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Supprimer 'functions/variograms.py'

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Kilian Vos 6 years ago
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functions/variograms.py
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"""This module contains all the functions needed for variogram analysis """
import sklearn.metrics.pairwise as pairwise
import numpy as np
def lagindices(pwdist, lag, tol):
'''
Input: (pwdist) square NumPy array of pairwise distances
(lag) the distance, h, between points
(tol) the tolerance we are comfortable with around (lag)
Output: (ind) list of tuples; the first element is the row of
(data) for one point, the second element is the row
of a point (lag)+/-(tol) away from the first point,
e.g., (3,5) corresponds fo data[3,:], and data[5,:]
'''
# grab the coordinates in a given range: lag +/- tolerance
i, j = np.where((pwdist >= lag - tol) & (pwdist < lag + tol))
# zip the coordinates into a list
indices = list(zip(i, j))
# take out the repeated elements,
# since p is a *symmetric* distance matrix
indices = np.array([i for i in indices if i[1] > i[0]])
return indices
def semivariance(data, indices):
'''
Input: (data) NumPy array where the fris t two columns
are the spatial coordinates, x and y, and
the third column is the variable of interest
(indices) indices of paired data points in (data)
Output: (z) semivariance value at lag (h) +/- (tol)
'''
# take the squared difference between
# the values of the variable of interest
z = [(data[i] - data[j])**2.0 for i, j in indices]
# the semivariance is half the mean squared difference
return np.mean(z) / 2.0
def semivariogram(t, data, lags, tol):
'''
Input: (data) NumPy array where the fris t two columns
are the spatial coordinates, x and y
(lag) the distance, h, between points
(tol) the tolerance we are comfortable with around (lag)
Output: (sv) <2xN> NumPy array of lags and semivariogram values
'''
return variogram(t, data, lags, tol, 'semivariogram')
def covariance(data, indices):
'''
Input: (data) NumPy array where the fris t two columns
are the spatial coordinates, x and y
(lag) the distance, h, between points
(tol) the tolerance we are comfortable with around (lag)
Output: (z) covariance value at lag (h) +/- (tol)
'''
# grab the indices of the points
# that are lag +/- tolerance apart
m_tail = np.mean([data[i] for i, j in indices])
m_head = np.mean([data[j] for i, j in indices])
m = m_tail * m_head
z = [data[i] * data[j] - m for i, j in indices]
return np.mean(z)
def covariogram(t, data, lags, tol):
'''
Input: (data) NumPy array where the fris t two columns
are the spatial coordinates, x and y
(lag) the distance, h, between points
(tol) the tolerance we are comfortable with around (lag)
Output: (cv) <2xN> NumPy array of lags and covariogram values
'''
return variogram(t, data, lags, tol, 'covariogram')
def variogram(t, data, lags, tol, method):
'''
Input: (data) NumPy array where the fris t two columns
are the spatial coordinates, x and y
(lag) the distance, h, between points
(tol) the tolerance we are comfortable with around (lag)
(method) either 'semivariogram', or 'covariogram'
Output: (cv) <2xN> NumPy array of lags and variogram values
'''
# calculate the pairwise distances
pwdist = pairwise.pairwise_distances(np.reshape(np.array(t), (-1,1)))
# create a list of lists of indices of points having the ~same lag
index = [lagindices(pwdist, lag, tol) for lag in lags]
# calculate the variogram at different lags given some tolerance
if method in ['semivariogram', 'semi', 'sv', 's']:
v = [semivariance(data, indices) for indices in index]
elif method in ['covariogram', 'cov', 'co', 'cv', 'c']:
v = [covariance(data, indices) for indices in index]
# bundle the semivariogram values with their lags
return np.array(list(zip(lags, v))).T
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