89 lines
1.9 KiB
Python
89 lines
1.9 KiB
Python
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# -*- coding: utf-8 -*-
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"""
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py.test module to test stats.py module.
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Created on Wed Aug 27 06:45:06 2014
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@author: rlabbe
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"""
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from __future__ import division
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from math import pi, exp
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import numpy as np
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from stats import gaussian, multivariate_gaussian, _to_cov
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from numpy.linalg import inv
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from numpy import linalg
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def near_equal(x,y):
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return abs(x-y) < 1.e-15
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def test_gaussian():
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import scipy.stats
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mean = 3.
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var = 1.5
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std = var**0.5
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for i in np.arange(-5,5,0.1):
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p0 = scipy.stats.norm(mean, std).pdf(i)
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p1 = gaussian(i, mean, var)
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assert near_equal(p0, p1)
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def norm_pdf_multivariate(x, mu, sigma):
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""" extremely literal transcription of the multivariate equation.
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Slow, but easy to verify by eye compared to my version."""
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n = len(x)
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sigma = _to_cov(sigma,n)
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det = linalg.det(sigma)
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norm_const = 1.0 / (pow((2*pi), n/2) * pow(det, .5))
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x_mu = x - mu
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result = exp(-0.5 * (x_mu.dot(inv(sigma)).dot(x_mu.T)))
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return norm_const * result
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def test_multivariate():
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from scipy.stats import multivariate_normal as mvn
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from numpy.random import rand
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mean = 3
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var = 1.5
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assert near_equal(mvn(mean,var).pdf(0.5),
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multivariate_gaussian(0.5, mean, var))
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mean = np.array([2.,17.])
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var = np.array([[10., 1.2], [1.2, 4.]])
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x = np.array([1,16])
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assert near_equal(mvn(mean,var).pdf(x),
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multivariate_gaussian(x, mean, var))
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for i in range(100):
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x = np.array([rand(), rand()])
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assert near_equal(mvn(mean,var).pdf(x),
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multivariate_gaussian(x, mean, var))
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assert near_equal(mvn(mean,var).pdf(x),
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norm_pdf_multivariate(x, mean, var))
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mean = np.array([1,2,3,4])
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var = np.eye(4)*rand()
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x = np.array([2,3,4,5])
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assert near_equal(mvn(mean,var).pdf(x),
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norm_pdf_multivariate(x, mean, var))
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