# Copyright (c) 2013,Vienna University of Technology,
# Department of Geodesy and Geoinformation
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'''
Created on Apr 17, 2013
@author: Christoph Paulik christoph.paulik@geo.tuwien.ac.at
@author: Sebastian Hahn sebastian.hahn@geo.tuwien.ac.at
@author: Alexander Gruber alexander.gruber@geo.tuwien.ac.at
'''
import numpy as np
import scipy.stats as sc_stats
[docs]def bias(x, y):
"""Bias
"""
return np.mean(x) - np.mean(y)
[docs]def rmsd(x, y):
"""Root-mean-square deviation
"""
return np.sqrt(RSS(x, y) / len(x))
[docs]def nrmsd(x, y):
"""Normalized root-mean-square deviation
"""
return rmsd(x, y) / (np.max([x, y]) - np.min([x, y]))
[docs]def ubrmsd(x, y):
"""Unbiased root-mean-square deviation
"""
return np.sqrt(np.sum(((x - np.mean(x)) - (y - np.mean(y))) ** 2) / len(x))
[docs]def mse(x, y):
"""Mean square error (MSE) as a decomposition of the RMSD into
individual error components
"""
MSEcorr = 2 * np.std(y) * np.std(x) * (1 - sc_stats.pearsonr(x, y)[0])
MSEbias = bias(x, y) ** 2
MSEvar = (np.std(x) - np.std(y)) ** 2
MSE = MSEcorr + MSEbias + MSEvar
return MSE, MSEcorr, MSEbias, MSEvar
[docs]def tcol_error(x, y, z):
"""Triple collocation error estimate
Parameters
----------
x : numpy.array
1D numpy array to calculate the errors
y : numpy.array
1D numpy array to calculate the errors
z : numpy.array
1D numpy array to calculate the errors
Returns
-------
triple collocation error for x : float
triple collocation error for y : float
triple collocation error for z : float
"""
e_x = np.sqrt(np.abs(np.mean((x - y) * (x - z))))
e_y = np.sqrt(np.abs(np.mean((y - x) * (y - z))))
e_z = np.sqrt(np.abs(np.mean((z - x) * (z - y))))
return e_x, e_y, e_z
[docs]def nash_sutcliffe(x, y):
"""Nash Sutcliffe model efficiency coefficient
Parameters
----------
x : numpy.array
1D numpy array to calculate the metric
y : numpy.array
1D numpy array to calculate the metric
Returns
-------
Nash Sutcliffe coefficient : float
Nash Sutcliffe model efficiency coefficient
"""
return 1 - (np.sum((x - y) ** 2)) / (np.sum((x - np.mean(x)) ** 2))
[docs]def pearsonr(x, y):
"""
Wrapper for scipy.stats.pearsonr
Parameters
----------
x : numpy.array
1D numpy array to calculate the metric
y : numpy.array
1D numpy array to calculate the metric
Returns
-------
Pearson's r : float
Pearson's correlation coefficent
p-value : float
2 tailed p-value
See Also
--------
scipy.stats.pearsonr
"""
return sc_stats.pearsonr(x, y)
[docs]def spearmanr(x, y):
"""
Wrapper for scipy.stats.spearmanr
Parameters
----------
x : numpy.array
1D numpy array to calculate the metric
y : numpy.array
1D numpy array to calculate the metric
Returns
-------
rho : float
Spearman correlation coefficient
p-value : float
The two-sided p-value for a hypothesis test whose null hypothesis
is that two sets of data are uncorrelated
See Also
--------
scipy.stats.spearmenr
"""
return sc_stats.spearmanr(x, y)
[docs]def kendalltau(x, y):
"""
Wrapper for scipy.stats.kendalltau
Parameters
----------
x : numpy.array
1D numpy array to calculate the metric
y : numpy.array
1D numpy array to calculate the metric
Returns
-------
Kendall's tau : float
The tau statistic
p-value : float
The two-sided p-value for a hypothesis test whose null hypothesis
is an absence of association, tau = 0.
See Also
--------
scipy.stats.kendalltau
"""
return sc_stats.kendalltau(x.tolist(), y.tolist())