"""
Defines the AbstractGrid class and child classes.
"""
from collections.abc import Sequence
__all__ = [
"AbstractGrid",
"CartesianGrid",
"NonUniformCartesianGrid",
]
import contextlib
import warnings
from abc import ABC, abstractmethod
from collections import namedtuple
from functools import cached_property
from typing import Union
import astropy.units as u
import numpy as np
import pandas as pd
import scipy.interpolate as interp
import xarray as xr
from scipy.spatial import distance
from plasmapy.utils.decorators.helpers import modify_docstring
def _detect_is_uniform_grid(pts0, pts1, pts2, tol: float = 1e-6):
r"""
Determine whether a grid is uniform (uniformly spaced) by computing the
variance of the grid gradients.
"""
variance = np.zeros([3])
dx = np.gradient(pts0, axis=0)
variance[0] = np.std(dx) / np.mean(dx)
dy = np.gradient(pts1, axis=1)
variance[1] = np.std(dy) / np.mean(dy)
dz = np.gradient(pts2, axis=2)
variance[2] = np.std(dz) / np.mean(dz)
return np.allclose(variance, 0.0, atol=tol)
[docs]
class AbstractGrid(ABC):
r"""
Abstract grid represents a 3D grid of positions. The grid is stored
as an `~numpy.ndarray`, while the units associated with each
dimension are stored separately.
There are two preferred methods to creating a grid object:
1. Initializing the grid by providing three 3D
`~astropy.units.Quantity` arrays of positions along each axis
(``xpoints``, ``ypoints``, ``zpoints``)
.. code-block:: python
AbstractGrid(xpoints, ypoints, zpoints)
2. A new grid can also be created using a syntax similar to
`numpy.linspace` by providing two three-element
`~astropy.units.Quantity` arrays of start and stop values and
setting the ``num`` keyword to the number of points along each axis.
.. code-block:: python
AbstractGrid(
start=[x0, y0, z0],
stop=[x1, y1, z1],
num=[Nx, Ny, Nz],
**kwargs,
)
In this case, any additional keyword arguments ``**kwargs`` provided
will be passed directly to `~numpy.linspace`.
"""
def __init__(self, *seeds: Sequence[int], num: int = 100, **kwargs) -> None:
# Initialize some variables
self._interpolator = None
self._is_uniform = None
# If three inputs are given, assume it's a user-provided grid
if len(seeds) == 3:
self._load_grid(seeds[0], seeds[1], seeds[2])
# If two inputs are given, assume they are start and stop arrays
# to create a new grid
# kwargs are passed to np.linspace in _make_grid()
elif len(seeds) == 2:
self._make_grid(seeds[0], seeds[1], num=num, **kwargs)
else:
raise TypeError(
f"{self.__class__.__name__} takes 2 or 3 "
f"positional arguments but {len(seeds)} were given"
)
def _validate(self) -> bool:
r"""
Checks to make sure that the grid parameters are
consistent with the coordinate system and units selected.
"""
return True
# A named tuple describing a key recognized by PlasmaPy to correspond to
# a particular physical quantity
RecognizedQuantity = namedtuple(
"RecognizedQuantities", ["key", "description", "unit"]
)
# These standard keys are used to refer to certain
# physical quantities. This dictionary also provides the expected unit.
_recognized_quantities_list = [
RecognizedQuantity("x", "x spatial position", u.m),
RecognizedQuantity("y", "y spatial position", u.m),
RecognizedQuantity("z", "z spatial position", u.m),
RecognizedQuantity("rho", "Mass density", u.kg / u.m**3),
RecognizedQuantity("E_x", "Electric field (x component)", u.V / u.m),
RecognizedQuantity("E_y", "Electric field (y component)", u.V / u.m),
RecognizedQuantity("E_z", "Electric field (z component)", u.V / u.m),
RecognizedQuantity("B_x", "Magnetic field (x component)", u.T),
RecognizedQuantity("B_y", "Magnetic field (y component)", u.T),
RecognizedQuantity("B_z", "Magnetic field (z component)", u.T),
RecognizedQuantity("phi", "Electric Scalar Potential", u.V),
]
# Create a dict of recognized quantities for fast access by key
_recognized_quantities = {}
for _rq in _recognized_quantities_list:
_recognized_quantities[_rq.key] = _rq
@property
def recognized_quantities(self):
r"""
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.
"""
return self._recognized_quantities
[docs]
def require_quantities(self, req_quantities, replace_with_zeros: bool = False):
r"""
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
------
KeyError
If ``replace_with_zeros`` is `False` and a required quantity
is missing.
KeyError
If ``replace_with_zeros`` is `True` but the
`~astropy.units.Quantity` is not in the list of recognized
quantities. In this case the units for the quantity are unknown,
so an array of zeros cannot be constructed.
"""
for rq in req_quantities:
# Error check that grid contains E and B variables required
if rq not in self.quantities:
# If missing, warn user and then replace with an array of zeros
if not replace_with_zeros:
raise KeyError(
f"{rq} is not specified for the provided "
"grid but is required."
)
elif rq not in self.recognized_quantities:
raise KeyError(
f"{rq} is not a recognized key, and "
"so cannot be automatically assumed "
"to be zero."
)
warnings.warn(
f"{rq} is not specified for the provided grid."
"This quantity will be assumed to be zero.",
RuntimeWarning,
)
unit = self.recognized_quantities[rq].unit
arg = {rq: np.zeros(self.shape) * unit}
self.add_quantities(**arg)
# *************************************************************************
# Fundamental properties of the grid
# *************************************************************************
def __repr__(self) -> str:
line_sep = "-----------------------------\n"
shape = list(self.shape)
coords = list(self.ds.coords.keys())
ax_units = self.units
ax_dtypes = [self.ds[i].dtype for i in coords]
coord_lbls = [f"{i}: {j}" for i, j in zip(coords, shape)]
s = f"*** Grid Summary ***\n{type(self)}\n"
s += f"Dimensions: ({', '.join(coord_lbls)})\n"
if self.is_uniform:
s += (
"Uniformly Spaced: (dax0, dax1, dax2) = "
f"({self.dax0:.3f}, {self.dax1:.3f}, {self.dax2:.3f})\n"
)
else:
s += "Non-Uniform Spacing\n"
s += line_sep + "Coordinates:\n"
for i in range(len(self.shape)):
s += f"\t-> {coords[i]} ({ax_units[i]}) {ax_dtypes[i]} ({shape[i]},)\n"
keys = self.quantities
rkeys = [k for k in keys if k in list(self.recognized_quantities.keys())]
nrkeys = [k for k in keys if k not in list(self.recognized_quantities.keys())]
s += line_sep + "Recognized Quantities:\n"
if not rkeys:
s += "-None-\n"
else:
for key in rkeys:
unit = self.ds[key].attrs["unit"]
dtype = self.ds[key].dtype
shape = self.ds[key].shape
s += f"\t-> {key} ({unit}) {dtype} {shape} \n"
s += line_sep + "Unrecognized Quantities:\n"
if not nrkeys:
s += "-None-\n"
else:
for key in nrkeys:
unit = self.ds[key].attrs["unit"]
dtype = self.ds[key].dtype
shape = self.ds[key].shape
s += f"\t-> {key} ({unit}) {dtype} {shape} \n"
return s
def __getitem__(self, key):
"""
Given a key, return the corresponding array as a `~astropy.units.Quantity`.
Returning with ``copy=False`` means that the array returned is a direct
reference to the underlying DataArray, so changes made will be reflected
in the underlying DataArray.
"""
return u.Quantity(self.ds[key].data, self.ds[key].attrs["unit"], copy=False)
@property
def is_uniform(self) -> bool:
"""
A boolean value reflecting whether or not the grid points are
uniformly spaced.
"""
if self._is_uniform is None:
raise ValueError(
"The `is_uniform` attribute is not accessible "
"before a grid has been loaded."
)
return self._is_uniform
@property
def shape(self):
r"""Shape of the grid."""
if self.is_uniform:
return (self.ax0.size, self.ax1.size, self.ax2.size)
return self.ds.coords["ax0"].shape
@property
def grids(self):
r"""
Three grids of vertex positions (in each coordinate), each having
shape (N0, N1, N2).
"""
if not self.is_uniform:
return (
self.ds["ax0"].data * self.unit0,
self.ds["ax1"].data * self.unit1,
self.ds["ax2"].data * self.unit2,
)
pts0, pts1, pts2 = np.meshgrid(self.ax0, self.ax1, self.ax2, indexing="ij")
return pts0, pts1, pts2
@property
def grid(self):
r"""
A single grid of vertex positions of shape (N0, N1, N2, 3).
Only defined for grids for which the ``unit`` property is defined.
"""
pts0, pts1, pts2 = self.grids
if self.is_uniform:
n0, n1, n2 = pts0.shape
grid = np.zeros([n0, n1, n2, 3]) * self.unit
else:
n = pts0.size
grid = np.zeros([n, 3]) * self.unit
grid[..., 0] = pts0
grid[..., 1] = pts1
grid[..., 2] = pts2
return grid
@property
def pts0(self):
r"""Array of positions in dimension 1."""
return self.grids[0]
@property
def pts1(self):
r"""Array of positions in dimension 2."""
return self.grids[1]
@property
def pts2(self):
r"""Array of positions in dimension 3."""
return self.grids[2]
@property
def units(self) -> list:
r"""A `list` of the units of each dimension."""
return self.ds.attrs["axis_units"]
@property
def unit0(self):
r"""Unit of dimension 1."""
return self.units[0]
@property
def unit1(self):
r"""Unit of dimension 2."""
return self.units[1]
@property
def unit2(self):
r"""Unit of dimension 3."""
return self.units[2]
@property
def unit(self):
r"""
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.
"""
if self.units[0] == self.units[1] == self.units[2]:
return self.units[0]
else:
raise ValueError(
f"Array dimensions do not all have the same units: {self.units}"
)
# *************************************************************************
# 1D axes and step sizes (valid only for uniform grids)
# *************************************************************************
@property
def si_scale_factors(self) -> list[float]:
"""
3-element list containing unitless scale factors for converting
the corresponding axis from its stored units to SI.
"""
return self._si_factors
def _get_ax(self, *, axis: int, si: bool = False):
"""
Helper function for retrieving axis values.
Parameters
----------
axis: int
Axis index for axis of interest (e.g. ``0`` for :attr:`ax0`).
si: bool
(Default: `False`) If `True` then convert the axis values to
their SI equivalent.
Returns
-------
~numpy.ndarray or `~astropy.units.Quantity`
If ``si==True`` then return a unitless `~numpy.ndarray`.
If ``si==False`` then return a `~astropy.units.Quantity`
array with the original units.
Raises
------
ValueError
If the grid is not uniform.
"""
ax_name = f"ax{axis}"
if not self.is_uniform:
raise ValueError(
"The axis properties are only valid on uniformly spaced grids."
)
vals = self.ds.coords[ax_name].to_numpy()
return vals * self.si_scale_factors[axis] if si else vals * self.units[axis]
def _get_dax(self, *, axis: int, si: bool = False):
"""
Helper function for calculating grid spacing.
See Also
--------
plasmapy.plasma.grids.AbstractGrid._get_ax
"""
ax = self._get_ax(axis=axis, si=si)
return np.mean(np.gradient(ax))
@property
def _ax0_si(self):
"""
The :attr:`ax0` axis without units, but scaled such that its values
correspond to SI values.
Only valid for uniform grids.
"""
return self._get_ax(axis=0, si=True)
@property
def ax0(self):
r"""
First axis of the grid.
Only valid for uniform grids.
"""
return self._get_ax(axis=0)
@property
def _ax1_si(self):
"""
The :attr:`ax1` axis without units, but scaled such that its values
correspond to SI values.
Only valid for uniform grids.
"""
return self._get_ax(axis=1, si=True)
@property
def ax1(self):
r"""
Second axis of the grid.
Only valid for uniform grids.
"""
return self._get_ax(axis=1)
@property
def _ax2_si(self):
"""
The :attr:`ax2` axis without units, but scaled such that its values
correspond to SI values.
Only valid for uniform grids.
"""
return self._get_ax(axis=2, si=True)
@property
def ax2(self):
r"""
Third axis of the grid.
Only valid for uniform grids.
"""
return self._get_ax(axis=2)
@property
def _dax0_si(self):
"""
Grid step size along axis :attr:`ax0` without units and scaled such
that its values correspond to SI values.
Only valid for uniform grids.
"""
return self._get_dax(axis=0, si=True)
@property
def dax0(self):
r"""
Grid step size along axis :attr:`ax0`.
Only valid for uniform grids.
"""
return self._get_dax(axis=0)
@property
def _dax1_si(self):
"""
Grid step size along axis :attr:`ax1` without units and scaled such
that its values correspond to SI values.
Only valid for uniform grids.
"""
return self._get_dax(axis=1, si=True)
@property
def dax1(self):
r"""
Grid step size along axis :attr:`ax1`.
Only valid for uniform grids.
"""
return self._get_dax(axis=1)
@property
def _dax2_si(self):
"""
Grid step size along axis :attr:`ax2` without units and scaled such
that its values correspond to SI values.
Only valid for uniform grids.
"""
return self._get_dax(axis=2, si=True)
@property
def dax2(self):
r"""
Grid step size along axis :attr:`ax2`.
Only valid for uniform grids.
"""
return self._get_dax(axis=2)
# *************************************************************************
# Loading and creating grids
# *************************************************************************
def _load_grid(
self,
pts0: u.Quantity,
pts1: u.Quantity,
pts2: u.Quantity,
):
r"""
Initialize the grid object from a user-supplied grid.
Parameters
----------
grid{0,1,2} : `~astropy.units.Quantity` array, shape (n0, n1, n2)
Grids of coordinate positions.
**kwargs : `~astropy.units.Quantity` array, shape (n0, n1, n2)
Quantities defined on the grid.
"""
# Validate input
if pts0.shape != pts1.shape or pts0.shape != pts2.shape:
raise ValueError(
"Provided arrays of grid points are of unequal "
f"shape: pts0 = {pts0.shape}, "
f"pts1 = {pts1.shape}, "
f"pts2 = {pts2.shape}."
)
self._is_uniform = _detect_is_uniform_grid(pts0, pts1, pts2)
# Create dataset
self.ds = xr.Dataset()
self.ds.attrs["axis_units"] = [pts0.unit, pts1.unit, pts2.unit]
# Store the conversion factors for each axis to SI
self._si_factors = [
pts0.unit.si.scale,
pts1.unit.si.scale,
pts2.unit.si.scale,
]
if self.is_uniform:
self.ds.coords["ax0"] = pts0[:, 0, 0]
self.ds.coords["ax1"] = pts1[0, :, 0]
self.ds.coords["ax2"] = pts2[0, 0, :]
else:
mdx = pd.MultiIndex.from_arrays(
[pts0.flatten(), pts1.flatten(), pts2.flatten()],
names=["ax0", "ax1", "ax2"],
)
self.ds.coords["ax"] = mdx
# Check to make sure that the object created satisfies any
# requirements: eg. units correspond to the coordinate system
self._validate()
[docs]
def add_quantities(self, **kwargs: u.Quantity) -> None:
r"""
Adds a quantity to the dataset as a new DataArray.
Parameters
----------
**kwargs : key, array pairs
The key will be used as the dataset key, while the array holds the
quantity.
"""
for key, quantity in kwargs.items():
# Check key against a list of "known" keys with pre-defined
# meanings (eg. E_x, n_e) and raise a warning if a "non-standard"
# key is being used so the user is aware.
if key in self.recognized_quantities:
try:
quantity.to(self.recognized_quantities[key].unit)
except u.UnitConversionError as ex:
raise ValueError(
f"Units provided for {key} ({quantity.unit}) "
"are not compatible with the correct units "
f"for that recognized key ({self.recognized_quantities[key]})."
) from ex
else:
warnings.warn(
f"Warning: {key} is not recognized quantity key", stacklevel=2
)
if self.is_uniform:
dims = ["ax0", "ax1", "ax2"]
coords = {
"ax0": self.ds.coords["ax0"],
"ax1": self.ds.coords["ax1"],
"ax2": self.ds.coords["ax2"],
}
# If grid is non-uniform, flatten quantity
else:
quantity = quantity.flatten() # noqa: PLW2901
dims = ["ax"]
coords = {"ax": self.ds.coords["ax"]}
if quantity.shape != self.shape:
raise ValueError(
f"Shape of quantity '{key}' {quantity.shape} "
f"does not match the grid shape {self.shape}."
)
data = xr.DataArray(
quantity, dims=dims, coords=coords, attrs={"unit": quantity.unit}
)
self.ds[key] = data
@property
def quantities(self):
r"""
A list of the keys corresponding to the quantities currently
defined on the grid.
"""
return list(self.ds.data_vars)
def _make_grid( # noqa: C901, PLR0912
self,
start: Union[float, u.Quantity],
stop: Union[float, u.Quantity],
num: int = 100,
units=None,
**kwargs,
):
r"""
Creates a grid based on ``start``, ``stop``, and ``num`` values
in a manner that mirrors the interface of the `numpy.linspace`
function.
Parameters
----------
start : number (`~astropy.units.Quantity`) or an array, list, or
tuple of three of the same.
Starting values for each dimension. If one value is given,
the same value will be used for all three dimensions.
stop : number (`~astropy.units..Quantity`) or an array, list, or
tuple of three of the same.
End values for each dimension. If one value is given,
the same value will be used for all three dimensions.
num : `int` or `list` or `tuple` of three `int` objects, optional
The number of points in each dimension. If a single integer is
given, the same number of points will be used in each dimension.
The default is 100.
**kwargs : Additional arguments
Any additional arguments will be passed directly to
`numpy.linspace`.
"""
# Store variables in dict for validation
var = {"stop": stop, "start": start, "num": num}
# Ensure that start and stop end up as a list of three u.Quantity objs
# and num a list of three integers
# TODO: python3.10: simplify using structural pattern matching
for k in ("start", "stop"):
# Convert tuple to list
if isinstance(var[k], tuple):
var[k] = list(var[k])
if isinstance(var[k], list):
if len(var[k]) == 1:
var[k] = var[k] * 3
# Make sure it's a list of quantities
if not all(isinstance(v, u.Quantity) for v in var[k]):
raise TypeError(
f"The argument `{k}` must be an "
"`astropy.units.Quantity` or a list of same, "
f"but a {type(var[k])} was given."
)
elif isinstance(var[k], u.Quantity):
# Extend to 3 elements if only one is given
# Case of >1 but != 3 is handled later
var[k] = [var[k]] * 3 if var[k].size == 1 else list(var[k])
else:
raise TypeError(
f"The argument `{k}` must be an "
"`astropy.units.Quantity` or a list of same, "
f"but a {type(var[k])} was given."
)
# Convert tuple to list
if isinstance(var["num"], tuple):
var["num"] = list(var["num"])
if isinstance(var["num"], list):
if len(var["num"]) == 1:
var["num"] = var["num"] * 3
elif isinstance(var["num"], int):
var["num"] = [var["num"]] * 3
else:
raise TypeError(
f"The argument `num` must be an int or list of "
f"same, but a {type(var[k])} was given."
)
# Check to make sure all lists now contain three values
# (throws exception if user supplies a list of two, say)
for k in var:
if len(var[k]) != 3:
raise TypeError(
f"{k} must be either a single value or a "
"list of three values, but "
f"({len(var[k])} values were given)."
)
# Take variables back out of dict
start = var["start"]
stop = var["stop"]
num = var["num"]
# Extract units from input arrays (if they are there), then
# remove the units from those arrays
units = []
for i in range(3):
# Determine unit for dimension
unit = start[i].unit
units.append(unit)
# Attempt to convert stop unit to start unit
try:
stop[i] = stop[i].to(unit)
except u.UnitConversionError as ex:
raise ValueError(
f"Units of {stop[i]} and {unit} are not compatible"
) from ex
# strip units
stop[i] = stop[i].value
start[i] = start[i].value
# Create coordinate mesh
pts0, pts1, pts2 = self._make_mesh(start, stop, num, **kwargs)
# Load into the dataset using the _load_grid function
self._load_grid(
pts0 * units[0],
pts1 * units[1],
pts2 * units[2],
)
def _make_mesh(self, start, stop, num: int, **kwargs):
r"""
Creates mesh as part of _make_grid(). Separated into its own function
so it can be re-implemented to make non-uniformly spaced meshes.
"""
# Construct the axis arrays
ax0 = np.linspace(start[0], stop[0], num=num[0], **kwargs)
ax1 = np.linspace(start[1], stop[1], num=num[1], **kwargs)
ax2 = np.linspace(start[2], stop[2], num=num[2], **kwargs)
# Construct the coordinate arrays
pts0, pts1, pts2 = np.meshgrid(ax0, ax1, ax2, indexing="ij")
return pts0, pts1, pts2
# *************************************************************************
# Methods
# *************************************************************************
[docs]
def on_grid(self, pos):
r"""
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 : `~numpy.ndarray` or `~astropy.units.Quantity` array, shape (n,3)
An array of positions in space, where the second dimension
corresponds to the three dimensions of the grid.
"""
if hasattr(pos, "unit"):
pos = pos.si.value
# Find the bounds
if self.is_uniform:
ax0_min, ax0_max = np.min(self.ax0.si.value), np.max(self.ax0.si.value)
ax1_min, ax1_max = np.min(self.ax1.si.value), np.max(self.ax1.si.value)
ax2_min, ax2_max = np.min(self.ax2.si.value), np.max(self.ax2.si.value)
else:
pts0, pts1, pts2 = self.grids
ax0_min, ax0_max = np.min(self.pts0).si.value, np.max(self.pts0).si.value
ax1_min, ax1_max = np.min(self.pts1).si.value, np.max(self.pts1).si.value
ax2_min, ax2_max = np.min(self.pts2).si.value, np.max(self.pts2).si.value
# Check each point elementwise against the bounds
on_grid = (
np.greater(ax0_min, pos[:, 0]).astype(np.int8)
+ np.less(ax0_max, pos[:, 0]).astype(np.int8)
+ np.greater(ax1_min, pos[:, 1]).astype(np.int8)
+ np.less(ax1_max, pos[:, 1]).astype(np.int8)
+ np.greater(ax2_min, pos[:, 2]).astype(np.int8)
+ np.less(ax2_max, pos[:, 2]).astype(np.int8)
)
return np.where(on_grid == 0, True, False) # noqa: FBT003
[docs]
@abstractmethod
def vector_intersects(self, p1, p2):
r"""
`True` if the vector from ``p1`` to ``p2`` intersects the grid,
and `False` otherwise.
The definition of 'intersects' is determined by the implementation
for each subclass.
"""
...
# *************************************************************************
# Interpolators
# *************************************************************************
# This property holds the list of quantity keys currently being interpolated
# It's used in the following cached properties
_interp_args = []
@cached_property
def _interp_quantities(self):
r"""Create a dimensionless array of quantities to be interpolated."""
nargs = len(self._interp_args)
# Load the arrays to be interpolated from and their units
if self.is_uniform:
nx, ny, nz = self.shape
_interp_quantities = np.zeros([nx, ny, nz, nargs])
else:
npoints = self.shape[0]
_interp_quantities = np.zeros([npoints, nargs])
for j, arg in enumerate(self._interp_args):
_interp_quantities[..., j] = self.ds[arg].to_numpy()
return _interp_quantities
@cached_property
def _interp_units(self):
r"""
Create a list of the units corresponding to the last dimension
in the `_interp_quantities` array.
"""
return [self.ds[arg].attrs["unit"] for arg in self._interp_args]
[docs]
@abstractmethod
def nearest_neighbor_interpolator(
self, pos: Union[np.ndarray, u.Quantity], *args, persistent: bool = False
):
r"""
Interpolate values on the grid using a nearest-neighbor scheme with
no higher-order weighting.
Parameters
----------
pos : `~numpy.ndarray` or `~astropy.units.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
`~numpy.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.
"""
...
def _persistent_interpolator_setup(self, pos, args, persistent):
r"""
Setup common to all persistent interpolators.
Parameters
----------
pos : `~numpy.ndarray` or `~astropy.units.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
`~numpy.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.
Returns
-------
pos: `~numpy.ndarray`
Position array with dimensions fixed, units converted to
standard and stripped.
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.
Raises
------
KeyError
A KeyError is raised if one of the args does not correspond
to a DataArray in the DataSet.
"""
# Condition pos
if isinstance(pos, u.Quantity):
pos = pos.to(u.m).value
elif self.unit != u.m:
pos *= self.unit.si.scale
# If a single point was given, add empty dimension
if pos.ndim == 1:
pos = np.reshape(pos, [1, 3])
# -- Validate args --
# must be np.ndarray or u.Quantity arrays of same shape as grid
for arg in args:
if arg not in self.quantities:
raise KeyError(
"Quantity arguments must correspond to "
"DataArrays in the DataSet. "
f"{arg} was not found. "
f"Existing keys are: {self.quantities}"
)
# If persistent, double check the arguments list hasn't changed
# If they have, run as non-persistent this time
if persistent and args != self._interp_args:
persistent = False
# Update _interp_args variable
self._interp_args = args
# If not persistent, clear the cached properties so they are re-created
# when called below
if not persistent:
with contextlib.suppress(AttributeError):
del self._interp_quantities
with contextlib.suppress(AttributeError):
del self._interp_units
return pos, args, persistent
def _fast_nearest_neighbor_interpolate(pos, ax):
"""
Find the indices in the axis `ax` that are closest to the
values in the array `pos`.
Assumes the axis `ax` is sorted in ascending order.
"""
# Find the index where each position would be inserted into the axis.
# This is equivalent to a nearest neighbor interpolation but always
# rounding to the next highest axis point.
indices = np.searchsorted(ax, pos)
# searchsorted can return an out-of-bound index on the top end, so replace
# that point with the closest in bound index
indices = np.where(indices == ax.size, ax.size - 1, indices)
# For any points that are closer to the point below than the point above,
# correct the index
return np.where(
np.abs(ax[indices] - pos) > np.abs(ax[indices - 1] - pos), indices - 1, indices
)
[docs]
class CartesianGrid(AbstractGrid):
r"""A uniformly spaced Cartesian grid."""
def _validate(self):
# Check that all units are lengths
for i in range(3):
try:
self.units[i].to(u.m)
except u.UnitConversionError as ex:
raise ValueError(
"Units of grid are not valid for a Cartesian "
f"grid: {self.units}."
) from ex
@property
def grid_resolution(self):
r"""
A scalar estimate of the grid resolution, calculated as the
the minima of [dax0, dax1, dax2].
"""
return min(self.dax0, self.dax1, self.dax2)
[docs]
def vector_intersects(self, p1, p2):
r"""
`True` if the vector from ``p1`` to ``p2`` intersects the grid,
and `False` otherwise.
This is a standard ray-box intersection algorithm.
"""
p1, p2 = p1.si.value, p2.si.value
# Calculate the minimum and maximum of each
Ax, Bx = np.min(self.pts0.si.value), np.max(self.pts0.si.value)
Ay, By = np.min(self.pts1.si.value), np.max(self.pts1.si.value)
Az, Bz = np.min(self.pts2.si.value), np.max(self.pts2.si.value)
A = np.array([Ax, Ay, Az])
B = np.array([Bx, By, Bz])
# Calculate the equation of the line from p1 to p2 such that
# r = p1 + t*D
D = np.abs(p2 - p1)
# Calculate the intersection points. These operations are just vectorized
# for convenience. Ignore div-by-zero: outputting infty's here is fine.
with np.errstate(divide="ignore"):
Tmin = (A - p1) / D
Tmax = (B - p1) / D
Tmin = np.max(Tmin)
Tmax = np.min(Tmax)
return Tmin < Tmax
[docs]
@modify_docstring(prepend=AbstractGrid.nearest_neighbor_interpolator.__doc__)
def nearest_neighbor_interpolator(
self, pos: Union[np.ndarray, u.Quantity], *args, persistent: bool = False
):
r""" """ # noqa: D419
# Shared setup
pos, args, persistent = self._persistent_interpolator_setup(
pos, args, persistent
)
ax0, ax1, ax2 = self._ax0_si, self._ax1_si, self._ax2_si
# Find particles that are off the grid
mask_particle_off = (
(pos[:, 0] < ax0.min())
| (pos[:, 0] > ax0.max())
| (pos[:, 1] < ax1.min())
| (pos[:, 1] > ax1.max())
| (pos[:, 2] < ax2.min())
| (pos[:, 2] > ax2.max())
)
# Interpolate nearest index to each point along each axis
i0 = _fast_nearest_neighbor_interpolate(pos[:, 0], ax0)
i1 = _fast_nearest_neighbor_interpolate(pos[:, 1], ax1)
i2 = _fast_nearest_neighbor_interpolate(pos[:, 2], ax2)
vals = self._interp_quantities[i0, i1, i2, :]
# Replace values of off-grid particles with NaN
vals[mask_particle_off, :] = np.nan
# Split output array into arrays with units
# Apply units to output arrays
output = [
vals[..., index] * self._interp_units[index] for index, _ in enumerate(args)
]
return output[0] if len(output) == 1 else tuple(output)
[docs]
def volume_averaged_interpolator(
self, pos: Union[np.ndarray, u.Quantity], *args, persistent: bool = False
):
r"""
Interpolate values on the grid using a volume-averaged scheme with
no higher-order weighting.
Parameters
----------
pos : `~numpy.ndarray` or `~astropy.units.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
`~numpy.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 :math:`dx \\times dy \\times dz`
(where :math:`dx`, :math:`dy`, and :math:`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.
"""
# Shared setup
pos, args, persistent = self._persistent_interpolator_setup(
pos, args, persistent
)
nparticles = pos.shape[0]
nargs = len(args)
# Load grid attributes (so this isn't repeated)
ax0, ax1, ax2 = self._ax0_si, self._ax1_si, self._ax2_si
dx, dy, dz = self._dax0_si, self._dax1_si, self._dax2_si
n0, n1, n2 = self.shape
# find cell nearest to each position
nearest_neighbor_index = np.zeros((nparticles, 3), dtype=np.int32)
nearest_neighbor_index[..., 0] = _fast_nearest_neighbor_interpolate(
pos[:, 0], ax0
)
nearest_neighbor_index[..., 1] = _fast_nearest_neighbor_interpolate(
pos[:, 1], ax1
)
nearest_neighbor_index[..., 2] = _fast_nearest_neighbor_interpolate(
pos[:, 2], ax2
)
# Create a mask for positions that are off the grid. The values at
# these points will be set to zero later.
mask_particle_off = (
(pos[:, 0] < ax0.min())
| (pos[:, 0] > ax0.max())
| (pos[:, 1] < ax1.min())
| (pos[:, 1] > ax1.max())
| (pos[:, 2] < ax2.min())
| (pos[:, 2] > ax2.max())
)
# Get the physical positions for the nearest neighbor cell
# for the each particle
xpos = ax0[nearest_neighbor_index[:, 0]]
ypos = ax1[nearest_neighbor_index[:, 1]]
zpos = ax2[nearest_neighbor_index[:, 2]]
nearest_neighbor_pos = np.array([xpos, ypos, zpos]).swapaxes(0, 1)
# Determine the indices for the grid cells bounding the particle
# - The imaginary cell centered on the particle will overlap with
# 1 to 8 surrounding cells
# - typically this is 8 but will be 4, 2, or 1 when the particle is
# near the boundary of the grid
bounding_cell_indices = np.empty((nparticles, 8, 3), dtype=np.int32)
lower_indices = np.where(
pos >= nearest_neighbor_pos,
nearest_neighbor_index,
nearest_neighbor_index - 1,
)
# populate x indices
bounding_cell_indices[:, 0:4, 0] = np.tile(
lower_indices[:, 0], (4, 1)
).swapaxes(0, 1)
bounding_cell_indices[:, 4:, 0] = bounding_cell_indices[:, 0:4, 0] + 1
# populate y indices
bounding_cell_indices[:, [0, 1, 4, 5], 1] = np.tile(
lower_indices[:, 1], (4, 1)
).swapaxes(0, 1)
bounding_cell_indices[:, [2, 3, 6, 7], 1] = (
bounding_cell_indices[:, [0, 1, 4, 5], 1] + 1
)
# populate z indices
bounding_cell_indices[:, 0::2, 2] = np.tile(
lower_indices[:, 2], (4, 1)
).swapaxes(0, 1)
bounding_cell_indices[:, 1::2, 2] = bounding_cell_indices[:, 0::2, 2] + 1
# Create a mask for cells whose locations would be off the grid,
# which occurs when the interpolation point is near the edge of the
# grid. These values will be weighted as zero later.
mask_cell_off = (
(bounding_cell_indices < 0).any(axis=2)
| (bounding_cell_indices[:, :, 0] >= n0)
| (bounding_cell_indices[:, :, 1] >= n1)
| (bounding_cell_indices[:, :, 2] >= n2)
)
# Zero any out of bounds indices so IndexError is not raised
# during indexing. This means an incorrect value will be retrieved
# but will not be used because of the zero weighting and the
# off the grid mask
bounding_cell_indices[mask_cell_off, :] = 0
# Calculate the volume of the overlap between the point volume
# and the volume of each of the surrounding vertices
lx = dx - np.abs(pos[:, None, 0] - ax0[bounding_cell_indices[..., 0]])
ly = dy - np.abs(pos[:, None, 1] - ax1[bounding_cell_indices[..., 1]])
lz = dz - np.abs(pos[:, None, 2] - ax2[bounding_cell_indices[..., 2]])
bounding_cell_weights = lx * ly * lz
# Set the weight for any off-grid vertices (cell or particle) to zero
bounding_cell_weights[mask_cell_off] = 0.0
bounding_cell_weights[mask_particle_off, ...] = 0.0
norms = np.sum(bounding_cell_weights, axis=1)
mask_norm_zero = norms == 0.0
bounding_cell_weights[~mask_norm_zero] = (
bounding_cell_weights[~mask_norm_zero, ...] / norms[~mask_norm_zero, None]
)
# Get the values of each of the interpolated quantities at each
# of the bounding vertices
vals = self._interp_quantities[
bounding_cell_indices[..., 0],
bounding_cell_indices[..., 1],
bounding_cell_indices[..., 2],
:,
]
# Construct a weighted average of the interpolated quantities
weighted_ave = np.sum(bounding_cell_weights[..., None] * vals, axis=1)
weighted_ave[mask_particle_off, :] = np.nan
# Split output array into arrays with units
# Apply units to output arrays
output = [
weighted_ave[..., arg] * self._interp_units[arg] for arg in range(nargs)
]
return output[0] if len(output) == 1 else tuple(output)