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// Lambert W
//
// lambert_w
//
// Lambert W function
//
// W(x) such that W*e^W = x
//
// Inputs: 1
// Outputs: 1
// Constants: 0
#include <math.h>
#include "ts.h"
ts_parameter_t const ts_lambert_w_p = { .n_inputs = 1, .n_outputs = 1, .n_constants = 0, .params_size = 0 };
uint_t ts_lambert_w_offset( ts_constant_t const *c )
{
( void )c;
return ( 0 );
}
int ts_lambert_w(
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_lambert_w_p );
(void)c;
for (uint_t i = 0; i < n; ++i)
{
fp_t xv = x[0][i];
if (xv < -1.0/exp(1.0))
{
y[0][i] = NAN;
continue;
}
if (xv == 0.0)
{
y[0][i] = 0.0;
continue;
}
/* Halley iteration for W(x) */
fp_t w = xv < 1.0 ? log(xv + 1.0) : log(xv);
for (uint_t j = 0; j < 10; ++j)
{
fp_t ew = exp(w);
fp_t f = w * ew - xv;
fp_t f1 = ew * (w + 1.0);
if (f1 == 0) break;
fp_t f2 = f1 * (w + 2.0);
w = w - f / f1 * (1.0 + f * f2 / (2.0 * f1 * f1));
}
y[0][i] = w;
}
return 0;
}
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