void Q_over_sqrt_Q_sqr(spinor * const R, double * const c,
const int n, spinor * const S,
const double rnorm, const double minev) {
int j;
double fact1, fact2, temp1, temp2, temp3, temp4, maxev, tnorm;
spinor *sv, *d, *dd, *aux, *aux3;
double ap_eps_sq = 0.;
sv=lock_Dov_WS_spinor(2);
d=lock_Dov_WS_spinor(3);
dd=lock_Dov_WS_spinor(4);
aux=lock_Dov_WS_spinor(5);
aux3=lock_Dov_WS_spinor(6);
eigenvalues_for_cg_computed = no_eigenvalues - 1;
if(eigenvalues_for_cg_computed < 0) eigenvalues_for_cg_computed = 0;
maxev=1.0;
fact1=4/(maxev-minev);
fact2=-2*(maxev+minev)/(maxev-minev);
zero_spinor_field(d, VOLUME);
zero_spinor_field(dd, VOLUME);
if(1) assign_sub_lowest_eigenvalues(aux3, S, no_eigenvalues-1, VOLUME);
else assign(aux3, S, VOLUME);
/* Check whether switch for adaptive precision is on */
/* this might be implemented again in the future */
/* Use the 'old' version using Clenshaw's recursion for the
Chebysheff polynomial
*/
if(1) {
for (j = n-1; j >= 1; j--) {
assign(sv, d, VOLUME);
if ( (j%10) == 0 ) {
assign_sub_lowest_eigenvalues(aux, d, no_eigenvalues-1, VOLUME);
}
else {
assign(aux, d, VOLUME);
}
norm_Q_sqr_psi(R, aux, rnorm);
/* printf("%d %e %e\n", j, R[0].s0.c0.re, R[0].s0.c0.im); */
/* printf("%e %e\n", R[0].s1.c0.re, R[0].s1.c0.im); */
temp1=-1.0;
temp2=c[j];
assign_mul_add_mul_add_mul_add_mul_r(d, R, dd, aux3, fact2, fact1, temp1, temp2, VOLUME);
assign(dd, sv, VOLUME);
}
if(1) assign_sub_lowest_eigenvalues(R, d, no_eigenvalues-1, VOLUME);
else assign(R, d, VOLUME);
norm_Q_sqr_psi(aux, R, rnorm);
temp1=-1.0;
temp2=c[0]/2.;
temp3=fact1/2.;
temp4=fact2/2.;
assign_mul_add_mul_add_mul_add_mul_r(aux, d, dd, aux3, temp3, temp4, temp1, temp2, VOLUME);
norm_Q_n_psi(R, aux, 1, rnorm);
}
else {
/* Use the adaptive precision version using the forward recursion
for the Chebysheff polynomial
*/
/* d = T_0(Q^2) */
assign(d, aux3, VOLUME);
/* dd = T_1(Q^2) */
norm_Q_sqr_psi(dd, d, rnorm);
temp3 = fact1/2.;
temp4 = fact2/2.;
assign_mul_add_mul_r(dd, d, temp3, temp4, VOLUME);
/* r = c_1 T_1(Q^2) + 1./2 c_0 */
temp1 = c[1];
temp2 = c[0]/2.;
mul_add_mul_r(R, dd, d, temp1, temp2, VOLUME);
temp1=-1.0;
for (j = 2; j <= n-1; j++) {
/* aux = T_j(Q^2) = 2 Q^2 T_{j-1}(Q^2) - T_{j-2}(Q^2) */
norm_Q_sqr_psi(aux, dd, rnorm);
assign_mul_add_mul_add_mul_r(aux, dd, d, fact1, fact2, temp1, VOLUME);
/* r = r + c_j T_j(Q^2) */
temp2 = c[j];
assign_add_mul_r(R, aux, temp2, VOLUME);
/* The stoppping criterio tnorm = |T_j(Q^2)| */
tnorm=square_norm(aux, VOLUME, 1);
tnorm*=(temp2*temp2);
/*
auxnorm=square_norm(R);
if(g_proc_id == g_stdio_proc){printf("j= %d\t|c T|^2= %g\t c_j= %g\t|r|^2= %g\n",j,tnorm,temp2,auxnorm); fflush( stdout);};
*/
if(tnorm < ap_eps_sq) break;
/* d = T_{j-1}(Q^2) */
assign(d, dd, VOLUME);
/* dd = T_{j}(Q^2) */
assign(dd, aux, VOLUME);
}
if(g_proc_id == g_stdio_proc && g_debug_level > 0) {
printf("Order of Chebysheff approximation = %d\n",j);
fflush( stdout);
}
/* r = Q r */
assign(aux, R, VOLUME);
norm_Q_n_psi(R, aux, 1, rnorm);
}
/* add in piece from projected subspace */
addproj_q_invsqrt(R, S, no_eigenvalues-1, VOLUME);
unlock_Dov_WS_spinor(2);
unlock_Dov_WS_spinor(3);
unlock_Dov_WS_spinor(4);
unlock_Dov_WS_spinor(5);
unlock_Dov_WS_spinor(6);
return;
}
void Ptilde_ndpsi(spinor *R_s, spinor *R_c, double *dd, int n,
spinor *S_s, spinor *S_c, matrix_mult_nd Qsq) {
int j;
double fact1, fact2, temp1, temp2, temp3, temp4;
spinor *svs_=NULL, *svs=NULL, *ds_=NULL, *ds=NULL, *dds_=NULL, *dds=NULL,
*auxs_=NULL, *auxs=NULL, *aux2s_=NULL, *aux2s=NULL, *aux3s_=NULL,
*aux3s=NULL;
spinor *svc_=NULL, *svc=NULL, *dc_=NULL, *dc=NULL, *ddc_=NULL,
*ddc=NULL, *auxc_=NULL, *auxc=NULL, *aux2c_=NULL, *aux2c=NULL,
*aux3c_=NULL, *aux3c=NULL;
svs_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
svs = (spinor *)(((unsigned long int)(svs_)+ALIGN_BASE)&~ALIGN_BASE);
ds_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
ds = (spinor *)(((unsigned long int)(ds_)+ALIGN_BASE)&~ALIGN_BASE);
dds_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
dds = (spinor *)(((unsigned long int)(dds_)+ALIGN_BASE)&~ALIGN_BASE);
auxs_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
auxs = (spinor *)(((unsigned long int)(auxs_)+ALIGN_BASE)&~ALIGN_BASE);
aux2s_= calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
aux2s = (spinor *)(((unsigned long int)(aux2s_)+ALIGN_BASE)&~ALIGN_BASE);
aux3s_= calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
aux3s = (spinor *)(((unsigned long int)(aux3s_)+ALIGN_BASE)&~ALIGN_BASE);
svc_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
svc = (spinor *)(((unsigned long int)(svc_)+ALIGN_BASE)&~ALIGN_BASE);
dc_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
dc = (spinor *)(((unsigned long int)(dc_)+ALIGN_BASE)&~ALIGN_BASE);
ddc_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
ddc = (spinor *)(((unsigned long int)(ddc_)+ALIGN_BASE)&~ALIGN_BASE);
auxc_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
auxc = (spinor *)(((unsigned long int)(auxc_)+ALIGN_BASE)&~ALIGN_BASE);
aux2c_= calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
aux2c = (spinor *)(((unsigned long int)(aux2c_)+ALIGN_BASE)&~ALIGN_BASE);
aux3c_= calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
aux3c = (spinor *)(((unsigned long int)(aux3c_)+ALIGN_BASE)&~ALIGN_BASE);
fact1=4/(phmc_cheb_evmax-phmc_cheb_evmin);
fact2=-2*(phmc_cheb_evmax+phmc_cheb_evmin)/(phmc_cheb_evmax-phmc_cheb_evmin);
zero_spinor_field(&ds[0],VOLUME/2);
zero_spinor_field(&dds[0],VOLUME/2);
zero_spinor_field(&dc[0],VOLUME/2);
zero_spinor_field(&ddc[0],VOLUME/2);
/* sub_low_ev(&aux3[0], &S[0]); */
assign(&aux3s[0], &S_s[0],VOLUME/2);
assign(&aux3c[0], &S_c[0],VOLUME/2);
/* Use the Clenshaw's recursion for the Chebysheff polynomial */
for (j=n-1; j>=1; j--) {
assign(&svs[0],&ds[0],VOLUME/2);
assign(&svc[0],&dc[0],VOLUME/2);
/*
* if ( (j%10) == 0 ) {
* sub_low_ev(&aux[0], &d[0]);
* } else { */
assign(&auxs[0], &ds[0], VOLUME/2);
assign(&auxc[0], &dc[0], VOLUME/2);
/* } */
Qsq(&R_s[0], &R_c[0], &auxs[0], &auxc[0]);
temp1=-1.0;
temp2=dd[j];
assign_mul_add_mul_add_mul_add_mul_r(&ds[0] , &R_s[0], &dds[0], &aux3s[0], fact2, fact1, temp1, temp2,VOLUME/2);
assign_mul_add_mul_add_mul_add_mul_r(&dc[0] , &R_c[0], &ddc[0], &aux3c[0], fact2, fact1, temp1, temp2,VOLUME/2);
assign(&dds[0], &svs[0],VOLUME/2);
assign(&ddc[0], &svc[0],VOLUME/2);
}
assign(&R_s[0], &ds[0],VOLUME/2);
assign(&R_c[0], &dc[0],VOLUME/2);
Qsq(&auxs[0], &auxc[0], &R_s[0], &R_c[0]);
temp1=-1.0;
temp2=dd[0]/2;
temp3=fact1/2;
temp4=fact2/2;
assign_mul_add_mul_add_mul_add_mul_r(&auxs[0], &ds[0], &dds[0], &aux3s[0], temp3, temp4, temp1, temp2,VOLUME/2);
assign_mul_add_mul_add_mul_add_mul_r(&auxc[0], &dc[0], &ddc[0], &aux3c[0], temp3, temp4, temp1, temp2,VOLUME/2);
assign(&R_s[0], &auxs[0],VOLUME/2);
assign(&R_c[0], &auxc[0],VOLUME/2);
free(svs_);
free(ds_);
free(dds_);
free(auxs_);
free(aux2s_);
free(aux3s_);
free(svc_);
free(dc_);
free(ddc_);
free(auxc_);
free(aux2c_);
free(aux3c_);
}
