waveformtools.grids

Classes to hold grid information

Classes

UniformGrid: grid info.: Stores information on the 2d grid in spherical polar coordinates.
GLGrid: grid info: Stores a Gauss-Legendre type grid on a spherical surface.

Classes

`GLGrid`([nphi, ntheta, nphi_act, ntheta_act, ...])	A class to store the coordinate grid on a sphere.
`UniformGrid`([nphi, ntheta, nphimax, ...])	A class to store the theta-phi grid info.

class waveformtools.grids.GLGrid(nphi=None, ntheta=None, nphi_act=None, ntheta_act=None, L=47, nghosts=2, integration_method='GL', grid_type='GL')[source]

A class to store the coordinate grid on a sphere.

Attributes:

nthetaint: Return the total number gridpoints along the theta direction, including the ghost zones at one iteration.
nphiint: Return the total number of gridpoints along the phi direction, including the ghost zones at one iteration.
nghostsint: Return the number of ghost zones
meshgridtuple of 2d array: The (\(\theta, \phi)\): coordinate meshes.
theta_1d1d array: Returns the coordinate value theta given the coordinate index.
phi_1d1d array: Returns the coordinate value theta given the coordinate index.
dthetafloat: The angular step size in the \(\theta\) direction.
dphifloat: Return the uniform angular stepping in \(\phi\) direction
npix_actint: Return the actual number of pixels,
meshgridtuple of 2darray: The (\(\theta, \phi)\): coordinate meshes.

Methods

`theta_1d`	Returns the coordinate value theta given the coordinate index.
`phi_1d`	Returns the coordinate value theta given the coordinate index.

Notes

The total number of points on the sphere is assumed to be \(2 (L+1)^2\)

\(N_\theta = L+1\)

\(N_\phi = 2(L+1)\)

This integrates out spherical harmonics of degree L exactly, given a regular function on the sphere.

In other words, given \(L+1\) points in the \(\theta\) direction, one can resolve spherical harmonics upto degree \(L\).

property L: Return the total number of pixels, including the ghost zones present at one iteration.

property dphi: Return the uniform angular stepping in \(\phi\) direction

property dtheta_1d: Return the non-uniform angular stepping in :math:` heta` direction

property grid_type

property integration_method: The default integration method

property meshgrid

The (\(\theta, \phi)\): coordinate meshes. Excludes the ghost zones.

Returns:

theta2d array: The \(\theta\) coordinate matrix for vectorization.
phi2d array: The \(\phi\) coordinate matrix for vectorization.

property nghosts: Return the number of ghost zones at each end in each direction

nphi()[source]: Return the total number of gridpoints along the phi direction, including the ghost zones at one iteration.

property nphi_act: Return the actual number of physical data points along the phi direction excluding the ghost and buffer zones at one iteration.

property npix: Return the total number of pixels, including the ghost zones present at one iteration.

property npix_act: Return the actual number of pixels, excluding the ghost zones present at one iteration

ntheta()[source]: Return the total number gridpoints along the theta direction, including the ghost zones at one iteration.

property ntheta_act: Return the actual number of physical data points along the theta direction excluding the ghost and buffer zones at one iteration.

property phi_1d

Returns the coordinate value theta given the coordinate index. The coordinate index lies in (0, nphi). The actual indices without the ghost and extra zones is (nghosts, nphi-nghosts).

Parameters:

phi_1dint / 1d array: The phi coordinate index or axis.

Returns:

phi_1dfloat or 1d array: The coordinate(s) \(\phi\) on the sphere.

property shape: Return the shape of the grif

property theta_1d

Returns the coordinate value theta given the coordinate index. The coordinate index ranges from (0, ntheta). The actual indices without the ghost and extra zones is (nghosts, ntheta-nghosts).

Parameters:

theta_indexint/ 1d array: The theta coordinate index or axis.

Returns:

theta_1dfloat: The coordinate(s) \(\theta\) on the sphere.

property weights: Return the integration weights along theta

property weights_grid: Return the integration weights on the coordinate mesh grid

class waveformtools.grids.UniformGrid(nphi=80, ntheta=41, nphimax=124, nthetamax=66, nghosts=2, integration_method='MP', grid_type='Uniform')[source]

A class to store the theta-phi grid info.

Attributes:

dphi
dtheta
grid_type
integration_method: The default integration method
meshgrid: The (\(\theta, \phi)\): coordinate meshes.
nbuffer
nphi_act: Return the actual number of valid pixels, excluding the ghost and buffer zones, along the phi axis at one iteration.
npix
npix_act
npix_max
ntheta_act: Return the actual number of valid pixels, excluding the ghost and buffer zones, along the theta axis at one iteration.
phi_1d: Returns the coordinate value theta given the coordinate index.
shape: Return the shape of the grif
theta_1d: Returns the coordinate value theta given the coordinate index.

Methods

`get_data_on_GLGrid`(func[, infoGL])	Get the data on a GLGrid given data on the uniform grid.
`to_GLGrid`()	Find the highest resolution closest equivalent GL grid of this grid

property dphi

property dtheta

get_data_on_GLGrid(func, infoGL=None)[source]

Get the data on a GLGrid given data on the uniform grid.

Parameters:

func2darray: The function to be interpolated onto the GLGrid
infoGLgrid_info, optional: The GLGrid onto which the function is to be interpolated. If not given, then the closeset equivalent GL grid to this instance of UniformGrid will be found and used.

Returns:

infoGLgrid_info: The GLGrid used for interpolation
func_on_GLGrid2darray: The function func values on the GLGrid

property grid_type

property integration_method: The default integration method

property meshgrid

The (\(\theta, \phi)\): coordinate meshes. Excludes the ghost zones.

Returns:

theta2d array: The \(\theta\) coordinate matrix for vectorization.
phi2d array: The \(\phi\) coordinate matrix for vectorization.

property nbuffer

property nphi_act: Return the actual number of valid pixels, excluding the ghost and buffer zones, along the phi axis at one iteration.

property npix

property npix_act

property npix_max

property ntheta_act: Return the actual number of valid pixels, excluding the ghost and buffer zones, along the theta axis at one iteration.

property phi_1d

Returns the coordinate value theta given the coordinate index. The coordinate index lies in (0, nphi). The actual indices without the ghost and extra zones is (nghosts, nphi-nghosts).

Parameters:

phi_1dint / 1d array: The phi coordinate index or axis.

Returns:

phi_1dfloat or 1d array: The coordinate(s) \(\phi\) on the sphere.

property shape: Return the shape of the grif

property theta_1d

Returns the coordinate value theta given the coordinate index. The coordinate index ranges from (0, ntheta). The actual indices without the ghost and extra zones is (nghosts, ntheta-nghosts).

Parameters:

theta_indexint/ 1d array: The theta coordinate index or axis.

Returns:

theta_1dfloat: The coordinate(s) \(\theta\) on the sphere.

to_GLGrid()[source]: Find the highest resolution closest equivalent GL grid of this grid