flag_spherlaguerre.c File Reference

#include "flag.h"
#include <math.h>
#include <stdlib.h>
#include <complex.h>
#include <fftw3.h>
#include <ssht.h>
#include <assert.h>

Go to the source code of this file.

Macros
#define	MIN(a, b)   ((a) < (b) ? (a) : (b))

Functions
double	eval_laguerre (double z, int n, int alpha)
double	eval_laguerre_rescaled (double z, int n, int alpha, double normfac)
long	factorial (int n)
long	factorial_range (int min, int max)
void	flag_spherlaguerre_quadrature (double *roots, double *weights, int N, int alpha)
double	flag_spherlaguerre_tau (double R, int N)
double	flag_spherlaguerre_Rmax (int N)
void	flag_spherlaguerre_sampling (double *nodes, double *weights, double tau, int N)
void	flag_spherlaguerre_allocate_sampling (double **nodes, double **weights, int N)
void	flag_spherlaguerre_analysis (double *fn, const double *f, const double *nodes, const double *weights, double tau, int N)
void	flag_spherlaguerre_synthesis (double *f, const double *fn, const double *nodes, int Nnodes, double tau, int N)
void	flag_spherlaguerre_synthesis_gen (double *f, const double *fn, const double *nodes, int Nnodes, double tau, int N, int alpha)
void	flag_spherlaguerre_mapped_analysis (complex double *fn, const complex double *f, const double *nodes, const double *weights, double tau, int N, int mapsize)
void	flag_spherlaguerre_mapped_synthesis (complex double *f, const complex double *fn, const double *nodes, int Nnodes, double tau, int N, int mapsize)
void	flag_spherlaguerre_basis (double *KN, const int N, const double *nodes, int Nnodes, double tau)
void	flag_spherbessel_sampling (double *nodes, double *weights, double R, int N)

Macro Definition Documentation

#define MIN	(		a,
			b
	)		((a) < (b) ? (a) : (b))

Definition at line 13 of file flag_spherlaguerre.c.

Function Documentation

double eval_laguerre	(	double	z,
		int	n,
		int	alpha
	)

Definition at line 16 of file flag_spherlaguerre.c.

double eval_laguerre_rescaled	(	double	z,
		int	n,
		int	alpha,
		double	normfac
	)

Definition at line 30 of file flag_spherlaguerre.c.

long factorial

(

int

n

)

Definition at line 44 of file flag_spherlaguerre.c.

long factorial_range	(	int	min,
		int	max
	)

Definition at line 52 of file flag_spherlaguerre.c.

void flag_spherbessel_sampling	(	double *	nodes,
		double *	weights,
		double	R,
		int	N
	)

Definition at line 479 of file flag_spherlaguerre.c.

void flag_spherlaguerre_allocate_sampling	(	double **	nodes,
		double **	weights,
		int	N
	)

Allocate spherical Laguerre sampling scheme.

Parameters

[out]	nodes	Nodes of the sampling.
[out]	weights	Weights for the SLAG quadrature.
[in]	N	Harmonic band-limit.

Return values

none

Definition at line 253 of file flag_spherlaguerre.c.

void flag_spherlaguerre_analysis	(	double *	fn,
		const double *	f,
		const double *	nodes,
		const double *	weights,
		double	tau,
		int	N
	)

Perform spherical Laguerre analysis.

Parameters

[out]	fn	SLAG coefficients.
[in]	f	Input dataset.
[in]	nodes	Nodes of the sampling.
[in]	weights	Weights for the SLAG quadrature.
[in]	N	Harmonic band-limit.

Return values

none

Definition at line 262 of file flag_spherlaguerre.c.

void flag_spherlaguerre_basis	(	double *	KN,
		const int	N,
		const double *	nodes,
		int	Nnodes,
		double	tau
	)

Compute the spherical-Laguerre basis functions on a grid of radii

Parameters

[out]	KN	Synthesised basis function.
[in]	N	SLAG band-limit.
[in]	nodes	Radii where the function must be calculated.
[in]	Nnodes	Number of radii.

Return values

none

Definition at line 443 of file flag_spherlaguerre.c.

void flag_spherlaguerre_mapped_analysis	(	complex double *	fn,
		const complex double *	f,
		const double *	weights,
		const double *	nodes,
		double	tau,
		int	N,
		int	mapsize
	)

Perform spherical Laguerre analysis. 3D mapped version - suitable for FLAG transform.

Parameters

[out]	fn	SLAG coefficients.
[in]	f	Input dataset.
[in]	nodes	Nodes of the sampling.
[in]	weights	Weights for the SLAG quadrature.
[in]	mapsize	Size of each layer (L^2 in FLAG).
[in]	N	Harmonic band-limit.

Return values

none

Definition at line 337 of file flag_spherlaguerre.c.

void flag_spherlaguerre_mapped_synthesis	(	complex double *	f,
		const complex double *	fn,
		const double *	nodes,
		int	Nnodes,
		double	tau,
		int	N,
		int	mapsize
	)

Perform spherical Laguerre synthesis. 3D mapped version - suitable for FLAG transform.

Parameters

[out]	f	Synthesised dataset.
[in]	fn	Input SLAG coefficients.
[in]	nodes	Nodes of the sampling.
[in]	mapsize	Size of each layer (L^2 in FLAG).
[in]	N	Harmonic band-limit.

Return values

none

Definition at line 389 of file flag_spherlaguerre.c.

void flag_spherlaguerre_quadrature	(	double *	roots,
		double *	weights,
		int	N,
		int	alpha
	)

Compute Gauss-Laguerre quadrature (nodes and weights).

Parameters

[out]	roots	Gauss-Laguerre nodes.
[out]	weights	Gauss-Laguerre weights.
[in]	N	Harmonic band-limit.

Return values

none

Definition at line 60 of file flag_spherlaguerre.c.

double flag_spherlaguerre_Rmax

(

int

N

)

Compute spherical Laguerre maximum R.

Parameters

[in]

N

Harmonic band-limit.

Return values

R	Radial limit / boundary.

Definition at line 160 of file flag_spherlaguerre.c.

void flag_spherlaguerre_sampling	(	double *	nodes,
		double *	weights,
		double	tau,
		int	N
	)

Compute spherical Laguerre sampling scheme.

Parameters

[out]	nodes	Nodes of the sampling.
[out]	weights	Weights for the SLAG quadrature.
[in]	R	Radial limit / boundary.
[in]	N	Harmonic band-limit.

Return values

none

Definition at line 236 of file flag_spherlaguerre.c.

void flag_spherlaguerre_synthesis	(	double *	f,
		const double *	fn,
		const double *	nodes,
		int	Nnodes,
		double	tau,
		int	N
	)

Perform spherical Laguerre synthesis.

Parameters

[out]	f	Synthesised dataset.
[in]	fn	Input SLAG coefficients.
[in]	nodes	Nodes of the sampling.
[in]	N	Harmonic band-limit.

Return values

none

Definition at line 297 of file flag_spherlaguerre.c.

void flag_spherlaguerre_synthesis_gen	(	double *	f,
		const double *	fn,
		const double *	nodes,
		int	Nnodes,
		double	tau,
		int	N,
		int	alpha
	)

Definition at line 303 of file flag_spherlaguerre.c.

double flag_spherlaguerre_tau	(	double	R,
		int	N
	)

Compute spherical Laguerre scaling factor tau.

Parameters

[in]	R	Radial limit / boundary.
[in]	N	Harmonic band-limit.

Return values

tau	Scaling factor for the SLAG sampling.

Definition at line 153 of file flag_spherlaguerre.c.