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#include <math.h>
#include <grass/gis.h>
#include <grass/vector.h>
#include <grass/glocale.h>
#include "global.h"
static double (*kernelfn)(double term, double bandwidth, double x);
/*********************** Gaussian ****************************/
/* probability for gaussian distribution */
double gaussian2dBySigma(double d, double sigma)
{
double res;
res = 1. / (2. * M_PI * sigma * sigma) * exp(-d * d / (2. * sigma * sigma));
return (res);
}
double gaussianFunction(double x, double sigma, double dimension)
{
return ((1. / (pow(2. * M_PI, dimension / 2.) * pow(sigma, dimension))) *
exp(-0.5 * pow(x / sigma, 2.)));
}
/* probability for gaussian distribution */
double gaussianKernel(double x, double termx)
{
return (termx * exp(-(x * x) / 2.));
}
/*
term1 = 1./(2.*M_PI*sigma*sigma)
term2 = 2.*sigma*sigma;
*/
double gaussian2dByTerms(double d, double term1, double term2)
{
double res;
res = term1 * exp(-d * d / term2);
return (res);
}
double segno(double x)
{
double y;
y = (x > 0 ? 1. : 0.) + (x < 0 ? -1. : 0.);
return y;
}
double kernel1(double d, double rs, double lambda)
{
double res;
double a = lambda - 1.;
if (lambda == 1.) {
res = 1. / (M_PI * (d * d + rs * rs));
}
else {
res = segno(a) * (a / M_PI) * (pow(rs, 2. * a)) *
(1 / pow(d * d + rs * rs, lambda));
}
/* res=1./(M_PI*(d*d+rs*rs)); */
return (res);
}
double invGaussian2d(double sigma, double prob)
{
double d;
d = sqrt(-2 * sigma * sigma * log(prob * M_PI * 2 * sigma * sigma));
return (d);
}
/* euclidean distance between vectors x and y of length n */
double euclidean_distance(double *x, double *y, int n)
{
int j;
double out = 0.0;
double tmp;
for (j = 0; j < n; j++) {
tmp = x[j] - y[j];
out += tmp * tmp;
}
return sqrt(out);
}
/*****************kernel density functions******************************/
double gaussianKernel4(double term, double bandwidth, double x)
{
/* term is set by setKernelFunction */
/* bandwidth is here SD */
/*
double term =
1. / (pow(bandwidth, dimension) * pow((2. * M_PI), dimension / 2.));
*/
x /= bandwidth;
/* SD = radius (bandwidth) / 4 */
return (term * exp((x * x) / -2.));
}
/* Note: these functions support currently only 1D and 2D, consider this for
* example before using them for 3d grid */
double uniformKernel(double term, double bandwidth, double x)
{
/* term is set by setKernelFunction */
if (x > bandwidth)
return 0;
/*
if (dimension == 2)
term = 2. / (M_PI * pow(bandwidth, 2));
else
term = 1. / bandwidth;
term *= (1. / 2);
x /= bandwidth;
*/
return term;
}
double triangularKernel(double term, double bandwidth, double x)
{
/* term is set by setKernelFunction */
if (x > bandwidth)
return 0;
/*
if (dimension == 2)
term = 3. / (M_PI * pow(bandwidth, 2));
else
term = 1. / bandwidth;
*/
x /= bandwidth;
return term * (1 - x);
}
double epanechnikovKernel(double term, double bandwidth, double x)
{
/* term is set by setKernelFunction */
if (x > bandwidth)
return 0;
/*
if (dimension == 2)
term = 8. / (M_PI * 3. * pow(bandwidth, 2));
else
term = 1. / bandwidth;
term *= (3. / 4.);
*/
x /= bandwidth;
/* return term * (3. / 4. * (1 - x * x)); */
return term * (1 - x * x);
}
double quarticKernel(double term, double bandwidth, double x)
{
/* term is set by setKernelFunction */
if (x > bandwidth)
return 0;
/*
if (dimension == 2)
term = 16. / (M_PI * 5. * pow(bandwidth, 2));
else
term = 1. / bandwidth;
term *= (15. / 16.);
*/
x /= bandwidth;
/* return term * (15. / 16. * pow(1 - x * x, 2)); */
return term * pow(1 - x * x, 2);
}
double triweightKernel(double term, double bandwidth, double x)
{
/* term is set by setKernelFunction */
if (x > bandwidth)
return 0;
/*
if (dimension == 2)
term = 128. / (M_PI * 35. * pow(bandwidth, 2));
else
term = 1. / bandwidth;
term *= (35. / 32);
*/
x /= bandwidth;
/* return term * (35. / 32 * pow(1 - x * x, 3)); */
return term * pow(1 - x * x, 3);
}
double cosineKernel(double term, double bandwidth, double x)
{
/* term is set by setKernelFunction */
if (x > bandwidth)
return 0;
/*
if (dimension == 2)
term = 1. / (2 * (M_PI / 2 - 1) * pow(bandwidth, 2));
else
term = 1. / bandwidth;
term *= (M_PI / 4.);
*/
x /= bandwidth;
/* return term * (M_PI / 4. * cos(M_PI / 2. * x)); */
return term * cos(M_PI / 2. * x);
}
double kernelFunction(double term, double bandwidth, double x)
{
return kernelfn(term, bandwidth, x);
}
void setKernelFunction(int function, int dimension, double bandwidth,
double *term)
{
switch (function) {
case KERNEL_UNIFORM:
kernelfn = uniformKernel;
if (dimension == 2)
*term = 2. / (M_PI * pow(bandwidth, 2));
else
*term = 1. / bandwidth;
*term *= (1. / 2);
break;
case KERNEL_TRIANGULAR:
kernelfn = triangularKernel;
if (dimension == 2)
*term = 3. / (M_PI * pow(bandwidth, 2));
else
*term = 1. / bandwidth;
break;
case KERNEL_EPANECHNIKOV:
kernelfn = epanechnikovKernel;
if (dimension == 2)
*term = 8. / (M_PI * 3. * pow(bandwidth, 2));
else
*term = 1. / bandwidth;
*term *= (3. / 4.);
break;
case KERNEL_QUARTIC:
kernelfn = quarticKernel;
if (dimension == 2)
*term = 16. / (M_PI * 5. * pow(bandwidth, 2));
else
*term = 1. / bandwidth;
*term *= (15. / 16.);
break;
case KERNEL_TRIWEIGHT:
kernelfn = triweightKernel;
if (dimension == 2)
*term = 128. / (M_PI * 35. * pow(bandwidth, 2));
else
*term = 1. / bandwidth;
*term *= (35. / 32);
break;
case KERNEL_GAUSSIAN:
kernelfn = gaussianKernel4;
*term =
1. / (pow(bandwidth, dimension) * pow((2. * M_PI), dimension / 2.));
break;
case KERNEL_COSINE:
kernelfn = cosineKernel;
if (dimension == 2)
*term = 1. / (2 * (M_PI / 2 - 1) * pow(bandwidth, 2));
else
*term = 1. / bandwidth;
*term *= (M_PI / 4.);
break;
default:
G_fatal_error("Unknown kernel function");
}
}
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