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/*
FITSPNG -- empirical distribution function
Copyright (C) 2019 Filip Hroch, Masaryk University, Brno, CZ
Fitspng 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.
Fitspng 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 Fitspng. If not, see <http://www.gnu.org/licenses/>.
*/
#include "fitspng.h"
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <float.h>
#include <string.h>
#include <assert.h>
#define EPSILON 2*FLT_EPSILON
#define CMP(x,y) ((x) < (y) ? -1 : ((x) > (y) ? 1 : 0))
static int fcmp(const void *u, const void *v)
{
return CMP(*(const float *) u, *(const float *) v);
/*
const float x = *(const float *) u;
const float y = *(const float *) v;
if( x < y )
return -1;
else if( x > y )
return 1;
else
return 0;
*/
}
/* alternative with modified data */
int ecdf(long n, const float *data, float *xcdf, float *ycdf)
{
assert(n > 0 && data);
long m = n * sizeof(float);
float *d;
if( (d = malloc(m)) == NULL )
perror("There is no room for data sort in CDF.");
memcpy(d,data,m);
qsort(d,n,sizeof(float),fcmp);
/* remove duplicities */
m = 1;
for(long i = 1; i < n; i++) {
if( fabsf(d[i] - d[m]) > EPSILON )
d[m++] = d[i];
}
/* setup CDF */
memcpy(xcdf,d,m*sizeof(float));
float h = 1.0 / (float)(m + 1);
for(long i = 0; i < m; i++) ycdf[i] = i*h;
free(d);
return m;
}
float quantile(long ncdf, const float *xcdf, const float *ycdf, float q)
{
long n = ncdf;
if( n == 0 )
return 0.0;
else if( n == 1 )
return xcdf[0];
if( q < ycdf[0] )
return xcdf[0];
else if( q > ycdf[n-1] )
return(xcdf[n-1]);
else {
float h = 1.0 / (float)(n + 1);
float r = q / h;
int m = roundf(r);
if( fabsf(m - r) < EPSILON )
return(xcdf[m]);
else {
int low = r;
int high = low + 1;
float dy = ycdf[high] - ycdf[low];
if( fabsf(dy) > EPSILON )
// inverse by linear interpolation
return((xcdf[high] - xcdf[low])/dy*(q - ycdf[low]) + xcdf[low]);
else {
// nearly singular
return((xcdf[high] + xcdf[low]) / 2);
}
}
}
}
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