void spline_coef(int *method, int *n, double *x, double *y,
double *b, double *c, double *d, double *e)
{
switch(*method) {
case 1:
periodic_spline(*n, x, y, b, c, d, e); break;
case 2:
natural_spline(*n, x, y, b, c, d); break;
case 3:
fmm_spline(*n, x, y, b, c, d); break;
}
}
void random_wave(double *wav_org, double *dist, int N, int flag, double *y, int NS){
/* wav_org - array of input wavelegnth
dist - array of photon number distribution
N - size of wav_org and dist
flag - interpolation degree : 0 (for line list) or 3 (for continious spectra)
y - output: randomly sampled wavelength
NS - size of y (number of sampling points)
*/
clock_t start = clock();
srand48((long)time(NULL));
int n, N_plus = N + 1; //number of extended data
if (flag == 0){ // no interpolation, step-like CDF, emission-line spectra
printf("Dealing with line list\n");
double *CDF = malloc(sizeof(double) * N_plus);
CDF[0] = 0;
for (n = 0; n < N; n++)
CDF[n+1] = CDF[n] + dist[n];
double total = CDF[N];
for (n = 0; n <= N; n++)
CDF[n] = CDF[n] / total; //normalization
unsigned long long ns;
double random;
int i, j, k;
//double *num_den = malloc(sizeof(double) * N);
for (ns = 0; ns < NS; ns ++) {
random = drand48();
i = 0;
j = N;
do{ // search algorithm (bi-section) to find position of random in CDF
k = (i+j)/2;
if (random < CDF[k])
j = k;
else i = k;
} while(j > i+1); //until random number falls into (CDF[i], CDF[i+1])
y[ns] = wav_org[i];
//num_den[i] ++;
}
/*---data analysis---*/
/*
FILE *num_den_file;
num_den_file = fopen("./num_den_cum.dat", "w+");
FILE *normalized_PDF_file;
normalized_PDF_file = fopen("./normalized_PDF.dat", "w+");
printf("Writing statistics to file\n");
for (n = 0; n < N; n++) {
fprintf(num_den_file, "%lf\t%le\n", wav_org[n], (double) num_den[n] / NS); //normalization
fprintf(normalized_PDF_file, "%lf\t%le\n", wav_org[n], dist[n] / total);
}
fclose(num_den_file);
fclose(normalized_PDF_file);
*/
}
if (flag == 3){ //continious spectra, data interpolation
/*---CDF; Data extension---*/
double *wav = malloc(sizeof(double) * N_plus);
double *CDF = malloc(sizeof(double) * N_plus);
double *delta_lambda = malloc(sizeof(double) * N);
double *flux = malloc(sizeof(double) * N);
/*---add a threshold where flux is too small---*/
double sum = 0;
for (n = 0; n < N; n++) {
flux[n] = dist[n];
sum += flux[n];
}
double threshold = sum * pow(10, -14); //15 decimal places for double precision
for (n = 0; n < N; n++)
if (flux[n] < threshold)
flux[n] = threshold;
//---delta lambda---
delta_lambda[0] = wav_org[1] - wav_org[0];
for (n = 1; n < N-1; n++)
delta_lambda[n] = (wav_org[n+1] - wav_org[n-1]) / 2;
delta_lambda[N-1] = wav_org[N-1] - wav_org[N-2];
//---CDF---
CDF[0] = 0;
CDF[1] = flux[0] * delta_lambda[0];
wav[0] = 1.5 * wav_org[0] - 0.5 * wav_org[1];
for (n = 1; n < N; n++) {
CDF[n+1] = CDF[n] + flux[n] * delta_lambda[n];
wav[n] = (wav_org[n-1] + wav_org[n]) / 2;
}
wav[N] = 1.5 * wav_org[N-1] - 0.5 * wav_org[N-2];
double total = CDF[N];
//printf("total = %le\n", total);
for (n = 0; n < N_plus; n++)
CDF[n] = CDF[n] / total;
free(flux);
/*---data output---
FILE *order_43;
order_43 = fopen("./order_43.dat", "w+");
for(n = 0; n < N_plus; n++)
fprintf(order_43, "%le\t%le\n", wav[n], CDF[n]);
fclose(order_43);
FILE *spec_43;
spec_43 = fopen("./spec_43.dat", "w+");
for(n = 0; n < N; n++)
fprintf(spec_43, "%le\t%le\n", wav_org[n], dist[n]);
fclose(spec_43); */
/*FILE *inter_43;
inter_43 = fopen("./inter_43.dat", "w+");*/
/*---interpolation---*/
unsigned long long ns;
double *b, *c, *d, *x;
b = malloc(sizeof(double) * N_plus);
c = malloc(sizeof(double) * N_plus);
d = malloc(sizeof(double) * N_plus);
natural_spline(N_plus, CDF, wav, b, c, d); //wav as a function of CDF
/*---sampling---*/
if (NS <= pow(10, 7)){
x = malloc(sizeof(double) * NS);
for (ns = 0; ns < NS; ns ++)
x[ns] = drand48();
printf("Sampling in progress\n");
spline_eval(&NS, x, y, &N_plus, CDF, wav, b, c, d); //returns y to be the sampling wavelength
/*for (n = 0; n < 500; n++)
printf("%le\t%16.14lf\n", x[n], y[n]);
for (n = 0; n < NS/10; n++)
fprintf(inter_43, "%le\t%16.14lf\n", x[n], y[n]);
fclose(inter_43); */
free(x);
}
else { //(NS > pow(10, 7))
int new_NS = pow(10, 7);
int progress, times, TIMES = (int)(NS / new_NS), tail = NS - new_NS * TIMES;
double ratio;
x = malloc(sizeof(double) * new_NS);
printf("Sampling in progress\n");
for (times = 0; times < TIMES; times ++){
for (ns = 0; ns < new_NS; ns ++)
x[ns] = drand48();
spline_eval(&new_NS, x, y, &N_plus, CDF, wav, b, c, d);
y += new_NS;
// Show the load bar.
ratio = (double)(times + 1) / TIMES;
printf("%3d%% [", (int)(ratio*100) );
for (progress = 0; progress < (int)(ratio * 50) ; progress++)
printf("=");
printf(">");
for (progress = (int)(ratio * 50); progress < 50; progress++)
printf(" ");
printf("]\r");
fflush(stdout);
}
free(x);
double *x2 = malloc(sizeof(double) * tail);
for (ns = 0; ns < tail; ns ++)
x2[ns] = drand48();
spline_eval(&tail, x2, y, &N_plus, CDF, wav, b, c, d);
printf("\n");
free(x2);
y -= new_NS * TIMES;
}
/*
FILE *wavelegnth_sam;
wavelegnth_sam = fopen("./wavelegnth_sam.dat", "w+");
for (ns = 0; ns < NS; ns++)
fprintf(wavelegnth_sam, "%lf\n", y[ns]);
fclose(wavelegnth_sam);
*/
/*---deallocate array memory---*/
free(b);
free(c);
free(d);
free(wav);
free(CDF);
free(delta_lambda);
}
clock_t ends = clock();
printf("%.2f s to return %.2le wavelegnths\n",(double) (ends - start) / CLOCKS_PER_SEC, (double)NS);
}
