#include <complex.h>
#include <math.h>
#include "ssht_types.h"

Macros
#define	ABS(x) ((x) >= 0 ? (x) : -(x))

Functions
void	gauleg (double x1, double x2, double x, double w, int n)

	SSHT_COMPLEX (double)

double	ssht_sampling_weight_dh (double theta_t, int L)

void	ssht_sampling_gl_thetas_weights (double thetas, double weights, int L)

int	ssht_sampling_mw_ntheta (int L)

double	ssht_sampling_mw_t2theta (int t, int L)

int	ssht_sampling_mw_nphi (int L)

double	ssht_sampling_mw_p2phi (int p, int L)

int	ssht_sampling_mw_n (int L)

double	ssht_sampling_mw_ss_t2theta (int t, int L)

int	ssht_sampling_mw_ss_ntheta (int L)

double	ssht_sampling_mw_ss_p2phi (int p, int L)

int	ssht_sampling_mw_ss_nphi (int L)

int	ssht_sampling_mw_ss_n (int L)

double	ssht_sampling_dh_t2theta (int t, int L)

int	ssht_sampling_dh_ntheta (int L)

double	ssht_sampling_dh_p2phi (int p, int L)

int	ssht_sampling_dh_nphi (int L)

int	ssht_sampling_dh_n (int L)

int	ssht_sampling_gl_ntheta (int L)

double	ssht_sampling_gl_p2phi (int p, int L)

int	ssht_sampling_gl_nphi (int L)

int	ssht_sampling_gl_n (int L)

Detailed Description

Functionality to define sample positions for various algorithms, to compute weights and to convert 1D and 2D harmonic indices.

Author: Jason McEwen

Definition in file ssht_sampling.c.

Macro Definition Documentation

◆ ABS

#define ABS ( x ) ((x) >= 0 ? (x) : -(x))

Definition at line 18 of file ssht_sampling.c.

Function Documentation

◆ gauleg()

void gauleg	(	double	x1,
		double	x2,
		double *	x,
		double *	w,
		int	n
	)

Given the lower and upper limits of integration x1 and x2, this routine returns arrays x[1..n] and w[1..n] of length n, containing the abscissas and weights of the Gauss-Legendre n-point quadrature formula.

Parameters

[in]	x1	Lower bound of range.
[in]	x2	Upper bound of range.
[out]	x	Node positions (i.e. roots of Legendre polynomials).
[out]	w	Corresponding weights.
[in]	n	Number of points (note memory must already be allocated for x and w to store n terms).

Author: Numerical recipes.

Definition at line 129 of file ssht_sampling.c.

References ABS.

Referenced by ssht_sampling_gl_thetas_weights().

◆ SSHT_COMPLEX()

SSHT_COMPLEX ( double )

Compute weights for toroidal extension.

Parameters

[in]	p	Integer index to compute weight for.
[out]	w	Corresponding weight.

Return values

Weight value computed.

Author: Jason McEwen

Definition at line 37 of file ssht_sampling.c.

References SSHT_PION2.

◆ ssht_sampling_dh_n()

int ssht_sampling_dh_n ( int L )

Compute total number of samples for Driscoll and Healy sampling.

Parameters

[in] L Harmonic band-limit.

Return values

n	Number of samples.

Author: Jason McEwen

Definition at line 425 of file ssht_sampling.c.

◆ ssht_sampling_dh_nphi()

int ssht_sampling_dh_nphi ( int L )

Compute number of phi samples for Driscoll and Healy sampling.

Parameters

[in] L Harmonic band-limit.

Return values

nphi	Number of phi samples.

Author: Jason McEwen

Definition at line 410 of file ssht_sampling.c.

◆ ssht_sampling_dh_ntheta()

int ssht_sampling_dh_ntheta ( int L )

Compute number of theta samples for Driscoll and Healy sampling.

Parameters

[in] L Harmonic band-limit.

Return values

ntheta Number of theta samples.

Author: Jason McEwen

Definition at line 376 of file ssht_sampling.c.

◆ ssht_sampling_dh_p2phi()

double ssht_sampling_dh_p2phi	(	int	p,
		int	L
	)

Convert phi index to angle for Driscoll and Healy sampling.

Note

p ranges from [0 .. 2*L-2] => 2*L-1 points in [0,2*pi).

Parameters

[in]	p	Phi index.
[in]	L	Harmonic band-limit.

Return values

phi	Phi angle.

Author: Jason McEwen

Definition at line 395 of file ssht_sampling.c.

References SSHT_PI.

◆ ssht_sampling_dh_t2theta()

double ssht_sampling_dh_t2theta	(	int	t,
		int	L
	)

Convert theta index to angle for Driscoll and Healy sampling.

Note

t ranges from [0 .. 2*L-1] => 2*L points in (0,pi).

Parameters

[in]	t	Theta index.
[in]	L	Harmonic band-limit.

Return values

theta Theta angle.

Author: Jason McEwen

Definition at line 361 of file ssht_sampling.c.

References SSHT_PI.

Referenced by ssht_core_dh_inverse_sov(), and ssht_core_dh_inverse_sov_real().

◆ ssht_sampling_gl_n()

int ssht_sampling_gl_n ( int L )

Compute total number of samples for Gauss-Legendre sampling.

Parameters

[in] L Harmonic band-limit.

Return values

n	Number of samples.

Author: Jason McEwen

Definition at line 489 of file ssht_sampling.c.

◆ ssht_sampling_gl_nphi()

int ssht_sampling_gl_nphi ( int L )

Compute number of phi samples for Gauss-Legendre sampling.

Parameters

[in] L Harmonic band-limit.

Return values

nphi	Number of phi samples.

Author: Jason McEwen

Definition at line 474 of file ssht_sampling.c.

◆ ssht_sampling_gl_ntheta()

int ssht_sampling_gl_ntheta ( int L )

Compute number of theta samples for Gauss-Legendre sampling.

Parameters

[in] L Harmonic band-limit.

Return values

ntheta Number of theta samples.

Author: Jason McEwen

Definition at line 440 of file ssht_sampling.c.

◆ ssht_sampling_gl_p2phi()

double ssht_sampling_gl_p2phi	(	int	p,
		int	L
	)

Convert phi index to angle for Gauss-Legendre sampling.

Note

p ranges from [0 .. 2*L-2] => 2*L-1 points in [0,2*pi).

Parameters

[in]	p	Phi index.
[in]	L	Harmonic band-limit.

Return values

phi	Phi angle.

Author: Jason McEwen

Definition at line 459 of file ssht_sampling.c.

References SSHT_PI.

◆ ssht_sampling_gl_thetas_weights()

void ssht_sampling_gl_thetas_weights	(	double *	thetas,
		double *	weights,
		int	L
	)

Compute Gauss-Legendre theta positions (roots of Legendre polynomials) and corresponding weights.

Parameters

[out]	thetas	L theta positions (memory must already be allocated to store the L theta positions).
[out]	weights	Corresponding weights (memory must already be allocated to store the L weights corresponding to each theta position).
[in]	L	Harmonic band-limit.

Return values

none

Author: Jason McEwen

Definition at line 94 of file ssht_sampling.c.

References gauleg().

Referenced by ssht_core_gl_forward_sov(), ssht_core_gl_forward_sov_real(), ssht_core_gl_inverse_sov(), and ssht_core_gl_inverse_sov_real().

◆ ssht_sampling_mw_n()

int ssht_sampling_mw_n ( int L )

Compute total number of samples for McEwen and Wiaux sampling.

/note Computes number of samples on sphere, not over extended domain.

Parameters

[in] L Harmonic band-limit.

Return values

n	Number of samples.

Author: Jason McEwen

Definition at line 249 of file ssht_sampling.c.

◆ ssht_sampling_mw_nphi()

int ssht_sampling_mw_nphi ( int L )

Compute number of phi samples for McEwen and Wiaux sampling.

Parameters

[in] L Harmonic band-limit.

Return values

nphi	Number of phi samples.

Author: Jason McEwen

Definition at line 212 of file ssht_sampling.c.

◆ ssht_sampling_mw_ntheta()

int ssht_sampling_mw_ntheta ( int L )

Compute number of theta samples for McEwen and Wiaux sampling.

/note Computes number of samples in (0,pi], not over extended domain.

Parameters

[in] L Harmonic band-limit.

Return values

ntheta Number of theta samples.

Author: Jason McEwen

Definition at line 178 of file ssht_sampling.c.

◆ ssht_sampling_mw_p2phi()

double ssht_sampling_mw_p2phi	(	int	p,
		int	L
	)

Convert phi index to angle for McEwen and Wiaux sampling.

Note

p ranges from [0 .. 2*L-2] => 2*L-1 points in [0,2*pi).

Parameters

[in]	p	Phi index.
[in]	L	Harmonic band-limit.

Return values

phi	Phi angle.

Author: Jason McEwen

Definition at line 231 of file ssht_sampling.c.

References SSHT_PI.

Referenced by ssht_adjoint_mw_forward_sov_sym_pole(), ssht_adjoint_mw_inverse_sov_sym_pole(), ssht_core_mw_forward_sov_conv_sym_pole(), and ssht_core_mw_inverse_sov_sym_pole().

◆ ssht_sampling_mw_ss_n()

int ssht_sampling_mw_ss_n ( int L )

Compute total number of samples for McEwen and Wiaux symmetric sampling.

/note Computes number of samples on sphere, not over extended domain.

Parameters

[in] L Harmonic band-limit.

Return values

n	Number of samples.

Author: Jason McEwen

Definition at line 342 of file ssht_sampling.c.

◆ ssht_sampling_mw_ss_nphi()

int ssht_sampling_mw_ss_nphi ( int L )

Compute number of phi samples for McEwen and Wiaux symmetric sampling.

Parameters

[in] L Harmonic band-limit.

Return values

nphi	Number of phi samples.

Author: Jason McEwen

Definition at line 323 of file ssht_sampling.c.

◆ ssht_sampling_mw_ss_ntheta()

int ssht_sampling_mw_ss_ntheta ( int L )

Compute number of theta samples for McEwen and Wiaux symmetric sampling.

/note Computes number of samples in [0,pi], not over extended domain.

Parameters

[in] L Harmonic band-limit.

Return values

ntheta Number of theta samples.

Author: Jason McEwen

Definition at line 288 of file ssht_sampling.c.

◆ ssht_sampling_mw_ss_p2phi()

double ssht_sampling_mw_ss_p2phi	(	int	p,
		int	L
	)

Convert phi index to angle for McEwen and Wiaux symmetric sampling.

Note

p ranges from [0 .. 2*L-1] => 2*L points in [0,2*pi).

Parameters

[in]	p	Phi index.
[in]	L	Harmonic band-limit.

Return values

phi	Phi angle.

Author: Jason McEwen

Definition at line 307 of file ssht_sampling.c.

References SSHT_PI.

Referenced by ssht_adjoint_mw_forward_sov_sym_ss_pole(), ssht_adjoint_mw_inverse_sov_sym_ss_pole(), ssht_core_mw_forward_sov_conv_sym_ss_pole(), and ssht_core_mw_inverse_sov_sym_ss_pole().

◆ ssht_sampling_mw_ss_t2theta()

double ssht_sampling_mw_ss_t2theta	(	int	t,
		int	L
	)

Convert theta index to angle for McEwen and Wiaux symmetric sampling.

Note

t ranges from [0 .. 2*L-1] => 2*L points in (0,2*pi).

Parameters

[in]	t	Theta index.
[in]	L	Harmonic band-limit.

Return values

theta Theta angle.

Author: Jason McEwen

Definition at line 269 of file ssht_sampling.c.

References SSHT_PI.

Referenced by ssht_core_mwdirect_inverse_ss().

◆ ssht_sampling_mw_t2theta()

double ssht_sampling_mw_t2theta	(	int	t,
		int	L
	)

Convert theta index to angle for McEwen and Wiaux sampling.

Note

t ranges from [0 .. 2*L-2] => 2*L-1 points in (0,2*pi).

Parameters

[in]	t	Theta index.
[in]	L	Harmonic band-limit.

Return values

theta Theta angle.

Author: Jason McEwen

Definition at line 197 of file ssht_sampling.c.

References SSHT_PI.

Referenced by ssht_core_mwdirect_inverse(), and ssht_core_mwdirect_inverse_sov().

◆ ssht_sampling_weight_dh()

double ssht_sampling_weight_dh	(	double	theta_t,
		int	L
	)

Compute Driscoll and Healy weights.

Parameters

[in]	theta_t	Theta value to compute weight for.
[in]	L	Harmonic band-limit. return w Weight value computed.

Author: Jason McEwen

Definition at line 65 of file ssht_sampling.c.

Macros

Functions

Detailed Description

Macro Definition Documentation

◆ ABS

Function Documentation

◆ gauleg()

◆ SSHT_COMPLEX()

◆ ssht_sampling_dh_n()

◆ ssht_sampling_dh_nphi()

◆ ssht_sampling_dh_ntheta()

◆ ssht_sampling_dh_p2phi()

◆ ssht_sampling_dh_t2theta()

◆ ssht_sampling_gl_n()

◆ ssht_sampling_gl_nphi()

◆ ssht_sampling_gl_ntheta()

◆ ssht_sampling_gl_p2phi()

◆ ssht_sampling_gl_thetas_weights()

◆ ssht_sampling_mw_n()

◆ ssht_sampling_mw_nphi()

◆ ssht_sampling_mw_ntheta()

◆ ssht_sampling_mw_p2phi()

◆ ssht_sampling_mw_ss_n()

◆ ssht_sampling_mw_ss_nphi()

◆ ssht_sampling_mw_ss_ntheta()

◆ ssht_sampling_mw_ss_p2phi()

◆ ssht_sampling_mw_ss_t2theta()

◆ ssht_sampling_mw_t2theta()

◆ ssht_sampling_weight_dh()