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#include "path.h"
#include <math.h>
#include <gsl/gsl_spline.h>
#include <stddef.h> /* for size_t */
#include <gsl/gsl_integration.h>
#include "pdg.h"
#include "vector.h"
#include <stdlib.h> /* for malloc(), calloc(), etc. */
#define N 100
static double foo(double s, double range, double theta0, int k)
{
return sqrt(2*pow(theta0,2)*range)*sin(M_PI*s*(k-0.5)/range)/(M_PI*(k-0.5));
}
double path_get_coefficient(unsigned int k, double *s, double *x, double theta0, size_t n)
{
size_t i;
double sum, range;
range = s[n-1];
sum = 0.0;
for (i = 1; i < n; i++) {
sum += (foo(s[i],range,theta0,k)*x[i] + foo(s[i-1],range,theta0,k)*x[i-1])*(s[i]-s[i-1])/2.0;
}
return sum*pow(k-0.5,2)*pow(M_PI,2)/pow(theta0*range,2);
}
path *path_init(double *pos, double *dir, double T0, double range, double theta0, getKineticEnergyFunc *fun, double *z1, double *z2, size_t n, double m)
{
size_t i, j;
double E, mom, beta, theta, phi;
double normal[3], k[3], tmp[3], tmp2[3];
path *p = malloc(sizeof(path));
p->theta0 = theta0;
p->pos[0] = pos[0];
p->pos[1] = pos[1];
p->pos[2] = pos[2];
p->dir[0] = dir[0];
p->dir[1] = dir[1];
p->dir[2] = dir[2];
double *s = malloc(sizeof(double)*N);
double *theta1 = calloc(N,sizeof(double));
double *theta2 = calloc(N,sizeof(double));
double *x = calloc(N,sizeof(double));
double *y = calloc(N,sizeof(double));
double *z = calloc(N,sizeof(double));
double *T = calloc(N,sizeof(double));
double *t = calloc(N,sizeof(double));
double *dx = calloc(N,sizeof(double));
double *dy = calloc(N,sizeof(double));
double *dz = calloc(N,sizeof(double));
dz[0] = 1.0;
for (i = 0; i < N; i++) {
s[i] = range*i/(N-1);
for (j = 0; j < n; j++) {
theta1[i] += z1[j]*foo(s[i],range,theta0,j+1);
theta2[i] += z2[j]*foo(s[i],range,theta0,j+1);
}
T[i] = fun(s[i],T0);
if (i > 0) {
theta = sqrt(theta1[i]*theta1[i] + theta2[i]*theta2[i]);
phi = atan2(theta2[i],theta1[i]);
dx[i] = (s[i]-s[i-1])*sin(theta)*cos(phi);
dy[i] = (s[i]-s[i-1])*sin(theta)*sin(phi);
dz[i] = (s[i]-s[i-1])*cos(theta);
/* Calculate total energy */
E = T[i] + m;
mom = sqrt(E*E - m*m);
beta = mom/E;
t[i] = t[i-1] + (s[i]-s[i-1])/(beta*SPEED_OF_LIGHT);
x[i] = x[i-1] + dx[i];
y[i] = y[i-1] + dy[i];
z[i] = z[i-1] + dz[i];
}
}
/* Now, we rotate and translate the path so that it starts at `pos` and
* points in the direction `dir`. */
/* We need to compute an arbitrary vector which is orthogonal to the
* direction vector. To do this, all we need is another vector not parallel
* to the direction. */
k[0] = 0.0;
k[1] = 0.0;
k[2] = 1.0;
/* If k is approximately equal to the unit vector in the z direction, we
* switch to the unit vector in the x direction. */
if (allclose(k,dir,3,1e-9,1e-9)) {
k[0] = 1.0;
k[1] = 0.0;
k[2] = 0.0;
}
/* Take the cross product between `k` and `dir` to get a vector orthogonal
* to `dir`. */
CROSS(normal,k,dir);
/* Make sure it's normalized. */
normalize(normal);
/* Compute the angle required to rotate the unit vector to `dir`. */
phi = acos(DOT(k,dir));
/* Now we rotate and translate all the positions and rotate all the
* directions. */
for (i = 0; i < N; i++) {
tmp[0] = x[i];
tmp[1] = y[i];
tmp[2] = z[i];
rotate(tmp2,tmp,normal,phi);
ADD(tmp2,tmp2,pos);
x[i] = tmp2[0];
y[i] = tmp2[1];
z[i] = tmp2[2];
tmp[0] = dx[i];
tmp[1] = dy[i];
tmp[2] = dz[i];
normalize(tmp);
rotate(tmp2,tmp,normal,phi);
dx[i] = tmp2[0];
dy[i] = tmp2[1];
dz[i] = tmp2[2];
}
for (i = 0; i < 8; i++) {
p->acc[i] = gsl_interp_accel_alloc();
p->spline[i] = gsl_spline_alloc(gsl_interp_linear,N);
}
gsl_spline_init(p->spline[0],s,x,N);
gsl_spline_init(p->spline[1],s,y,N);
gsl_spline_init(p->spline[2],s,z,N);
gsl_spline_init(p->spline[3],s,T,N);
gsl_spline_init(p->spline[4],s,t,N);
gsl_spline_init(p->spline[5],s,dx,N);
gsl_spline_init(p->spline[6],s,dy,N);
gsl_spline_init(p->spline[7],s,dz,N);
free(s);
free(theta1);
free(theta2);
free(x);
free(y);
free(z);
free(T);
free(t);
free(dx);
free(dy);
free(dz);
return p;
}
void path_eval(path *p, double s, double *pos, double *dir, double *T, double *t, double *theta0)
{
if (s > p->spline[0]->x[p->spline[0]->size-1])
s = p->spline[0]->x[p->spline[0]->size-1];
pos[0] = gsl_spline_eval(p->spline[0],s,p->acc[0]);
pos[1] = gsl_spline_eval(p->spline[1],s,p->acc[1]);
pos[2] = gsl_spline_eval(p->spline[2],s,p->acc[2]);
*T = gsl_spline_eval(p->spline[3],s,p->acc[3]);
*t = gsl_spline_eval(p->spline[4],s,p->acc[4]);
dir[0] = gsl_spline_eval(p->spline[5],s,p->acc[5]);
dir[1] = gsl_spline_eval(p->spline[6],s,p->acc[6]);
dir[2] = gsl_spline_eval(p->spline[7],s,p->acc[7]);
/* FIXME: This should be the *residual* scattering RMS. */
*theta0 = p->theta0*sqrt(s);
}
void path_free(path *p)
{
size_t i;
for (i = 0; i < 5; i++) {
gsl_interp_accel_free(p->acc[i]);
gsl_spline_free(p->spline[i]);
}
free(p);
}
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