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// Gaussian Quantile
//
// gaussian_quantile
//
// Gaussian quantile function (inverse CDF)
//
// Q(p) = Φ^(-1)(p)
//
// Inputs: 1
// Outputs: 1
// Constants: 0
#include <math.h>
#include "ts.h"
ts_parameter_t const ts_gaussian_quantile_p = { .n_inputs = 1, .n_outputs = 1, .n_constants = 0, .params_size = 0 };
uint_t ts_gaussian_quantile_offset( ts_constant_t const *c )
{
( void )c;
return ( 0 );
}
int ts_gaussian_quantile(
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_gaussian_quantile_p );
(void)c;
/* Peter Acklam's approximation for inverse normal CDF */
/* Coefficients for rational approximation */
fp_t const a[] = {
-3.969683028665376e+01, 2.209460984245205e+02,
-2.759285104469687e+02, 1.383577518672690e+02,
-3.066479806614716e+01, 2.506628277459239e+00
};
fp_t const b[] = {
-5.447609879822406e+01, 1.615858368580409e+02,
-1.556989798598866e+02, 6.680131188771972e+01,
-1.328068155288572e+01
};
fp_t const cc[] = {
-7.784894002430993e-03, 3.223964580411365e-01,
-2.400758277161838e+00, -2.549732539343734e+00,
4.374664141464968e+00, 2.938163982698783e+00
};
fp_t const d[] = {
7.784695709041462e-03, 3.224671290700398e-01,
2.445134137142996e+00, 3.754408661907416e+00
};
fp_t const p_low = 0.02425;
fp_t const p_high = 1.0 - p_low;
for (uint_t i = 0; i < n; ++i)
{
fp_t p = x[0][i];
if (p <= 0.0)
{
y[0][i] = -INFINITY;
continue;
}
if (p >= 1.0)
{
y[0][i] = INFINITY;
continue;
}
fp_t q, r;
if (p < p_low) {
q = sqrt(-2.0 * log(p));
y[0][i] = -(((((cc[0]*q + cc[1])*q + cc[2])*q + cc[3])*q + cc[4])*q + cc[5]) /
((((d[0]*q + d[1])*q + d[2])*q + d[3])*q + 1.0);
} else if (p <= p_high) {
q = p - 0.5;
r = q * q;
y[0][i] = (((((a[0]*r + a[1])*r + a[2])*r + a[3])*r + a[4])*r + a[5])*q /
(((((b[0]*r + b[1])*r + b[2])*r + b[3])*r + b[4])*r + 1.0);
} else {
q = sqrt(-2.0 * log(1.0 - p));
y[0][i] = (((((cc[0]*q + cc[1])*q + cc[2])*q + cc[3])*q + cc[4])*q + cc[5]) /
((((d[0]*q + d[1])*q + d[2])*q + d[3])*q + 1.0);
}
}
return 0;
}
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