#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <stdbool.h>
#include "so3/so3_error.h"
#include "so3/so3_types.h"

Include dependency graph for so3_sampling.c:

Macros
#define	MAX(a, b) ((a > b) ? (a) : (b))

Functions
int	so3_sampling_nalpha (const so3_parameters_t *)

int	so3_sampling_nbeta (const so3_parameters_t *)

int	so3_sampling_ngamma (const so3_parameters_t *)

complex double	so3_sampling_weight (const so3_parameters_t *parameters, int p)

int	so3_sampling_f_size (const so3_parameters_t *parameters)

int	so3_sampling_n (const so3_parameters_t *parameters)

double	so3_sampling_a2alpha (int a, const so3_parameters_t *parameters)

double	so3_sampling_b2beta (int b, const so3_parameters_t *parameters)

double	so3_sampling_g2gamma (int g, const so3_parameters_t *parameters)

int	so3_sampling_flmn_size (const so3_parameters_t *parameters)

void	so3_sampling_elmn2ind (int ind, int el, int m, int n, const so3_parameters_t parameters)

void	so3_sampling_ind2elmn (int el, int m, int n, int ind, const so3_parameters_t parameters)

void	so3_sampling_elmn2ind_real (int ind, int el, int m, int n, const so3_parameters_t parameters)

void	so3_sampling_ind2elmn_real (int el, int m, int n, int ind, const so3_parameters_t parameters)

void	so3_sampling_n_loop_values (int n_start, int n_stop, int n_inc, const so3_parameters_t parameters)

void	so3_sampling_el_loop_values (int el_start, int el_stop, int el_inc, const int n, const so3_parameters_t parameters)

void	so3_sampling_m_loop_values (int m_start, int m_stop, int *m_inc, const int el)

bool	so3_sampling_is_i_in_loop_range (const int i, const int i_start, const int i_stop, const int i_inc)

bool	so3_sampling_is_elmn_non_zero (const int el, const int m, const int n, const so3_parameters_t *parameters)

int	so3_sampling_is_elmn_non_zero_return_int (const int el, const int m, const int n, const so3_parameters_t *parameters)

Macro Definition Documentation

◆ MAX

#define MAX	(	a,
		b
	)	((a > b) ? (a) : (b))

Function Documentation

◆ so3_sampling_a2alpha()

double so3_sampling_a2alpha	(	int	a,
		const so3_parameters_t *	parameters
	)

Convert alpha index to angle for a given sampling scheme.

Note

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

Parameters

[in]	a	Alpha index.
[in]	parameters	A parameters object with (at least) the following fields: L, sampling_scheme

Return values

alpha Alpha angle.

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_b2beta()

double so3_sampling_b2beta	(	int	b,
		const so3_parameters_t *	parameters
	)

Convert beta index to angle for a given sampling scheme.

Note

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

Parameters

[in]	b	Beta index.
[in]	parameters	A parameters object with (at least) the following fields: L, sampling_scheme

Return values

beta	Beta angle.

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_el_loop_values()

void so3_sampling_el_loop_values	(	int *	el_start,
		int *	el_stop,
		int *	el_inc,
		const int	n,
		const so3_parameters_t *	parameters
	)

Calculates the starting, stopping and increment of el that a applicable for a flmn. This is useful for looping over the whole array

Parameters

[out]	el_start	starting el.
[out]	el_stop	stopping el.
[out]	el_inc	increment in el.
[in]	n	The value of n the loop is being applied to.
[in]	parameters	A parameters object with (at least) the following fields: L, N, storage The reality flag is ignored. Use so3_sampling_ind2elmn instead.

Return values

none	example: so3_sampling_el_loop_values(&el_start, &el_stop, &el_inc, n, &parameters); for (el = el_start; el <= el_stop; el +=el_inc){}

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_elmn2ind()

void so3_sampling_elmn2ind	(	int *	ind,
		int	el,
		int	m,
		int	n,
		const so3_parameters_t *	parameters
	)

Convert (el,m,n) harmonic indices to 1D index used to access flmn array.

Note

Index ranges are as follows:

el ranges from [0 .. L-1].
m ranges from [-el .. el].
n ranges from [-el' .. el'], where el' = min{el, N}
ind ranges from [0 .. (2*N)(L**2-N(N-1)/3)-1] for compact storage methods and from [0 .. (2*N-1)*L**2-1] for 0-padded storage methods.

Parameters

[out]	ind	1D index to access flmn array.
[in]	el	Harmonic index.
[in]	m	Azimuthal harmonic index.
[in]	n	Orientational harmonic index.
[in]	parameters	A parameters object with (at least) the following fields: L, N, storage, n_order The reality flag is ignored. Use instead. none Martin Büttner

Author: Jason McEwen

◆ so3_sampling_elmn2ind_real()

void so3_sampling_elmn2ind_real	(	int *	ind,
		int	el,
		int	m,
		int	n,
		const so3_parameters_t *	parameters
	)

Convert (el,m,n) harmonic indices to 1D index used to access flmn array for a real signal.

Note

Index ranges are as follows:

el ranges from [0 .. L-1].
m ranges from [-el .. el].
n ranges from [0 .. el'], where el' = min{el, N}
ind ranges from [0 .. N*(L*L-(N-1)*(2*N-1)/6)-1] for compact storage methods and from [0 .. N*L*L-1] for 0-padded storage methods.

Parameters

[out]	ind	1D index to access flmn array.
[in]	el	Harmonic index
[in]	m	Azimuthal harmonic index.
[in]	n	Orientational harmonic index.
[in]	parameters	A parameters object with (at least) the following fields: L, N, storage The reality flag is ignored. Use so3_sampling_elmn2ind instead.

Return values

none

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_f_size()

int so3_sampling_f_size ( const so3_parameters_t * parameters )

Compute size of the signal buffer f to be passed to the forward and returned from the inverse transform function for a given sampling scheme.

Note: Computes number of samples on rotation group, not over extended domain.; This includes degenerate samples on the poles which are the same for each value of phi. To get the logical number of samples (i.e. ignoring without degeneracy) use so3_sampling_n, instead.

Parameters

[in] parameters A parameters object with (at least) the following fields: L, N, sampling_scheme

Return values

n	Number of samples stored in the signal buffers.

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_flmn_size()

int so3_sampling_flmn_size ( const so3_parameters_t * parameters )

Get storage size of flmn array for different storage methods.

Parameters

[in] parameters A parameters object with (at least) the following fields: L, N, storage, reality

Return values

Number of coefficients to be stored.

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_g2gamma()

double so3_sampling_g2gamma	(	int	g,
		const so3_parameters_t *	parameters
	)

Convert gamma index to angle for a given sampling scheme.

Note

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

Parameters

[in]	g	Gamma index.
[in]	parameters	A parameters object with (at least) the following fields: N, sampling_scheme

Return values

gamma Gamma angle.

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_ind2elmn()

void so3_sampling_ind2elmn	(	int *	el,
		int *	m,
		int *	n,
		int	ind,
		const so3_parameters_t *	parameters
	)

Convert 1D index used to access flmn array to (el,m,n) harmonic indices.

Note

Index ranges are as follows:

el ranges from [0 .. L-1].
m ranges from [-el .. el].
n ranges from [-el' .. el'], where el' = min{el, N}
ind ranges from [0 .. (2*N)(L**2-N(N-1)/3)-1] for compact storage methods and from [0 .. (2*N-1)*L**2-1] for 0-padded storage methods.

Parameters

[out]	el	Harmonic index.
[out]	m	Azimuthal harmonic index.
[out]	n	Orientational harmonic index.
[in]	ind	1D index to access flm array.
[in]	parameters	A parameters object with (at least) the following fields: L, N, storage The reality flag is ignored. Use so3_sampling_ind2elmn_real instead.

Return values

none

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_ind2elmn_real()

void so3_sampling_ind2elmn_real	(	int *	el,
		int *	m,
		int *	n,
		int	ind,
		const so3_parameters_t *	parameters
	)

Convert 1D index used to access flmn array to (el,m,n) harmonic indices for a real signal.

Note

Index ranges are as follows:

el ranges from [0 .. L-1].
m ranges from [-el .. el].
n ranges from [0 .. el'], where el' = min{el, N}
ind ranges from [0 .. N*(L*L-(N-1)*(2*N-1)/6)-1] for compact storage methods and from [0 .. N*L*L-1] for 0-padded storage methods.

Parameters

[out]	el	Harmonic index.
[out]	m	Azimuthal harmonic index.
[out]	n	Orientational harmonic index.
[in]	ind	1D index to access flm array.
[in]	parameters	A parameters object with (at least) the following fields: L, N, storage The reality flag is ignored. Use so3_sampling_ind2elmn instead.

Return values

none

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_is_elmn_non_zero()

bool so3_sampling_is_elmn_non_zero	(	const int	el,
		const int	m,
		const int	n,
		const so3_parameters_t *	parameters
	)

Queries if (el,m,n) harmonic indices are non zero in this setting

Note

Index ranges are as follows:

el ranges from [0 .. L-1].
m ranges from [-el .. el].
n ranges from [-el' .. el'], where el' = min{el, N}
ind ranges from [0 .. (2*N)(L**2-N(N-1)/3)-1] for compact storage methods and from [0 .. (2*N-1)*L**2-1] for 0-padded storage methods.

Parameters

[in]	el	Harmonic index.
[in]	m	Azimuthal harmonic index.
[in]	n	Orientational harmonic index.
[in]	parameters	A parameters object with (at least) the following fields: L, N, storage, n_order, reality

Return values

none

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_is_elmn_non_zero_return_int()

int so3_sampling_is_elmn_non_zero_return_int	(	const int	el,
		const int	m,
		const int	n,
		const so3_parameters_t *	parameters
	)

◆ so3_sampling_is_i_in_loop_range()

bool so3_sampling_is_i_in_loop_range	(	const int	i,
		const int	i_start,
		const int	i_stop,
		const int	i_inc
	)

Queries if integer i would be covered in a loop for (i=i_start; i<=i_stop; i += i_inc)

Parameters

[in]	i	integer to query
[in]	i_start	starting point
[in]	i_stop	stoping point
[in]	i_inc	incrementing step

Return values

none

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_m_loop_values()

void so3_sampling_m_loop_values	(	int *	m_start,
		int *	m_stop,
		int *	m_inc,
		const int	el
	)

Calculates the starting, stopping and increment of m that a applicable for a flmn. This is useful for looping over the whole array

Parameters

[out]	m_start	starting m.
[out]	m_stop	stopping m.
[out]	m_inc	increment in m.
[in]	el	The value of el the loop is being applied to.

Return values

none	example: so3_sampling_el_loop_values(&m_start, &m_stop, &m_inc, el); for (m = m_start; m <= m_stop; m +=m_inc){}

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_n()

int so3_sampling_n ( const so3_parameters_t * parameters )

Compute total number of samples for a given sampling scheme.

Note: Computes number of samples on rotation group, not over extended domain.; This returns the logical number of samples (without degeneracy), and not the size of the signal buffer used in the transform functions. Use so3_sampling_f_size to get the actual size of the signal buffer.

Parameters

[in] parameters A parameters object with (at least) the following fields: L, N, sampling_scheme

Return values

n	Number of samples.

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_n_loop_values()

void so3_sampling_n_loop_values	(	int *	n_start,
		int *	n_stop,
		int *	n_inc,
		const so3_parameters_t *	parameters
	)

Calculates the starting, stopping and increment of n that a applicable for a flmn. This is useful for looping over the whole array

Parameters

[out]	n_start	starting n.
[out]	n_stop	stopping n.
[out]	n_inc	increment in n.
[in]	parameters	A parameters object with (at least) the following fields: L, N, storage The reality flag is ignored. Use so3_sampling_ind2elmn instead. example: so3_sampling_n_loop_values(&n_start, &n_stop, &n_inc, parameters); for (n = n_start; n <= n_stop; n += n_inc) {}

Return values

none

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_nalpha()

int so3_sampling_nalpha ( const so3_parameters_t * parameters )

Compute number of alpha samples for a given sampling scheme.

Parameters

[in] parameters A parameters object with (at least) the following fields: L, sampling_scheme

Return values

nalpha Number of alpha samples.

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_nbeta()

int so3_sampling_nbeta ( const so3_parameters_t * parameters )

Compute number of beta samples for a given sampling scheme.

Note: Computes number of samples in (0,pi], not over extended domain.

Parameters

[in] parameters A parameters object with (at least) the following fields: L, sampling_scheme

Return values

nbeta Number of beta samples.

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_ngamma()

int so3_sampling_ngamma ( const so3_parameters_t * parameters )

Compute number of gamma samples for a given sampling scheme.

Parameters

[in] parameters A parameters object with (at least) the following fields: B, sampling_scheme

Return values

ngamma Number of gamma samples.

Author: Martin Büttner; Jason McEwen

◆ so3_sampling_weight()

complex double so3_sampling_weight	(	const so3_parameters_t *	parameters,
		int	p
	)

Compute conjugate weights for toroidal extension.

Parameters

[in]	parameters	A parameters object with (at least) sampling_scheme
[in]	p	Integer index to compute weight for.

Return values

Corresponding conjugate weight.

Author: Jason McEwen

Macros

Functions

Macro Definition Documentation

◆ MAX

Function Documentation

◆ so3_sampling_a2alpha()

◆ so3_sampling_b2beta()

◆ so3_sampling_el_loop_values()

◆ so3_sampling_elmn2ind()

◆ so3_sampling_elmn2ind_real()

◆ so3_sampling_f_size()

◆ so3_sampling_flmn_size()

◆ so3_sampling_g2gamma()

◆ so3_sampling_ind2elmn()

◆ so3_sampling_ind2elmn_real()

◆ so3_sampling_is_elmn_non_zero()

◆ so3_sampling_is_elmn_non_zero_return_int()

◆ so3_sampling_is_i_in_loop_range()

◆ so3_sampling_m_loop_values()

◆ so3_sampling_n()

◆ so3_sampling_n_loop_values()

◆ so3_sampling_nalpha()

◆ so3_sampling_nbeta()

◆ so3_sampling_ngamma()

◆ so3_sampling_weight()