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chebyshev_polynomial.c
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chebyshev_polynomial.c
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/***********************************************************************
*
* Copyright (C) 2003,2005,2006,2007,2008 Mauro Papinutto, Ines Wetzorke,
* Karl Jansen, Carsten Urbach
*
* This file is part of tmLQCD.
*
* tmLQCD is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* tmLQCD is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with tmLQCD. If not, see <http://www.gnu.org/licenses/>.
***********************************************************************/
#ifdef HAVE_CONFIG_H
#include "tmlqcd_config.h"
#endif
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "global.h"
#include "linalg_eo.h"
#include "start.h"
#include "operator/tm_operators.h"
#include "operator/tm_operators_nd.h"
#include "chebyshev_polynomial.h"
#define PI 3.141592653589793
double cheb_evmin, cheb_evmax;
double func(double u, double exponent){
return pow(u,exponent);
}
void chebyshev_polynomial(double aa, double bb, double c[], int n, double exponent){
int k,j;
double fac,bpa,bma,*f;
double inv_n;
inv_n=1./(double)n;
f=calloc(n,sizeof(double));/*vector(0,n-1);*/
fflush(stdout);
bma=0.5*(bb-aa);
bpa=0.5*(bb+aa);
for (k=0;k<n;k++) {
double y=cos(PI*(k+0.5)*inv_n);
f[k]=func(y*bma+bpa,exponent);
}
fac=2.0*inv_n;
for (j=0;j<n;j++) {
double sum=0.0;
for (k=0;k<n;k++)
sum += f[k]*cos(PI*j*(k+0.5)*inv_n);
c[j]=fac*sum;
}
free(f);
}
#undef PI
/****************************************************************************
*
* computation of (Q^dagger Q)^(1/4) on a vector
* by using the chebyshev approximation for the function ()^1/4
* subtraction of low-lying eigenvalues is not yet implemented for this
*
**************************************************************************/
void QdaggerQ_power(spinor *R_s, spinor *R_c, double *c, int n, spinor *S_s, spinor *S_c)
{
int j;
double fact1, fact2, temp, 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;
#if ( defined SSE || defined SSE2 )
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);
#else
svs_=calloc(VOLUMEPLUSRAND, sizeof(spinor));
svs = svs_;
ds_=calloc(VOLUMEPLUSRAND, sizeof(spinor));
ds = ds_;
dds_=calloc(VOLUMEPLUSRAND, sizeof(spinor));
dds = dds_;
auxs_=calloc(VOLUMEPLUSRAND, sizeof(spinor));
auxs = auxs_;
aux2s_=calloc(VOLUMEPLUSRAND, sizeof(spinor));
aux2s = aux2s_;
aux3s_=calloc(VOLUMEPLUSRAND, sizeof(spinor));
aux3s = aux3s_;
svc_=calloc(VOLUMEPLUSRAND, sizeof(spinor));
svc = svc_;
dc_=calloc(VOLUMEPLUSRAND, sizeof(spinor));
dc = dc_;
ddc_=calloc(VOLUMEPLUSRAND, sizeof(spinor));
ddc = ddc_;
auxc_=calloc(VOLUMEPLUSRAND, sizeof(spinor));
auxc = auxc_;
aux2c_=calloc(VOLUMEPLUSRAND, sizeof(spinor));
aux2c = aux2c_;
aux3c_=calloc(VOLUMEPLUSRAND, sizeof(spinor));
aux3c = aux3c_;
#endif
cheb_evmax=1.;
fact1=4/(cheb_evmax-cheb_evmin);
fact2=-2*(cheb_evmax+cheb_evmin)/(cheb_evmax-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);
/* } */
Qtm_dagger_ndpsi(&aux2s[0], &aux2c[0], &auxs[0], &auxc[0]);
Qtm_ndpsi(&R_s[0], &R_c[0], &aux2s[0], &aux2c[0]);
temp1=-1.0;
temp2=c[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);
}
/* sub_low_ev(&R[0],&d[0]); */
assign(&R_s[0], &ds[0],VOLUME/2);
assign(&R_c[0], &dc[0],VOLUME/2);
Qtm_dagger_ndpsi(&aux2s[0], &aux2c[0], &R_s[0], &R_c[0]);
Qtm_ndpsi(&auxs[0], &auxc[0], &aux2s[0], &aux2c[0]);
temp1=-1.0;
temp2=c[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);
/* addproj_q_invsqrt(&R[0], &S[0]); */
/*
#ifndef _SOLVER_OUTPUT
if(g_proc_id == g_stdio_proc){
printf("Order of Chebysheff approximation = %d\n",j);
fflush( stdout);};
#endif
*/
free(svs_);
free(ds_);
free(dds_);
free(auxs_);
free(aux2s_);
free(aux3s_);
free(svc_);
free(dc_);
free(ddc_);
free(auxc_);
free(aux2c_);
free(aux3c_);
}
/**************************************************************************
*
* The externally accessible function is
*
* void degree_of_polynomial(void)
* Computation of (QdaggerQ)^1/4
* by using the chebyshev approximation for the function ()^1/4
*
*
*******************************************************************************/
double stopeps=5.0e-16;
int dop_n_cheby=0;
double * dop_cheby_coef;
void degree_of_polynomial(const int repro){
int i;
double temp;
static int ini=0;
spinor *ss=NULL, *ss_=NULL, *auxs=NULL, *auxs_=NULL,
*aux2s=NULL, *aux2s_=NULL, *aux3s=NULL, *aux3s_=NULL;
spinor *sc=NULL, *sc_=NULL, *auxc=NULL, *auxc_=NULL, *aux2c=NULL,
*aux2c_=NULL, *aux3c=NULL, *aux3c_=NULL;
if(ini==0){
dop_cheby_coef = calloc(N_CHEBYMAX,sizeof(double));
ini=1;
}
#if ( defined SSE || defined SSE2 || defined SSE3)
ss_ = calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
auxs_ = calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
aux2s_= calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
aux3s_= calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
ss = (spinor *)(((unsigned long int)(ss_)+ALIGN_BASE)&~ALIGN_BASE);
auxs = (spinor *)(((unsigned long int)(auxs_)+ALIGN_BASE)&~ALIGN_BASE);
aux2s = (spinor *)(((unsigned long int)(aux2s_)+ALIGN_BASE)&~ALIGN_BASE);
aux3s = (spinor *)(((unsigned long int)(aux3s_)+ALIGN_BASE)&~ALIGN_BASE);
sc_ = calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
auxc_ = calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
aux2c_= calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
aux3c_= calloc(VOLUMEPLUSRAND/2+1, sizeof(spinor));
sc = (spinor *)(((unsigned long int)(sc_)+ALIGN_BASE)&~ALIGN_BASE);
auxc = (spinor *)(((unsigned long int)(auxc_)+ALIGN_BASE)&~ALIGN_BASE);
aux2c = (spinor *)(((unsigned long int)(aux2c_)+ALIGN_BASE)&~ALIGN_BASE);
aux3c = (spinor *)(((unsigned long int)(aux3c_)+ALIGN_BASE)&~ALIGN_BASE);
#else
ss =calloc(VOLUMEPLUSRAND/2, sizeof(spinor));
auxs =calloc(VOLUMEPLUSRAND/2, sizeof(spinor));
aux2s=calloc(VOLUMEPLUSRAND/2, sizeof(spinor));
aux3s=calloc(VOLUMEPLUSRAND/2, sizeof(spinor));
sc =calloc(VOLUMEPLUSRAND/2, sizeof(spinor));
auxc =calloc(VOLUMEPLUSRAND/2, sizeof(spinor));
aux2c=calloc(VOLUMEPLUSRAND/2, sizeof(spinor));
aux3c=calloc(VOLUMEPLUSRAND/2, sizeof(spinor));
#endif
chebyshev_polynomial(cheb_evmin, cheb_evmax, dop_cheby_coef, N_CHEBYMAX, 0.25);
temp=1.0;
random_spinor_field_eo(ss, repro, RN_GAUSS);
random_spinor_field_eo(sc, repro, RN_GAUSS);
/* assign(&sc[0], &ss[0],VOLUME/2);
Qtm_pm_psi(&auxs[0], &ss[0]);
temp=square_norm(&auxs[0],VOLUME/2, 1);
printf("||auxs Carsten||=%e\n",temp);
Qtm_dagger_ndpsi(&aux3s[0], &aux3c[0], &ss[0], &sc[0]);
Qtm_ndpsi(&auxs[0], &auxc[0], &aux3s[0], &aux3c[0]);
temp=square_norm(&auxs[0],VOLUME/2, 1);
printf("||auxs own||=%e\n",temp);
temp=square_norm(&auxc[0],VOLUME/2, 1);
printf("||auxc own||=%e\n",temp); */
/* if(g_proc_id == g_stdio_proc) {
printf("\ndetermine the degree of the polynomial:\n");
fflush(stdout);
} */
dop_n_cheby=(int)5./sqrt(cheb_evmin);
for(i = 0;i < 1 ; i++){
/* printf("n_cheby=%d i=%d\n", dop_n_cheby, i); */
if (dop_n_cheby >= N_CHEBYMAX) {
if(g_proc_id == g_stdio_proc){
printf("Error: n_cheby=%d > N_CHEBYMAX=%d\n",dop_n_cheby,N_CHEBYMAX);
printf("Increase n_chebymax\n");
}
/* errorhandler(35,"degree_of_polynomial"); */
}
QdaggerQ_power(&aux3s[0], &aux3c[0], dop_cheby_coef, dop_n_cheby, &ss[0], &sc[0]);
QdaggerQ_power(&auxs[0], &auxc[0], dop_cheby_coef, dop_n_cheby, &aux3s[0], &aux3c[0]);
QdaggerQ_power(&aux3s[0], &aux3c[0], dop_cheby_coef, dop_n_cheby, &auxs[0], &auxc[0]);
QdaggerQ_power(&auxs[0], &auxc[0], dop_cheby_coef, dop_n_cheby, &aux3s[0], &aux3c[0]);
/* temp=square_norm(&auxs[0],VOLUME/2, 1);
printf("||auxs||=%e\n",temp);
temp=square_norm(&auxc[0],VOLUME/2, 1);
printf("||auxc||=%e\n",temp); */
Qtm_dagger_ndpsi(&aux2s[0], &aux2c[0], &ss[0], &sc[0]);
Qtm_ndpsi(&aux3s[0], &aux3c[0], &aux2s[0], &aux2c[0]);
/* temp=square_norm(&aux3s[0],VOLUME/2, 1);
printf("||auxs_3||=%e\n",temp);
temp=square_norm(&aux3c[0],VOLUME/2, 1);
printf("||auxc_3||=%e\n",temp); */
diff(&auxs[0],&auxs[0],&aux3s[0],VOLUME/2);
temp=square_norm(&auxs[0],VOLUME/2)/square_norm(&aux3s[0],VOLUME/2, 1)/4.0;
if(g_proc_id == g_stdio_proc) {
printf("difference=%e\n",temp);
diff(&auxc[0],&auxc[0],&aux3c[0],VOLUME/2);
temp=square_norm(&auxc[0],VOLUME/2)/square_norm(&aux3c[0],VOLUME/2, 1)/4.0;
printf("difference=%e\n",temp);
}
if(temp < stopeps ) break;
dop_n_cheby*=1.05;
}
free(ss_);
free(auxs_);
free(aux2s_);
free(aux3s_);
free(sc_);
free(auxc_);
free(aux2c_);
free(aux3c_);
}