ShepardIDWInterpolator¶
- class photutils.utils.ShepardIDWInterpolator(coordinates, values, weights=None, leafsize=10)[source]¶
Bases:
object
Class to perform Inverse Distance Weighted (IDW) interpolation.
This interpolator uses a modified version of Shepard’s method (see the Notes section for details).
- Parameters:
- coordinatesfloat, 1D array_like, or NxM array_like
Coordinates of the known data points. In general, it is expected that these coordinates are in a form of a NxM-like array where N is the number of points and M is dimension of the coordinate space. When M=1 (1D space), then the
coordinates
parameter may be entered as a 1D array or, if only one data point is available,coordinates
can be a scalar number representing the 1D coordinate of the data point.Note
If the dimensionality of
coordinates
is larger than 2, e.g., if it is of the form N1 x N2 x N3 x … x Nn x M, then it will be flattened to form an array of size NxM where N = N1 * N2 * … * Nn.- valuesfloat or 1D array_like
Values of the data points corresponding to each coordinate provided in
coordinates
. In general a 1D array is expected. When a single data point is available, thenvalues
can be a scalar number.Note
If the dimensionality of
values
is larger than 1 then it will be flattened.- weightsfloat or 1D array_like, optional
Weights to be associated with each data value. These weights, if provided, will be combined with inverse distance weights (see the Notes section for details). When
weights
isNone
(default), then only inverse distance weights will be used. When provided, this input parameter must have the same form asvalues
.- leafsizefloat, optional
The number of points at which the k-d tree algorithm switches over to brute-force.
leafsize
must be positive. Seescipy.spatial.cKDTree
for further information.
Notes
This interpolator uses a slightly modified version of Shepard’s method. The essential difference is the introduction of a “regularization” parameter (
reg
) that is used when computing the inverse distance weights:\[w_i = 1 / (d(x, x_i)^{power} + r)\]By supplying a positive regularization parameter one can avoid singularities at the locations of the data points as well as control the “smoothness” of the interpolation (e.g., make the weights of the neighbors less varied). The “smoothness” of interpolation can also be controlled by the power parameter (
power
).Examples
This class can can be instantiated using the following syntax:
>>> from photutils.utils import ShepardIDWInterpolator as idw
Example of interpolating 1D data:
>>> import numpy as np >>> rng = np.random.default_rng(0) >>> x = rng.random(100) # 100 random values >>> y = np.sin(x) >>> f = idw(x, y) >>> f(0.4) 0.38937843420912366 >>> np.sin(0.4) 0.3894183423086505 >>> xi = rng.random(4) # 4 random values >>> xi array([0.47998792, 0.23237292, 0.80188058, 0.92353016]) >>> f(xi) array([0.46577097, 0.22837422, 0.71856662, 0.80125391]) >>> np.sin(xi) array([0.46176846, 0.23028731, 0.71866503, 0.7977353 ])
NOTE: In the last example,
xi
may be aNx1
array instead of a 1D vector.Example of interpolating 2D data:
>>> rng = np.random.default_rng(0) >>> pos = rng.random((1000, 2)) >>> val = np.sin(pos[:, 0] + pos[:, 1]) >>> f = idw(pos, val) >>> f([0.5, 0.6]) 0.8948257014687874 >>> np.sin(0.5 + 0.6) 0.8912073600614354
Methods Summary
__call__
(positions[, n_neighbors, eps, ...])Evaluate the interpolator at the given positions.
Methods Documentation
- __call__(positions, n_neighbors=8, eps=0.0, power=1.0, reg=0.0, conf_dist=1e-12, dtype=<class 'float'>)[source]¶
Evaluate the interpolator at the given positions.
- Parameters:
- positionsfloat, 1D array_like, or NxM array_like
Coordinates of the position(s) at which the interpolator should be evaluated. In general, it is expected that these coordinates are in a form of a NxM-like array where N is the number of points and M is dimension of the coordinate space. When M=1 (1D space), then the
positions
parameter may be input as a 1D-like array or, if only one data point is available,positions
can be a scalar number representing the 1D coordinate of the data point.Note
If the dimensionality of the
positions
argument is larger than 2, e.g., if it is of the form N1 x N2 x N3 x … x Nn x M, then it will be flattened to form an array of size NxM where N = N1 * N2 * … * Nn.Warning
The dimensionality of
positions
must match the dimensionality of thecoordinates
used during the initialization of the interpolator.- n_neighborsint, optional
The maximum number of nearest neighbors to use during the interpolation.
- epsfloat, optional
Set to use approximate nearest neighbors; the kth neighbor is guaranteed to be no further than (1 +
eps
) times the distance to the real k-th nearest neighbor. Seescipy.spatial.cKDTree.query
for further information.- powerfloat, optional
The power of the inverse distance used for the interpolation weights. See the Notes section for more details.
- regfloat, optional
The regularization parameter. It may be used to control the smoothness of the interpolator. See the Notes section for more details.
- conf_distfloat, optional
The confusion distance below which the interpolator should use the value of the closest data point instead of attempting to interpolate. This is used to avoid singularities at the known data points, especially if
reg
is 0.0.- dtypedata-type, optional
The data type of the output interpolated values. If
None
then the type will be inferred from the type of thevalues
parameter used during the initialization of the interpolator.