desc.geometry.ZernikeRZToroidalSection

class desc.geometry.ZernikeRZToroidalSection(R_lmn=None, Z_lmn=None, modes_R=None, modes_Z=None, spectral_indexing='ansi', sym='auto', L=None, M=None, zeta=0.0, name='', check_orientation=True)Source

A toroidal cross section represented by a Zernike polynomial in R,Z.

Parameters:

• R_lmn (array-like, shape(k,)) – zernike coefficients

• Z_lmn (array-like, shape(k,)) – zernike coefficients

• modes_R (array-like, shape(k,2)) – radial and poloidal mode numbers [l,m] for R_lmn

• modes_Z (array-like, shape(k,2)) – radial and poloidal mode numbers [l,m] for Z_lmn. If None defaults to modes_R.

• sym (bool) – whether to enforce stellarator symmetry. Default is “auto” which enforces if modes are symmetric. If True, non-symmetric modes will be truncated.

• spectral_indexing ({'ansi', 'fringe'}) –

  Indexing method, default value = 'ansi'

  For L=0, all methods are equivalent and give a “chevron” shaped basis (only the outer edge of the zernike pyramid of width M). For L>0, the indexing scheme defines order of the basis functions:

  'ansi': ANSI indexing fills in the pyramid with triangles of decreasing size, ending in a triangle shape. For L == M, the traditional ANSI pyramid indexing is recovered. For L>M, adds rows to the bottom of the pyramid, increasing L while keeping M constant, giving a “house” shape

  'fringe': Fringe indexing fills in the pyramid with chevrons of decreasing size, ending in a diamond shape for L=2*M where the traditional fringe/U of Arizona indexing is recovered. For L > 2*M, adds chevrons to the bottom, making a hexagonal diamond

• L (int or None) – Maximum radial and poloidal mode numbers. Defaults to max from modes_R and modes_Z.

• M (int or None) – Maximum radial and poloidal mode numbers. Defaults to max from modes_R and modes_Z.

• zeta (float [0,2pi)) – toroidal angle for the section.

• name (str) – name for this surface

• check_orientation (bool) – ensure that this surface has a right handed orientation. Do not set to False unless you are sure the parameterization you have given is right handed (ie, e_theta x e_zeta points outward from the surface).

Methods

change_resolution(*args, **kwargs)	Change the maximum radial and poloidal resolution.
compute(names[, grid, params, transforms, ...])	Compute the quantity given by name on grid.
copy([deepcopy])	Return a (deep)copy of this object.
equiv(other)	Compare equivalence between DESC objects.
get_coeffs(l[, m])	Get Zernike coefficients for given mode number(s).
load(load_from[, file_format])	Initialize from file.
pack_params(p)	Convert a dictionary of parameters into a single array.
save(file_name[, file_format, file_mode])	Save the object.
set_coeffs(l[, m, R, Z])	Set specific Zernike coefficients.
unpack_params(x)	Convert a single array of concatenated parameters into a dictionary.

Attributes

L	Maximum radial mode number.
M	Maximum poloidal mode number.
N	Maximum toroidal mode number.
R_basis	Spectral basis for R.
R_lmn	Spectral coefficients for R.
Z_basis	Spectral basis for Z.
Z_lmn	Spectral coefficients for Z.
dim_x	total number of optimizable parameters.
dimensions	dictionary of integers of sizes of each optimizable parameter.
name	Name of the surface.
optimizable_params	string names of parameters that have been declared optimizable.
params_dict	dictionary of arrays of optimizable parameters.
spectral_indexing	Type of spectral indexing for Zernike basis.
sym	Whether or not the surface is stellarator symmetric.
x_idx	arrays of indices for each parameter in concatenated array.
zeta	Toroidal angle.