4.2.5 pde.grids.cartesian module
Cartesian grids of arbitrary dimension.
- class CartesianGrid(bounds, shape, periodic=False)[source]
Bases:
GridBased-dimensional Cartesian grid with uniform discretization for each axis
The grids can be thought of as a collection of n-dimensional boxes, called cells, of equal length in each dimension. The bounds then defined the total volume covered by these cells, while the cell coordinates give the location of the box centers. We index the boxes starting from 0 along each dimension. Consequently, the cell \(i-\frac12\) corresponds to the left edge of the covered interval and the index \(i+\frac12\) corresponds to the right edge, when the dimension is covered by d boxes.
In particular, the discretization along dimension \(k\) is defined as
\[\begin{split}x^{(k)}_i &= x^{(k)}_\mathrm{min} + \left(i + \frac12\right) \Delta x^{(k)} \quad \text{for} \quad i = 0, \ldots, N^{(k)} - 1 \\ \Delta x^{(k)} &= \frac{x^{(k)}_\mathrm{max} - x^{(k)}_\mathrm{min}}{N^{(k)}}\end{split}\]where \(N^{(k)}\) is the number of cells along this dimension. Consequently, cells have dimension \(\Delta x^{(k)}\) and cover the interval \([x^{(k)}_\mathrm{min}, x^{(k)}_\mathrm{max}]\).
- Parameters:
bounds (list of tuple) – Give the coordinate range for each axis. This should be a tuple of two number (lower and upper bound) for each axis. The length of bounds thus determines the grid dimension.
shape (list) – The number of support points for each axis. The length of shape needs to match the grid dimension.
periodic (bool or list) – Specifies which axes possess periodic boundary conditions. This is either a list of booleans defining periodicity for each individual axis or a single boolean value specifying the same periodicity for all axes.
- boundary_names: dict[str, tuple[int, bool]] = {'back': (2, False), 'bottom': (1, False), 'front': (2, True), 'left': (0, False), 'right': (0, True), 'top': (1, True)}
Names of boundaries to select them conveniently
- Type:
- property cell_volume_data
size associated with each cell
- difference_vector(p1, p2, *, coords='grid')[source]
return Cartesian vector(s) pointing from p1 to p2
In case of periodic boundary conditions, the shortest vector is returned.
- Parameters:
p1 (
ndarray) – First point(s)p2 (
ndarray) – Second point(s)coords (str) – The coordinate system in which the points are specified. Valid values are cartesian, cell, and grid; see
transform().
- Returns:
The difference vectors between the points with periodic boundary conditions applied.
- Return type:
- classmethod from_bounds(bounds, shape, periodic)[source]
- Parameters:
bounds (tuple) – Give the coordinate range for each axis. This should be a tuple of two number (lower and upper bound) for each axis. The length of bounds thus determines the grid dimension.
shape (tuple) – The number of support points for each axis. The length of shape needs to match the grid dimension.
periodic (bool or list) – Specifies which axes possess periodic boundary conditions. This is either a list of booleans defining periodicity for each individual axis or a single boolean value specifying the same periodicity for all axes.
- Returns:
representing the region chosen by bounds
- Return type:
- classmethod from_state(state)[source]
create a field from a stored state.
- Parameters:
state (dict) – The state from which the grid is reconstructed.
- Returns:
the grid re-created from the state data
- Return type:
- get_line_data(data, extract='auto')[source]
return a line cut through the given data
- Parameters:
data (
ndarray) – The values at the grid pointsextract (str) –
Determines which cut is done through the grid. Possible choices are (default is cut_0):
cut_#: return values along the axis specified by # and use the mid point along all other axes.
project_#: average values for all axes, except axis #.
Here, # can either be a zero-based index (from 0 to dim-1) or a letter denoting the axis.
- Returns:
A dictionary with information about the line cut, which is convenient for plotting.
- Return type:
- get_random_point(*, boundary_distance=0, coords='cartesian', rng=None)[source]
return a random point within the grid
- Parameters:
boundary_distance (float) – The minimal distance this point needs to have from all boundaries.
coords (str) – Determines the coordinate system in which the point is specified. Valid values are cartesian, cell, and grid; see
transform().rng (
Generator) – Random number generator (default:default_rng())
- Returns:
The coordinates of the point
- Return type:
- get_vector_data(data, **kwargs)[source]
return data to visualize vector field
- Parameters:
data (
ndarray) – The vectorial values at the grid points**kwargs – Arguments forwarded to
get_image_data().
- Returns:
A dictionary with information about the data convenient for plotting.
- Return type:
- iter_mirror_points(point, with_self=False, only_periodic=True)[source]
generates all mirror points corresponding to point
- plot(*args, title=None, filename=None, action='auto', ax_style=None, fig_style=None, ax=None, **kwargs)[source]
visualize the grid
- Parameters:
title (str) – Title of the plot. If omitted, the title might be chosen automatically.
filename (str, optional) – If given, the plot is written to the specified file.
action (str) – Decides what to do with the final figure. If the argument is set to show,
matplotlib.pyplot.show()will be called to show the plot. If the value is none, the figure will be created, but not necessarily shown. The value close closes the figure, after saving it to a file when filename is given. The default value auto implies that the plot is shown if it is not a nested plot call.ax_style (dict) – Dictionary with properties that will be changed on the axis after the plot has been drawn by calling
matplotlib.pyplot.setp(). A special item i this dictionary is use_offset, which is flag that can be used to control whether offset are shown along the axes of the plot.fig_style (dict) – Dictionary with properties that will be changed on the figure after the plot has been drawn by calling
matplotlib.pyplot.setp(). For instance, using fig_style={‘dpi’: 200} increases the resolution of the figure.ax (
matplotlib.axes.Axes) – Figure axes to be used for plotting. The special value “create” creates a new figure, while “reuse” attempts to reuse an existing figure, which is the default.**kwargs – Extra arguments are passed on the to the matplotlib plotting routines, e.g., to set the color of the lines
- class UnitGrid(shape, periodic=False)[source]
Bases:
CartesianGridd-dimensional Cartesian grid with unit discretization in all directions
The grids can be thought of as a collection of d-dimensional cells of unit length. The shape parameter determines how many boxes there are in each direction. The cells are enumerated starting with 0, so the last cell has index \(n-1\) if there are \(n\) cells along a dimension. A given cell \(i\) extends from coordinates \(i\) to \(i + 1\), so the midpoint is at \(i + \frac12\), which is the cell coordinate. Taken together, the cells covers the interval \([0, n]\) along this dimension.
- Parameters:
shape (list) – The number of support points for each axis. The dimension of the grid is given by len(shape).
periodic (bool or list) – Specifies which axes possess periodic boundary conditions. This is either a list of booleans defining periodicity for each individual axis or a single boolean value specifying the same periodicity for all axes.
- to_cartesian()[source]
convert unit grid to
CartesianGrid- Returns:
The equivalent cartesian grid
- Return type: