All these function perform a global spherical harmonic transform. More...

Macros
#define	SH_to_grad_spat(shtns, S, Gt, Gp) SHsph_to_spat(shtns, S, Gt, Gp)
	Compute the spatial representation of the gradient of a scalar SH field. Alias for SHsph_to_spat.

#define	SH_to_grad_spat_l(shtns, S, Gt, Gp, ltr) SHsph_to_spat_l(shtns, S, Gt, Gp, ltr)
	Compute the spatial representation of the gradient of a scalar SH field. Alias for SHsph_to_spat_l.

#define	SH_to_grad_spat_ml(shtns, im, S, Gt, Gp, ltr) SHsph_to_spat_ml(shtns, im, S, Gt, Gp, ltr)
	Compute the spatial representation of the gradient of a scalar SH field. Alias for SHsph_to_spat_l.

Scalar transforms
void	spat_to_SH (shtns_cfg shtns, double Vr, cplx Qlm)
	transform the scalar field Vr into its spherical harmonic representation Qlm. More...

void	SH_to_spat (shtns_cfg shtns, cplx Qlm, double Vr)
	transform the spherical harmonic coefficients Qlm into its spatial representation Vr. More...

void	SH_to_spat_cplx (shtns_cfg shtns, cplx alm, cplx z)
	complex scalar synthesis. More...

void	spat_cplx_to_SH (shtns_cfg shtns, cplx z, cplx alm)
	complex scalar analysis. More...

2D vector transforms
void	spat_to_SHsphtor (shtns_cfg, double Vt, double Vp, cplx Slm, cplx Tlm)
	transform the theta and phi components (Vt,Vp) of a vector into its spheroidal-toroidal spherical harmonic representation (Slm,Tlm). More...

void	SHsphtor_to_spat (shtns_cfg, cplx Slm, cplx Tlm, double Vt, double Vp)
	transform spheroidal-toroidal spherical harmonic coefficients (Slm,Tlm) to the spatial theta and phi components (Vt,Vp). More...

void	SHsph_to_spat (shtns_cfg, cplx Slm, double Vt, double *Vp)
	transform spheroidal spherical harmonic coefficients Slm to the spatial theta and phi components (Vt,Vp), effectively computing the gradient of S. More...

void	SHtor_to_spat (shtns_cfg, cplx Tlm, double Vt, double *Vp)
	transform toroidal spherical harmonic coefficients Tlm to the spatial theta and phi components (Vt,Vp). More...

3D transforms (combine scalar and vector)
void	spat_to_SHqst (shtns_cfg, double Vr, double Vt, double Vp, cplx Qlm, cplx Slm, cplx Tlm)
	3D vector transform from spherical coordinates to radial-spheroidal-toroidal spectral components (see Radial - Spheroidal - Toroidal decomposition). More...

void	SHqst_to_spat (shtns_cfg, cplx Qlm, cplx Slm, cplx Tlm, double Vr, double Vt, double Vp)
	3D vector transform from spherical coordinates to radial-spheroidal-toroidal spectral components (see Radial - Spheroidal - Toroidal decomposition). More...

Truncated transforms at given degree l
wiht l <= lmax used for setup.
void	spat_to_SH_l (shtns_cfg, double Vr, cplx Qlm, int ltr)

void	SH_to_spat_l (shtns_cfg, cplx Qlm, double Vr, int ltr)

void	SHsphtor_to_spat_l (shtns_cfg, cplx Slm, cplx Tlm, double Vt, double Vp, int ltr)

void	SHsph_to_spat_l (shtns_cfg, cplx Slm, double Vt, double *Vp, int ltr)

void	SHtor_to_spat_l (shtns_cfg, cplx Tlm, double Vt, double *Vp, int ltr)

void	spat_to_SHsphtor_l (shtns_cfg, double Vt, double Vp, cplx Slm, cplx Tlm, int ltr)

void	spat_to_SHqst_l (shtns_cfg, double Vr, double Vt, double Vp, cplx Qlm, cplx Slm, cplx Tlm, int ltr)

void	SHqst_to_spat_l (shtns_cfg, cplx Qlm, cplx Slm, cplx Tlm, double Vr, double Vt, double Vp, int ltr)

Legendre transform at given m (no fft) and truncated at given degree l <= lmax
void	spat_to_SH_ml (shtns_cfg, int im, cplx Vr, cplx Ql, int ltr)

void	SH_to_spat_ml (shtns_cfg, int im, cplx Ql, cplx Vr, int ltr)

void	spat_to_SHsphtor_ml (shtns_cfg, int im, cplx Vt, cplx Vp, cplx Sl, cplx Tl, int ltr)

void	SHsphtor_to_spat_ml (shtns_cfg, int im, cplx Sl, cplx Tl, cplx Vt, cplx Vp, int ltr)

void	SHsph_to_spat_ml (shtns_cfg, int im, cplx Sl, cplx Vt, cplx *Vp, int ltr)

void	SHtor_to_spat_ml (shtns_cfg, int im, cplx Tl, cplx Vt, cplx *Vp, int ltr)

void	spat_to_SHqst_ml (shtns_cfg, int im, cplx Vr, cplx Vt, cplx Vp, cplx Ql, cplx Sl, cplx Tl, int ltr)

void	SHqst_to_spat_ml (shtns_cfg, int im, cplx Ql, cplx Sl, cplx Tl, cplx Vr, cplx Vt, cplx Vp, int ltr)

Detailed Description

All these function perform a global spherical harmonic transform.

Their first argument is a shtns_cfg variable (which is a pointer to a shtns_info struct) obtained by a previous call to shtns_create or shtns_init.

See Also: Spatial data layouts and grids used by SHTns; Spherical Harmonics storage and normalization; Vector Spherical Harmonics as implemented in SHTns

Function Documentation

void SH_to_spat	(	shtns_cfg	shtns,
		cplx *	Qlm,
		double *	Vr
	)

transform the spherical harmonic coefficients Qlm into its spatial representation Vr.

Parameters

[in]	shtns	= a configuration created by shtns_create with a grid set by shtns_set_grid or shtns_set_grid_auto
[in]	Qlm	= spherical harmonics coefficients : cplx array of size shtns->nlm.
[out]	Vr	= spatial scalar field : double array of size shtns->nspat.

Examples:: SHT_example.c.

void SH_to_spat_cplx	(	shtns_cfg	shtns,
		cplx *	alm,
		cplx *	z
	)

complex scalar synthesis.

Parameters

[in]	shtns	= a configuration created by shtns_create with a grid set by shtns_set_grid or shtns_set_grid_auto
[in]	alm[l*(l+1)+m]	is the SH coefficient of order l and degree m (with -l <= m <= l) [total of (LMAX+1)^2 coefficients]
[out]	z	= complex spatial field

complex scalar synthesis.

in: alm[l*(l+1)+m] is the SH coefficients of order l and degree m (with -l <= m <= l) for a total of (LMAX+1)^2 coefficients. out: complex spatial field.

void SHqst_to_spat	(	shtns_cfg	,
		cplx *	Qlm,
		cplx *	Slm,
		cplx *	Tlm,
		double *	Vr,
		double *	Vt,
		double *	Vp
	)

3D vector transform from spherical coordinates to radial-spheroidal-toroidal spectral components (see Radial - Spheroidal - Toroidal decomposition).

They should be prefered over separate calls to scalar and 2D vector transforms as they are often significantly faster.

void SHsph_to_spat	(	shtns_cfg	,
		cplx *	Slm,
		double *	Vt,
		double *	Vp
	)

transform spheroidal spherical harmonic coefficients Slm to the spatial theta and phi components (Vt,Vp), effectively computing the gradient of S.

See Also: Vector Spherical Harmonics as implemented in SHTns

void SHsphtor_to_spat	(	shtns_cfg	,
		cplx *	Slm,
		cplx *	Tlm,
		double *	Vt,
		double *	Vp
	)

transform spheroidal-toroidal spherical harmonic coefficients (Slm,Tlm) to the spatial theta and phi components (Vt,Vp).

See Also: Vector Spherical Harmonics as implemented in SHTns

Examples:: SHT_example.c.

void SHtor_to_spat	(	shtns_cfg	,
		cplx *	Tlm,
		double *	Vt,
		double *	Vp
	)

transform toroidal spherical harmonic coefficients Tlm to the spatial theta and phi components (Vt,Vp).

See Also: Vector Spherical Harmonics as implemented in SHTns

Examples:: SHT_example.c.

void spat_cplx_to_SH	(	shtns_cfg	shtns,
		cplx *	z,
		cplx *	alm
	)

complex scalar analysis.

Parameters

[in]	shtns	= a configuration created by shtns_create with a grid set by shtns_set_grid or shtns_set_grid_auto
[in]	z	= complex spatial field
[out]	alm[l*(l+1)+m]	is the SH coefficient of order l and degree m (with -l <= m <= l) [total of (LMAX+1)^2 coefficients]

complex scalar analysis.

in: complex spatial field. out: alm[l*(l+1)+m] is the SH coefficients of order l and degree m (with -l <= m <= l) for a total of (LMAX+1)^2 coefficients.

void spat_to_SH	(	shtns_cfg	shtns,
		double *	Vr,
		cplx *	Qlm
	)

transform the scalar field Vr into its spherical harmonic representation Qlm.

Parameters

[in]	shtns	= a configuration created by shtns_create with a grid set by shtns_set_grid or shtns_set_grid_auto
[in]	Vr	= spatial scalar field : double array of size shtns->nspat.
[out]	Qlm	= spherical harmonics coefficients : cplx array of size shtns->nlm.

Examples:: SHT_example.c.

void spat_to_SHqst	(	shtns_cfg	,
		double *	Vr,
		double *	Vt,
		double *	Vp,
		cplx *	Qlm,
		cplx *	Slm,
		cplx *	Tlm
	)

3D vector transform from spherical coordinates to radial-spheroidal-toroidal spectral components (see Radial - Spheroidal - Toroidal decomposition).

They should be prefered over separate calls to scalar and 2D vector transforms as they are often significantly faster.

void spat_to_SHsphtor	(	shtns_cfg	,
		double *	Vt,
		double *	Vp,
		cplx *	Slm,
		cplx *	Tlm
	)

transform the theta and phi components (Vt,Vp) of a vector into its spheroidal-toroidal spherical harmonic representation (Slm,Tlm).

See Also: Vector Spherical Harmonics as implemented in SHTns

Macros

Scalar transforms

2D vector transforms

3D transforms (combine scalar and vector)

Truncated transforms at given degree l

Legendre transform at given m (no fft) and truncated at given degree l <= lmax

Detailed Description

Function Documentation