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pfft.c
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pfft.c
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#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include "pfft.h"
double pi = acos(-1);
double sinc(double x) {
return sin(x)/x;
}
struct pair {
int a;
float b;
};
void zip(int * as, float * bs, struct pair * ps, int n) {
for(int i=0; i<n; i++) {
ps[i].a=as[i];
ps[i].b=bs[i];
}
}
int comp(const void * a, const void * b) {
if (((struct pair *)a)->b < ((struct pair *)b)->b) return -1;
if (((struct pair *)a)->b == ((struct pair *)b)->b) return 0;
if (((struct pair *)a)->b > ((struct pair *)b)->b) return 1;
//return ((struct pair *)a)->b - ((struct pair *)b)->b;
}
int nearby1D(struct pair * ps,int natom,double L,int xi, float x,double rc,int * n) {
struct pair p = {.a = 0, .b = x};
struct pair * ptr = bsearch(&p,ps,natom,sizeof(struct pair),comp);
uintptr_t pi = ptr-ps;
int count = 0;
int j;
for(j=pi+1; j<natom; j++) {
if(ps[j].b - x < rc) {
n[count]=ps[j].a;
count++;
} else break;
}
if(j==natom) {
for(j=0; j<pi; j++) {
if(ps[j].b + L - x < rc) {
n[count]=ps[j].a;
count++;
} else break;
}
}
//for(j=pi-1; j>=0; j--) {
// if(x - ps[j].b < rc) {
// n[count]=ps[j].a;
// count++;
// } else break;
//}
//if(j==-1) {
// for(j=natom-1; j>pi; j--) {
// if(x - ps[j].b + L < rc) {
// n[count]=ps[j].a;
// count++;
// } else break;
// }
//}
return count;
}
int compi(const void * a, const void * b) {
return (*(int *)a) - (*(int *)b);
}
int intersect(int * a, int na, int * b, int nb, int * n) {
qsort(a,na,sizeof(int),compi);
qsort(b,nb,sizeof(int),compi);
int count = 0;
int ai=0;
int bi=0;
while(ai<na && bi<nb) {
if(a[ai]==b[bi]) {
n[count]=a[ai];
count++;
ai++;
bi++;
continue;
} else if (a[ai]>b[bi]) {
bi++;
} else {
ai++;
}
}
return count;
}
struct bins {
int n;
double l;
int space;
int *** bin;
int *** counts;
double * xs;
double * ys;
double * zs;
double * bs;
};
//assumes square system
struct bins * bin(struct partsys ps, double rc) {
int n = floor(ps.uc[0]/rc);
struct bins * b = malloc(sizeof(struct bins));
b->n=n;
b->l=ps.uc[0]/n;
b->space = ceil(2.0*ps.natom/(1.0*n*n));
b->bin = &((int ***) malloc((n+2)*sizeof(int **)))[1];
b->counts = &((int ***) malloc((n+2)*sizeof(int **)))[1];
b->xs = malloc(ps.natom * sizeof(double));
b->ys = malloc(ps.natom * sizeof(double));
b->zs = malloc(ps.natom * sizeof(double));
b->bs = malloc(ps.natom * sizeof(double));
for (int i=0; i<n; i++) {
b->bin[i] = &((int **) malloc((n+2)*sizeof(int *)))[1];
b->counts[i] = &((int **) malloc((n+2)*sizeof(int *)))[1];
for (int j=0; j<n; j++) {
b->bin[i][j] = malloc(b->space*sizeof(int));
b->counts[i][j] = malloc(sizeof(int));
*(b->counts[i][j]) = 0;
}
b->bin[i][-1]=b->bin[i][n-1];
b->bin[i][n]=b->bin[i][0];
b->counts[i][-1]=b->counts[i][n-1];
b->counts[i][n]=b->counts[i][0];
}
b->bin[-1]=b->bin[n-1];
b->bin[n]=b->bin[0];
b->counts[-1]=b->counts[n-1];
b->counts[n]=b->counts[0];
for(int i=0; i<ps.natom; i++) {
int bx = ((int) floor(ps.xs[i]/b->l) + n) % n;
int by = ((int) floor(ps.ys[i]/b->l) + n) % n;
b->bin[bx][by][*(b->counts[bx][by])]=i;
*(b->counts[bx][by]) = (*(b->counts[bx][by]))+1;
b->xs[i]=ps.xs[i]-bx*b->l;
b->ys[i]=ps.ys[i]-by*b->l;
b->zs[i]=ps.zs[i];
b->bs[i]=ps.bs[i];
}
return b;
}
void freeBins(struct bins * b) {
for (int i=-1; i<b->n+1; i++) {
for (int j=-1; j<b->n+1; j++) {
free(b->bin[i][j]);
free(b->counts[i][j]);
}
free(&b->bin[i][-1]);
free(&b->counts[i][-1]);
}
free(&b->bin[-1]);
free(&b->counts[-1]);
free(b->xs);
free(b->ys);
free(b->zs);
free(b->bs);
free(b);
}
//rc = ds*rci
void term1a(struct partsys ps, double rc, struct result res) {
int ns[ps.natom];
for(int i=0; i<ps.natom; i++)
ns[i]=i;
struct pair * srtx = malloc(ps.natom*sizeof(struct pair));
struct pair * srty = malloc(ps.natom*sizeof(struct pair));
zip(ns,ps.xs,srtx,ps.natom);
zip(ns,ps.ys,srty,ps.natom);
qsort(srtx,ps.natom,sizeof(struct pair),comp);
qsort(srty,ps.natom,sizeof(struct pair),comp);
#pragma omp parallel for
for(int qi=0; qi<res.nqs; qi++) {
for(int i=0; i<ps.natom; i++) {
int nx[ps.natom];
int nnx = nearby1D(srtx,ps.natom,ps.uc[0],i,ps.xs[i],rc,nx);
int ny[ps.natom];
int nny = nearby1D(srty,ps.natom,ps.uc[1],i,ps.ys[i],rc,ny);
int jis[ps.natom];
int nj = intersect(nx, nnx, ny, nny, jis);
if(i%1480==0)
fprintf(stderr,"%d",i/1480);
for(int k=0; k<nj; k++) {
int j = jis[k];
double dx = ps.xs[j] - ps.xs[i];
double dy = ps.ys[j] - ps.ys[i];
if(dx*dx+dy*dy<rc*rc) {
double dz = ps.zs[j] - ps.zs[i];
double dr = sqrt(dx*dx + dy*dy + dz*dz);
res.is[qi]+=2*ps.bs[i]*ps.bs[j]*sinc(res.qs[qi]*dr);
}
}
}
}
free(srtx);
free(srty);
}
void term1abin(struct partsys ps, double rc, struct result res) {
struct bins * b = bin(ps,rc);
#pragma omp parallel for
for(int qi=0; qi<res.nqs; qi++) {
for(int xi=0; xi<b->n; xi++) {
fprintf(stderr,"xi=%d\n",xi);
for(int yi=0; yi<b->n; yi++) {
fprintf(stderr,"yi=%d\n",yi);
for(int ai=0; ai<*(b->counts[xi][yi]); ai++) {
//+x bin
for(int aj=0; aj<*(b->counts[xi+1][yi]); aj++) {
double dx = b->l + b->xs[aj] - b->xs[ai];
double dy = b->ys[aj] - b->ys[ai];
if(dx*dx+dy*dy<rc*rc) {
double dz = b->zs[aj] - b->zs[ai];
double dr = sqrt(dx*dx + dy*dy + dz*dz);
res.is[qi]+=2*b->bs[ai]*b->bs[aj]*sinc(res.qs[qi]*dr);
}
}
//+y bin
for(int aj=0; aj<*(b->counts[xi][yi+1]); aj++) {
double dx = b->xs[aj] - b->xs[ai];
double dy = b->l + b->ys[aj] - b->ys[ai];
if(dx*dx+dy*dy<rc*rc) {
double dz = b->zs[aj] - b->zs[ai];
double dr = sqrt(dx*dx + dy*dy + dz*dz);
res.is[qi]+=2*b->bs[ai]*b->bs[aj]*sinc(res.qs[qi]*dr);
}
}
//+xy bin
for(int aj=0; aj<*(b->counts[xi+1][yi+1]); aj++) {
double dx = b->l + b->xs[aj] - b->xs[ai];
double dy = b->l + b->ys[aj] - b->ys[ai];
if(dx*dx+dy*dy<rc*rc) {
double dz = b->zs[aj] - b->zs[ai];
double dr = sqrt(dx*dx + dy*dy + dz*dz);
res.is[qi]+=2*b->bs[ai]*b->bs[aj]*sinc(res.qs[qi]*dr);
}
}
//-y bin
for(int aj=0; aj<*(b->counts[xi][yi-1]); aj++) {
double dx = b->xs[aj] - b->xs[ai];
double dy = -(b->l) + b->ys[aj] - b->ys[ai];
if(dx*dx+dy*dy<rc*rc) {
double dz = b->zs[aj] - b->zs[ai];
double dr = sqrt(dx*dx + dy*dy + dz*dz);
res.is[qi]+=2*b->bs[ai]*b->bs[aj]*sinc(res.qs[qi]*dr);
}
}
//same bin
for(int aj=0; aj<*(b->counts[xi][yi]); aj++) {
if(b->xs[aj] > b->xs[ai]) {
double dx = b->xs[aj] - b->xs[ai];
double dy = b->ys[aj] - b->ys[ai];
if(dx*dx+dy*dy<rc*rc) {
double dz = b->zs[aj] - b->zs[ai];
double dr = sqrt(dx*dx + dy*dy + dz*dz);
res.is[qi]+=2*b->bs[ai]*b->bs[aj]*sinc(res.qs[qi]*dr);
}
} else if((b->xs[aj] == b->xs[ai]) && (b->ys[aj] > b->ys[ai])){
double dx = b->xs[aj] - b->xs[ai];
double dy = b->ys[aj] - b->ys[ai];
if(dx*dx+dy*dy<rc*rc) {
double dz = b->zs[aj] - b->zs[ai];
double dr = sqrt(dx*dx + dy*dy + dz*dz);
res.is[qi]+=2*b->bs[ai]*b->bs[aj]*sinc(res.qs[qi]*dr);
}
}
}
}
}
}
}
freeBins(b);
}
//rci is the index of the first ring OUTSIDE the cutoff
void term1b(struct partsys ps, struct betaz * bz, double bw, int rci, double ds, int simax, struct result res) {
#pragma omp parallel for
for (int qi=0; qi<res.nqs; qi++) {
for(int i=0; i<ps.natom; i++) {
if(i%1480==0) fprintf(stderr,"%d",i/1480);
double base = ps.bs[i]*ds*2*pi*(bz->dz);
for (int si=rci; si<=simax; si++) {
double s = ds*0.5+ds*si;
for (int zi=-bz->maxbin; zi<=bz->maxbin; zi++) {
double deltaz = zi*(bz->dz) - ps.zs[i];
//res.is[qi]+=ps.bs[i]*(bz->dz)*ds*2*pi*s*(bz->beta[zi])*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
res.is[qi]+=base*s*(bz->beta[zi])*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
}
//end caps
{
//top
double z = ((bz->maxbin + 0.5)*(bz->dz) + ps.uc[2]/2.0)/2.0;
double dz = ps.uc[2]/2.0 - (bz->maxbin + 0.5)*(bz->dz);
double deltaz = z - ps.zs[i];
res.is[qi]+=ps.bs[i]*dz*ds*2*pi*s*bw*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
//bottom
z *= -1;
deltaz = z - ps.zs[i];
res.is[qi]+=ps.bs[i]*dz*ds*2*pi*s*bw*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
}
}
}
}
}
void term234(struct betaz * bz, double * uc, double bw, double ds, int simax, struct result res) {
for(int qi=0; qi<res.nqs; qi++) {
for(int si=0; si<=simax; si++) {
double s = ds*0.5+ds*si;
for(int zi=-bz->maxbin; zi<=bz->maxbin; zi++) {
for(int zj=-bz->maxbin; zj<=bz->maxbin; zj++) {
double deltaz = (zi-zj)*bz->dz;
res.is[qi]+=2*pi*s*bw*uc[0]*uc[1]*bz->dz*bz->dz*ds*(-2*bz->beta[zi]+bw)*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
}
//end caps (j)
{
//top (j)
double z2 = ((bz->maxbin + 0.5)*(bz->dz) + uc[2]/2.0)/2.0;
double dz2 = uc[2]/2.0 - (bz->maxbin + 0.5)*(bz->dz);
double deltaz = zi*bz->dz - z2;
res.is[qi]+=2*pi*s*bw*uc[0]*uc[1]*bz->dz*dz2*ds*(-2*bz->beta[zi]+bw)*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
//bottom (j)
z2 *= -1;
deltaz = zi*bz->dz - z2;
res.is[qi]+=2*pi*s*bw*uc[0]*uc[1]*bz->dz*dz2*ds*(-2*bz->beta[zi]+bw)*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
}
}
//end caps (i)
{
//top (i)
double z1 = ((bz->maxbin + 0.5)*(bz->dz) + uc[2]/2.0)/2.0;
double dz1 = uc[2]/2.0 - (bz->maxbin + 0.5)*(bz->dz);
for(int zj=-bz->maxbin; zj<=bz->maxbin; zj++) {
double deltaz = z1 - zj*bz->dz;
res.is[qi]+=2*pi*s*bw*uc[0]*uc[1]*dz1*bz->dz*ds*(-2*bw+bw)*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
}
//end caps (j)
{
//top (j)
double z2 = ((bz->maxbin + 0.5)*(bz->dz) + uc[2]/2.0)/2.0;
double dz2 = uc[2]/2.0 - (bz->maxbin + 0.5)*(bz->dz);
double deltaz = z1 - z2;
res.is[qi]+=2*pi*s*bw*uc[0]*uc[1]*dz1*dz2*ds*(-2*bw+bw)*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
//bottom (j)
z2 *= -1;
deltaz = z1 - z2;
res.is[qi]+=2*pi*s*bw*uc[0]*uc[1]*dz1*dz2*ds*(-2*bw+bw)*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
}
//bottom (i)
z1 *= -1;
for(int zj=-bz->maxbin; zj<=bz->maxbin; zj++) {
double deltaz = z1 - zj*bz->dz;
res.is[qi]+=2*pi*s*bw*uc[0]*uc[1]*dz1*bz->dz*ds*(-2*bw+bw)*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
}
//end caps (j)
{
//top (j)
double z2 = ((bz->maxbin + 0.5)*(bz->dz) + uc[2]/2.0)/2.0;
double dz2 = uc[2]/2.0 - (bz->maxbin + 0.5)*(bz->dz);
double deltaz = z1 - z2;
res.is[qi]+=2*pi*s*bw*uc[0]*uc[1]*dz1*dz2*ds*(-2*bw+bw)*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
//bottom (j)
z2 *= -1;
deltaz = z1 - z2;
res.is[qi]+=2*pi*s*bw*uc[0]*uc[1]*dz1*dz2*ds*(-2*bw+bw)*sinc(res.qs[qi]*sqrt(s*s+deltaz*deltaz));
}
}
}
}
}
//smax = (simax+1)*ds
void termHighS(struct partsys ps, double bw, double smax, struct result res) {
double sum=0;
for(int i=0; i<ps.natom; i++)
sum+=ps.bs[i];
for(int qi=0; qi<res.nqs; qi++) {
res.is[qi]+=2*pi*(sum - ps.uc[0]*ps.uc[1]*ps.uc[2]*bw)*(sum-ps.uc[0]*ps.uc[1]*ps.uc[2]*bw)*cos(res.qs[qi]*smax)/(res.qs[qi]*res.qs[qi]*ps.uc[0]*ps.uc[1]);
}
}
void pfft(struct partsys ps, struct betaz * bz, double bw, int rci, double ds, int simax, struct result res) {
fprintf(stderr,"a");
//term1a(ps, ds*rci, res);
term1abin(ps, ds*rci, res);
fprintf(stderr,"b");
term1b(ps, bz, bw, rci, ds, simax, res);
fprintf(stderr,"2");
term234(bz, ps.uc, bw, ds, simax, res);
fprintf(stderr,"H");
termHighS(ps, bw, (simax+1)*ds, res);
}