CartesianGrid
- class plasmapy.plasma.grids.CartesianGrid(*seeds, num=100, **kwargs)
Bases:
plasmapy.plasma.grids.AbstractGrid
A uniformly spaced Cartesian grid.
Attributes Summary
First axis of the grid.
Second axis of the grid.
Third axis of the grid.
Grid step size along axis
ax0
.Grid step size along axis
ax1
.Grid step size along axis
ax2
.A single grid of vertex positions of shape (N0, N1, N2, 3).
A scalar estimate of the grid resolution.
Three grids of vertex positions (in each coordinate), each having shape (N0, N1, N2).
A nearest-neighbor interpolator that returns the nearest grid index to a position.
A boolean value reflecting whether or not the grid points are uniformly spaced.
Array of positions in dimension 1.
Array of positions in dimension 2.
Array of positions in dimension 3.
A list of the keys corresponding to the quantities currently defined on the grid.
A dictionary of standard key names representing particular physical quantities.
Shape of the grid
3-element list containing unitless scale factors for converting the corresponding axis from its stored units to SI.
The unit for the entire grid.
Unit of dimension 1.
Unit of dimension 2.
Unit of dimension 3.
A
list
of the units of each dimension.Methods Summary
add_quantities
(**kwargs)Adds a quantity to the dataset as a new DataArray.
interpolate_indices
(pos)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 fromp1
top2
intersects the grid, andFalse
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.
- 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.
Methods Documentation
- add_quantities(**kwargs)
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: Union[numpy.ndarray, astropy.units.quantity.Quantity])
Interpolate the nearest grid indices to a position using a nearest-neighbor interpolator.
- Parameters
pos (
ndarray
orQuantity
array, shape (n,3)) – An array of positions in space, where the second dimension corresponds to the three dimensions of the grid. If andarray
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 thatgrid[ix,iy,iz,:]
∼pos[n,:]
- Return type
ndarray
, shape (n,3)
- nearest_neighbor_interpolator(pos: Union[numpy.ndarray, astropy.units.quantity.Quantity], *args, persistent=False)
Interpolate values on the grid using a nearest-neighbor scheme with no higher-order weighting.
- Parameters
pos (
ndarray
orQuantity
array, shape (n,3)) – An array of positions in space, where the second dimension corresponds to the three dimensions of the grid. If anndarray
is provided, units will be assumed to match those of the grid.*args (
str
) – Strings that correspond to DataArrays in the datasetpersistent (
bool
) – IfTrue
, 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 toFalse
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.
- 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
- Raises
- vector_intersects(p1, p2)
True
if the vector fromp1
top2
intersects the grid, andFalse
otherwise.This is a standard ray-box intersection algorithm.
- volume_averaged_interpolator(pos: Union[numpy.ndarray, astropy.units.quantity.Quantity], *args, persistent=False)
Interpolate values on the grid using a volume-averaged scheme with no higher-order weighting.
- Parameters
pos (
ndarray
orQuantity
array, shape (n,3)) – An array of positions in space, where the second dimension corresponds to the three dimensions of the grid. If andarray
is provided, units will be assumed to match those of the grid.*args (
str
) – Strings that correspond to DataArrays in the datasetpersistent (
bool
) – IfTrue
, 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 toFalse
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.