def test_probability_density_without_noise():
"""Test probability density of MVN with not invertible covariance."""
random_state = check_random_state(0)
n_samples = 10
x = np.linspace(0, 1, n_samples)[:, np.newaxis]
y = np.ones((n_samples, 1))
samples = np.hstack((x, y))
mvn = MVN(random_state=random_state)
mvn.from_samples(samples)
assert_array_almost_equal(mvn.mean, np.array([0.5, 1.0]), decimal=2)
assert_equal(mvn.covariance[1, 1], 0.0)
p_training = mvn.to_probability_density(samples)
p_test = mvn.to_probability_density(samples + 1)
assert_true(np.all(p_training > p_test))
def test_probability_density_without_noise():
"""Test probability density of MVN with not invertible covariance."""
random_state = check_random_state(0)
n_samples = 10
x = np.linspace(0, 1, n_samples)[:, np.newaxis]
y = np.ones((n_samples, 1))
samples = np.hstack((x, y))
mvn = MVN(random_state=random_state)
mvn.from_samples(samples)
assert_array_almost_equal(mvn.mean, np.array([0.5, 1.0]), decimal=2)
assert_equal(mvn.covariance[1, 1], 0.0)
p_training = mvn.to_probability_density(samples)
p_test = mvn.to_probability_density(samples + 1)
assert_true(np.all(p_training > p_test))
def test_probability_density():
"""Test PDF of MVN."""
random_state = check_random_state(0)
mvn = MVN(mean, covariance, random_state=random_state)
x = np.linspace(-100, 100, 201)
X = np.vstack(map(np.ravel, np.meshgrid(x, x))).T
p = mvn.to_probability_density(X)
approx_int = np.sum(p) * ((x[-1] - x[0]) / 201) ** 2
assert_less(np.abs(1.0 - approx_int), 0.01)
def test_probability_density():
"""Test PDF of MVN."""
random_state = check_random_state(0)
mvn = MVN(mean, covariance, random_state=random_state)
x = np.linspace(-100, 100, 201)
X = np.vstack(map(np.ravel, np.meshgrid(x, x))).T
p = mvn.to_probability_density(X)
approx_int = np.sum(p) * ((x[-1] - x[0]) / 201)**2
assert_less(np.abs(1.0 - approx_int), 0.01)
"""
========================================================
Confidence Interval of a 1D Standard Normal Distribution
========================================================
We plot the 0.6827 confidence interval of a standard normal distribution in
one dimension. The confidence interval is marked by green lines and the
region outside of the confidence interval is marked by red lines.
"""
print(__doc__)
import matplotlib.pyplot as plt
import numpy as np
from gmr import MVN
mvn = MVN(mean=[0.0], covariance=[[1.0]])
alpha = 0.6827
X = np.linspace(-3, 3, 101)[:, np.newaxis]
P = mvn.to_probability_density(X)
for x, p in zip(X, P):
conf = mvn.is_in_confidence_region(x, alpha)
color = "g" if conf else "r"
plt.plot([x[0], x[0]], [0, p], color=color)
plt.plot(X.ravel(), P)
plt.xlabel("x")
plt.ylabel("Probability Density $p(x)$")
plt.show()
