moment_factorial_from_upfactorial.h File Reference

Falling-factorial moments from rising-factorial moments, via the Lah numbers. More...

#include <vector>
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/matrix.h"
#include "line/util/population.h"
#include "line/api/moment/moment_lah.h"

Include dependency graph for moment_factorial_from_upfactorial.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::moment

Functions
template<class T>
std::vector< T >	line::moment::moment_factorial_from_upfactorial (const std::vector< T > &fp)
	f_0 = 1; f_i = sum_k (-1)^(i-k) L(i,k) fp_k for i >= 1.

Detailed Description

Falling-factorial moments from rising-factorial moments, via the Lah numbers.

Templated port of matlab/src/api/moment/moment_factorial_from_upfactorial.m. Every operation is integer or rational, so the exact instantiation returns the transform with no rounding at all. That matters more here than almost anywhere else in the API: the alternating binomial sums of the moment conversions cancel catastrophically in double arithmetic once the order grows.

Definition in file moment_factorial_from_upfactorial.h.