Rotation of spherical harmonics, using an on-the-fly algorithm (does not store the rotation matrix) inspired by the GUMEROV's algorithm to generate the Wigner-d matrices describing rotation of Spherical Harmonics. More...

Functions
shtns_rot	shtns_rotation_create (const int lmax, const int mmax, int norm)
	Allocate memory and precompute some recurrence coefficients for rotation (independent of angle).

void	shtns_rotation_destroy (shtns_rot r)
	Release memory allocated for the rotation object.

void	shtns_rotation_set_angles_ZYZ (shtns_rot r, double alpha, double beta, double gamma)
	Set the rotation angles, and compute associated Legendre functions, given the 3 intrinsic Euler angles in ZYZ convention.

void	shtns_rotation_set_angles_ZXZ (shtns_rot r, double alpha, double beta, double gamma)
	Set the rotation angles, and compute associated Legendre functions, given the 3 intrinsic Euler angles in ZXZ convention.

void	shtns_rotation_set_angle_axis (shtns_rot r, double theta, double Vx, double Vy, double Vz)
	Sets a rotation by angle theta around axis of cartesian coordinates (Vx,Vy,Vz), and compute associated Legendre functions.

int	quarter_wigner_d_matrix (shtns_rot r, const int l, double *mx, const int compressed)

int	shtns_rotation_wigner_d_matrix (shtns_rot r, const int l, double *mx)
	Generate spherical-harmonic rotation matrix for given degree l and orthonormal convention (Wigner-d matrix)

void	shtns_rotation_apply_real (shtns_rot r, cplx Qlm, cplx Rlm)
	apply rotation to the orthonormal spherical harmonic expansion Qlm of a real field, store the result into Rlm (can be the same as Qlm)

void	shtns_rotation_apply_cplx (shtns_rot r, cplx Zlm, cplx Rlm)
	rotate Zlm, store the result in Rlm, without ever storing the wigner-d matrices (on-the-fly operation)

Detailed Description

Rotation of spherical harmonics, using an on-the-fly algorithm (does not store the rotation matrix) inspired by the GUMEROV's algorithm to generate the Wigner-d matrices describing rotation of Spherical Harmonics.

See https://arxiv.org/abs/1403.7698 or https://doi.org/10.1007/978-3-319-13230-3_5 Thanks to Alex J. Yuffa, ayuff.nosp@m.a@gm.nosp@m.ail.c.nosp@m.om for his suggestions and help.

These functions are more accurate and faster than the pseudo-spectral rotations of Gimbutas and do not require mmax=lmax. Note that if mmax<lmax, the rotations are apprixmate only, with the quality of the approximation decreasing with increasing 'beta' angle (rotation angle around Y-axis).

Function Documentation

◆ shtns_rotation_apply_cplx()

void shtns_rotation_apply_cplx	(	shtns_rot	r,
		cplx *	Zlm,
		cplx *	Rlm
	)

rotate Zlm, store the result in Rlm, without ever storing the wigner-d matrices (on-the-fly operation)

apply rotation to the orthonormal spherical harmonic expansion Zlm of a complex-valued field, store the result into Rlm (can be the same as Zlm)

◆ shtns_rotation_create()

shtns_rot shtns_rotation_create	(	const int	lmax,
		const int	mmax,
		int	norm
	)

Allocate memory and precompute some recurrence coefficients for rotation (independent of angle).

Creation of a spherical harmonic rotation object for degrees and orders up to lmax and mmax respectively.

Setting mmax < lmax will result in approximate rotations if not aligned with the z-axis, while mmax=lmax leads to exact rotations.

◆ shtns_rotation_set_angle_axis()

void shtns_rotation_set_angle_axis	(	shtns_rot	r,
		double	theta,
		double	Vx,
		double	Vy,
		double	Vz
	)

Sets a rotation by angle theta around axis of cartesian coordinates (Vx,Vy,Vz), and compute associated Legendre functions.

Defines a rotation of angle theta around axis of cartesian coordinates (Vx,Vy,Vz).

◆ shtns_rotation_set_angles_ZXZ()

void shtns_rotation_set_angles_ZXZ	(	shtns_rot	r,
		double	alpha,
		double	beta,
		double	gamma
	)

Set the rotation angles, and compute associated Legendre functions, given the 3 intrinsic Euler angles in ZXZ convention.

Defines a rotation parameterized by the 3 intrinsic Euler angles with ZXZ convention.

◆ shtns_rotation_set_angles_ZYZ()

void shtns_rotation_set_angles_ZYZ	(	shtns_rot	r,
		double	alpha,
		double	beta,
		double	gamma
	)

Set the rotation angles, and compute associated Legendre functions, given the 3 intrinsic Euler angles in ZYZ convention.

Defines a rotation parameterized by the 3 intrinsic Euler angles with ZYZ convention.

◆ shtns_rotation_wigner_d_matrix()

int shtns_rotation_wigner_d_matrix	(	shtns_rot	r,
		const int	l,
		double *	mx
	)

Generate spherical-harmonic rotation matrix for given degree l and orthonormal convention (Wigner-d matrix)

Parameters

[out] mx is an (2*l+1)*(2*l+1) array that will be filled with the Wigner-d matrix elements (rotation matrix along Y-axis in orthonormal spherical harmonic space).

Returns: 0 if error, or 2*l+1 (size of the square matrix) otherwise.

Warning: The returned rotation matrix only applies to orthonormal convention (see Normalization)

Functions