dedalus.core.basis
Abstract and built-in classes for spectral bases.
Module Contents
- class Jacobi(coord, size, bounds, a, b, a0=None, b0=None, dealias=(1,), library=None)
Jacobi polynomial basis.
- group_shape = (1,)
- native_bounds = ()
- transforms
- default_dct = 'fftw_dct'
- default_library = 'matrix'
- transform_plan(grid_size)
Build transform plan.
- elements_to_groups(grid_space, elements)
- valid_elements(tensorsig, grid_space, elements)
- Jacobi_matrix(size)
- product_matrix(arg_basis, out_basis, i)
- derivative_basis(order=1)
- Legendre(*args, **kw)
- Ultraspherical(*args, alpha, alpha0=None, **kw)
- ChebyshevT(*args, **kw)
- ChebyshevU(*args, **kw)
- ChebyshevV(*args, **kw)
- Chebyshev
- Fourier(*args, dtype=None, **kw)
Factory function dispatching to RealFourier and ComplexFourier based on provided dtype.
- class ComplexFourier(coord, size, bounds, dealias=(1,), library=None)
Fourier complex exponential basis. Modes: [exp(0j*x), exp(1j*x), exp(2j*x), …]
- group_shape = (1,)
- transforms
- valid_elements(tensorsig, grid_space, elements)
- product_matrix(arg_basis, out_basis, i)
- class RealFourier(coord, size, bounds, dealias=(1,), library=None)
Fourier real sine/cosine basis. Modes: [cos(0*x), -sin(0*x), cos(1*x), -sin(1*x), …]
- group_shape = (2,)
- transforms
- valid_elements(tensorsig, grid_space, elements)
- product_matrix(arg_basis, out_basis, i)
- class AnnulusBasis(coordsystem, shape, dtype, radii=(1, 2), k=0, alpha=(- 0.5, - 0.5), dealias=(1, 1), azimuth_library=None, radius_library=None)
Abstract base class for spectral bases.
- transforms
- subaxis_dependence = (False, True)
- radial_basis()
- global_grid_radius(scale)
- local_grid_radius(scale)
- global_radius_weights(scale=None)
- local_radius_weights(scale=None)
- constant_mode_value()
- transform_plan(grid_size, k)
Build transform plan.
- radial_transform_factor(scale, data_axis, dk)
- forward_transform_radius(field, axis, gdata, cdata)
- backward_transform_radius(field, axis, cdata, gdata)
- interpolation(m, spintotal, position)
- operator_matrix(op, m, spintotal, size=None)
- jacobi_conversion(m, dk, size=None)
- conversion_matrix(m, spintotal, dk)
- class DiskBasis(coordsystem, shape, dtype, radius=1, k=0, alpha=0, dealias=(1, 1), azimuth_library=None, radius_library=None)
Abstract base class for spectral bases.
- transforms
- subaxis_dependence = (True, True)
- default_library = 'matrix'
- radial_basis()
- global_grid_radius(scale)
- local_grid_radius(scale)
- global_radius_weights(scale=None)
- local_radius_weights(scale=None)
- constant_mode_value()
- transform_plan(grid_shape, axis, s)
Build transform plan.
- abstract forward_transform_radius_Nmax0(field, axis, gdata, cdata)
- forward_transform_radius(field, axis, gdata, cdata)
- abstract backward_transform_radius_Nmax0(field, axis, cdata, gdata)
- backward_transform_radius(field, axis, cdata, gdata)
- conversion_matrix(m, spintotal, dk)
- operator_matrix(op, m, spin, size=None)
- interpolation(m, spintotal, position)
- radius_multiplication_matrix(m, spintotal, order, d)
- class SphereBasis(coordsystem, shape, dtype, radius=1, dealias=(1, 1), azimuth_library=None, colatitude_library=None)
Abstract base class for spectral bases.
- dim = 2
- dims = ['azimuth', 'colatitude']
- subaxis_dependence = [True, True]
- transforms
- constant_mode_value
- default_library = 'matrix'
- latitude_basis()
- matrix_dependence(matrix_coupling)
- global_shape(grid_space, scales)
- chunk_shape(grid_space)
- elements_to_groups(grid_space, elements)
- m_maps()
Tuple of (m, mg_slice, mc_slice, ell_slice) for all local m’s when the colatitude axis is local.
- ell_reversed()
- ell_maps()
Tuple of (ell, m_slice, ell_slice) for all local ells in coeff space. m_slice and ell_slice are local slices along the phi and theta axes.
Data for each ell should be sliced as:
- for ell, m_slice, ell_slice in ell_maps:
ell_data = data[m_slice, ell_slice]
- global_grids(scales=None)
Global grids.
- global_grid_colatitude(scale)
- global_grid_spacing(axis, scales=None)
Global grids spacings.
- local_grid_spacing(axis, scales=None)
Local grids spacings.
- local_grids(scales=None)
Local grids.
- local_grid_colatitude(scale)
- global_colatitude_weights(scale=None)
- local_colatitude_weights(scale=None)
- transform_plan(Ntheta, s)
Build transform plan.
- forward_transform_azimuth_Mmax0(field, axis, gdata, cdata)
- forward_transform_azimuth(field, axis, gdata, cdata)
- forward_transform_radius(field, axis, gdata, cdata)
- backward_transform_azimuth_Mmax0(field, axis, cdata, gdata)
- backward_transform_azimuth(field, axis, cdata, gdata)
- backward_transform_radius(field, axis, cdata, gdata)
- forward_transform_colatitude_Lmax0(field, axis, gdata, cdata)
- forward_transform_colatitude(field, axis, gdata, cdata)
- backward_transform_colatitude_Lmax0(field, axis, cdata, gdata)
- backward_transform_colatitude(field, axis, cdata, gdata)
- static k(l, s, mu)
- k_vector(mu, m, s, local_l)
- valid_elements(tensorsig, grid_space, elements)
- ell_size(m)
- operator_matrix(op, m, spintotal, size=None)
- sine_multiplication_matrix(m, spintotal, order, size=None)
- class ShellBasis(coordsystem, shape, dtype, radii=(1, 2), k=0, alpha=(- 0.5, - 0.5), dealias=(1, 1, 1), azimuth_library=None, colatitude_library=None, radius_library=None)
Abstract base class for spectral bases.
- property meridional_basis
- forward_transform_radius(field, axis, gdata, cdata)
- backward_transform_radius(field, axis, cdata, gdata)
- build_ncc_matrix(product, subproblem, ncc_cutoff, max_ncc_terms)
- build_meridional_ncc_matrix(product, subproblem, ncc_cutoff, max_ncc_terms)
- class BallBasis(coordsystem, shape, dtype, radius=1, k=0, alpha=0, dealias=(1, 1, 1), azimuth_library=None, colatitude_library=None, radius_library=None)
Abstract base class for spectral bases.
- transforms
- default_library = 'matrix'
- transform_plan(grid_shape, regindex, axis, regtotal, k, alpha)
Build transform plan.
- forward_transform_radius(field, axis, gdata, cdata)
- backward_transform_radius(field, axis, cdata, gdata)