ssht_sampling_mod Module Reference

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

Functions/Subroutines
real(dp)	ssht_sampling_weight_dh (theta_t, L)
	Compute Discoll and Healy weights.
complex(dpc)	ssht_sampling_weight_mw (p)
	Compute weights for toroidal extension.
subroutine	ssht_sampling_gl_thetas_weights (thetas, weights, L)
	Compute theta positions (roots of Legendre polynomials) and corresponding weights.
subroutine	gauleg (x1, x2, x, w, 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.
real(dp)	ssht_sampling_dh_t2theta (t, L)
	Convert theta index to angle for Driscoll and Healy sampling.
real(dp)	ssht_sampling_dh_p2phi (p, L)
	Convert phi index to angle for Driscoll and Healy sampling.
real(dp)	ssht_sampling_gl_p2phi (p, L)
	Convert phi index to angle for Gauss-Legendre sampling.
real(dp)	ssht_sampling_mw_t2theta (t, L)
	Convert theta index to angle for McEwen and Wiaux sampling.
real(dp)	ssht_sampling_mw_p2phi (p, L)
	Convert phi index to angle for McEwen and Wiaux sampling.
real(dp)	ssht_sampling_mweo_t2theta (t, L)
	Convert theta index to angle for McEwen and Wiaux even-odd sampling.
real(dp)	ssht_sampling_mweo_p2phi (p, L)
	Convert phi index to angle for McEwen and Wiaux even-odd sampling.
subroutine	ssht_sampling_elm2ind (ind, el, m)
	Convert (el,m) harmonic indices to 1D index used to access flm array.
subroutine	ssht_sampling_ind2elm (el, m, ind)
	Convert 1D index used to access flm array to (el,m) harmonic indices.
Variables
integer, parameter	SSHT_SAMPLING_DH = 1
	Flag to indicate Driscoll and Healy sampling.
integer, parameter	SSHT_SAMPLING_GL = 2
	Flag to indicate Gauss-Legendre sampling.
integer, parameter	SSHT_SAMPLING_MW = 3
	Flag to indicate McEwen and Wiaux sampling.
integer, parameter	SSHT_SAMPLING_MWEO = 4
	Flag to indicate McEwen and Wiaux sampling for even-odd algorithm.
integer, parameter	SSHT_SAMPLING_DEFAULT = SSHT_SAMPLING_MW
	Flag to indicate default sampling (McEwen and Wiaux sampling).

Detailed Description

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

Author:: Jason McEwen

Function/Subroutine Documentation

subroutine ssht_sampling_mod::gauleg	(	real(dp),intent(in)	x1,
		real(dp),intent(in)	x2,
		real(dp),dimension(1:n),intent(out)	x,
		real(dp),dimension(1:n),intent(out)	w,
		integer,intent(in)	n
	)			`[private]`

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.

Variables:

x1: Lower bound of range [input].
x2: Upper bound of range [input].
x: Node positions (i.e. roots of Legendre polynomials) [output].
w: Corresponding weights [output].
n: Number of points [input].

Author:: Numerical recipes.

Definition at line 208 of file ssht_sampling_mod.f90.

Referenced by ssht_sampling_gl_thetas_weights().

real(dp) ssht_sampling_mod::ssht_sampling_dh_p2phi	(	integer,intent(in)	p,
		integer,intent(in)	L
	)

Convert phi index to angle for Driscoll and Healy sampling.

Notes:

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

Variables:

p: Phi index [input].
L: Harmonic band-limit [input].
phi: Phi angle [output].

Author:: Jason McEwen

Definition at line 299 of file ssht_sampling_mod.f90.

References ssht_types_mod::PI.

Referenced by ssht_core_mod::ssht_core_dh_forward_sov_direct(), ssht_core_mod::ssht_core_dh_inverse_direct(), ssht_core_mod::ssht_core_dh_inverse_direct_factored(), and ssht_core_mod::ssht_core_dh_inverse_sov_direct().

real(dp) ssht_sampling_mod::ssht_sampling_dh_t2theta	(	integer,intent(in)	t,
		integer,intent(in)	L
	)

Convert theta index to angle for Driscoll and Healy sampling.

Notes:

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

Variables:

t: Theta index [input].
L: Harmonic band-limit [input].
theta: Theta angle [output].

Author:: Jason McEwen

Definition at line 269 of file ssht_sampling_mod.f90.

References ssht_types_mod::PI.

subroutine ssht_sampling_mod::ssht_sampling_elm2ind	(	integer,intent(out)	ind,
		integer,intent(in)	el,
		integer,intent(in)	m
	)

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

Notes:

el ranges from [0 .. L-1].
m ranges from [-el .. el].
ind ranges from [0 .. L**2-1].

Variables:

ind: 1D index to access flm array [output].
el: Harmonic index [input].
m: Azimuthal harmonic index [input].

Author:: Jason McEwen

Definition at line 486 of file ssht_sampling_mod.f90.

real(dp) ssht_sampling_mod::ssht_sampling_gl_p2phi	(	integer,intent(in)	p,
		integer,intent(in)	L
	)

Convert phi index to angle for Gauss-Legendre sampling.

Notes:

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

Variables:

p: Phi index [input].
L: Harmonic band-limit [input].
phi: Phi angle [output].

Author:: Jason McEwen

Definition at line 329 of file ssht_sampling_mod.f90.

References ssht_types_mod::PI.

subroutine ssht_sampling_mod::ssht_sampling_gl_thetas_weights	(	real(dp),dimension(0:l-1),intent(out)	thetas,
		real(dp),dimension(0:l-1),intent(out)	weights,
		integer,intent(in)	L
	)