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// Chi-Squared PDF
//
// chi_squared_pdf - χ² probability density
//
// f(x; k) = x^(k/2-1) * e^(-x/2) / (2^(k/2) * Γ(k/2)), for x > 0
//
// Inputs: 1
// Outputs: 1 (PDF value)
// Constants: 1 (degrees of freedom)
#include <math.h>
#include "ts.h"
typedef struct {
fp_t k;
} ts_chi_squared_pdf_params_t;
ts_parameter_t const ts_chi_squared_pdf_p = { .n_inputs = 1, .n_outputs = 1, .n_constants = 1, .params_size = sizeof(ts_chi_squared_pdf_params_t) };
uint_t ts_chi_squared_pdf_offset( ts_constant_t const *c )
{
( void )c;
return ( 0 );
}
int ts_chi_squared_pdf(
fp_t * const *y, uint_t y_n,
fp_t const * const *x, uint_t x_n,
uint_t n, ts_constant_t const *c
)
{
TS_PROLOGUE( ts_chi_squared_pdf_p );
if ( !c ) return -1;
fp_t k = ((ts_chi_squared_pdf_params_t *)c)->k;
if ( k <= 0 )
{
for( uint_t i = 0; i < n; ++i ) y[0][i] = 0;
return -1;
}
for( uint_t i = 0; i < n; ++i )
{
fp_t xi = x[0][i];
y[0][i] = xi > 0 ? pow( xi, k / 2.0 - 1.0 ) * exp( -xi / 2.0 ) / ( pow( 2.0, k / 2.0 ) * tgamma( k / 2.0 ) ) : 0.0;
}
return 0;
}
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