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Grids: Non-Uniform Grids

Some data cannot be easily represented on a grid of uniformly spaced vertices. It is still possible to create a grid object to represent such a dataset.

[1]:
%matplotlib inline

import astropy.units as u
import matplotlib.pyplot as plt
import numpy as np

from plasmapy.plasma import grids
[2]:
grid = grids.NonUniformCartesianGrid(
    np.array([-1, -1, -1]) * u.cm, np.array([1, 1, 1]) * u.cm, num=(50, 50, 50)
)

Currently, all non-uniform data is stored as an unordered 1D array of points. Therefore, although the dataset created above falls approximately on a Cartesian grid, its treatment is identical to a completely unordered set of points

[3]:
grid.shape
[3]:
(125000,)

Many of the properties defined for uniform grids are inaccessible for non-uniform grids. For example, it is not possible to pull out an axis. However, the following properties still apply

[4]:
print(f"Grid points: {grid.grid.shape}")
print(f"Units: {grid.units}")
Grid points: (125000, 3)
Units: [Unit("cm"), Unit("cm"), Unit("cm")]

Properties can be added in the same way as on uniform grids.

[5]:
Bx = np.random.rand(*grid.shape) * u.T
grid.add_quantities(B_x=Bx)
print(grid)
*** Grid Summary ***
<class 'plasmapy.plasma.grids.NonUniformCartesianGrid'>
Dimensions: (ax: 125000)
Non-Uniform Spacing
-----------------------------
Coordinates:
        -> ax (cm) object (125000,)
-----------------------------
Recognized Quantities:
        -> B_x (T) float64 (125000,)
-----------------------------
Unrecognized Quantities:
-None-

Methods

Many of the methods defined for uniform grids also work for non-uniform grids, however there is usually a substantial performance penalty in the non-uniform case.

For example, grid.on_grid behaves similarly. In this case, the boundaries of the grid are defined by the furthest point away from the origin in each direction.

[6]:
pos = np.array([[0.1, -0.3, 0], [3, 0, 0]]) * u.cm
print(grid.on_grid(pos))
[ True False]

The same definition is used to define the grid boundaries in grid.vector_intersects

[7]:
pt0 = np.array([3, 0, 0]) * u.cm
pt1 = np.array([-3, 0, 0]) * u.cm
pt2 = np.array([3, 10, 0]) * u.cm

print(f"Line from pt0 to pt1 intersects: {grid.vector_intersects(pt0, pt1)}")
print(f"Line from pt0 to pt2 intersects: {grid.vector_intersects(pt0, pt2)}")
Line from pt0 to pt1 intersects: True
Line from pt0 to pt2 intersects: False

Interpolating Quantities

Nearest-neighbor interpolation also works identically. However, volume-weighted interpolation is not implemented for non-uniform grids.

[8]:
pos = np.array([[0.1, -0.3, 0], [0.5, 0.25, 0.8]]) * u.cm
print(f"Pos shape: {pos.shape}")
print(f"Position 1: {pos[0,:]}")
print(f"Position 2: {pos[1,:]}")

Bx_vals = grid.nearest_neighbor_interpolator(pos, "B_x")
print(f"Bx at position 1: {Bx_vals[0]:.2f}")
Pos shape: (2, 3)
Position 1: [ 0.1 -0.3  0. ] cm
Position 2: [0.5  0.25 0.8 ] cm
Bx at position 1: 0.23 T
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