dedalus.libraries.dedalus_sphere.sphere

Module Contents

dtype = 'longdouble'

quadrature(Lmax, dtype=dtype)

Generates the Gauss quadrature grid and weights for spherical harmonics transform.

Returns cos_theta, weights

Will integrate polynomials on (-1,+1) exactly up to degree = 2*Lmax+1.

Parameters:

Lmax (int >=0; spherical-harmonic degree.)

spin2Jacobi(Lmax, m, s, ds=None, dm=None)

harmonics(Lmax, m, s, cos_theta, **kwargs)

Gives spin-wieghted spherical harmonic functions on the Gauss quaduature grid. Returns an array with

shape = ( Lmax - Lmin(m,s) + 1, len(z) )

or (Lmax - Lmin(m,s) + 1,) if z is a single point.

Parameters:

• Lmax (int >=0; spherical-harmonic degree.)

• m,s (int) – spherical harmonic parameters.

• cos_theta (np.ndarray or float.)

• dtype (output dtype. internal dtype = ‘longdouble’.)

operator(name, dtype=dtype)

Interface to base ShereOperator class.

class SphereOperator(name, radius=1, dtype=dtype)

property radius

property dtype

static identity(dtype=dtype)

static parity(dtype=dtype)

static L(dtype=dtype)

static M(dtype=dtype)

static S(dtype=dtype)

class SphereCodomain(dL=0, dm=0, ds=0, pi=0)

Base class for Jacobi codomain.

codomain = JacobiCodomain(dn,da,db,pi)

n’, a’, b’ = codomain(n,a,b)

if pi == 0:

n’, a’, b’ = n+dn, a+da, b+db

if pi == 1:

n’, a’, b’ = n+dn, b+da, a+db

pi_0 + pi_1 = pi_0 XOR pi_1

Variables:

__arrow (stores dn,da,db,pi.)

self[0:3]: returns dn,da,db,pi respectively.

str(self): displays codomain mapping.

self + other: combines codomains.

self(n,a,b): evaluates current codomain.

-self: inverse codomain.

n*self: iterated codomain addition.

self == other: determines equivalent codomains (a,b,pi).

self | other: determines codomain compatiblity and returns larger-n space.