dedalus.core.basis
==================

.. py:module:: dedalus.core.basis

.. autoapi-nested-parse::

   Abstract and built-in classes for spectral bases.









Module Contents
---------------

.. py: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.


   .. py:method:: backward_transform_radius(field, axis, cdata, gdata)


   .. py:method:: constant_mode_value()


   .. py:method:: conversion_matrix(m, spintotal, dk)


   .. py:method:: forward_transform_radius(field, axis, gdata, cdata)


   .. py:method:: global_grid_radius(dist, scale)


   .. py:method:: global_radius_weights(dist, scale=None)


   .. py:method:: interpolation(m, spintotal, position)


   .. py:method:: jacobi_conversion(m, dk, size=None)


   .. py:method:: local_grid_radius(dist, scale)


   .. py:method:: local_radius_weights(dist, scale=None)


   .. py:method:: operator_matrix(op, m, spintotal, size=None)


   .. py:method:: radial_basis()


   .. py:method:: radial_transform_factor(scale, data_axis, dk)


   .. py:method:: transform_plan(dist, grid_size, k)

      Build transform plan.



   .. py:attribute:: alpha


   .. py:attribute:: azimuth_library
      :value: None



   .. py:attribute:: coordsys


   .. py:attribute:: dR
      :value: 1



   .. py:attribute:: dealias
      :value: (1, 1)



   .. py:attribute:: dtype


   .. py:attribute:: grid_params


   .. py:attribute:: inner_edge


   .. py:attribute:: k
      :value: 0



   .. py:attribute:: outer_edge


   .. py:attribute:: radii
      :value: (1, 2)



   .. py:attribute:: radius_library
      :value: None



   .. py:attribute:: rho
      :value: 3.0



   .. py:attribute:: shape


   .. py:attribute:: subaxis_dependence
      :value: (False, True)



   .. py:attribute:: transforms


   .. py:attribute:: volume


.. py: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.


   .. py:method:: backward_transform_radius(field, axis, cdata, gdata)


   .. py:method:: forward_transform_radius(field, axis, gdata, cdata)


   .. py:method:: transform_plan(dist, grid_shape, regindex, axis, regtotal, k, alpha)

      Build transform plan.



   .. py:attribute:: alpha
      :value: 0



   .. py:attribute:: azimuth_library
      :value: None



   .. py:attribute:: backward_transforms


   .. py:attribute:: colatitude_library
      :value: None



   .. py:attribute:: coordsys


   .. py:attribute:: dealias
      :value: (1, 1, 1)



   .. py:attribute:: default_library
      :value: 'matrix'



   .. py:attribute:: dtype


   .. py:attribute:: forward_transforms


   .. py:attribute:: grid_params


   .. py:attribute:: k
      :value: 0



   .. py:attribute:: radial_basis


   .. py:attribute:: radius
      :value: 1



   .. py:attribute:: radius_library
      :value: None



   .. py:attribute:: shape


   .. py:attribute:: surface


   .. py:attribute:: transforms


   .. py:attribute:: volume


.. py:class:: CardinalBasis(coord, size)



   Cardinal basis.


   .. py:method:: backward_transform(field, axis, cdata, gdata)

      Backward transform field data.



   .. py:method:: chunk_shape(grid_space)


   .. py:method:: elements_to_groups(grid_space, elements)


   .. py:method:: forward_transform(field, axis, gdata, cdata)

      Forward transform field data.



   .. py:method:: global_grid(dist, scale)

      Global grid.



   .. py:method:: global_grids(dist, scales)

      Global grids.



   .. py:method:: global_shape(grid_space, scales)


   .. py:method:: local_grid(dist, scale)

      Local grid.



   .. py:method:: local_grids(dist, scales)

      Local grids.



   .. py:method:: local_modes(dist)

      Local grid.



   .. py:method:: matrix_dependence(matrix_coupling)


   .. py:method:: valid_elements(tensorsig, grid_space, elements)


   .. py:attribute:: coord


   .. py:attribute:: coordsys


   .. py:attribute:: dealias
      :value: (1,)



   .. py:attribute:: dim
      :value: 1



   .. py:attribute:: group_shape
      :value: (1,)



   .. py:attribute:: shape


   .. py:attribute:: size


   .. py:attribute:: subaxis_dependence
      :value: [False]



.. py:class:: ComplexFourier(coord, size, bounds, dealias=(1, ), library=None)



   Fourier complex exponential basis.
   Modes: [exp(0j*x), exp(1j*x), exp(2j*x), ...]


   .. py:method:: product_matrix(arg_basis, out_basis, i)


   .. py:method:: valid_elements(tensorsig, grid_space, elements)


   .. py:attribute:: group_shape
      :value: (1,)



   .. py:attribute:: transforms


.. py: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.


   .. py:method:: backward_transform_radius(field, axis, cdata, gdata)


   .. py:method:: backward_transform_radius_Nmax0(field, axis, cdata, gdata)
      :abstractmethod:



   .. py:method:: constant_mode_value()


   .. py:method:: conversion_matrix(m, spintotal, dk)


   .. py:method:: forward_transform_radius(field, axis, gdata, cdata)


   .. py:method:: forward_transform_radius_Nmax0(field, axis, gdata, cdata)
      :abstractmethod:



   .. py:method:: global_grid_radius(dist, scale)


   .. py:method:: global_radius_weights(dist, scale=None)


   .. py:method:: interpolation(m, spintotal, position)


   .. py:method:: local_grid_radius(dist, scale)


   .. py:method:: local_radius_weights(dist, scale=None)


   .. py:method:: operator_matrix(op, m, spin, size=None)


   .. py:method:: radial_basis()


   .. py:method:: radius_multiplication_matrix(m, spintotal, order, d)


   .. py:method:: transform_plan(dist, grid_shape, axis, s)

      Build transform plan.



   .. py:attribute:: alpha
      :value: 0



   .. py:attribute:: azimuth_library
      :value: None



   .. py:attribute:: coordsys


   .. py:attribute:: dealias
      :value: (1, 1)



   .. py:attribute:: default_library
      :value: 'matrix'



   .. py:attribute:: dtype


   .. py:attribute:: edge


   .. py:attribute:: grid_params


   .. py:attribute:: k
      :value: 0



   .. py:attribute:: radial_COV


   .. py:attribute:: radius
      :value: 1



   .. py:attribute:: radius_library
      :value: None



   .. py:attribute:: shape


   .. py:attribute:: subaxis_dependence
      :value: (True, True)



   .. py:attribute:: transforms


   .. py:attribute:: volume


.. py:class:: Jacobi(coord, size, bounds, a, b, a0=None, b0=None, dealias=(1, ), library=None)



   Jacobi polynomial basis.


   .. py:method:: Jacobi_matrix(size)


   .. py:method:: derivative_basis(order=1)


   .. py:method:: elements_to_groups(grid_space, elements)


   .. py:method:: product_matrix(arg_basis, out_basis, i)


   .. py:method:: transform_plan(dist, grid_size)

      Build transform plan.



   .. py:method:: valid_elements(tensorsig, grid_space, elements)


   .. py:attribute:: a


   .. py:attribute:: a0
      :value: None



   .. py:attribute:: b


   .. py:attribute:: b0
      :value: None



   .. py:attribute:: bounds


   .. py:attribute:: constant_mode_value


   .. py:attribute:: coord


   .. py:attribute:: dealias
      :value: (1,)



   .. py:attribute:: default_dct
      :value: 'fftw_dct'



   .. py:attribute:: default_library
      :value: 'matrix'



   .. py:attribute:: grid_params


   .. py:attribute:: group_shape
      :value: (1,)



   .. py:attribute:: library
      :value: None



   .. py:attribute:: native_bounds


   .. py:attribute:: size


   .. py:attribute:: transforms


.. py: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), ...]


   .. py:method:: product_matrix(arg_basis, out_basis, i)


   .. py:method:: valid_elements(tensorsig, grid_space, elements)


   .. py:attribute:: group_shape
      :value: (2,)



   .. py:attribute:: transforms


.. py: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.


   .. py:method:: backward_transform_radius(field, axis, cdata, gdata)


   .. py:method:: build_meridional_ncc_matrix(product, subproblem, ncc_cutoff, max_ncc_terms)


   .. py:method:: build_ncc_matrix(product, subproblem, ncc_cutoff, max_ncc_terms)


   .. py:method:: forward_transform_radius(field, axis, gdata, cdata)


   .. py:attribute:: alpha


   .. py:attribute:: azimuth_library
      :value: None



   .. py:attribute:: backward_transforms


   .. py:attribute:: colatitude_library
      :value: None



   .. py:attribute:: coordsys


   .. py:attribute:: dealias
      :value: (1, 1, 1)



   .. py:attribute:: dtype


   .. py:attribute:: forward_transforms


   .. py:attribute:: grid_params


   .. py:attribute:: inner_surface


   .. py:attribute:: k
      :value: 0



   .. py:property:: meridional_basis


   .. py:attribute:: outer_surface


   .. py:attribute:: radial_basis


   .. py:attribute:: radii
      :value: (1, 2)



   .. py:attribute:: radius_library
      :value: None



   .. py:attribute:: shape


   .. py:attribute:: volume


.. py:class:: SphereBasis(coordsys, shape, dtype, radius=1, dealias=(1, 1), azimuth_library=None, colatitude_library=None)



   Abstract base class for spectral bases.


   .. py:method:: backward_transform_azimuth(field, axis, cdata, gdata)


   .. py:method:: backward_transform_azimuth_Mmax0(field, axis, cdata, gdata)


   .. py:method:: backward_transform_colatitude(field, axis, cdata, gdata)


   .. py:method:: backward_transform_colatitude_Lmax0(field, axis, cdata, gdata)


   .. py:method:: backward_transform_radius(field, axis, cdata, gdata)


   .. py:method:: chunk_shape(grid_space)


   .. py:method:: elements_to_groups(grid_space, elements)


   .. py:method:: 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]



   .. py:method:: ell_reversed(dist)


   .. py:method:: ell_size(m)


   .. py:method:: forward_transform_azimuth(field, axis, gdata, cdata)


   .. py:method:: forward_transform_azimuth_Mmax0(field, axis, gdata, cdata)


   .. py:method:: forward_transform_colatitude(field, axis, gdata, cdata)


   .. py:method:: forward_transform_colatitude_Lmax0(field, axis, gdata, cdata)


   .. py:method:: forward_transform_radius(field, axis, gdata, cdata)


   .. py:method:: global_colatitude_weights(dist, scale=None)


   .. py:method:: global_grid_colatitude(dist, scale)


   .. py:method:: global_grid_spacing(dist, subaxis, scales)

      Global grids spacings.



   .. py:method:: global_grids(dist, scales)

      Global grids.



   .. py:method:: global_shape(grid_space, scales)


   .. py:method:: k(l, s, mu)
      :staticmethod:



   .. py:method:: k_vector(mu, m, s, local_l)


   .. py:method:: latitude_basis()


   .. py:method:: local_colatitude_weights(dist, scale=None)


   .. py:method:: local_grid_colatitude(dist, scale)


   .. py:method:: local_grid_spacing(dist, subaxis, scales)

      Local grids spacings.



   .. py:method:: local_grids(dist, scales)

      Local grids.



   .. py:method:: m_maps(dist)

      Tuple of (m, mg_slice, mc_slice, ell_slice) for all local m's when
      the colatitude axis is local.



   .. py:method:: matrix_dependence(matrix_coupling)


   .. py:method:: operator_matrix(op, m, spintotal, size=None)


   .. py:method:: sine_multiplication_matrix(m, spintotal, order, size=None)


   .. py:method:: transform_plan(dist, Ntheta, s)

      Build transform plan.



   .. py:method:: valid_elements(tensorsig, grid_space, elements)


   .. py:attribute:: azimuth_library
      :value: None



   .. py:attribute:: backward_transforms


   .. py:attribute:: colatitude_library
      :value: None



   .. py:attribute:: constant_mode_value


   .. py:attribute:: coordsys


   .. py:attribute:: dealias
      :value: (1, 1)



   .. py:attribute:: default_library
      :value: 'matrix'



   .. py:attribute:: dim
      :value: 2



   .. py:attribute:: dims
      :value: ['azimuth', 'colatitude']



   .. py:attribute:: dtype


   .. py:attribute:: forward_transforms


   .. py:attribute:: grid_params


   .. py:attribute:: radius
      :value: 1



   .. py:attribute:: shape


   .. py:attribute:: subaxis_dependence
      :value: [True, True]



   .. py:attribute:: transforms


   .. py:attribute:: volume


.. py:function:: ChebyshevT(*args, **kw)

.. py:function:: ChebyshevU(*args, **kw)

.. py:function:: ChebyshevV(*args, **kw)

.. py:function:: Fourier(*args, dtype=None, **kw)

   Factory function dispatching to RealFourier and ComplexFourier based on provided dtype.


.. py:function:: Legendre(*args, **kw)

.. py:function:: Ultraspherical(*args, alpha, alpha0=None, **kw)

.. py:data:: Chebyshev