desc.basis.ZernikePolynomial

class desc.basis.ZernikePolynomial(L, M, sym=False, spectral_indexing='ansi')Source

2D basis set for analytic functions in a unit disc.

Parameters:

• L (int) – Maximum radial resolution. Use L=-1 for default based on M.

• M (int) – Maximum poloidal resolution.

• sym ({'cos', 'sin', False}) –

  • 'cos' for cos(m*t-n*z) symmetry

  • 'sin' for sin(m*t-n*z) symmetry

  • False for no symmetry (Default)

• 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.

Methods

change_resolution(L, M[, sym])	Change resolution of the basis to the given resolutions.
copy([deepcopy])	Return a (deep)copy of this object.
equiv(other)	Compare equivalence between DESC objects.
evaluate(grid[, derivatives, modes])	Evaluate basis functions at specified nodes.
get_idx([L, M, N, error])	Get the index of the 'modes' array corresponding to given mode numbers.
load(load_from[, file_format])	Initialize from file.
save(file_name[, file_format, file_mode])	Save the object.

Attributes

L	Maximum radial resolution.
M	Maximum poloidal resolution.
N	Maximum toroidal resolution.
NFP	Number of field periods.
fft_poloidal	whether this basis is compatible with fft in the poloidal direction.
fft_toroidal	whether this basis is compatible with fft in the toroidal direction.
inverse_LM_idx	Indices of unique_LM_idx that recover the LM mode pairs.
inverse_L_idx	Indices of unique_L_idx that recover the radial modes.
inverse_M_idx	Indices of unique_M_idx that recover the poloidal modes.
inverse_N_idx	Indices of unique_N_idx that recover the toroidal modes.
modes	Mode numbers [l,m,n].
num_modes	Total number of modes in the spectral basis.
spectral_indexing	Type of indexing used for the spectral basis.
sym	Type of symmetry.
unique_LM_idx	Indices of unique radial/poloidal mode pairs.
unique_L_idx	Indices of unique radial modes.
unique_M_idx	Indices of unique poloidal modes.
unique_N_idx	Indices of unique toroidal modes.