalar_product_re(&u, t_ptr, t_ptr, VOLUME);
_co_eq_co_ti_re(&omega, &w, 1./u);
/*
if(g_cart_id==0) fprintf(stdout, "i\nw =\t%25.16e +i %25.16e\n"\
"u =\t%25.16e\nomega =\t%25.16e +i %25.16e\n", w.re, w.im, u, omega.re, omega.im);
*/
/* the new r1 */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, t_ptr+iix, &omega);
_fv_eq_fv_mi_fv(r1_ptr+iix, s_ptr+iix, spinor1);
iix+=24;
}
spinor_scalar_product_re(&norm, r1_ptr, r1_ptr, VOLUME);
if(g_cart_id==0) fprintf(stdout, "# [%d] residuum after iteration %d: %25.16e\n", g_cart_id, niter, norm);
if(norm<=solver_precision*normb) break;
/* the new x */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, s_ptr+iix, &omega);
_fv_pl_eq_fv(x_ptr+iix, spinor1);
_fv_eq_fv_ti_co(spinor1, p_ptr+iix, &alpha);
_fv_pl_eq_fv(x_ptr+iix, spinor1);
iix+=24;
}
spinor_scalar_product_co(&w, r2_ptr, r1_ptr, VOLUME);
_co_eq_co_ti_co_inv(&w2, &w, &r0rn);
_co_eq_co_ti_co_inv(&w3, &alpha, &omega);
_co_eq_co_ti_co(&beta, &w2, &w3);
r0rn.re = w.re; r0rn.im = w.im;
/*
if(g_cart_id==0) fprintf(stdout, "\nw =\t%25.16e +i %25.16e\n"\
"w2 =\t%25.16e +i %25.16e\nw3 =\t%25.16e +i %25.16e\nbeta =\t%25.16e +i %25.16e\n", w.re, w.im, w2.re, w2.im, w3.re, w3.im, beta.re, beta.im);
*/
/* the new p */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, p2_ptr+iix, &omega);
_fv_eq_fv_mi_fv(spinor1, p_ptr+iix, spinor1);
_fv_eq_fv_ti_co(spinor2, spinor1, &beta);
_fv_eq_fv_pl_fv(p_ptr+iix, r1_ptr+iix, spinor2);
iix+=24;
}
xchange_field(p_ptr);
/* the new p2 */
Qf5(aux, p_ptr, -g_mu);
xchange_field(aux);
Qf5(p2_ptr, aux, g_mu);
}
/*******************************
* get final solution
*******************************/
xchange_field(x_ptr);
Qf5(aux, x_ptr, -g_mu);
memcpy((void*)x_ptr, (void*)aux, 24*VOLUME*sizeof(double));
xchange_field(x_ptr);
/*************************
* output
*************************/
if(norm<=solver_precision*normb && niter<=niter_max) {
if(g_cart_id==0) {
fprintf(stdout, "# BiCGStab converged after %d steps with relative residuum %e\n", niter, norm/normb);
}
} else {
if(g_cart_id==0) {
fprintf(stdout, "# No convergence in BiCGStab; after %d steps relative residuum is %e\n", niter, norm/normb);
}
return(-3);
}
/*************************
* check the solution
*************************/
Q_phi_tbc(p_ptr, x_ptr);
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_mi_eq_fv(p_ptr+iix, phi+iix);
iix+=24;
}
spinor_scalar_product_re(&norm, p_ptr, p_ptr, VOLUME);
if(g_cart_id==0) {
fprintf(stdout, "# true relative squared residuum is %e\n", norm/normb);
}
return(niter);
}
int invert_Q_Wilson(double *xi, double *phi, int kwork) {
int ix, niter, iix;
double *r1_ptr = (double*)NULL;
double *r2_ptr = (double*)NULL;
double *s_ptr = (double*)NULL;
double *t_ptr = (double*)NULL;
double *x_ptr = (double*)NULL;
double *p_ptr = (double*)NULL;
double *p2_ptr = (double*)NULL;
double u, norm, normb;
double spinor1[24], spinor2[24];
complex alpha, beta, omega;
complex w, w2, w3, r0rn;
/*************************
* set the fields
*************************/
r1_ptr = g_spinor_field[kwork];
r2_ptr = g_spinor_field[kwork+1];
s_ptr = g_spinor_field[kwork+2];
t_ptr = g_spinor_field[kwork+3];
p_ptr = g_spinor_field[kwork+4];
p2_ptr = g_spinor_field[kwork+5];
x_ptr = xi;
if( r1_ptr==(double*)NULL || r2_ptr==(double*)NULL || s_ptr==(double*)NULL || t_ptr==(double*)NULL ||
p_ptr==(double*)NULL || x_ptr==(double*)NULL || phi==(double*)NULL ) return(-2);
/*************************
* initialize
*************************/
alpha.re = 0.; alpha.im = 0.;
beta.re = 0.; beta.im = 0.;
omega.re = 0.; omega.im = 0.;
w.re = 0.; w.im = 0.;
w2.re = 0.; w2.im = 0.;
w3.re = 0.; w3.im = 0.;
u = 0.;
/* normb */
spinor_scalar_product_re(&normb, phi, phi, VOLUME);
if(g_cart_id==0) fprintf(stdout, "# norm of r.-h. side: %e\n", normb);
/* p = phi - D xi */
Q_Wilson_phi(p_ptr, xi);
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_mi_fv(p_ptr+iix, phi+iix, p_ptr+iix);
iix+=24;
}
xchange_field(p_ptr);
/* check the norm */
spinor_scalar_product_re(&norm, p_ptr, p_ptr, VOLUME);
//if(g_cart_id==0) fprintf(stdout, "norm = %25.16e\n", norm);
if(norm<=solver_precision*normb) {
if(g_cart_id==0) fprintf(stdout, "start spinor solves to requested precision\n");
return(0);
}
/* r1 = p = r2 */
memcpy((void*)r1_ptr, (void*)p_ptr, 24*VOLUME*sizeof(double));
memcpy((void*)r2_ptr, (void*)p_ptr, 24*VOLUME*sizeof(double));
/* p2 = D p */
Q_Wilson_phi(p2_ptr, p_ptr);
/*************************
* start iteration
*************************/
for(niter=0; niter<=niter_max; niter++) {
spinor_scalar_product_co(&r0rn, r2_ptr, r1_ptr, VOLUME);
spinor_scalar_product_co(&w, r2_ptr, p2_ptr, VOLUME);
_co_eq_co_ti_co_inv(&alpha, &r0rn, &w);
//if(g_cart_id==0) fprintf(stdout, "\nr0rn =\t%25.16e +i %25.16e\n"\
// "w =\t%25.16e +i %25.16e\nalpha =\t%25.16e +i %25.16e\n", r0rn.re, r0rn.im, w.re, w.im, alpha.re, alpha.im);
/* the new complete s */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, p2_ptr+iix, &alpha);
_fv_eq_fv_mi_fv(s_ptr+iix, r1_ptr+iix, spinor1);
iix+=24;
}
xchange_field(s_ptr);
/* the new t */
Q_Wilson_phi(t_ptr, s_ptr);
spinor_scalar_product_co(&w, t_ptr, s_ptr, VOLUME);
spinor_scalar_product_re(&u, t_ptr, t_ptr, VOLUME);
_co_eq_co_ti_re(&omega, &w, 1./u);
//if(g_cart_id==0) fprintf(stdout, "i\nw =\t%25.16e +i %25.16e\n"\
// "u =\t%25.16e\nomega =\t%25.16e +i %25.16e\n", w.re, w.im, u, omega.re, omega.im);
/* the new r1 */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, t_ptr+iix, &omega);
_fv_eq_fv_mi_fv(r1_ptr+iix, s_ptr+iix, spinor1);
iix+=24;
}
spinor_scalar_product_re(&norm, r1_ptr, r1_ptr, VOLUME);
if(g_cart_id==0) {
fprintf(stdout, "# [%d] residuum after iteration %d: %25.16e\n", g_cart_id, niter, norm);
fflush(stdout);
}
if(norm<=solver_precision*normb) break;
/* the new x */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, s_ptr+iix, &omega);
_fv_pl_eq_fv(x_ptr+iix, spinor1);
_fv_eq_fv_ti_co(spinor1, p_ptr+iix, &alpha);
_fv_pl_eq_fv(x_ptr+iix, spinor1);
iix+=24;
}
spinor_scalar_product_co(&w, r2_ptr, r1_ptr, VOLUME);
_co_eq_co_ti_co_inv(&w2, &w, &r0rn);
_co_eq_co_ti_co_inv(&w3, &alpha, &omega);
_co_eq_co_ti_co(&beta, &w2, &w3);
r0rn.re = w.re; r0rn.im = w.im;
//spinor_scalar_product_re(&norm, r1_ptr, r1_ptr, VOLUME);
//if(g_cart_id==0) fprintf(stdout, "# [%d] (1) norm of r1 = %25.16e\n", g_cart_id, norm);
//spinor_scalar_product_re(&norm, r2_ptr, r2_ptr, VOLUME);
//if(g_cart_id==0) fprintf(stdout, "# [%d] (1) norm of r2 = %25.16e\n", g_cart_id, norm);
//if(g_cart_id==0) fprintf(stdout, "\n(1) w =\t%25.16e +i %25.16e\n"\
// "(1) w2 =\t%25.16e +i %25.16e\n(1) w3 =\t%25.16e +i %25.16e\n(1) beta =\t%25.16e +i %25.16e\n", w.re, w.im, w2.re, w2.im, w3.re, w3.im, beta.re, beta.im);
/* the new p */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, p2_ptr+iix, &omega);
_fv_eq_fv_mi_fv(spinor1, p_ptr+iix, spinor1);
_fv_eq_fv_ti_co(spinor2, spinor1, &beta);
_fv_eq_fv_pl_fv(p_ptr+iix, r1_ptr+iix, spinor2);
iix+=24;
}
xchange_field(p_ptr);
/* the new p2 */
Q_Wilson_phi(p2_ptr, p_ptr);
}
/*************************
* output
*************************/
if(norm<=solver_precision*normb && niter<=niter_max) {
if(g_cart_id==0) {
fprintf(stdout, "# BiCGStab converged after %d steps with relative residuum %e\n", niter, norm/normb);
}
} else {
if(g_cart_id==0) {
fprintf(stdout, "# No convergence in BiCGStab; after %d steps relative residuum is %e\n", niter, norm/normb);
}
return(-3);
}
/*************************
* check the solution
*************************/
xchange_field(x_ptr);
Q_Wilson_phi(p_ptr, x_ptr);
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_mi_eq_fv(p_ptr+iix, phi+iix);
iix+=24;
}
spinor_scalar_product_re(&norm, p_ptr, p_ptr, VOLUME);
if(g_cart_id==0) {
fprintf(stdout, "# true relative squared residuum is %e\n", norm/normb);
}
return(niter);
}
/****************************************************************
* invert_Q_Wilson_her
****************************************************************/
int invert_Q_Wilson_her(double *xi, double *phi, int kwork) {
int ix, niter, iix;
double *r_ptr = (double*)NULL;
double *s_ptr = (double*)NULL;
double *x_ptr = (double*)NULL;
double *p_ptr = (double*)NULL;
double norm, normb;
double spinor1[24], spinor2[24];
complex alpha, w;
double beta, r0r0, rnrn;
/*************************
* set the fields
*************************/
r_ptr = g_spinor_field[kwork];
s_ptr = g_spinor_field[kwork+1];
p_ptr = g_spinor_field[kwork+2];
x_ptr = xi;
if( r_ptr==(double*)NULL || s_ptr==(double*)NULL || p_ptr==(double*)NULL || x_ptr==(double*)NULL || phi==(double*)NULL ) return(-2);
/*************************
* initialize
*************************/
alpha.re = 0.; alpha.im = 0.;
beta = 0.;
w.re = 0.; w.im = 0.;
/* normb */
spinor_scalar_product_re(&normb, phi, phi, VOLUME);
if(g_cart_id==0) fprintf(stdout, "# norm of r.-h. side: %e\n", normb);
/* p = gamma5 phi - g5 D_W xi */
Q_g5_Wilson_phi(p_ptr, xi);
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_gamma_ti_fv(spinor1, 5, phi+iix);
_fv_eq_fv_mi_fv(p_ptr+iix, spinor1, p_ptr+iix);
iix+=24;
}
xchange_field(p_ptr);
/* check the norm */
spinor_scalar_product_re(&norm, p_ptr, p_ptr, VOLUME);
/* if(g_cart_id==0) fprintf(stdout, "norm = %25.16e\n", norm); */
if(norm<=solver_precision*normb) {
if(g_cart_id==0) fprintf(stdout, "start spinor solves to requested precision\n");
return(0);
}
/* r1 = p */
memcpy((void*)r_ptr, (void*)p_ptr, 24*VOLUME*sizeof(double));
/* r0p0 = <r0, r0> */
spinor_scalar_product_re(&rnrn, r_ptr, r_ptr, VOLUME);
Q_g5_Wilson_phi(s_ptr, p_ptr);
/*************************
* start iteration
*************************/
for(niter=0; niter<=niter_max; niter++) {
r0r0 = rnrn;
// w = (p, A p)
spinor_scalar_product_co(&w, p_ptr, s_ptr, VOLUME);
alpha.re = rnrn / ( w.re*w.re + w.im*w.im );
alpha.im = -alpha.re * w.im;
alpha.re *= w.re;
/* the new r */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, s_ptr+iix, &alpha);
_fv_eq_fv_mi_fv(r_ptr+iix, r_ptr+iix, spinor1);
iix+=24;
}
/* the new x */
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_co(spinor1, p_ptr+iix, &alpha);
_fv_pl_eq_fv(x_ptr+iix, spinor1);
iix+=24;
}
spinor_scalar_product_re(&rnrn, r_ptr, r_ptr, VOLUME);
if(g_cart_id==0) fprintf(stdout, "# [%d] residuum after iteration %d: %25.16e\n", g_cart_id, niter, rnrn);
if(rnrn<=solver_precision*normb) {
norm = rnrn;
break;
}
/* the new p */
beta = rnrn / r0r0;
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_eq_fv_ti_re(spinor1, p_ptr+iix, beta);
_fv_eq_fv_pl_fv(p_ptr+iix, r_ptr+iix, spinor1);
iix+=24;
}
xchange_field(p_ptr);
/* the new s */
Q_g5_Wilson_phi(s_ptr, p_ptr);
} // of loop on niter
/*******************************
* exchane final solution
*******************************/
xchange_field(x_ptr);
/*************************
* output
*************************/
if(norm<=solver_precision*normb && niter<=niter_max) {
if(g_cart_id==0) {
fprintf(stdout, "# CGher converged after %d steps with relative residuum %e\n", niter, norm/normb);
}
} else {
if(g_cart_id==0) {
fprintf(stdout, "# No convergence in CGher; after %d steps relative residuum is %e\n", niter, norm/normb);
}
return(-3);
}
/*************************
* check the solution
*************************/
Q_Wilson_phi(p_ptr, x_ptr);
iix=0;
for(ix=0; ix<VOLUME; ix++) {
_fv_mi_eq_fv(p_ptr+iix, phi+iix);
iix+=24;
}
spinor_scalar_product_re(&norm, p_ptr, p_ptr, VOLUME);
if(g_cart_id==0) {
fprintf(stdout, "# true relative squared residuum is %e\n", norm/normb);
}
return(niter);
}
} /* end of namespace cvc */