dedalus.core.basis
Abstract and built-in classes for spectral bases.
Module Contents
- class AnnulusBasis(coordsys, 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.
- backward_transform_radius(field, axis, cdata, gdata)
- constant_mode_value()
- conversion_matrix(m, spintotal, dk)
- forward_transform_radius(field, axis, gdata, cdata)
- global_grid_radius(dist, scale)
- global_radius_weights(dist, scale=None)
- interpolation(m, spintotal, position)
- jacobi_conversion(m, dk, size=None)
- local_grid_radius(dist, scale)
- local_radius_weights(dist, scale=None)
- operator_matrix(op, m, spintotal, size=None)
- radial_basis()
- radial_transform_factor(scale, data_axis, dk)
- transform_plan(dist, grid_size, k)
Build transform plan.
- alpha
- azimuth_library = None
- coordsys
- dR = 1
- dealias = (1, 1)
- dtype
- grid_params
- inner_edge
- k = 0
- outer_edge
- radii = (1, 2)
- radius_library = None
- rho = 3.0
- shape
- subaxis_dependence = (False, True)
- transforms
- volume
- class BallBasis(coordsys, 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.
- backward_transform_radius(field, axis, cdata, gdata)
- forward_transform_radius(field, axis, gdata, cdata)
- transform_plan(dist, grid_shape, regindex, axis, regtotal, k, alpha)
Build transform plan.
- alpha = 0
- azimuth_library = None
- backward_transforms
- colatitude_library = None
- coordsys
- dealias = (1, 1, 1)
- default_library = 'matrix'
- dtype
- forward_transforms
- grid_params
- k = 0
- radial_basis
- radius = 1
- radius_library = None
- shape
- surface
- transforms
- volume
- class CardinalBasis(coord, size)
Cardinal basis.
- backward_transform(field, axis, cdata, gdata)
Backward transform field data.
- chunk_shape(grid_space)
- elements_to_groups(grid_space, elements)
- forward_transform(field, axis, gdata, cdata)
Forward transform field data.
- global_grid(dist, scale)
Global grid.
- global_grids(dist, scales)
Global grids.
- global_shape(grid_space, scales)
- local_grid(dist, scale)
Local grid.
- local_grids(dist, scales)
Local grids.
- local_modes(dist)
Local grid.
- matrix_dependence(matrix_coupling)
- valid_elements(tensorsig, grid_space, elements)
- coord
- coordsys
- dealias = (1,)
- dim = 1
- group_shape = (1,)
- shape
- size
- subaxis_dependence = [False]
- class ComplexFourier(coord, size, bounds, dealias=(1,), library=None)
Fourier complex exponential basis. Modes: [exp(0j*x), exp(1j*x), exp(2j*x), …]
- product_matrix(arg_basis, out_basis, i)
- valid_elements(tensorsig, grid_space, elements)
- group_shape = (1,)
- transforms
- class DiskBasis(coordsys, shape, dtype, radius=1, k=0, alpha=0, dealias=(1, 1), azimuth_library=None, radius_library=None)
Abstract base class for spectral bases.
- backward_transform_radius(field, axis, cdata, gdata)
- abstractmethod backward_transform_radius_Nmax0(field, axis, cdata, gdata)
- constant_mode_value()
- conversion_matrix(m, spintotal, dk)
- forward_transform_radius(field, axis, gdata, cdata)
- abstractmethod forward_transform_radius_Nmax0(field, axis, gdata, cdata)
- global_grid_radius(dist, scale)
- global_radius_weights(dist, scale=None)
- interpolation(m, spintotal, position)
- local_grid_radius(dist, scale)
- local_radius_weights(dist, scale=None)
- operator_matrix(op, m, spin, size=None)
- radial_basis()
- radius_multiplication_matrix(m, spintotal, order, d)
- transform_plan(dist, grid_shape, axis, s)
Build transform plan.
- alpha = 0
- azimuth_library = None
- coordsys
- dealias = (1, 1)
- default_library = 'matrix'
- dtype
- edge
- grid_params
- k = 0
- radial_COV
- radius = 1
- radius_library = None
- shape
- subaxis_dependence = (True, True)
- transforms
- volume
- class Jacobi(coord, size, bounds, a, b, a0=None, b0=None, dealias=(1,), library=None)
Jacobi polynomial basis.
- Jacobi_matrix(size)
- derivative_basis(order=1)
- elements_to_groups(grid_space, elements)
- product_matrix(arg_basis, out_basis, i)
- transform_plan(dist, grid_size)
Build transform plan.
- valid_elements(tensorsig, grid_space, elements)
- a
- a0 = None
- b
- b0 = None
- bounds
- constant_mode_value
- coord
- dealias = (1,)
- default_dct = 'fftw_dct'
- default_library = 'matrix'
- grid_params
- group_shape = (1,)
- library = None
- native_bounds
- size
- transforms
- 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), …]
- product_matrix(arg_basis, out_basis, i)
- valid_elements(tensorsig, grid_space, elements)
- group_shape = (2,)
- transforms
- class ShellBasis(coordsys, 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.
- backward_transform_radius(field, axis, cdata, gdata)
- build_meridional_ncc_matrix(product, subproblem, ncc_cutoff, max_ncc_terms)
- build_ncc_matrix(product, subproblem, ncc_cutoff, max_ncc_terms)
- forward_transform_radius(field, axis, gdata, cdata)
- alpha
- azimuth_library = None
- backward_transforms
- colatitude_library = None
- coordsys
- dealias = (1, 1, 1)
- dtype
- forward_transforms
- grid_params
- inner_surface
- k = 0
- property meridional_basis
- outer_surface
- radial_basis
- radii = (1, 2)
- radius_library = None
- shape
- volume
- class SphereBasis(coordsys, shape, dtype, radius=1, dealias=(1, 1), azimuth_library=None, colatitude_library=None)
Abstract base class for spectral bases.
- backward_transform_azimuth(field, axis, cdata, gdata)
- backward_transform_azimuth_Mmax0(field, axis, cdata, gdata)
- backward_transform_colatitude(field, axis, cdata, gdata)
- backward_transform_colatitude_Lmax0(field, axis, cdata, gdata)
- backward_transform_radius(field, axis, cdata, gdata)
- chunk_shape(grid_space)
- elements_to_groups(grid_space, elements)
- ell_maps(dist)
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]
- ell_reversed(dist)
- ell_size(m)
- forward_transform_azimuth(field, axis, gdata, cdata)
- forward_transform_azimuth_Mmax0(field, axis, gdata, cdata)
- forward_transform_colatitude(field, axis, gdata, cdata)
- forward_transform_colatitude_Lmax0(field, axis, gdata, cdata)
- forward_transform_radius(field, axis, gdata, cdata)
- global_colatitude_weights(dist, scale=None)
- global_grid_colatitude(dist, scale)
- global_grid_spacing(dist, subaxis, scales)
Global grids spacings.
- global_grids(dist, scales)
Global grids.
- global_shape(grid_space, scales)
- static k(l, s, mu)
- k_vector(mu, m, s, local_l)
- latitude_basis()
- local_colatitude_weights(dist, scale=None)
- local_grid_colatitude(dist, scale)
- local_grid_spacing(dist, subaxis, scales)
Local grids spacings.
- local_grids(dist, scales)
Local grids.
- m_maps(dist)
Tuple of (m, mg_slice, mc_slice, ell_slice) for all local m’s when the colatitude axis is local.
- matrix_dependence(matrix_coupling)
- operator_matrix(op, m, spintotal, size=None)
- sine_multiplication_matrix(m, spintotal, order, size=None)
- transform_plan(dist, Ntheta, s)
Build transform plan.
- valid_elements(tensorsig, grid_space, elements)
- azimuth_library = None
- backward_transforms
- colatitude_library = None
- constant_mode_value
- coordsys
- dealias = (1, 1)
- default_library = 'matrix'
- dim = 2
- dims = ['azimuth', 'colatitude']
- dtype
- forward_transforms
- grid_params
- radius = 1
- shape
- subaxis_dependence = [True, True]
- transforms
- volume
- ChebyshevT(*args, **kw)
- ChebyshevU(*args, **kw)
- ChebyshevV(*args, **kw)
- Fourier(*args, dtype=None, **kw)
Factory function dispatching to RealFourier and ComplexFourier based on provided dtype.
- Legendre(*args, **kw)
- Ultraspherical(*args, alpha, alpha0=None, **kw)
- Chebyshev