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"""
This is a module for inverse distance weighting (IDW) Spatial Interpolation
"""
import numpy as np
from ..utils.distance import haversine, euclidean
from ..base import Base
class IDW(Base):
"""A class that is declared for performing IDW Interpolation.
For more information on how this method works, kindly refer to
https://en.wikipedia.org/wiki/Inverse_distance_weighting
Parameters
----------
exponent : positive float, optional
The rate of fall of values from source data points.
Higher the exponent, lower is the value when we move
across space. Default value is 2.
Attributes
----------
Interpolated Values : {array-like, 2D matrix}, shape(resolution, resolution)
This contains all the interpolated values when the interpolation is performed
over a grid, instead of interpolation over a set of points.
X : {array-like, 2D matrix}, shape(n_samples, 2)
Set of all the coordinates available for interpolation.
y : array-like, shape(n_samples,)
Set of all the available values at the specified X coordinates.
result : array_like, shape(n_to_predict, )
Set of all the interpolated values when interpolating over a given
set of data points.
"""
def __init__(
self, exponent=2, resolution="standard", coordinate_type="Euclidean"
):
super().__init__(resolution, coordinate_type)
self.exponent = exponent
self.interpolated_values = None
self.X = None
self.y = None
self.result = None
if self.coordinate_type == "Geographic":
self.distance = haversine
elif self.coordinate_type == "Euclidean":
self.distance = euclidean
else:
raise NotImplementedError(
"Only Geographic and Euclidean Coordinates are available"
)
def _fit(self, X, y):
"""This function is for the IDW Class.
This is not expected to be called directly
"""
self.X = X
self.y = y
return self
def _predict_grid(self, x1lim, x2lim):
"""Gridded interpolation for natural neighbors interpolation. This function should not
be called directly.
"""
lims = (*x1lim, *x2lim)
x1min, x1max, x2min, x2max = lims
x1 = np.linspace(x1min, x1max, self.resolution)
x2 = np.linspace(x2min, x2max, self.resolution)
X1, X2 = np.meshgrid(x1, x2)
return self._predict(np.array([X1.ravel(), X2.ravel()]).T)
def _predict(self, X):
"""The function call to predict using the interpolated data
in IDW interpolation. This should not be called directly.
"""
dist = self.distance(self.X, X)
weights = 1 / np.power(dist, self.exponent)
result = (weights * self.y[:, None]).sum(axis=0) / weights.sum(axis=0)
# if point is from train data, ground truth must not change
for i in range(X.shape[0]):
mask = np.equal(X[i], self.X).all(axis=1)
if mask.any():
result[i] = (self.y * mask).sum()
return result
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