# CartesianGrid

class plasmapy.plasma.grids.CartesianGrid(*seeds, num=100, **kwargs)

A uniformly spaced Cartesian grid.

Attributes Summary

 ax0 First axis of the grid. ax1 Second axis of the grid. ax2 Third axis of the grid. dax0 Grid step size along axis ax0. dax1 Grid step size along axis ax1. dax2 Grid step size along axis ax2. grid A single grid of vertex positions of shape (N0, N1, N2, 3). grid_resolution A scalar estimate of the grid resolution. grids Three grids of vertex positions (in each coordinate), each having shape (N0, N1, N2). interpolator A nearest-neighbor interpolator that returns the nearest grid index to a position. is_uniform A boolean value reflecting whether or not the grid points are uniformly spaced. pts0 Array of positions in dimension 1. pts1 Array of positions in dimension 2. pts2 Array of positions in dimension 3. quantities A list of the keys corresponding to the quantities currently defined on the grid. recognized_quantities A dictionary of standard key names representing particular physical quantities. shape Shape of the grid si_scale_factors 3-element list containing unitless scale factors for converting the corresponding axis from its stored units to SI. unit The unit for the entire grid. unit0 Unit of dimension 1. unit1 Unit of dimension 2. unit2 Unit of dimension 3. units A list of the units of each dimension.

Methods Summary

 add_quantities(**kwargs) Adds a quantity to the dataset as a new DataArray. Interpolate the nearest grid indices to a position using a nearest-neighbor interpolator. nearest_neighbor_interpolator(pos, *args[, ...]) Interpolate values on the grid using a nearest-neighbor scheme with no higher-order weighting. on_grid(pos) Given a list of positions, determines which are in the region bounded by the grid points. require_quantities(req_quantities[, ...]) Check to make sure that a list of required quantities are present. vector_intersects(p1, p2) True if the vector from p1 to p2 intersects the grid, and False otherwise. volume_averaged_interpolator(pos, *args[, ...]) Interpolate values on the grid using a volume-averaged scheme with no higher-order weighting.

Attributes Documentation

ax0

First axis of the grid.

Only valid for uniform grids.

ax1

Second axis of the grid.

Only valid for uniform grids.

ax2

Third axis of the grid.

Only valid for uniform grids.

dax0

Grid step size along axis ax0.

Only valid for uniform grids.

dax1

Grid step size along axis ax1.

Only valid for uniform grids.

dax2

Grid step size along axis ax2.

Only valid for uniform grids.

grid

A single grid of vertex positions of shape (N0, N1, N2, 3).

Only defined for grids for which the unit property is defined.

grid_resolution

A scalar estimate of the grid resolution.

For uniform grids, this is the minima of [dax0, dax1, dax2].

For non-uniform grids, it is the closest spacing between any two points.

grids

Three grids of vertex positions (in each coordinate), each having shape (N0, N1, N2).

interpolator

A nearest-neighbor interpolator that returns the nearest grid index to a position.

is_uniform

A boolean value reflecting whether or not the grid points are uniformly spaced.

pts0

Array of positions in dimension 1.

pts1

Array of positions in dimension 2.

pts2

Array of positions in dimension 3.

quantities

A list of the keys corresponding to the quantities currently defined on the grid.

recognized_quantities

A dictionary of standard key names representing particular physical quantities. Using these keys allows these quantities to be recognized automatically by other PlasmaPy functions. Each entry contains a tuple containing a description and the unit associated with the quantity.

shape

Shape of the grid

si_scale_factors

3-element list containing unitless scale factors for converting the corresponding axis from its stored units to SI.

unit

The unit for the entire grid. Only valid if all dimensions of the grid have the same units.

Raises

ValueError – If all grid dimensions do not have identical units.

unit0

Unit of dimension 1.

unit1

Unit of dimension 2.

unit2

Unit of dimension 3.

units

A list of the units of each dimension.

Methods Documentation

Adds a quantity to the dataset as a new DataArray.

Parameters
• key – The key will be used as the dataset key, while the array holds the quantity.

• arguments (array pairs as keyword) – The key will be used as the dataset key, while the array holds the quantity.

interpolate_indices(pos: )

Interpolate the nearest grid indices to a position using a nearest-neighbor interpolator.

Parameters

pos (ndarray or Quantity array, shape (n,3)) – An array of positions in space, where the second dimension corresponds to the three dimensions of the grid. If a ndarray is provided, units will be assumed to match those of the grid.

Returns

i – An array of indices corresponding to the positions such that i[n,:] = ix,iy,iz such that grid[ix,iy,iz,:]pos[n,:]

Return type

ndarray, shape (n,3)

nearest_neighbor_interpolator(pos: , *args, persistent=False)

Interpolate values on the grid using a nearest-neighbor scheme with no higher-order weighting.

Parameters
• pos (ndarray or Quantity array, shape (n,3)) – An array of positions in space, where the second dimension corresponds to the three dimensions of the grid. If an ndarray is provided, units will be assumed to match those of the grid.

• *args (str) – Strings that correspond to DataArrays in the dataset

• persistent (bool) – If True, the interpolator will assume the grid and its contents have not changed since the last interpolation. This substantially speeds up the interpolation when many interpolations are performed on the same grid in a loop. persistent overrides to False if the arguments list has changed since the last call.

on_grid(pos)

Given a list of positions, determines which are in the region bounded by the grid points.

For non-uniform grids, “on grid” is defined as being bounded by grid points in all axes.

Parameters

pos (ndarray or Quantity array, shape (n,3)) – An array of positions in space, where the second dimension corresponds to the three dimensions of the grid.

require_quantities(req_quantities, replace_with_zeros=False)

Check to make sure that a list of required quantities are present. Optionally, can create missing quantities and fill them with an array of zeros.

Parameters
• req_quantities (list of str) – A list of quantity keys that are required.

• replace_with_zeros (bool, optional) – If true, missing quantities will be replaced with an array of zeros. If false, an exception will be raised instead. The default is False.

Raises
vector_intersects(p1, p2)

True if the vector from p1 to p2 intersects the grid, and False otherwise.

This is a standard ray-box intersection algorithm.

volume_averaged_interpolator(pos: , *args, persistent=False)

Interpolate values on the grid using a volume-averaged scheme with no higher-order weighting.

Parameters
• pos (ndarray or Quantity array, shape (n,3)) – An array of positions in space, where the second dimension corresponds to the three dimensions of the grid. If a ndarray is provided, units will be assumed to match those of the grid.

• *args (str) – Strings that correspond to DataArrays in the dataset

• persistent (bool) – If True, the interpolator will assume the grid and its contents have not changed since the last interpolation. This substantially speeds up the interpolation when many interpolations are performed on the same grid in a loop. persistent overrides to False if the arguments list has changed since the last call.

Notes

This interpolator approximates the value of a quantity at a given interpolation point using a weighted sum of the values at the eight grid vertices that surround the point. The weighting factors are calculated by defining a volume $$dx \times dy \times dz$$ (where $$dx$$, $$dy$$, and $$dz$$ are the grid spacings in each direction) around each grid vertex and around the interpolation point. The contribution of each grid vertex is then weighted by the fraction of the volume surrounding the interpolation point that overlaps the volume surrounding that vertex. This effectively introduces a linear interpolation between grid vertices.

This implementation of this algorithm assumes that the grid is uniformly spaced and Cartesian.