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ssht_adjoint.c File Reference
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <complex.h>
#include <fftw3.h>
#include "ssht_types.h"
#include "ssht_error.h"
#include "ssht_dl.h"
#include "ssht_sampling.h"
#include "ssht_adjoint.h"

Go to the source code of this file.

Functions

void ssht_adjoint_mw_inverse_sov_sym (SSHT_COMPLEX(double) *flm, const SSHT_COMPLEX(double) *f, int L, int spin, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_inverse_sov_sym_real (SSHT_COMPLEX(double) *flm, const double *f, int L, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_forward_sov_sym (SSHT_COMPLEX(double) *f, const SSHT_COMPLEX(double) *flm, int L, int spin, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_forward_sov_sym_real (double *f, const SSHT_COMPLEX(double) *flm, int L, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_forward_sov_sym_pole (SSHT_COMPLEX(double) *f, SSHT_COMPLEX(double) *f_sp, double *phi_sp, SSHT_COMPLEX(double) *flm, int L, int spin, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_forward_sov_sym_real_pole (double *f, double *f_sp, SSHT_COMPLEX(double) *flm, int L, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_inverse_sov_sym_pole (SSHT_COMPLEX(double) *flm, SSHT_COMPLEX(double) *f, SSHT_COMPLEX(double) f_sp, double phi_sp, int L, int spin, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_inverse_sov_sym_real_pole (SSHT_COMPLEX(double) *flm, double *f, double f_sp, int L, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_inverse_sov_sym_ss (SSHT_COMPLEX(double) *flm, SSHT_COMPLEX(double) *f, int L, int spin, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_inverse_sov_sym_ss_real (SSHT_COMPLEX(double) *flm, double *f, int L, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_forward_sov_sym_ss (SSHT_COMPLEX(double) *f, SSHT_COMPLEX(double) *flm, int L, int spin, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_forward_sov_sym_ss_real (double *f, SSHT_COMPLEX(double) *flm, int L, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_forward_sov_sym_ss_pole (SSHT_COMPLEX(double) *f, SSHT_COMPLEX(double) *f_np, double *phi_np, SSHT_COMPLEX(double) *f_sp, double *phi_sp, SSHT_COMPLEX(double) *flm, int L, int spin, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_forward_sov_sym_ss_real_pole (double *f, double *f_np, double *f_sp, SSHT_COMPLEX(double) *flm, int L, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_inverse_sov_sym_ss_pole (SSHT_COMPLEX(double) *flm, SSHT_COMPLEX(double) *f, SSHT_COMPLEX(double) f_np, double phi_np, SSHT_COMPLEX(double) f_sp, double phi_sp, int L, int spin, ssht_dl_method_t dl_method, int verbosity)
 
void ssht_adjoint_mw_inverse_sov_sym_ss_real_pole (SSHT_COMPLEX(double) *flm, double *f, double f_np, double f_sp, int L, ssht_dl_method_t dl_method, int verbosity)
 

Detailed Description

Algorithms to perform fast adjoint of spin spherical harmonic transforms on the sphere.

Author
Jason McEwen

Definition in file ssht_adjoint.c.

Function Documentation

◆ ssht_adjoint_mw_forward_sov_sym()

void ssht_adjoint_mw_forward_sov_sym ( SSHT_COMPLEX(double) *  f,
const SSHT_COMPLEX(double) *  flm,
int  L,
int  spin,
ssht_dl_method_t  dl_method,
int  verbosity 
)

Compute adjoint of forward transform for MW method using separation of variables, fast Fourier transforms, performing convolution with weights as product in transformed space and exploiting all symmetries (for complex spin signal).

Parameters
[out]fFunction on sphere.
[in]flmHarmonic coefficients.
[in]LHarmonic band-limit.
[in]spinSpin number.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 597 of file ssht_adjoint.c.

References SSHT_COMPLEX, ssht_dl_beta_risbo_eighth_table(), ssht_dl_beta_risbo_fill_eighth2quarter_table(), ssht_dl_calloc(), ssht_dl_get_offset(), ssht_dl_get_stride(), ssht_dl_halfpi_trapani_eighth_table(), ssht_dl_halfpi_trapani_fill_eighth2quarter_table(), SSHT_DL_QUARTER, SSHT_DL_QUARTER_EXTENDED, SSHT_DL_RISBO, SSHT_DL_TRAPANI, SSHT_ERROR_GENERIC, SSHT_ERROR_MEM_ALLOC_CHECK, SSHT_PI, SSHT_PION2, and SSHT_PROMPT.

Referenced by ssht_adjoint_mw_forward_sov_sym_pole().

◆ ssht_adjoint_mw_forward_sov_sym_pole()

void ssht_adjoint_mw_forward_sov_sym_pole ( SSHT_COMPLEX(double) *  f,
SSHT_COMPLEX(double) *  f_sp,
double *  phi_sp,
SSHT_COMPLEX(double) *  flm,
int  L,
int  spin,
ssht_dl_method_t  dl_method,
int  verbosity 
)

South pole wrapper for adjoint forward transform for MW method. The South pole is defined by a single sample and its corresponding phi angle, rather than specifying samples for all phi at the South pole (which are simply related by the rotation of a spin function in its tangent plane).

Parameters
[out]fFunction on sphere (excluding South pole).
[out]f_spFunction sample on South pole.
[out]phi_spPhi angle corresponding to quoted sample at South pole.
[in]flmHarmonic coefficients.
[in]LHarmonic band-limit.
[in]spinSpin number.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 1304 of file ssht_adjoint.c.

References ssht_adjoint_mw_forward_sov_sym(), SSHT_COMPLEX, SSHT_ERROR_MEM_ALLOC_CHECK, and ssht_sampling_mw_p2phi().

◆ ssht_adjoint_mw_forward_sov_sym_real()

void ssht_adjoint_mw_forward_sov_sym_real ( double *  f,
const SSHT_COMPLEX(double) *  flm,
int  L,
ssht_dl_method_t  dl_method,
int  verbosity 
)

Compute adjoint of forward transform for MW method of real scalar signal using separation of variables, fast Fourier transforms, performing convolution with weights as product in transformed space and exploiting all symmetries (including additional symmetries for real signals).

Parameters
[out]fFunction on sphere.
[in]flmHarmonic coefficients.
[in]LHarmonic band-limit.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 946 of file ssht_adjoint.c.

References SSHT_COMPLEX, ssht_dl_beta_risbo_eighth_table(), ssht_dl_beta_risbo_fill_eighth2quarter_table(), ssht_dl_calloc(), ssht_dl_get_offset(), ssht_dl_get_stride(), ssht_dl_halfpi_trapani_eighth_table(), ssht_dl_halfpi_trapani_fill_eighth2quarter_table(), SSHT_DL_QUARTER, SSHT_DL_QUARTER_EXTENDED, SSHT_DL_RISBO, SSHT_DL_TRAPANI, SSHT_ERROR_GENERIC, SSHT_ERROR_MEM_ALLOC_CHECK, SSHT_PI, SSHT_PION2, and SSHT_PROMPT.

Referenced by ssht_adjoint_mw_forward_sov_sym_real_pole().

◆ ssht_adjoint_mw_forward_sov_sym_real_pole()

void ssht_adjoint_mw_forward_sov_sym_real_pole ( double *  f,
double *  f_sp,
SSHT_COMPLEX(double) *  flm,
int  L,
ssht_dl_method_t  dl_method,
int  verbosity 
)

South pole wrapper for adjoint forward transform of real scalar function for MW method. The South pole is defined by a single sample, rather than specifying samples for all phi at the South pole (which for a scalar function are identical).

Parameters
[out]fFunction on sphere (excluding South pole).
[out]f_spFunction sample on South pole.
[in]flmHarmonic coefficients.
[in]LHarmonic band-limit.
[in]spinSpin number.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 1350 of file ssht_adjoint.c.

References ssht_adjoint_mw_forward_sov_sym_real(), and SSHT_ERROR_MEM_ALLOC_CHECK.

◆ ssht_adjoint_mw_forward_sov_sym_ss()

void ssht_adjoint_mw_forward_sov_sym_ss ( SSHT_COMPLEX(double) *  f,
SSHT_COMPLEX(double) *  flm,
int  L,
int  spin,
ssht_dl_method_t  dl_method,
int  verbosity 
)

Compute adjoint of forward transform for MW method with symmetric sampling using separation of variables, fast Fourier transforms, performing convolution with weights as product in transformed space and exploiting all symmetries (for complex spin signal).

Parameters
[out]fFunction on sphere.
[in]flmHarmonic coefficients.
[in]LHarmonic band-limit.
[in]spinSpin number.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 2034 of file ssht_adjoint.c.

References SSHT_COMPLEX, ssht_dl_beta_risbo_eighth_table(), ssht_dl_beta_risbo_fill_eighth2quarter_table(), ssht_dl_calloc(), ssht_dl_get_offset(), ssht_dl_get_stride(), ssht_dl_halfpi_trapani_eighth_table(), ssht_dl_halfpi_trapani_fill_eighth2quarter_table(), SSHT_DL_QUARTER, SSHT_DL_QUARTER_EXTENDED, SSHT_DL_RISBO, SSHT_DL_TRAPANI, SSHT_ERROR_GENERIC, SSHT_ERROR_MEM_ALLOC_CHECK, SSHT_PI, SSHT_PION2, and SSHT_PROMPT.

Referenced by ssht_adjoint_mw_forward_sov_sym_ss_pole().

◆ ssht_adjoint_mw_forward_sov_sym_ss_pole()

void ssht_adjoint_mw_forward_sov_sym_ss_pole ( SSHT_COMPLEX(double) *  f,
SSHT_COMPLEX(double) *  f_np,
double *  phi_np,
SSHT_COMPLEX(double) *  f_sp,
double *  phi_sp,
SSHT_COMPLEX(double) *  flm,
int  L,
int  spin,
ssht_dl_method_t  dl_method,
int  verbosity 
)

North-South pole wrapper for adjoint forward transform for MW method with symmetric sampling. The poles are defined by single samples and their corresponding phi angle, rather than specifying samples for all phi at the poles (which are simply related by the rotation of a spin function in its tangent plane).

Parameters
[out]fFunction on sphere (excluding poles).
[out]f_npFunction sample on North pole.
[out]phi_npPhi angle corresponding to quoted sample at North pole.
[out]f_spFunction sample on South pole.
[out]phi_spPhi angle corresponding to quoted sample at South pole.
[in]flmHarmonic coefficients.
[in]LHarmonic band-limit.
[in]spinSpin number.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 2731 of file ssht_adjoint.c.

References ssht_adjoint_mw_forward_sov_sym_ss(), SSHT_COMPLEX, SSHT_ERROR_MEM_ALLOC_CHECK, and ssht_sampling_mw_ss_p2phi().

◆ ssht_adjoint_mw_forward_sov_sym_ss_real()

void ssht_adjoint_mw_forward_sov_sym_ss_real ( double *  f,
SSHT_COMPLEX(double) *  flm,
int  L,
ssht_dl_method_t  dl_method,
int  verbosity 
)

Compute adjoint of forward transform for MW method with symmetric sampling of real scalar signal using separation of variables, fast Fourier transforms, performing convolution with weights as product in transformed space and exploiting all symmetries (including additional symmetries for real signals).

Parameters
[out]fFunction on sphere.
[in]flmHarmonic coefficients.
[in]LHarmonic band-limit.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 2378 of file ssht_adjoint.c.

References SSHT_COMPLEX, ssht_dl_beta_risbo_eighth_table(), ssht_dl_beta_risbo_fill_eighth2quarter_table(), ssht_dl_calloc(), ssht_dl_get_offset(), ssht_dl_get_stride(), ssht_dl_halfpi_trapani_eighth_table(), ssht_dl_halfpi_trapani_fill_eighth2quarter_table(), SSHT_DL_QUARTER, SSHT_DL_QUARTER_EXTENDED, SSHT_DL_RISBO, SSHT_DL_TRAPANI, SSHT_ERROR_GENERIC, SSHT_ERROR_MEM_ALLOC_CHECK, SSHT_PI, SSHT_PION2, and SSHT_PROMPT.

Referenced by ssht_adjoint_mw_forward_sov_sym_ss_real_pole().

◆ ssht_adjoint_mw_forward_sov_sym_ss_real_pole()

void ssht_adjoint_mw_forward_sov_sym_ss_real_pole ( double *  f,
double *  f_np,
double *  f_sp,
SSHT_COMPLEX(double) *  flm,
int  L,
ssht_dl_method_t  dl_method,
int  verbosity 
)

North-South pole wrapper for adjoint forward transform of real scalar function for MW method with symmetric sampling. The poles are defined by single samples, rather than specifying samples for all phi at the poles (which for a scalar function are identical).

Parameters
[out]fFunction on sphere (excluding poles).
[out]f_spFunction sample on South pole.
[out]f_npFunction sample on North pole.
[in]flmHarmonic coefficients.
[in]LHarmonic band-limit.
[in]spinSpin number.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 2783 of file ssht_adjoint.c.

References ssht_adjoint_mw_forward_sov_sym_ss_real(), and SSHT_ERROR_MEM_ALLOC_CHECK.

◆ ssht_adjoint_mw_inverse_sov_sym()

void ssht_adjoint_mw_inverse_sov_sym ( SSHT_COMPLEX(double) *  flm,
const SSHT_COMPLEX(double) *  f,
int  L,
int  spin,
ssht_dl_method_t  dl_method,
int  verbosity 
)

Compute adjoint of inverse transform for MW method using separation of variables, fast Fourier transforms and exploiting all symmetries (for complex spin signal).

Parameters
[out]flmHarmonic coefficients.
[in]fFunction on sphere.
[in]LHarmonic band-limit.
[in]spinSpin number.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 48 of file ssht_adjoint.c.

References SSHT_COMPLEX, ssht_dl_calloc(), ssht_dl_get_offset(), ssht_dl_get_stride(), SSHT_DL_QUARTER, SSHT_DL_QUARTER_EXTENDED, SSHT_DL_RISBO, SSHT_ERROR_MEM_ALLOC_CHECK, SSHT_PI, SSHT_PION2, and SSHT_PROMPT.

Referenced by ssht_adjoint_mw_inverse_sov_sym_pole().

◆ ssht_adjoint_mw_inverse_sov_sym_pole()

void ssht_adjoint_mw_inverse_sov_sym_pole ( SSHT_COMPLEX(double) *  flm,
SSHT_COMPLEX(double) *  f,
SSHT_COMPLEX(double)  f_sp,
double  phi_sp,
int  L,
int  spin,
ssht_dl_method_t  dl_method,
int  verbosity 
)

South pole wrapper for adjoint inverse transform for MW method. The South pole is defined by a single sample and its corresponding phi angle, rather than specifying samples for all phi at the South pole (which are simply related by the rotation of a spin function in its tangent plane).

Parameters
[out]flmHarmonic coefficients.
[in]fFunction on sphere (excluding South pole).
[in]f_spFunction sample on South pole.
[in]phi_spPhi angle corresponding to quoted sample at South pole.
[in]LHarmonic band-limit.
[in]spinSpin number.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 1398 of file ssht_adjoint.c.

References ssht_adjoint_mw_inverse_sov_sym(), SSHT_COMPLEX, SSHT_ERROR_MEM_ALLOC_CHECK, and ssht_sampling_mw_p2phi().

◆ ssht_adjoint_mw_inverse_sov_sym_real()

void ssht_adjoint_mw_inverse_sov_sym_real ( SSHT_COMPLEX(double) *  flm,
const double *  f,
int  L,
ssht_dl_method_t  dl_method,
int  verbosity 
)

Compute adjoint of inverse transform for MW method of real scalar signal using separation of variables, fast Fourier transforms and exploiting all symmetries (including additional symmetries for real signals).

Parameters
[out]flmHarmonic coefficients.
[in]fFunction on sphere.
[in]LHarmonic band-limit.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 325 of file ssht_adjoint.c.

References SSHT_COMPLEX, ssht_dl_calloc(), ssht_dl_get_offset(), ssht_dl_get_stride(), SSHT_DL_QUARTER, SSHT_DL_QUARTER_EXTENDED, SSHT_DL_RISBO, SSHT_ERROR_MEM_ALLOC_CHECK, SSHT_PI, SSHT_PION2, and SSHT_PROMPT.

Referenced by ssht_adjoint_mw_inverse_sov_sym_real_pole().

◆ ssht_adjoint_mw_inverse_sov_sym_real_pole()

void ssht_adjoint_mw_inverse_sov_sym_real_pole ( SSHT_COMPLEX(double) *  flm,
double *  f,
double  f_sp,
int  L,
ssht_dl_method_t  dl_method,
int  verbosity 
)

South pole wrapper for adjoint inverse transform of real scalar function for MW method. The South pole is defined by a single sample, rather than specifying samples for all phi at the South pole (which for a scalar function are identical).

Parameters
[out]flmHarmonic coefficients.
[in]fFunction on sphere (excluding South pole).
[in]f_spFunction sample on South pole.
[in]LHarmonic band-limit.
[in]spinSpin number.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 1446 of file ssht_adjoint.c.

References ssht_adjoint_mw_inverse_sov_sym_real(), and SSHT_ERROR_MEM_ALLOC_CHECK.

◆ ssht_adjoint_mw_inverse_sov_sym_ss()

void ssht_adjoint_mw_inverse_sov_sym_ss ( SSHT_COMPLEX(double) *  flm,
SSHT_COMPLEX(double) *  f,
int  L,
int  spin,
ssht_dl_method_t  dl_method,
int  verbosity 
)

Compute adjoint of inverse transform for MW method with symmetric sampling using separation of variables, fast Fourier transforms and exploiting all symmetries (for complex spin signal).

Parameters
[out]flmHarmonic coefficients.
[in]fFunction on sphere.
[in]LHarmonic band-limit.
[in]spinSpin number.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 1495 of file ssht_adjoint.c.

References SSHT_COMPLEX, ssht_dl_calloc(), ssht_dl_get_offset(), ssht_dl_get_stride(), SSHT_DL_QUARTER, SSHT_DL_QUARTER_EXTENDED, SSHT_DL_RISBO, SSHT_ERROR_MEM_ALLOC_CHECK, SSHT_PI, SSHT_PION2, and SSHT_PROMPT.

Referenced by ssht_adjoint_mw_inverse_sov_sym_ss_pole().

◆ ssht_adjoint_mw_inverse_sov_sym_ss_pole()

void ssht_adjoint_mw_inverse_sov_sym_ss_pole ( SSHT_COMPLEX(double) *  flm,
SSHT_COMPLEX(double) *  f,
SSHT_COMPLEX(double)  f_np,
double  phi_np,
SSHT_COMPLEX(double)  f_sp,
double  phi_sp,
int  L,
int  spin,
ssht_dl_method_t  dl_method,
int  verbosity 
)

North-South pole wrapper for adjoint inverse transform for MW method with symmetric sampling. The poles are defined by single samples and their corresponding phi angle, rather than specifying samples for all phi at the poles (which are simply related by the rotation of a spin function in its tangent plane).

Parameters
[out]flmHarmonic coefficients.
[in]fFunction on sphere (excluding poles).
[in]f_npFunction sample on North pole.
[in]phi_npPhi angle corresponding to quoted sample at North pole.
[in]f_spFunction sample on South pole.
[in]phi_spPhi angle corresponding to quoted sample at South pole.
[in]LHarmonic band-limit.
[in]spinSpin number.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 2838 of file ssht_adjoint.c.

References ssht_adjoint_mw_inverse_sov_sym_ss(), SSHT_COMPLEX, SSHT_ERROR_MEM_ALLOC_CHECK, and ssht_sampling_mw_ss_p2phi().

◆ ssht_adjoint_mw_inverse_sov_sym_ss_real()

void ssht_adjoint_mw_inverse_sov_sym_ss_real ( SSHT_COMPLEX(double) *  flm,
double *  f,
int  L,
ssht_dl_method_t  dl_method,
int  verbosity 
)

Compute adjoint of inverse transform for MW method with symmetric sampling of real scalar signal using separation of variables, fast Fourier transforms and exploiting all symmetries (including additional symmetries for real signals).

Parameters
[out]flmHarmonic coefficients.
[in]fFunction on sphere.
[in]LHarmonic band-limit.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 1773 of file ssht_adjoint.c.

References SSHT_COMPLEX, ssht_dl_calloc(), ssht_dl_get_offset(), ssht_dl_get_stride(), SSHT_DL_QUARTER, SSHT_DL_QUARTER_EXTENDED, SSHT_DL_RISBO, SSHT_ERROR_MEM_ALLOC_CHECK, SSHT_PION2, and SSHT_PROMPT.

Referenced by ssht_adjoint_mw_inverse_sov_sym_ss_real_pole().

◆ ssht_adjoint_mw_inverse_sov_sym_ss_real_pole()

void ssht_adjoint_mw_inverse_sov_sym_ss_real_pole ( SSHT_COMPLEX(double) *  flm,
double *  f,
double  f_np,
double  f_sp,
int  L,
ssht_dl_method_t  dl_method,
int  verbosity 
)

North-South pole wrapper for adjoint inverse transform of real scalar function for MW method with symmetric sampling. The poles are defined by single samples, rather than specifying samples for all phi at the poles (which for a scalar function are identical).

Parameters
[out]flmHarmonic coefficients.
[in]fFunction on sphere (excluding poles).
[in]f_npFunction sample on North pole.
[in]f_spFunction sample on South pole.
[in]LHarmonic band-limit.
[in]spinSpin number.
[in]dl_methodMethod to use when compute Wigner functions.
[in]verbosityVerbosiity flag in range [0,5].
Return values
none
Author
Jason McEwen

Definition at line 2891 of file ssht_adjoint.c.

References ssht_adjoint_mw_inverse_sov_sym_ss_real(), and SSHT_ERROR_MEM_ALLOC_CHECK.