lib/legendre.c


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// Legendre
//
// legendre
//
// Legendre polynomial
//
// P_n(x) via recurrence relation
//
// Inputs:    2
// Outputs:   1
// Constants: 0


#include <math.h>
#include "ts.h"


ts_parameter_t const ts_legendre_p = { .n_inputs = 2, .n_outputs = 1, .n_constants = 0, .params_size = 0 };

uint_t ts_legendre_offset( ts_constant_t const *c )
{
	( void )c;
	return ( 0 );
}

int ts_legendre(
	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_legendre_p );
	(void)c;
    for( uint_t i = 0; i < n; ++i )
    {
        fp_t xv = x[0][i];
        if (x[1][i] < 0) { y[0][i] = 0; continue; }
        uint_t n_val = (uint_t)x[1][i];
        if( n_val == 0 )
        {
            y[0][i] = 1.0;
        }
        else if( n_val == 1 )
        {
            y[0][i] = xv;
        }
        else
        {
            fp_t p0 = 1.0;
            fp_t p1 = xv;
            for( uint_t k = 2; k <= n_val; ++k )
            {
                fp_t p2 = ((2.0 * (fp_t)k - 1.0) * xv * p1 - (fp_t)(k - 1) * p0) / (fp_t)k;
                p0 = p1;
                p1 = p2;
            }
            y[0][i] = p1;
        }
    }
	return 0;
}