static ERL_NIF_TERM kurtosis(ErlNifEnv * env, int argc, const ERL_NIF_TERM argv[]) {
double_list dl = alloc_double_list(env, argv[0]);
ARG_ERROR_IF_DL_IS_NULL(dl);
ERL_NIF_TERM final = enif_make_double(env, gsl_stats_kurtosis(dl.list, 1, dl.length));
free_double_list(dl);
return final;
}
void
test_basic(const size_t n, const double data[], const double tol)
{
gsl_rstat_workspace *rstat_workspace_p = gsl_rstat_alloc();
const double expected_mean = gsl_stats_mean(data, 1, n);
const double expected_var = gsl_stats_variance(data, 1, n);
const double expected_sd = gsl_stats_sd(data, 1, n);
const double expected_sd_mean = expected_sd / sqrt((double) n);
const double expected_skew = gsl_stats_skew(data, 1, n);
const double expected_kurtosis = gsl_stats_kurtosis(data, 1, n);
double expected_rms = 0.0;
double mean, var, sd, sd_mean, rms, skew, kurtosis;
size_t i, num;
int status;
/* compute expected rms */
for (i = 0; i < n; ++i)
expected_rms += data[i] * data[i];
expected_rms = sqrt(expected_rms / n);
/* add data to rstat workspace */
for (i = 0; i < n; ++i)
gsl_rstat_add(data[i], rstat_workspace_p);
mean = gsl_rstat_mean(rstat_workspace_p);
var = gsl_rstat_variance(rstat_workspace_p);
sd = gsl_rstat_sd(rstat_workspace_p);
sd_mean = gsl_rstat_sd_mean(rstat_workspace_p);
rms = gsl_rstat_rms(rstat_workspace_p);
skew = gsl_rstat_skew(rstat_workspace_p);
kurtosis = gsl_rstat_kurtosis(rstat_workspace_p);
num = gsl_rstat_n(rstat_workspace_p);
gsl_test_int(num, n, "n n=%zu" , n);
gsl_test_rel(mean, expected_mean, tol, "mean n=%zu", n);
gsl_test_rel(var, expected_var, tol, "variance n=%zu", n);
gsl_test_rel(sd, expected_sd, tol, "stddev n=%zu", n);
gsl_test_rel(sd_mean, expected_sd_mean, tol, "stddev_mean n=%zu", n);
gsl_test_rel(rms, expected_rms, tol, "rms n=%zu", n);
gsl_test_rel(skew, expected_skew, tol, "skew n=%zu", n);
gsl_test_rel(kurtosis, expected_kurtosis, tol, "kurtosis n=%zu", n);
status = gsl_rstat_reset(rstat_workspace_p);
gsl_test_int(status, GSL_SUCCESS, "rstat returned success");
num = gsl_rstat_n(rstat_workspace_p);
gsl_test_int(num, 0, "n n=%zu" , n);
gsl_rstat_free(rstat_workspace_p);
}
CAMLprim value ml_gsl_stats_kurtosis(value ow, value data)
{
size_t len = Double_array_length(data);
double result;
if(ow == Val_none)
result = gsl_stats_kurtosis(Double_array_val(data), 1, len);
else {
value w = Unoption(ow);
check_array_size(data, w);
result = gsl_stats_wkurtosis(Double_array_val(w), 1,
Double_array_val(data), 1, len);
}
return copy_double(result);
}
void
test_basic(const size_t n, const double data[], const double tol)
{
gsl_rstat_workspace *rstat_workspace_p = gsl_rstat_alloc();
const double expected_mean = gsl_stats_mean(data, 1, n);
const double expected_var = gsl_stats_variance(data, 1, n);
const double expected_sd = gsl_stats_sd(data, 1, n);
const double expected_skew = gsl_stats_skew(data, 1, n);
const double expected_kurtosis = gsl_stats_kurtosis(data, 1, n);
double expected_rms = 0.0;
double mean, var, sd, rms, skew, kurtosis;
size_t i;
/* compute expected rms */
for (i = 0; i < n; ++i)
expected_rms += data[i] * data[i];
expected_rms = sqrt(expected_rms / n);
/* add data to rstat workspace */
for (i = 0; i < n; ++i)
gsl_rstat_add(data[i], rstat_workspace_p);
mean = gsl_rstat_mean(rstat_workspace_p);
var = gsl_rstat_variance(rstat_workspace_p);
sd = gsl_rstat_sd(rstat_workspace_p);
rms = gsl_rstat_rms(rstat_workspace_p);
skew = gsl_rstat_skew(rstat_workspace_p);
kurtosis = gsl_rstat_kurtosis(rstat_workspace_p);
gsl_test_rel(mean, expected_mean, tol, "mean n=%zu", n);
gsl_test_rel(var, expected_var, tol, "variance n=%zu", n);
gsl_test_rel(sd, expected_sd, tol, "stddev n=%zu", n);
gsl_test_rel(rms, expected_rms, tol, "rms n=%zu", n);
gsl_test_rel(skew, expected_skew, tol, "skew n=%zu", n);
gsl_test_rel(kurtosis, expected_kurtosis, tol, "kurtosis n=%zu", n);
gsl_rstat_free(rstat_workspace_p);
}
int
main()
{
gsl_rng *r = gsl_rng_alloc(gsl_rng_default);
const double tol1 = 1.0e-8;
const double tol2 = 1.0e-3;
gsl_ieee_env_setup();
{
const size_t N = 2000000;
double *data = random_data(N, r);
double data2[] = { 4.0, 7.0, 13.0, 16.0 };
size_t i;
test_basic(2, data, tol1);
test_basic(100, data, tol1);
test_basic(1000, data, tol1);
test_basic(10000, data, tol1);
test_basic(50000, data, tol1);
test_basic(80000, data, tol1);
test_basic(1500000, data, tol1);
test_basic(2000000, data, tol1);
for (i = 0; i < 4; ++i)
data2[i] += 1.0e9;
test_basic(4, data2, tol1);
free(data);
}
{
/* dataset from Jain and Chlamtac paper */
const size_t n_jain = 20;
const double data_jain[] = { 0.02, 0.15, 0.74, 3.39, 0.83,
22.37, 10.15, 15.43, 38.62, 15.92,
34.60, 10.28, 1.47, 0.40, 0.05,
11.39, 0.27, 0.42, 0.09, 11.37 };
double expected_jain = 4.44063435326;
test_quantile(0.5, data_jain, n_jain, expected_jain, tol1, "jain");
}
{
size_t n = 1000000;
double *data = malloc(n * sizeof(double));
double *sorted_data = malloc(n * sizeof(double));
gsl_rstat_workspace *rstat_workspace_p = gsl_rstat_alloc();
double p;
size_t i;
for (i = 0; i < n; ++i)
{
data[i] = gsl_ran_gaussian_tail(r, 1.3, 1.0);
gsl_rstat_add(data[i], rstat_workspace_p);
}
memcpy(sorted_data, data, n * sizeof(double));
gsl_sort(sorted_data, 1, n);
/* test quantile calculation */
for (p = 0.1; p <= 0.9; p += 0.1)
{
double expected = gsl_stats_quantile_from_sorted_data(sorted_data, 1, n, p);
test_quantile(p, data, n, expected, tol2, "gauss");
}
/* test mean, variance */
{
const double expected_mean = gsl_stats_mean(data, 1, n);
const double expected_var = gsl_stats_variance(data, 1, n);
const double expected_sd = gsl_stats_sd(data, 1, n);
const double expected_skew = gsl_stats_skew(data, 1, n);
const double expected_kurtosis = gsl_stats_kurtosis(data, 1, n);
const double expected_median = gsl_stats_quantile_from_sorted_data(sorted_data, 1, n, 0.5);
const double mean = gsl_rstat_mean(rstat_workspace_p);
const double var = gsl_rstat_variance(rstat_workspace_p);
const double sd = gsl_rstat_sd(rstat_workspace_p);
const double skew = gsl_rstat_skew(rstat_workspace_p);
const double kurtosis = gsl_rstat_kurtosis(rstat_workspace_p);
const double median = gsl_rstat_median(rstat_workspace_p);
gsl_test_rel(mean, expected_mean, tol1, "mean");
gsl_test_rel(var, expected_var, tol1, "variance");
gsl_test_rel(sd, expected_sd, tol1, "stddev");
gsl_test_rel(skew, expected_skew, tol1, "skew");
gsl_test_rel(kurtosis, expected_kurtosis, tol1, "kurtosis");
gsl_test_abs(median, expected_median, tol2, "median");
}
free(data);
free(sorted_data);
gsl_rstat_free(rstat_workspace_p);
}
gsl_rng_free(r);
exit (gsl_test_summary());
}
int main (void)
{
int i, j, warn, counter;
double lim[15];
lim[0]=0.01;
//lim[1]=0.02;
lim[1]=0.03;
//lim[3]=0.04;
lim[2]=0.05;
//lim[5]=0.09;
lim[3]=0.11;
//lim[7]=0.14;
lim[4]=0.17;
//lim[9]=0.208;
lim[5]=0.26;
//lim[11]=0.32;
lim[6]=0.4;
//lim[13]=0.51;
lim[7]=0.64;
//lim[15]=0.8;
lim[8]=1.0;
//lim[17]=1.25;
lim[9]=1.56;
//lim[19]=1.95;
lim[10]=2.44;
//lim[21]=3.05;
lim[11]=3.81;
//lim[23]=4.76;
lim[12]=5.96;
//lim[25]=7.45;
lim[13]=9.31;
//lim[27]=11.64;
lim[14]=14.55;
//lim[29]=18.18;
counter = 0.0;
double pos[N],vel[N],err[N],vel_sq, sum;
double mean, median, skew, sd, kurtosis, error, sum1, sum2;
FILE *velo, *sig, *script;
velo = fopen("organized.dat", "r");
sig = fopen("sigma.dat","w");
for(i=0.0; i<N; i++)
{
fscanf(velo, "%lf %lf %lf", &pos[i], &vel[i], &err[i]);
}
//printf ("The sample mean is %g\n", mean);
fclose(velo);
for(j=0.0; j<14.0; j=j+1.0)
{
counter = 0.0;
for(i = 0.0;(i)<=N; i++)
{
if( lim[j] <= pos[i] && pos[i] < lim[(j)+1] )
{
counter++;
gsl_sort (vel, 1, counter);
mean = gsl_stats_mean(vel, 1, counter);
median = gsl_stats_median_from_sorted_data (vel, 1, counter);
sd = gsl_stats_sd (vel, 1, counter);
skew = gsl_stats_skew(vel, 1, counter);
kurtosis = gsl_stats_kurtosis (vel, 1, counter);
sum1 = (vel[i]-mean)*(vel[i]-mean);
sum1++;
sum2 = (vel[i]-mean)*err[i];
sum2++;
error = 1.0/(sqrt(counter)) * pow(sum1,-0.5) * sum2;
}
}
printf("Particulas entre %lf y %lf es %d\n",lim[j],lim[j+1], counter);
printf("Error %lf\n", error);
printf ("The sample mean is %g\n", mean);
printf ("The median is %g\n", median);
printf ("Standard deviation is %g\n", sd);
printf ("Skewness is %g\n", skew);
printf ("kurtosis is %g\n\n", kurtosis);
//printf("Sigma in the bin is: %.2f\n\n", sig);
fprintf(sig, "%lf\t %lf\t %lf\t %d\n", (lim[j]+lim[j+1])*0.5, sd, error, counter);
}
fclose(sig);
script = fopen( "script1.gpl", "w" );
fprintf(script, "set grid\nset terminal png\nset output 'Sigma_vs_rad.png'\nset nokey\n");
fprintf( script, "set title 'Sigma vs Radius'\n" );
fprintf( script, "set logscale x\n" );
fprintf( script, "set xlabel 'Radius in Arcmin'\n" );
fprintf( script, "set xrange [0.01:20]\n" );
//fprintf( script, "set logscale x 10\n" );
fprintf( script, "set ylabel 'Sigma (km/s)'\n" );
fprintf( script, "plot 'sigma.dat' u 1:2:3 pt 7 ps 1 with errorbars\n");
fclose(script);
warn = system("gnuplot script1.gpl");
return(warn);
}
int main (void)
{
int i, j, warn, lim[13], counter;
lim[0]=0.0;
lim[1]=1.0;
lim[2]=2.0;
lim[3]=3.0;
lim[4]=4.0;
lim[5]=5.0;
lim[6]=8.0;
lim[7]=12.0;
lim[8]=16.0;
lim[9]=20.0;
lim[10]=24.0;
lim[11]=28.0;
lim[12]=45.0;
counter = 0.0;
double pos[N],vel[N],err[N],vel_sq, sum;
double mean, median, skew, sd, kurtosis;
FILE *velo, *sig, *script;
velo = fopen("velocity.dat", "r");
sig = fopen("sigma.dat","w");
for(i=0.0; i<N; i++)
{
fscanf(velo, "%lf %lf %lf", &pos[i], &vel[i], &err[i]);
}
//printf ("The sample mean is %g\n", mean);
fclose(velo);
for(j=0.0; j<12.0; j=j+1.0)
{
counter = 0.0;
for(i = 0.0;(i)<=N; i++)
{
if( lim[j] <= pos[i] && pos[i] < lim[(j)+1] )
{
counter++;
gsl_sort (vel, 1, counter);
mean = gsl_stats_mean(vel, 1, counter);
median = gsl_stats_median_from_sorted_data (vel, 1, counter);
sd = gsl_stats_sd (vel, 1, counter);
skew = gsl_stats_skew(vel, 1, counter);
kurtosis = gsl_stats_kurtosis (vel, 1, counter);
}
}
printf("Particulas entre %d y %d es %d\n",lim[j],lim[j +1], counter);
printf ("The sample mean is %g\n", mean);
printf ("The median is %g\n", median);
printf ("Standard deviation is %g\n", sd);
printf ("Skewness is %g\n", skew);
printf ("kurtosis is %g\n\n", kurtosis);
//printf("Sigma in the bin is: %.2f\n\n", sig);
fprintf(sig, "%.2f\t %.2f\n", (lim[j]+lim[j+1])*0.5, sd);
}
fclose(sig);
script = fopen( "script1.gpl", "w" );
fprintf(script, "set grid\nset terminal png\nset output 'Sigma_vs_rad.png'\nset nokey\n");
fprintf( script, "set title 'Sigma vs Radius'\n" );
//fprintf( script, "set logscale x\n" );
fprintf( script, "set xlabel 'Radius in Arcmin'\n" );
//fprintf( script, "set yrange [25:100]\n" );
fprintf( script, "set ylabel 'Sigma (km/s)'\n" );
fprintf( script, "plot 'sigma.dat' u 1:2 pt 7 ps 1\n");
fclose(script);
warn = system("gnuplot script1.gpl");
return(warn);
}
