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projektAI/venv/Lib/site-packages/scipy/stats/tests/test_multivariate.py

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"""
Test functions for multivariate normal distributions.
"""
import pickle
from numpy.testing import (assert_allclose, assert_almost_equal,
assert_array_almost_equal, assert_equal,
assert_array_less, assert_)
import pytest
from pytest import raises as assert_raises
from .test_continuous_basic import check_distribution_rvs
import numpy
import numpy as np
import scipy.linalg
from scipy.stats._multivariate import (_PSD,
_lnB,
_cho_inv_batch,
multivariate_normal_frozen)
from scipy.stats import (multivariate_normal, multivariate_hypergeom,
matrix_normal, special_ortho_group, ortho_group,
random_correlation, unitary_group, dirichlet,
beta, wishart, multinomial, invwishart, chi2,
invgamma, norm, uniform, ks_2samp, kstest, binom,
hypergeom, multivariate_t, cauchy, normaltest)
from scipy.integrate import romb
from scipy.special import multigammaln
from .common_tests import check_random_state_property
from unittest.mock import patch
class TestMultivariateNormal(object):
def test_input_shape(self):
mu = np.arange(3)
cov = np.identity(2)
assert_raises(ValueError, multivariate_normal.pdf, (0, 1), mu, cov)
assert_raises(ValueError, multivariate_normal.pdf, (0, 1, 2), mu, cov)
assert_raises(ValueError, multivariate_normal.cdf, (0, 1), mu, cov)
assert_raises(ValueError, multivariate_normal.cdf, (0, 1, 2), mu, cov)
def test_scalar_values(self):
np.random.seed(1234)
# When evaluated on scalar data, the pdf should return a scalar
x, mean, cov = 1.5, 1.7, 2.5
pdf = multivariate_normal.pdf(x, mean, cov)
assert_equal(pdf.ndim, 0)
# When evaluated on a single vector, the pdf should return a scalar
x = np.random.randn(5)
mean = np.random.randn(5)
cov = np.abs(np.random.randn(5)) # Diagonal values for cov. matrix
pdf = multivariate_normal.pdf(x, mean, cov)
assert_equal(pdf.ndim, 0)
# When evaluated on scalar data, the cdf should return a scalar
x, mean, cov = 1.5, 1.7, 2.5
cdf = multivariate_normal.cdf(x, mean, cov)
assert_equal(cdf.ndim, 0)
# When evaluated on a single vector, the cdf should return a scalar
x = np.random.randn(5)
mean = np.random.randn(5)
cov = np.abs(np.random.randn(5)) # Diagonal values for cov. matrix
cdf = multivariate_normal.cdf(x, mean, cov)
assert_equal(cdf.ndim, 0)
def test_logpdf(self):
# Check that the log of the pdf is in fact the logpdf
np.random.seed(1234)
x = np.random.randn(5)
mean = np.random.randn(5)
cov = np.abs(np.random.randn(5))
d1 = multivariate_normal.logpdf(x, mean, cov)
d2 = multivariate_normal.pdf(x, mean, cov)
assert_allclose(d1, np.log(d2))
def test_logpdf_default_values(self):
# Check that the log of the pdf is in fact the logpdf
# with default parameters Mean=None and cov = 1
np.random.seed(1234)
x = np.random.randn(5)
d1 = multivariate_normal.logpdf(x)
d2 = multivariate_normal.pdf(x)
# check whether default values are being used
d3 = multivariate_normal.logpdf(x, None, 1)
d4 = multivariate_normal.pdf(x, None, 1)
assert_allclose(d1, np.log(d2))
assert_allclose(d3, np.log(d4))
def test_logcdf(self):
# Check that the log of the cdf is in fact the logcdf
np.random.seed(1234)
x = np.random.randn(5)
mean = np.random.randn(5)
cov = np.abs(np.random.randn(5))
d1 = multivariate_normal.logcdf(x, mean, cov)
d2 = multivariate_normal.cdf(x, mean, cov)
assert_allclose(d1, np.log(d2))
def test_logcdf_default_values(self):
# Check that the log of the cdf is in fact the logcdf
# with default parameters Mean=None and cov = 1
np.random.seed(1234)
x = np.random.randn(5)
d1 = multivariate_normal.logcdf(x)
d2 = multivariate_normal.cdf(x)
# check whether default values are being used
d3 = multivariate_normal.logcdf(x, None, 1)
d4 = multivariate_normal.cdf(x, None, 1)
assert_allclose(d1, np.log(d2))
assert_allclose(d3, np.log(d4))
def test_rank(self):
# Check that the rank is detected correctly.
np.random.seed(1234)
n = 4
mean = np.random.randn(n)
for expected_rank in range(1, n + 1):
s = np.random.randn(n, expected_rank)
cov = np.dot(s, s.T)
distn = multivariate_normal(mean, cov, allow_singular=True)
assert_equal(distn.cov_info.rank, expected_rank)
def test_degenerate_distributions(self):
def _sample_orthonormal_matrix(n):
M = np.random.randn(n, n)
u, s, v = scipy.linalg.svd(M)
return u
for n in range(1, 5):
x = np.random.randn(n)
for k in range(1, n + 1):
# Sample a small covariance matrix.
s = np.random.randn(k, k)
cov_kk = np.dot(s, s.T)
# Embed the small covariance matrix into a larger low rank matrix.
cov_nn = np.zeros((n, n))
cov_nn[:k, :k] = cov_kk
# Define a rotation of the larger low rank matrix.
u = _sample_orthonormal_matrix(n)
cov_rr = np.dot(u, np.dot(cov_nn, u.T))
y = np.dot(u, x)
# Check some identities.
distn_kk = multivariate_normal(np.zeros(k), cov_kk,
allow_singular=True)
distn_nn = multivariate_normal(np.zeros(n), cov_nn,
allow_singular=True)
distn_rr = multivariate_normal(np.zeros(n), cov_rr,
allow_singular=True)
assert_equal(distn_kk.cov_info.rank, k)
assert_equal(distn_nn.cov_info.rank, k)
assert_equal(distn_rr.cov_info.rank, k)
pdf_kk = distn_kk.pdf(x[:k])
pdf_nn = distn_nn.pdf(x)
pdf_rr = distn_rr.pdf(y)
assert_allclose(pdf_kk, pdf_nn)
assert_allclose(pdf_kk, pdf_rr)
logpdf_kk = distn_kk.logpdf(x[:k])
logpdf_nn = distn_nn.logpdf(x)
logpdf_rr = distn_rr.logpdf(y)
assert_allclose(logpdf_kk, logpdf_nn)
assert_allclose(logpdf_kk, logpdf_rr)
def test_large_pseudo_determinant(self):
# Check that large pseudo-determinants are handled appropriately.
# Construct a singular diagonal covariance matrix
# whose pseudo determinant overflows double precision.
large_total_log = 1000.0
npos = 100
nzero = 2
large_entry = np.exp(large_total_log / npos)
n = npos + nzero
cov = np.zeros((n, n), dtype=float)
np.fill_diagonal(cov, large_entry)
cov[-nzero:, -nzero:] = 0
# Check some determinants.
assert_equal(scipy.linalg.det(cov), 0)
assert_equal(scipy.linalg.det(cov[:npos, :npos]), np.inf)
assert_allclose(np.linalg.slogdet(cov[:npos, :npos]),
(1, large_total_log))
# Check the pseudo-determinant.
psd = _PSD(cov)
assert_allclose(psd.log_pdet, large_total_log)
def test_broadcasting(self):
np.random.seed(1234)
n = 4
# Construct a random covariance matrix.
data = np.random.randn(n, n)
cov = np.dot(data, data.T)
mean = np.random.randn(n)
# Construct an ndarray which can be interpreted as
# a 2x3 array whose elements are random data vectors.
X = np.random.randn(2, 3, n)
# Check that multiple data points can be evaluated at once.
desired_pdf = multivariate_normal.pdf(X, mean, cov)
desired_cdf = multivariate_normal.cdf(X, mean, cov)
for i in range(2):
for j in range(3):
actual = multivariate_normal.pdf(X[i, j], mean, cov)
assert_allclose(actual, desired_pdf[i,j])
# Repeat for cdf
actual = multivariate_normal.cdf(X[i, j], mean, cov)
assert_allclose(actual, desired_cdf[i,j], rtol=1e-3)
def test_normal_1D(self):
# The probability density function for a 1D normal variable should
# agree with the standard normal distribution in scipy.stats.distributions
x = np.linspace(0, 2, 10)
mean, cov = 1.2, 0.9
scale = cov**0.5
d1 = norm.pdf(x, mean, scale)
d2 = multivariate_normal.pdf(x, mean, cov)
assert_allclose(d1, d2)
# The same should hold for the cumulative distribution function
d1 = norm.cdf(x, mean, scale)
d2 = multivariate_normal.cdf(x, mean, cov)
assert_allclose(d1, d2)
def test_marginalization(self):
# Integrating out one of the variables of a 2D Gaussian should
# yield a 1D Gaussian
mean = np.array([2.5, 3.5])
cov = np.array([[.5, 0.2], [0.2, .6]])
n = 2 ** 8 + 1 # Number of samples
delta = 6 / (n - 1) # Grid spacing
v = np.linspace(0, 6, n)
xv, yv = np.meshgrid(v, v)
pos = np.empty((n, n, 2))
pos[:, :, 0] = xv
pos[:, :, 1] = yv
pdf = multivariate_normal.pdf(pos, mean, cov)
# Marginalize over x and y axis
margin_x = romb(pdf, delta, axis=0)
margin_y = romb(pdf, delta, axis=1)
# Compare with standard normal distribution
gauss_x = norm.pdf(v, loc=mean[0], scale=cov[0, 0] ** 0.5)
gauss_y = norm.pdf(v, loc=mean[1], scale=cov[1, 1] ** 0.5)
assert_allclose(margin_x, gauss_x, rtol=1e-2, atol=1e-2)
assert_allclose(margin_y, gauss_y, rtol=1e-2, atol=1e-2)
def test_frozen(self):
# The frozen distribution should agree with the regular one
np.random.seed(1234)
x = np.random.randn(5)
mean = np.random.randn(5)
cov = np.abs(np.random.randn(5))
norm_frozen = multivariate_normal(mean, cov)
assert_allclose(norm_frozen.pdf(x), multivariate_normal.pdf(x, mean, cov))
assert_allclose(norm_frozen.logpdf(x),
multivariate_normal.logpdf(x, mean, cov))
assert_allclose(norm_frozen.cdf(x), multivariate_normal.cdf(x, mean, cov))
assert_allclose(norm_frozen.logcdf(x),
multivariate_normal.logcdf(x, mean, cov))
def test_pseudodet_pinv(self):
# Make sure that pseudo-inverse and pseudo-det agree on cutoff
# Assemble random covariance matrix with large and small eigenvalues
np.random.seed(1234)
n = 7
x = np.random.randn(n, n)
cov = np.dot(x, x.T)
s, u = scipy.linalg.eigh(cov)
s = np.full(n, 0.5)
s[0] = 1.0
s[-1] = 1e-7
cov = np.dot(u, np.dot(np.diag(s), u.T))
# Set cond so that the lowest eigenvalue is below the cutoff
cond = 1e-5
psd = _PSD(cov, cond=cond)
psd_pinv = _PSD(psd.pinv, cond=cond)
# Check that the log pseudo-determinant agrees with the sum
# of the logs of all but the smallest eigenvalue
assert_allclose(psd.log_pdet, np.sum(np.log(s[:-1])))
# Check that the pseudo-determinant of the pseudo-inverse
# agrees with 1 / pseudo-determinant
assert_allclose(-psd.log_pdet, psd_pinv.log_pdet)
def test_exception_nonsquare_cov(self):
cov = [[1, 2, 3], [4, 5, 6]]
assert_raises(ValueError, _PSD, cov)
def test_exception_nonfinite_cov(self):
cov_nan = [[1, 0], [0, np.nan]]
assert_raises(ValueError, _PSD, cov_nan)
cov_inf = [[1, 0], [0, np.inf]]
assert_raises(ValueError, _PSD, cov_inf)
def test_exception_non_psd_cov(self):
cov = [[1, 0], [0, -1]]
assert_raises(ValueError, _PSD, cov)
def test_exception_singular_cov(self):
np.random.seed(1234)
x = np.random.randn(5)
mean = np.random.randn(5)
cov = np.ones((5, 5))
e = np.linalg.LinAlgError
assert_raises(e, multivariate_normal, mean, cov)
assert_raises(e, multivariate_normal.pdf, x, mean, cov)
assert_raises(e, multivariate_normal.logpdf, x, mean, cov)
assert_raises(e, multivariate_normal.cdf, x, mean, cov)
assert_raises(e, multivariate_normal.logcdf, x, mean, cov)
def test_R_values(self):
# Compare the multivariate pdf with some values precomputed
# in R version 3.0.1 (2013-05-16) on Mac OS X 10.6.
# The values below were generated by the following R-script:
# > library(mnormt)
# > x <- seq(0, 2, length=5)
# > y <- 3*x - 2
# > z <- x + cos(y)
# > mu <- c(1, 3, 2)
# > Sigma <- matrix(c(1,2,0,2,5,0.5,0,0.5,3), 3, 3)
# > r_pdf <- dmnorm(cbind(x,y,z), mu, Sigma)
r_pdf = np.array([0.0002214706, 0.0013819953, 0.0049138692,
0.0103803050, 0.0140250800])
x = np.linspace(0, 2, 5)
y = 3 * x - 2
z = x + np.cos(y)
r = np.array([x, y, z]).T
mean = np.array([1, 3, 2], 'd')
cov = np.array([[1, 2, 0], [2, 5, .5], [0, .5, 3]], 'd')
pdf = multivariate_normal.pdf(r, mean, cov)
assert_allclose(pdf, r_pdf, atol=1e-10)
# Compare the multivariate cdf with some values precomputed
# in R version 3.3.2 (2016-10-31) on Debian GNU/Linux.
# The values below were generated by the following R-script:
# > library(mnormt)
# > x <- seq(0, 2, length=5)
# > y <- 3*x - 2
# > z <- x + cos(y)
# > mu <- c(1, 3, 2)
# > Sigma <- matrix(c(1,2,0,2,5,0.5,0,0.5,3), 3, 3)
# > r_cdf <- pmnorm(cbind(x,y,z), mu, Sigma)
r_cdf = np.array([0.0017866215, 0.0267142892, 0.0857098761,
0.1063242573, 0.2501068509])
cdf = multivariate_normal.cdf(r, mean, cov)
assert_allclose(cdf, r_cdf, atol=1e-5)
# Also test bivariate cdf with some values precomputed
# in R version 3.3.2 (2016-10-31) on Debian GNU/Linux.
# The values below were generated by the following R-script:
# > library(mnormt)
# > x <- seq(0, 2, length=5)
# > y <- 3*x - 2
# > mu <- c(1, 3)
# > Sigma <- matrix(c(1,2,2,5), 2, 2)
# > r_cdf2 <- pmnorm(cbind(x,y), mu, Sigma)
r_cdf2 = np.array([0.01262147, 0.05838989, 0.18389571,
0.40696599, 0.66470577])
r2 = np.array([x, y]).T
mean2 = np.array([1, 3], 'd')
cov2 = np.array([[1, 2], [2, 5]], 'd')
cdf2 = multivariate_normal.cdf(r2, mean2, cov2)
assert_allclose(cdf2, r_cdf2, atol=1e-5)
def test_multivariate_normal_rvs_zero_covariance(self):
mean = np.zeros(2)
covariance = np.zeros((2, 2))
model = multivariate_normal(mean, covariance, allow_singular=True)
sample = model.rvs()
assert_equal(sample, [0, 0])
def test_rvs_shape(self):
# Check that rvs parses the mean and covariance correctly, and returns
# an array of the right shape
N = 300
d = 4
sample = multivariate_normal.rvs(mean=np.zeros(d), cov=1, size=N)
assert_equal(sample.shape, (N, d))
sample = multivariate_normal.rvs(mean=None,
cov=np.array([[2, .1], [.1, 1]]),
size=N)
assert_equal(sample.shape, (N, 2))
u = multivariate_normal(mean=0, cov=1)
sample = u.rvs(N)
assert_equal(sample.shape, (N, ))
def test_large_sample(self):
# Generate large sample and compare sample mean and sample covariance
# with mean and covariance matrix.
np.random.seed(2846)
n = 3
mean = np.random.randn(n)
M = np.random.randn(n, n)
cov = np.dot(M, M.T)
size = 5000
sample = multivariate_normal.rvs(mean, cov, size)
assert_allclose(numpy.cov(sample.T), cov, rtol=1e-1)
assert_allclose(sample.mean(0), mean, rtol=1e-1)
def test_entropy(self):
np.random.seed(2846)
n = 3
mean = np.random.randn(n)
M = np.random.randn(n, n)
cov = np.dot(M, M.T)
rv = multivariate_normal(mean, cov)
# Check that frozen distribution agrees with entropy function
assert_almost_equal(rv.entropy(), multivariate_normal.entropy(mean, cov))
# Compare entropy with manually computed expression involving
# the sum of the logs of the eigenvalues of the covariance matrix
eigs = np.linalg.eig(cov)[0]
desired = 1 / 2 * (n * (np.log(2 * np.pi) + 1) + np.sum(np.log(eigs)))
assert_almost_equal(desired, rv.entropy())
def test_lnB(self):
alpha = np.array([1, 1, 1])
desired = .5 # e^lnB = 1/2 for [1, 1, 1]
assert_almost_equal(np.exp(_lnB(alpha)), desired)
class TestMatrixNormal(object):
def test_bad_input(self):
# Check that bad inputs raise errors
num_rows = 4
num_cols = 3
M = np.full((num_rows,num_cols), 0.3)
U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
# Incorrect dimensions
assert_raises(ValueError, matrix_normal, np.zeros((5,4,3)))
assert_raises(ValueError, matrix_normal, M, np.zeros(10), V)
assert_raises(ValueError, matrix_normal, M, U, np.zeros(10))
assert_raises(ValueError, matrix_normal, M, U, U)
assert_raises(ValueError, matrix_normal, M, V, V)
assert_raises(ValueError, matrix_normal, M.T, U, V)
# Singular covariance
e = np.linalg.LinAlgError
assert_raises(e, matrix_normal, M, U, np.ones((num_cols, num_cols)))
assert_raises(e, matrix_normal, M, np.ones((num_rows, num_rows)), V)
def test_default_inputs(self):
# Check that default argument handling works
num_rows = 4
num_cols = 3
M = np.full((num_rows,num_cols), 0.3)
U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
Z = np.zeros((num_rows, num_cols))
Zr = np.zeros((num_rows, 1))
Zc = np.zeros((1, num_cols))
Ir = np.identity(num_rows)
Ic = np.identity(num_cols)
I1 = np.identity(1)
assert_equal(matrix_normal.rvs(mean=M, rowcov=U, colcov=V).shape,
(num_rows, num_cols))
assert_equal(matrix_normal.rvs(mean=M).shape,
(num_rows, num_cols))
assert_equal(matrix_normal.rvs(rowcov=U).shape,
(num_rows, 1))
assert_equal(matrix_normal.rvs(colcov=V).shape,
(1, num_cols))
assert_equal(matrix_normal.rvs(mean=M, colcov=V).shape,
(num_rows, num_cols))
assert_equal(matrix_normal.rvs(mean=M, rowcov=U).shape,
(num_rows, num_cols))
assert_equal(matrix_normal.rvs(rowcov=U, colcov=V).shape,
(num_rows, num_cols))
assert_equal(matrix_normal(mean=M).rowcov, Ir)
assert_equal(matrix_normal(mean=M).colcov, Ic)
assert_equal(matrix_normal(rowcov=U).mean, Zr)
assert_equal(matrix_normal(rowcov=U).colcov, I1)
assert_equal(matrix_normal(colcov=V).mean, Zc)
assert_equal(matrix_normal(colcov=V).rowcov, I1)
assert_equal(matrix_normal(mean=M, rowcov=U).colcov, Ic)
assert_equal(matrix_normal(mean=M, colcov=V).rowcov, Ir)
assert_equal(matrix_normal(rowcov=U, colcov=V).mean, Z)
def test_covariance_expansion(self):
# Check that covariance can be specified with scalar or vector
num_rows = 4
num_cols = 3
M = np.full((num_rows, num_cols), 0.3)
Uv = np.full(num_rows, 0.2)
Us = 0.2
Vv = np.full(num_cols, 0.1)
Vs = 0.1
Ir = np.identity(num_rows)
Ic = np.identity(num_cols)
assert_equal(matrix_normal(mean=M, rowcov=Uv, colcov=Vv).rowcov,
0.2*Ir)
assert_equal(matrix_normal(mean=M, rowcov=Uv, colcov=Vv).colcov,
0.1*Ic)
assert_equal(matrix_normal(mean=M, rowcov=Us, colcov=Vs).rowcov,
0.2*Ir)
assert_equal(matrix_normal(mean=M, rowcov=Us, colcov=Vs).colcov,
0.1*Ic)
def test_frozen_matrix_normal(self):
for i in range(1,5):
for j in range(1,5):
M = np.full((i,j), 0.3)
U = 0.5 * np.identity(i) + np.full((i,i), 0.5)
V = 0.7 * np.identity(j) + np.full((j,j), 0.3)
frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
rvs1 = frozen.rvs(random_state=1234)
rvs2 = matrix_normal.rvs(mean=M, rowcov=U, colcov=V,
random_state=1234)
assert_equal(rvs1, rvs2)
X = frozen.rvs(random_state=1234)
pdf1 = frozen.pdf(X)
pdf2 = matrix_normal.pdf(X, mean=M, rowcov=U, colcov=V)
assert_equal(pdf1, pdf2)
logpdf1 = frozen.logpdf(X)
logpdf2 = matrix_normal.logpdf(X, mean=M, rowcov=U, colcov=V)
assert_equal(logpdf1, logpdf2)
def test_matches_multivariate(self):
# Check that the pdfs match those obtained by vectorising and
# treating as a multivariate normal.
for i in range(1,5):
for j in range(1,5):
M = np.full((i,j), 0.3)
U = 0.5 * np.identity(i) + np.full((i,i), 0.5)
V = 0.7 * np.identity(j) + np.full((j,j), 0.3)
frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
X = frozen.rvs(random_state=1234)
pdf1 = frozen.pdf(X)
logpdf1 = frozen.logpdf(X)
vecX = X.T.flatten()
vecM = M.T.flatten()
cov = np.kron(V,U)
pdf2 = multivariate_normal.pdf(vecX, mean=vecM, cov=cov)
logpdf2 = multivariate_normal.logpdf(vecX, mean=vecM, cov=cov)
assert_allclose(pdf1, pdf2, rtol=1E-10)
assert_allclose(logpdf1, logpdf2, rtol=1E-10)
def test_array_input(self):
# Check array of inputs has the same output as the separate entries.
num_rows = 4
num_cols = 3
M = np.full((num_rows,num_cols), 0.3)
U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
N = 10
frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
X1 = frozen.rvs(size=N, random_state=1234)
X2 = frozen.rvs(size=N, random_state=4321)
X = np.concatenate((X1[np.newaxis,:,:,:],X2[np.newaxis,:,:,:]), axis=0)
assert_equal(X.shape, (2, N, num_rows, num_cols))
array_logpdf = frozen.logpdf(X)
assert_equal(array_logpdf.shape, (2, N))
for i in range(2):
for j in range(N):
separate_logpdf = matrix_normal.logpdf(X[i,j], mean=M,
rowcov=U, colcov=V)
assert_allclose(separate_logpdf, array_logpdf[i,j], 1E-10)
def test_moments(self):
# Check that the sample moments match the parameters
num_rows = 4
num_cols = 3
M = np.full((num_rows,num_cols), 0.3)
U = 0.5 * np.identity(num_rows) + np.full((num_rows, num_rows), 0.5)
V = 0.7 * np.identity(num_cols) + np.full((num_cols, num_cols), 0.3)
N = 1000
frozen = matrix_normal(mean=M, rowcov=U, colcov=V)
X = frozen.rvs(size=N, random_state=1234)
sample_mean = np.mean(X,axis=0)
assert_allclose(sample_mean, M, atol=0.1)
sample_colcov = np.cov(X.reshape(N*num_rows,num_cols).T)
assert_allclose(sample_colcov, V, atol=0.1)
sample_rowcov = np.cov(np.swapaxes(X,1,2).reshape(
N*num_cols,num_rows).T)
assert_allclose(sample_rowcov, U, atol=0.1)
class TestDirichlet(object):
def test_frozen_dirichlet(self):
np.random.seed(2846)
n = np.random.randint(1, 32)
alpha = np.random.uniform(10e-10, 100, n)
d = dirichlet(alpha)
assert_equal(d.var(), dirichlet.var(alpha))
assert_equal(d.mean(), dirichlet.mean(alpha))
assert_equal(d.entropy(), dirichlet.entropy(alpha))
num_tests = 10
for i in range(num_tests):
x = np.random.uniform(10e-10, 100, n)
x /= np.sum(x)
assert_equal(d.pdf(x[:-1]), dirichlet.pdf(x[:-1], alpha))
assert_equal(d.logpdf(x[:-1]), dirichlet.logpdf(x[:-1], alpha))
def test_numpy_rvs_shape_compatibility(self):
np.random.seed(2846)
alpha = np.array([1.0, 2.0, 3.0])
x = np.random.dirichlet(alpha, size=7)
assert_equal(x.shape, (7, 3))
assert_raises(ValueError, dirichlet.pdf, x, alpha)
assert_raises(ValueError, dirichlet.logpdf, x, alpha)
dirichlet.pdf(x.T, alpha)
dirichlet.pdf(x.T[:-1], alpha)
dirichlet.logpdf(x.T, alpha)
dirichlet.logpdf(x.T[:-1], alpha)
def test_alpha_with_zeros(self):
np.random.seed(2846)
alpha = [1.0, 0.0, 3.0]
# don't pass invalid alpha to np.random.dirichlet
x = np.random.dirichlet(np.maximum(1e-9, alpha), size=7).T
assert_raises(ValueError, dirichlet.pdf, x, alpha)
assert_raises(ValueError, dirichlet.logpdf, x, alpha)
def test_alpha_with_negative_entries(self):
np.random.seed(2846)
alpha = [1.0, -2.0, 3.0]
# don't pass invalid alpha to np.random.dirichlet
x = np.random.dirichlet(np.maximum(1e-9, alpha), size=7).T
assert_raises(ValueError, dirichlet.pdf, x, alpha)
assert_raises(ValueError, dirichlet.logpdf, x, alpha)
def test_data_with_zeros(self):
alpha = np.array([1.0, 2.0, 3.0, 4.0])
x = np.array([0.1, 0.0, 0.2, 0.7])
dirichlet.pdf(x, alpha)
dirichlet.logpdf(x, alpha)
alpha = np.array([1.0, 1.0, 1.0, 1.0])
assert_almost_equal(dirichlet.pdf(x, alpha), 6)
assert_almost_equal(dirichlet.logpdf(x, alpha), np.log(6))
def test_data_with_zeros_and_small_alpha(self):
alpha = np.array([1.0, 0.5, 3.0, 4.0])
x = np.array([0.1, 0.0, 0.2, 0.7])
assert_raises(ValueError, dirichlet.pdf, x, alpha)
assert_raises(ValueError, dirichlet.logpdf, x, alpha)
def test_data_with_negative_entries(self):
alpha = np.array([1.0, 2.0, 3.0, 4.0])
x = np.array([0.1, -0.1, 0.3, 0.7])
assert_raises(ValueError, dirichlet.pdf, x, alpha)
assert_raises(ValueError, dirichlet.logpdf, x, alpha)
def test_data_with_too_large_entries(self):
alpha = np.array([1.0, 2.0, 3.0, 4.0])
x = np.array([0.1, 1.1, 0.3, 0.7])
assert_raises(ValueError, dirichlet.pdf, x, alpha)
assert_raises(ValueError, dirichlet.logpdf, x, alpha)
def test_data_too_deep_c(self):
alpha = np.array([1.0, 2.0, 3.0])
x = np.full((2, 7, 7), 1 / 14)
assert_raises(ValueError, dirichlet.pdf, x, alpha)
assert_raises(ValueError, dirichlet.logpdf, x, alpha)
def test_alpha_too_deep(self):
alpha = np.array([[1.0, 2.0], [3.0, 4.0]])
x = np.full((2, 2, 7), 1 / 4)
assert_raises(ValueError, dirichlet.pdf, x, alpha)
assert_raises(ValueError, dirichlet.logpdf, x, alpha)
def test_alpha_correct_depth(self):
alpha = np.array([1.0, 2.0, 3.0])
x = np.full((3, 7), 1 / 3)
dirichlet.pdf(x, alpha)
dirichlet.logpdf(x, alpha)
def test_non_simplex_data(self):
alpha = np.array([1.0, 2.0, 3.0])
x = np.full((3, 7), 1 / 2)
assert_raises(ValueError, dirichlet.pdf, x, alpha)
assert_raises(ValueError, dirichlet.logpdf, x, alpha)
def test_data_vector_too_short(self):
alpha = np.array([1.0, 2.0, 3.0, 4.0])
x = np.full((2, 7), 1 / 2)
assert_raises(ValueError, dirichlet.pdf, x, alpha)
assert_raises(ValueError, dirichlet.logpdf, x, alpha)
def test_data_vector_too_long(self):
alpha = np.array([1.0, 2.0, 3.0, 4.0])
x = np.full((5, 7), 1 / 5)
assert_raises(ValueError, dirichlet.pdf, x, alpha)
assert_raises(ValueError, dirichlet.logpdf, x, alpha)
def test_mean_and_var(self):
alpha = np.array([1., 0.8, 0.2])
d = dirichlet(alpha)
expected_var = [1. / 12., 0.08, 0.03]
expected_mean = [0.5, 0.4, 0.1]
assert_array_almost_equal(d.var(), expected_var)
assert_array_almost_equal(d.mean(), expected_mean)
def test_scalar_values(self):
alpha = np.array([0.2])
d = dirichlet(alpha)
# For alpha of length 1, mean and var should be scalar instead of array
assert_equal(d.mean().ndim, 0)
assert_equal(d.var().ndim, 0)
assert_equal(d.pdf([1.]).ndim, 0)
assert_equal(d.logpdf([1.]).ndim, 0)
def test_K_and_K_minus_1_calls_equal(self):
# Test that calls with K and K-1 entries yield the same results.
np.random.seed(2846)
n = np.random.randint(1, 32)
alpha = np.random.uniform(10e-10, 100, n)
d = dirichlet(alpha)
num_tests = 10
for i in range(num_tests):
x = np.random.uniform(10e-10, 100, n)
x /= np.sum(x)
assert_almost_equal(d.pdf(x[:-1]), d.pdf(x))
def test_multiple_entry_calls(self):
# Test that calls with multiple x vectors as matrix work
np.random.seed(2846)
n = np.random.randint(1, 32)
alpha = np.random.uniform(10e-10, 100, n)
d = dirichlet(alpha)
num_tests = 10
num_multiple = 5
xm = None
for i in range(num_tests):
for m in range(num_multiple):
x = np.random.uniform(10e-10, 100, n)
x /= np.sum(x)
if xm is not None:
xm = np.vstack((xm, x))
else:
xm = x
rm = d.pdf(xm.T)
rs = None
for xs in xm:
r = d.pdf(xs)
if rs is not None:
rs = np.append(rs, r)
else:
rs = r
assert_array_almost_equal(rm, rs)
def test_2D_dirichlet_is_beta(self):
np.random.seed(2846)
alpha = np.random.uniform(10e-10, 100, 2)
d = dirichlet(alpha)
b = beta(alpha[0], alpha[1])
num_tests = 10
for i in range(num_tests):
x = np.random.uniform(10e-10, 100, 2)
x /= np.sum(x)
assert_almost_equal(b.pdf(x), d.pdf([x]))
assert_almost_equal(b.mean(), d.mean()[0])
assert_almost_equal(b.var(), d.var()[0])
def test_multivariate_normal_dimensions_mismatch():
# Regression test for GH #3493. Check that setting up a PDF with a mean of
# length M and a covariance matrix of size (N, N), where M != N, raises a
# ValueError with an informative error message.
mu = np.array([0.0, 0.0])
sigma = np.array([[1.0]])
assert_raises(ValueError, multivariate_normal, mu, sigma)
# A simple check that the right error message was passed along. Checking
# that the entire message is there, word for word, would be somewhat
# fragile, so we just check for the leading part.
try:
multivariate_normal(mu, sigma)
except ValueError as e:
msg = "Dimension mismatch"
assert_equal(str(e)[:len(msg)], msg)
class TestWishart(object):
def test_scale_dimensions(self):
# Test that we can call the Wishart with various scale dimensions
# Test case: dim=1, scale=1
true_scale = np.array(1, ndmin=2)
scales = [
1, # scalar
[1], # iterable
np.array(1), # 0-dim
np.r_[1], # 1-dim
np.array(1, ndmin=2) # 2-dim
]
for scale in scales:
w = wishart(1, scale)
assert_equal(w.scale, true_scale)
assert_equal(w.scale.shape, true_scale.shape)
# Test case: dim=2, scale=[[1,0]
# [0,2]
true_scale = np.array([[1,0],
[0,2]])
scales = [
[1,2], # iterable
np.r_[1,2], # 1-dim
np.array([[1,0], # 2-dim
[0,2]])
]
for scale in scales:
w = wishart(2, scale)
assert_equal(w.scale, true_scale)
assert_equal(w.scale.shape, true_scale.shape)
# We cannot call with a df < dim
assert_raises(ValueError, wishart, 1, np.eye(2))
# We cannot call with a 3-dimension array
scale = np.array(1, ndmin=3)
assert_raises(ValueError, wishart, 1, scale)
def test_quantile_dimensions(self):
# Test that we can call the Wishart rvs with various quantile dimensions
# If dim == 1, consider x.shape = [1,1,1]
X = [
1, # scalar
[1], # iterable
np.array(1), # 0-dim
np.r_[1], # 1-dim
np.array(1, ndmin=2), # 2-dim
np.array([1], ndmin=3) # 3-dim
]
w = wishart(1,1)
density = w.pdf(np.array(1, ndmin=3))
for x in X:
assert_equal(w.pdf(x), density)
# If dim == 1, consider x.shape = [1,1,*]
X = [
[1,2,3], # iterable
np.r_[1,2,3], # 1-dim
np.array([1,2,3], ndmin=3) # 3-dim
]
w = wishart(1,1)
density = w.pdf(np.array([1,2,3], ndmin=3))
for x in X:
assert_equal(w.pdf(x), density)
# If dim == 2, consider x.shape = [2,2,1]
# where x[:,:,*] = np.eye(1)*2
X = [
2, # scalar
[2,2], # iterable
np.array(2), # 0-dim
np.r_[2,2], # 1-dim
np.array([[2,0],
[0,2]]), # 2-dim
np.array([[2,0],
[0,2]])[:,:,np.newaxis] # 3-dim
]
w = wishart(2,np.eye(2))
density = w.pdf(np.array([[2,0],
[0,2]])[:,:,np.newaxis])
for x in X:
assert_equal(w.pdf(x), density)
def test_frozen(self):
# Test that the frozen and non-frozen Wishart gives the same answers
# Construct an arbitrary positive definite scale matrix
dim = 4
scale = np.diag(np.arange(dim)+1)
scale[np.tril_indices(dim, k=-1)] = np.arange(dim * (dim-1) // 2)
scale = np.dot(scale.T, scale)
# Construct a collection of positive definite matrices to test the PDF
X = []
for i in range(5):
x = np.diag(np.arange(dim)+(i+1)**2)
x[np.tril_indices(dim, k=-1)] = np.arange(dim * (dim-1) // 2)
x = np.dot(x.T, x)
X.append(x)
X = np.array(X).T
# Construct a 1D and 2D set of parameters
parameters = [
(10, 1, np.linspace(0.1, 10, 5)), # 1D case
(10, scale, X)
]
for (df, scale, x) in parameters:
w = wishart(df, scale)
assert_equal(w.var(), wishart.var(df, scale))
assert_equal(w.mean(), wishart.mean(df, scale))
assert_equal(w.mode(), wishart.mode(df, scale))
assert_equal(w.entropy(), wishart.entropy(df, scale))
assert_equal(w.pdf(x), wishart.pdf(x, df, scale))
def test_1D_is_chisquared(self):
# The 1-dimensional Wishart with an identity scale matrix is just a
# chi-squared distribution.
# Test variance, mean, entropy, pdf
# Kolgomorov-Smirnov test for rvs
np.random.seed(482974)
sn = 500
dim = 1
scale = np.eye(dim)
df_range = np.arange(1, 10, 2, dtype=float)
X = np.linspace(0.1,10,num=10)
for df in df_range:
w = wishart(df, scale)
c = chi2(df)
# Statistics
assert_allclose(w.var(), c.var())
assert_allclose(w.mean(), c.mean())
assert_allclose(w.entropy(), c.entropy())
# PDF
assert_allclose(w.pdf(X), c.pdf(X))
# rvs
rvs = w.rvs(size=sn)
args = (df,)
alpha = 0.01
check_distribution_rvs('chi2', args, alpha, rvs)
def test_is_scaled_chisquared(self):
# The 2-dimensional Wishart with an arbitrary scale matrix can be
# transformed to a scaled chi-squared distribution.
# For :math:`S \sim W_p(V,n)` and :math:`\lambda \in \mathbb{R}^p` we have
# :math:`\lambda' S \lambda \sim \lambda' V \lambda \times \chi^2(n)`
np.random.seed(482974)
sn = 500
df = 10
dim = 4
# Construct an arbitrary positive definite matrix
scale = np.diag(np.arange(4)+1)
scale[np.tril_indices(4, k=-1)] = np.arange(6)
scale = np.dot(scale.T, scale)
# Use :math:`\lambda = [1, \dots, 1]'`
lamda = np.ones((dim,1))
sigma_lamda = lamda.T.dot(scale).dot(lamda).squeeze()
w = wishart(df, sigma_lamda)
c = chi2(df, scale=sigma_lamda)
# Statistics
assert_allclose(w.var(), c.var())
assert_allclose(w.mean(), c.mean())
assert_allclose(w.entropy(), c.entropy())
# PDF
X = np.linspace(0.1,10,num=10)
assert_allclose(w.pdf(X), c.pdf(X))
# rvs
rvs = w.rvs(size=sn)
args = (df,0,sigma_lamda)
alpha = 0.01
check_distribution_rvs('chi2', args, alpha, rvs)
class TestMultinomial(object):
def test_logpmf(self):
vals1 = multinomial.logpmf((3,4), 7, (0.3, 0.7))
assert_allclose(vals1, -1.483270127243324, rtol=1e-8)
vals2 = multinomial.logpmf([3, 4], 0, [.3, .7])
assert_allclose(vals2, np.NAN, rtol=1e-8)
vals3 = multinomial.logpmf([3, 4], 0, [-2, 3])
assert_allclose(vals3, np.NAN, rtol=1e-8)
def test_reduces_binomial(self):
# test that the multinomial pmf reduces to the binomial pmf in the 2d
# case
val1 = multinomial.logpmf((3, 4), 7, (0.3, 0.7))
val2 = binom.logpmf(3, 7, 0.3)
assert_allclose(val1, val2, rtol=1e-8)
val1 = multinomial.pmf((6, 8), 14, (0.1, 0.9))
val2 = binom.pmf(6, 14, 0.1)
assert_allclose(val1, val2, rtol=1e-8)
def test_R(self):
# test against the values produced by this R code
# (https://stat.ethz.ch/R-manual/R-devel/library/stats/html/Multinom.html)
# X <- t(as.matrix(expand.grid(0:3, 0:3))); X <- X[, colSums(X) <= 3]
# X <- rbind(X, 3:3 - colSums(X)); dimnames(X) <- list(letters[1:3], NULL)
# X
# apply(X, 2, function(x) dmultinom(x, prob = c(1,2,5)))
n, p = 3, [1./8, 2./8, 5./8]
r_vals = {(0, 0, 3): 0.244140625, (1, 0, 2): 0.146484375,
(2, 0, 1): 0.029296875, (3, 0, 0): 0.001953125,
(0, 1, 2): 0.292968750, (1, 1, 1): 0.117187500,
(2, 1, 0): 0.011718750, (0, 2, 1): 0.117187500,
(1, 2, 0): 0.023437500, (0, 3, 0): 0.015625000}
for x in r_vals:
assert_allclose(multinomial.pmf(x, n, p), r_vals[x], atol=1e-14)
def test_rvs_np(self):
# test that .rvs agrees w/numpy
sc_rvs = multinomial.rvs(3, [1/4.]*3, size=7, random_state=123)
rndm = np.random.RandomState(123)
np_rvs = rndm.multinomial(3, [1/4.]*3, size=7)
assert_equal(sc_rvs, np_rvs)
def test_pmf(self):
vals0 = multinomial.pmf((5,), 5, (1,))
assert_allclose(vals0, 1, rtol=1e-8)
vals1 = multinomial.pmf((3,4), 7, (.3, .7))
assert_allclose(vals1, .22689449999999994, rtol=1e-8)
vals2 = multinomial.pmf([[[3,5],[0,8]], [[-1, 9], [1, 1]]], 8,
(.1, .9))
assert_allclose(vals2, [[.03306744, .43046721], [0, 0]], rtol=1e-8)
x = np.empty((0,2), dtype=np.float64)
vals3 = multinomial.pmf(x, 4, (.3, .7))
assert_equal(vals3, np.empty([], dtype=np.float64))
vals4 = multinomial.pmf([1,2], 4, (.3, .7))
assert_allclose(vals4, 0, rtol=1e-8)
vals5 = multinomial.pmf([3, 3, 0], 6, [2/3.0, 1/3.0, 0])
assert_allclose(vals5, 0.219478737997, rtol=1e-8)
def test_pmf_broadcasting(self):
vals0 = multinomial.pmf([1, 2], 3, [[.1, .9], [.2, .8]])
assert_allclose(vals0, [.243, .384], rtol=1e-8)
vals1 = multinomial.pmf([1, 2], [3, 4], [.1, .9])
assert_allclose(vals1, [.243, 0], rtol=1e-8)
vals2 = multinomial.pmf([[[1, 2], [1, 1]]], 3, [.1, .9])
assert_allclose(vals2, [[.243, 0]], rtol=1e-8)
vals3 = multinomial.pmf([1, 2], [[[3], [4]]], [.1, .9])
assert_allclose(vals3, [[[.243], [0]]], rtol=1e-8)
vals4 = multinomial.pmf([[1, 2], [1,1]], [[[[3]]]], [.1, .9])
assert_allclose(vals4, [[[[.243, 0]]]], rtol=1e-8)
def test_cov(self):
cov1 = multinomial.cov(5, (.2, .3, .5))
cov2 = [[5*.2*.8, -5*.2*.3, -5*.2*.5],
[-5*.3*.2, 5*.3*.7, -5*.3*.5],
[-5*.5*.2, -5*.5*.3, 5*.5*.5]]
assert_allclose(cov1, cov2, rtol=1e-8)
def test_cov_broadcasting(self):
cov1 = multinomial.cov(5, [[.1, .9], [.2, .8]])
cov2 = [[[.45, -.45],[-.45, .45]], [[.8, -.8], [-.8, .8]]]
assert_allclose(cov1, cov2, rtol=1e-8)
cov3 = multinomial.cov([4, 5], [.1, .9])
cov4 = [[[.36, -.36], [-.36, .36]], [[.45, -.45], [-.45, .45]]]
assert_allclose(cov3, cov4, rtol=1e-8)
cov5 = multinomial.cov([4, 5], [[.3, .7], [.4, .6]])
cov6 = [[[4*.3*.7, -4*.3*.7], [-4*.3*.7, 4*.3*.7]],
[[5*.4*.6, -5*.4*.6], [-5*.4*.6, 5*.4*.6]]]
assert_allclose(cov5, cov6, rtol=1e-8)
def test_entropy(self):
# this is equivalent to a binomial distribution with n=2, so the
# entropy .77899774929 is easily computed "by hand"
ent0 = multinomial.entropy(2, [.2, .8])
assert_allclose(ent0, binom.entropy(2, .2), rtol=1e-8)
def test_entropy_broadcasting(self):
ent0 = multinomial.entropy([2, 3], [.2, .3])
assert_allclose(ent0, [binom.entropy(2, .2), binom.entropy(3, .2)],
rtol=1e-8)
ent1 = multinomial.entropy([7, 8], [[.3, .7], [.4, .6]])
assert_allclose(ent1, [binom.entropy(7, .3), binom.entropy(8, .4)],
rtol=1e-8)
ent2 = multinomial.entropy([[7], [8]], [[.3, .7], [.4, .6]])
assert_allclose(ent2,
[[binom.entropy(7, .3), binom.entropy(7, .4)],
[binom.entropy(8, .3), binom.entropy(8, .4)]],
rtol=1e-8)
def test_mean(self):
mean1 = multinomial.mean(5, [.2, .8])
assert_allclose(mean1, [5*.2, 5*.8], rtol=1e-8)
def test_mean_broadcasting(self):
mean1 = multinomial.mean([5, 6], [.2, .8])
assert_allclose(mean1, [[5*.2, 5*.8], [6*.2, 6*.8]], rtol=1e-8)
def test_frozen(self):
# The frozen distribution should agree with the regular one
np.random.seed(1234)
n = 12
pvals = (.1, .2, .3, .4)
x = [[0,0,0,12],[0,0,1,11],[0,1,1,10],[1,1,1,9],[1,1,2,8]]
x = np.asarray(x, dtype=np.float64)
mn_frozen = multinomial(n, pvals)
assert_allclose(mn_frozen.pmf(x), multinomial.pmf(x, n, pvals))
assert_allclose(mn_frozen.logpmf(x), multinomial.logpmf(x, n, pvals))
assert_allclose(mn_frozen.entropy(), multinomial.entropy(n, pvals))
class TestInvwishart(object):
def test_frozen(self):
# Test that the frozen and non-frozen inverse Wishart gives the same
# answers
# Construct an arbitrary positive definite scale matrix
dim = 4
scale = np.diag(np.arange(dim)+1)
scale[np.tril_indices(dim, k=-1)] = np.arange(dim*(dim-1)/2)
scale = np.dot(scale.T, scale)
# Construct a collection of positive definite matrices to test the PDF
X = []
for i in range(5):
x = np.diag(np.arange(dim)+(i+1)**2)
x[np.tril_indices(dim, k=-1)] = np.arange(dim*(dim-1)/2)
x = np.dot(x.T, x)
X.append(x)
X = np.array(X).T
# Construct a 1D and 2D set of parameters
parameters = [
(10, 1, np.linspace(0.1, 10, 5)), # 1D case
(10, scale, X)
]
for (df, scale, x) in parameters:
iw = invwishart(df, scale)
assert_equal(iw.var(), invwishart.var(df, scale))
assert_equal(iw.mean(), invwishart.mean(df, scale))
assert_equal(iw.mode(), invwishart.mode(df, scale))
assert_allclose(iw.pdf(x), invwishart.pdf(x, df, scale))
def test_1D_is_invgamma(self):
# The 1-dimensional inverse Wishart with an identity scale matrix is
# just an inverse gamma distribution.
# Test variance, mean, pdf
# Kolgomorov-Smirnov test for rvs
np.random.seed(482974)
sn = 500
dim = 1
scale = np.eye(dim)
df_range = np.arange(5, 20, 2, dtype=float)
X = np.linspace(0.1,10,num=10)
for df in df_range:
iw = invwishart(df, scale)
ig = invgamma(df/2, scale=1./2)
# Statistics
assert_allclose(iw.var(), ig.var())
assert_allclose(iw.mean(), ig.mean())
# PDF
assert_allclose(iw.pdf(X), ig.pdf(X))
# rvs
rvs = iw.rvs(size=sn)
args = (df/2, 0, 1./2)
alpha = 0.01
check_distribution_rvs('invgamma', args, alpha, rvs)
def test_wishart_invwishart_2D_rvs(self):
dim = 3
df = 10
# Construct a simple non-diagonal positive definite matrix
scale = np.eye(dim)
scale[0,1] = 0.5
scale[1,0] = 0.5
# Construct frozen Wishart and inverse Wishart random variables
w = wishart(df, scale)
iw = invwishart(df, scale)
# Get the generated random variables from a known seed
np.random.seed(248042)
w_rvs = wishart.rvs(df, scale)
np.random.seed(248042)
frozen_w_rvs = w.rvs()
np.random.seed(248042)
iw_rvs = invwishart.rvs(df, scale)
np.random.seed(248042)
frozen_iw_rvs = iw.rvs()
# Manually calculate what it should be, based on the Bartlett (1933)
# decomposition of a Wishart into D A A' D', where D is the Cholesky
# factorization of the scale matrix and A is the lower triangular matrix
# with the square root of chi^2 variates on the diagonal and N(0,1)
# variates in the lower triangle.
np.random.seed(248042)
covariances = np.random.normal(size=3)
variances = np.r_[
np.random.chisquare(df),
np.random.chisquare(df-1),
np.random.chisquare(df-2),
]**0.5
# Construct the lower-triangular A matrix
A = np.diag(variances)
A[np.tril_indices(dim, k=-1)] = covariances
# Wishart random variate
D = np.linalg.cholesky(scale)
DA = D.dot(A)
manual_w_rvs = np.dot(DA, DA.T)
# inverse Wishart random variate
# Supposing that the inverse wishart has scale matrix `scale`, then the
# random variate is the inverse of a random variate drawn from a Wishart
# distribution with scale matrix `inv_scale = np.linalg.inv(scale)`
iD = np.linalg.cholesky(np.linalg.inv(scale))
iDA = iD.dot(A)
manual_iw_rvs = np.linalg.inv(np.dot(iDA, iDA.T))
# Test for equality
assert_allclose(w_rvs, manual_w_rvs)
assert_allclose(frozen_w_rvs, manual_w_rvs)
assert_allclose(iw_rvs, manual_iw_rvs)
assert_allclose(frozen_iw_rvs, manual_iw_rvs)
def test_cho_inv_batch(self):
"""Regression test for gh-8844."""
a0 = np.array([[2, 1, 0, 0.5],
[1, 2, 0.5, 0.5],
[0, 0.5, 3, 1],
[0.5, 0.5, 1, 2]])
a1 = np.array([[2, -1, 0, 0.5],
[-1, 2, 0.5, 0.5],
[0, 0.5, 3, 1],
[0.5, 0.5, 1, 4]])
a = np.array([a0, a1])
ainv = a.copy()
_cho_inv_batch(ainv)
ident = np.eye(4)
assert_allclose(a[0].dot(ainv[0]), ident, atol=1e-15)
assert_allclose(a[1].dot(ainv[1]), ident, atol=1e-15)
def test_logpdf_4x4(self):
"""Regression test for gh-8844."""
X = np.array([[2, 1, 0, 0.5],
[1, 2, 0.5, 0.5],
[0, 0.5, 3, 1],
[0.5, 0.5, 1, 2]])
Psi = np.array([[9, 7, 3, 1],
[7, 9, 5, 1],
[3, 5, 8, 2],
[1, 1, 2, 9]])
nu = 6
prob = invwishart.logpdf(X, nu, Psi)
# Explicit calculation from the formula on wikipedia.
p = X.shape[0]
sig, logdetX = np.linalg.slogdet(X)
sig, logdetPsi = np.linalg.slogdet(Psi)
M = np.linalg.solve(X, Psi)
expected = ((nu/2)*logdetPsi
- (nu*p/2)*np.log(2)
- multigammaln(nu/2, p)
- (nu + p + 1)/2*logdetX
- 0.5*M.trace())
assert_allclose(prob, expected)
class TestSpecialOrthoGroup(object):
def test_reproducibility(self):
np.random.seed(514)
x = special_ortho_group.rvs(3)
expected = np.array([[-0.99394515, -0.04527879, 0.10011432],
[0.04821555, -0.99846897, 0.02711042],
[0.09873351, 0.03177334, 0.99460653]])
assert_array_almost_equal(x, expected)
random_state = np.random.RandomState(seed=514)
x = special_ortho_group.rvs(3, random_state=random_state)
assert_array_almost_equal(x, expected)
def test_invalid_dim(self):
assert_raises(ValueError, special_ortho_group.rvs, None)
assert_raises(ValueError, special_ortho_group.rvs, (2, 2))
assert_raises(ValueError, special_ortho_group.rvs, 1)
assert_raises(ValueError, special_ortho_group.rvs, 2.5)
def test_frozen_matrix(self):
dim = 7
frozen = special_ortho_group(dim)
rvs1 = frozen.rvs(random_state=1234)
rvs2 = special_ortho_group.rvs(dim, random_state=1234)
assert_equal(rvs1, rvs2)
def test_det_and_ortho(self):
xs = [special_ortho_group.rvs(dim)
for dim in range(2,12)
for i in range(3)]
# Test that determinants are always +1
dets = [np.linalg.det(x) for x in xs]
assert_allclose(dets, [1.]*30, rtol=1e-13)
# Test that these are orthogonal matrices
for x in xs:
assert_array_almost_equal(np.dot(x, x.T),
np.eye(x.shape[0]))
def test_haar(self):
# Test that the distribution is constant under rotation
# Every column should have the same distribution
# Additionally, the distribution should be invariant under another rotation
# Generate samples
dim = 5
samples = 1000 # Not too many, or the test takes too long
ks_prob = .05
np.random.seed(514)
xs = special_ortho_group.rvs(dim, size=samples)
# Dot a few rows (0, 1, 2) with unit vectors (0, 2, 4, 3),
# effectively picking off entries in the matrices of xs.
# These projections should all have the same disribution,
# establishing rotational invariance. We use the two-sided
# KS test to confirm this.
# We could instead test that angles between random vectors
# are uniformly distributed, but the below is sufficient.
# It is not feasible to consider all pairs, so pick a few.
els = ((0,0), (0,2), (1,4), (2,3))
#proj = {(er, ec): [x[er][ec] for x in xs] for er, ec in els}
proj = dict(((er, ec), sorted([x[er][ec] for x in xs])) for er, ec in els)
pairs = [(e0, e1) for e0 in els for e1 in els if e0 > e1]
ks_tests = [ks_2samp(proj[p0], proj[p1])[1] for (p0, p1) in pairs]
assert_array_less([ks_prob]*len(pairs), ks_tests)
class TestOrthoGroup(object):
def test_reproducibility(self):
np.random.seed(515)
x = ortho_group.rvs(3)
x2 = ortho_group.rvs(3, random_state=515)
# Note this matrix has det -1, distinguishing O(N) from SO(N)
assert_almost_equal(np.linalg.det(x), -1)
expected = np.array([[0.94449759, -0.21678569, -0.24683651],
[-0.13147569, -0.93800245, 0.3207266],
[0.30106219, 0.27047251, 0.9144431]])
assert_array_almost_equal(x, expected)
assert_array_almost_equal(x2, expected)
def test_invalid_dim(self):
assert_raises(ValueError, ortho_group.rvs, None)
assert_raises(ValueError, ortho_group.rvs, (2, 2))
assert_raises(ValueError, ortho_group.rvs, 1)
assert_raises(ValueError, ortho_group.rvs, 2.5)
def test_det_and_ortho(self):
xs = [[ortho_group.rvs(dim)
for i in range(10)]
for dim in range(2,12)]
# Test that abs determinants are always +1
dets = np.array([[np.linalg.det(x) for x in xx] for xx in xs])
assert_allclose(np.fabs(dets), np.ones(dets.shape), rtol=1e-13)
# Test that we get both positive and negative determinants
# Check that we have at least one and less than 10 negative dets in a sample of 10. The rest are positive by the previous test.
# Test each dimension separately
assert_array_less([0]*10, [np.nonzero(d < 0)[0].shape[0] for d in dets])
assert_array_less([np.nonzero(d < 0)[0].shape[0] for d in dets], [10]*10)
# Test that these are orthogonal matrices
for xx in xs:
for x in xx:
assert_array_almost_equal(np.dot(x, x.T),
np.eye(x.shape[0]))
def test_haar(self):
# Test that the distribution is constant under rotation
# Every column should have the same distribution
# Additionally, the distribution should be invariant under another rotation
# Generate samples
dim = 5
samples = 1000 # Not too many, or the test takes too long
ks_prob = .05
np.random.seed(518) # Note that the test is sensitive to seed too
xs = ortho_group.rvs(dim, size=samples)
# Dot a few rows (0, 1, 2) with unit vectors (0, 2, 4, 3),
# effectively picking off entries in the matrices of xs.
# These projections should all have the same disribution,
# establishing rotational invariance. We use the two-sided
# KS test to confirm this.
# We could instead test that angles between random vectors
# are uniformly distributed, but the below is sufficient.
# It is not feasible to consider all pairs, so pick a few.
els = ((0,0), (0,2), (1,4), (2,3))
#proj = {(er, ec): [x[er][ec] for x in xs] for er, ec in els}
proj = dict(((er, ec), sorted([x[er][ec] for x in xs])) for er, ec in els)
pairs = [(e0, e1) for e0 in els for e1 in els if e0 > e1]
ks_tests = [ks_2samp(proj[p0], proj[p1])[1] for (p0, p1) in pairs]
assert_array_less([ks_prob]*len(pairs), ks_tests)
@pytest.mark.slow
def test_pairwise_distances(self):
# Test that the distribution of pairwise distances is close to correct.
np.random.seed(514)
def random_ortho(dim):
u, _s, v = np.linalg.svd(np.random.normal(size=(dim, dim)))
return np.dot(u, v)
for dim in range(2, 6):
def generate_test_statistics(rvs, N=1000, eps=1e-10):
stats = np.array([
np.sum((rvs(dim=dim) - rvs(dim=dim))**2)
for _ in range(N)
])
# Add a bit of noise to account for numeric accuracy.
stats += np.random.uniform(-eps, eps, size=stats.shape)
return stats
expected = generate_test_statistics(random_ortho)
actual = generate_test_statistics(scipy.stats.ortho_group.rvs)
_D, p = scipy.stats.ks_2samp(expected, actual)
assert_array_less(.05, p)
class TestRandomCorrelation(object):
def test_reproducibility(self):
np.random.seed(514)
eigs = (.5, .8, 1.2, 1.5)
x = random_correlation.rvs(eigs)
x2 = random_correlation.rvs(eigs, random_state=514)
expected = np.array([[1., -0.20387311, 0.18366501, -0.04953711],
[-0.20387311, 1., -0.24351129, 0.06703474],
[0.18366501, -0.24351129, 1., 0.38530195],
[-0.04953711, 0.06703474, 0.38530195, 1.]])
assert_array_almost_equal(x, expected)
assert_array_almost_equal(x2, expected)
def test_invalid_eigs(self):
assert_raises(ValueError, random_correlation.rvs, None)
assert_raises(ValueError, random_correlation.rvs, 'test')
assert_raises(ValueError, random_correlation.rvs, 2.5)
assert_raises(ValueError, random_correlation.rvs, [2.5])
assert_raises(ValueError, random_correlation.rvs, [[1,2],[3,4]])
assert_raises(ValueError, random_correlation.rvs, [2.5, -.5])
assert_raises(ValueError, random_correlation.rvs, [1, 2, .1])
def test_definition(self):
# Test the definition of a correlation matrix in several dimensions:
#
# 1. Det is product of eigenvalues (and positive by construction
# in examples)
# 2. 1's on diagonal
# 3. Matrix is symmetric
def norm(i, e):
return i*e/sum(e)
np.random.seed(123)
eigs = [norm(i, np.random.uniform(size=i)) for i in range(2, 6)]
eigs.append([4,0,0,0])
ones = [[1.]*len(e) for e in eigs]
xs = [random_correlation.rvs(e) for e in eigs]
# Test that determinants are products of eigenvalues
# These are positive by construction
# Could also test that the eigenvalues themselves are correct,
# but this seems sufficient.
dets = [np.fabs(np.linalg.det(x)) for x in xs]
dets_known = [np.prod(e) for e in eigs]
assert_allclose(dets, dets_known, rtol=1e-13, atol=1e-13)
# Test for 1's on the diagonal
diags = [np.diag(x) for x in xs]
for a, b in zip(diags, ones):
assert_allclose(a, b, rtol=1e-13)
# Correlation matrices are symmetric
for x in xs:
assert_allclose(x, x.T, rtol=1e-13)
def test_to_corr(self):
# Check some corner cases in to_corr
# ajj == 1
m = np.array([[0.1, 0], [0, 1]], dtype=float)
m = random_correlation._to_corr(m)
assert_allclose(m, np.array([[1, 0], [0, 0.1]]))
# Floating point overflow; fails to compute the correct
# rotation, but should still produce some valid rotation
# rather than infs/nans
with np.errstate(over='ignore'):
g = np.array([[0, 1], [-1, 0]])
m0 = np.array([[1e300, 0], [0, np.nextafter(1, 0)]], dtype=float)
m = random_correlation._to_corr(m0.copy())
assert_allclose(m, g.T.dot(m0).dot(g))
m0 = np.array([[0.9, 1e300], [1e300, 1.1]], dtype=float)
m = random_correlation._to_corr(m0.copy())
assert_allclose(m, g.T.dot(m0).dot(g))
# Zero discriminant; should set the first diag entry to 1
m0 = np.array([[2, 1], [1, 2]], dtype=float)
m = random_correlation._to_corr(m0.copy())
assert_allclose(m[0,0], 1)
# Slightly negative discriminant; should be approx correct still
m0 = np.array([[2 + 1e-7, 1], [1, 2]], dtype=float)
m = random_correlation._to_corr(m0.copy())
assert_allclose(m[0,0], 1)
class TestUnitaryGroup(object):
def test_reproducibility(self):
np.random.seed(514)
x = unitary_group.rvs(3)
x2 = unitary_group.rvs(3, random_state=514)
expected = np.array([[0.308771+0.360312j, 0.044021+0.622082j, 0.160327+0.600173j],
[0.732757+0.297107j, 0.076692-0.4614j, -0.394349+0.022613j],
[-0.148844+0.357037j, -0.284602-0.557949j, 0.607051+0.299257j]])
assert_array_almost_equal(x, expected)
assert_array_almost_equal(x2, expected)
def test_invalid_dim(self):
assert_raises(ValueError, unitary_group.rvs, None)
assert_raises(ValueError, unitary_group.rvs, (2, 2))
assert_raises(ValueError, unitary_group.rvs, 1)
assert_raises(ValueError, unitary_group.rvs, 2.5)
def test_unitarity(self):
xs = [unitary_group.rvs(dim)
for dim in range(2,12)
for i in range(3)]
# Test that these are unitary matrices
for x in xs:
assert_allclose(np.dot(x, x.conj().T), np.eye(x.shape[0]), atol=1e-15)
def test_haar(self):
# Test that the eigenvalues, which lie on the unit circle in
# the complex plane, are uncorrelated.
# Generate samples
dim = 5
samples = 1000 # Not too many, or the test takes too long
np.random.seed(514) # Note that the test is sensitive to seed too
xs = unitary_group.rvs(dim, size=samples)
# The angles "x" of the eigenvalues should be uniformly distributed
# Overall this seems to be a necessary but weak test of the distribution.
eigs = np.vstack([scipy.linalg.eigvals(x) for x in xs])
x = np.arctan2(eigs.imag, eigs.real)
res = kstest(x.ravel(), uniform(-np.pi, 2*np.pi).cdf)
assert_(res.pvalue > 0.05)
class TestMultivariateT:
# These tests were created by running vpa(mvtpdf(...)) in MATLAB. The
# function takes no `mu` parameter. The tests were run as
#
# >> ans = vpa(mvtpdf(x - mu, shape, df));
#
PDF_TESTS = [(
# x
[
[1, 2],
[4, 1],
[2, 1],
[2, 4],
[1, 4],
[4, 1],
[3, 2],
[3, 3],
[4, 4],
[5, 1],
],
# loc
[0, 0],
# shape
[
[1, 0],
[0, 1]
],
# df
4,
# ans
[
0.013972450422333741737457302178882,
0.0010998721906793330026219646100571,
0.013972450422333741737457302178882,
0.00073682844024025606101402363634634,
0.0010998721906793330026219646100571,
0.0010998721906793330026219646100571,
0.0020732579600816823488240725481546,
0.00095660371505271429414668515889275,
0.00021831953784896498569831346792114,
0.00037725616140301147447000396084604
]
), (
# x
[
[0.9718, 0.1298, 0.8134],
[0.4922, 0.5522, 0.7185],
[0.3010, 0.1491, 0.5008],
[0.5971, 0.2585, 0.8940],
[0.5434, 0.5287, 0.9507],
],
# loc
[-1, 1, 50],
# shape
[
[1.0000, 0.5000, 0.2500],
[0.5000, 1.0000, -0.1000],
[0.2500, -0.1000, 1.0000],
],
# df
8,
# ans
[
0.00000000000000069609279697467772867405511133763,
0.00000000000000073700739052207366474839369535934,
0.00000000000000069522909962669171512174435447027,
0.00000000000000074212293557998314091880208889767,
0.00000000000000077039675154022118593323030449058,
]
)]
@pytest.mark.parametrize("x, loc, shape, df, ans", PDF_TESTS)
def test_pdf_correctness(self, x, loc, shape, df, ans):
dist = multivariate_t(loc, shape, df, seed=0)
val = dist.pdf(x)
assert_array_almost_equal(val, ans)
@pytest.mark.parametrize("x, loc, shape, df, ans", PDF_TESTS)
def test_logpdf_correct(self, x, loc, shape, df, ans):
dist = multivariate_t(loc, shape, df, seed=0)
val1 = dist.pdf(x)
val2 = dist.logpdf(x)
assert_array_almost_equal(np.log(val1), val2)
# https://github.com/scipy/scipy/issues/10042#issuecomment-576795195
def test_mvt_with_df_one_is_cauchy(self):
x = [9, 7, 4, 1, -3, 9, 0, -3, -1, 3]
val = multivariate_t.pdf(x, df=1)
ans = cauchy.pdf(x)
assert_array_almost_equal(val, ans)
def test_mvt_with_high_df_is_approx_normal(self):
# `normaltest` returns the chi-squared statistic and the associated
# p-value. The null hypothesis is that `x` came from a normal
# distribution, so a low p-value represents rejecting the null, i.e.
# that it is unlikely that `x` came a normal distribution.
P_VAL_MIN = 0.1
dist = multivariate_t(0, 1, df=100000, seed=1)
samples = dist.rvs(size=100000)
_, p = normaltest(samples)
assert (p > P_VAL_MIN)
dist = multivariate_t([-2, 3], [[10, -1], [-1, 10]], df=100000,
seed=42)
samples = dist.rvs(size=100000)
_, p = normaltest(samples)
assert ((p > P_VAL_MIN).all())
@patch('scipy.stats.multivariate_normal._logpdf')
def test_mvt_with_inf_df_calls_normal(self, mock):
dist = multivariate_t(0, 1, df=np.inf, seed=7)
assert isinstance(dist, multivariate_normal_frozen)
multivariate_t.pdf(0, df=np.inf)
assert mock.call_count == 1
multivariate_t.logpdf(0, df=np.inf)
assert mock.call_count == 2
def test_shape_correctness(self):
# pdf and logpdf should return scalar when the
# number of samples in x is one.
dim = 4
loc = np.zeros(dim)
shape = np.eye(dim)
df = 4.5
x = np.zeros(dim)
res = multivariate_t(loc, shape, df).pdf(x)
assert np.isscalar(res)
res = multivariate_t(loc, shape, df).logpdf(x)
assert np.isscalar(res)
# pdf() and logpdf() should return probabilities of shape
# (n_samples,) when x has n_samples.
n_samples = 7
x = np.random.random((n_samples, dim))
res = multivariate_t(loc, shape, df).pdf(x)
assert (res.shape == (n_samples,))
res = multivariate_t(loc, shape, df).logpdf(x)
assert (res.shape == (n_samples,))
# rvs() should return scalar unless a size argument is applied.
res = multivariate_t(np.zeros(1), np.eye(1), 1).rvs()
assert np.isscalar(res)
# rvs() should return vector of shape (size,) if size argument
# is applied.
size = 7
res = multivariate_t(np.zeros(1), np.eye(1), 1).rvs(size=size)
assert (res.shape == (size,))
def test_default_arguments(self):
dist = multivariate_t()
assert_equal(dist.loc, [0])
assert_equal(dist.shape, [[1]])
assert (dist.df == 1)
DEFAULT_ARGS_TESTS = [
(None, None, None, 0, 1, 1),
(None, None, 7, 0, 1, 7),
(None, [[7, 0], [0, 7]], None, [0, 0], [[7, 0], [0, 7]], 1),
(None, [[7, 0], [0, 7]], 7, [0, 0], [[7, 0], [0, 7]], 7),
([7, 7], None, None, [7, 7], [[1, 0], [0, 1]], 1),
([7, 7], None, 7, [7, 7], [[1, 0], [0, 1]], 7),
([7, 7], [[7, 0], [0, 7]], None, [7, 7], [[7, 0], [0, 7]], 1),
([7, 7], [[7, 0], [0, 7]], 7, [7, 7], [[7, 0], [0, 7]], 7)
]
@pytest.mark.parametrize("loc, shape, df, loc_ans, shape_ans, df_ans", DEFAULT_ARGS_TESTS)
def test_default_args(self, loc, shape, df, loc_ans, shape_ans, df_ans):
dist = multivariate_t(loc=loc, shape=shape, df=df)
assert_equal(dist.loc, loc_ans)
assert_equal(dist.shape, shape_ans)
assert (dist.df == df_ans)
ARGS_SHAPES_TESTS = [
(-1, 2, 3, [-1], [[2]], 3),
([-1], [2], 3, [-1], [[2]], 3),
(np.array([-1]), np.array([2]), 3, [-1], [[2]], 3)
]
@pytest.mark.parametrize("loc, shape, df, loc_ans, shape_ans, df_ans", ARGS_SHAPES_TESTS)
def test_scalar_list_and_ndarray_arguments(self, loc, shape, df, loc_ans, shape_ans, df_ans):
dist = multivariate_t(loc, shape, df)
assert_equal(dist.loc, loc_ans)
assert_equal(dist.shape, shape_ans)
assert_equal(dist.df, df_ans)
def test_argument_error_handling(self):
# `loc` should be a one-dimensional vector.
loc = [[1, 1]]
assert_raises(ValueError,
multivariate_t,
**dict(loc=loc))
# `shape` should be scalar or square matrix.
shape = [[1, 1], [2, 2], [3, 3]]
assert_raises(ValueError,
multivariate_t,
**dict(loc=loc, shape=shape))
# `df` should be greater than zero.
loc = np.zeros(2)
shape = np.eye(2)
df = -1
assert_raises(ValueError,
multivariate_t,
**dict(loc=loc, shape=shape, df=df))
df = 0
assert_raises(ValueError,
multivariate_t,
**dict(loc=loc, shape=shape, df=df))
def test_reproducibility(self):
rng = np.random.RandomState(4)
loc = rng.uniform(size=3)
shape = np.eye(3)
dist1 = multivariate_t(loc, shape, df=3, seed=2)
dist2 = multivariate_t(loc, shape, df=3, seed=2)
samples1 = dist1.rvs(size=10)
samples2 = dist2.rvs(size=10)
assert_equal(samples1, samples2)
def test_allow_singular(self):
# Make shape singular and verify error was raised.
args = dict(loc=[0,0], shape=[[0,0],[0,1]], df=1, allow_singular=False)
assert_raises(np.linalg.LinAlgError, multivariate_t, **args)
class TestMultivariateHypergeom:
@pytest.mark.parametrize(
"x, m, n, expected",
[
# Ground truth value from R dmvhyper
([3, 4], [5, 10], 7, -1.119814),
# test for `n=0`
([3, 4], [5, 10], 0, np.NINF),
# test for `x < 0`
([-3, 4], [5, 10], 7, np.NINF),
# test for `m < 0` (RuntimeWarning issue)
([3, 4], [-5, 10], 7, np.nan),
# test for all `m < 0` and `x.sum() != n`
([[1, 2], [3, 4]], [[-4, -6], [-5, -10]],
[3, 7], [np.nan, np.nan]),
# test for `x < 0` and `m < 0` (RuntimeWarning issue)
([-3, 4], [-5, 10], 1, np.nan),
# test for `x > m`
([1, 11], [10, 1], 12, np.nan),
# test for `m < 0` (RuntimeWarning issue)
([1, 11], [10, -1], 12, np.nan),
# test for `n < 0`
([3, 4], [5, 10], -7, np.nan),
# test for `x.sum() != n`
([3, 3], [5, 10], 7, np.NINF)
]
)
def test_logpmf(self, x, m, n, expected):
vals = multivariate_hypergeom.logpmf(x, m, n)
assert_allclose(vals, expected, rtol=1e-6)
def test_reduces_hypergeom(self):
# test that the multivariate_hypergeom pmf reduces to the
# hypergeom pmf in the 2d case.
val1 = multivariate_hypergeom.pmf(x=[3, 1], m=[10, 5], n=4)
val2 = hypergeom.pmf(k=3, M=15, n=4, N=10)
assert_allclose(val1, val2, rtol=1e-8)
val1 = multivariate_hypergeom.pmf(x=[7, 3], m=[15, 10], n=10)
val2 = hypergeom.pmf(k=7, M=25, n=10, N=15)
assert_allclose(val1, val2, rtol=1e-8)
def test_rvs(self):
# test if `rvs` is unbiased and large sample size converges
# to the true mean.
rv = multivariate_hypergeom(m=[3, 5], n=4)
rvs = rv.rvs(size=1000, random_state=123)
assert_allclose(rvs.mean(0), rv.mean(), rtol=1e-2)
def test_rvs_broadcasting(self):
rv = multivariate_hypergeom(m=[[3, 5], [5, 10]], n=[4, 9])
rvs = rv.rvs(size=(1000, 2), random_state=123)
assert_allclose(rvs.mean(0), rv.mean(), rtol=1e-2)
@pytest.mark.parametrize(
"x, m, n, expected",
[
([5], [5], 5, 1),
([3, 4], [5, 10], 7, 0.3263403),
# Ground truth value from R dmvhyper
([[[3, 5], [0, 8]], [[-1, 9], [1, 1]]],
[5, 10], [[8, 8], [8, 2]],
[[0.3916084, 0.006993007], [0, 0.4761905]]),
# test with empty arrays.
(np.array([], np.int_), np.array([], np.int_), 0, []),
([1, 2], [4, 5], 5, 0),
# Ground truth value from R dmvhyper
([3, 3, 0], [5, 6, 7], 6, 0.01077354)
]
)
def test_pmf(self, x, m, n, expected):
vals = multivariate_hypergeom.pmf(x, m, n)
assert_allclose(vals, expected, rtol=1e-7)
@pytest.mark.parametrize(
"x, m, n, expected",
[
([3, 4], [[5, 10], [10, 15]], 7, [0.3263403, 0.3407531]),
([[1], [2]], [[3], [4]], [1, 3], [1., 0.]),
([[[1], [2]]], [[3], [4]], [1, 3], [[1., 0.]]),
([[1], [2]], [[[[3]]]], [1, 3], [[[1., 0.]]])
]
)
def test_pmf_broadcasting(self, x, m, n, expected):
vals = multivariate_hypergeom.pmf(x, m, n)
assert_allclose(vals, expected, rtol=1e-7)
def test_cov(self):
cov1 = multivariate_hypergeom.cov(m=[3, 7, 10], n=12)
cov2 = [[0.64421053, -0.26526316, -0.37894737],
[-0.26526316, 1.14947368, -0.88421053],
[-0.37894737, -0.88421053, 1.26315789]]
assert_allclose(cov1, cov2, rtol=1e-8)
def test_cov_broadcasting(self):
cov1 = multivariate_hypergeom.cov(m=[[7, 9], [10, 15]], n=[8, 12])
cov2 = [[[1.05, -1.05], [-1.05, 1.05]],
[[1.56, -1.56], [-1.56, 1.56]]]
assert_allclose(cov1, cov2, rtol=1e-8)
cov3 = multivariate_hypergeom.cov(m=[[4], [5]], n=[4, 5])
cov4 = [[[0.]], [[0.]]]
assert_allclose(cov3, cov4, rtol=1e-8)
cov5 = multivariate_hypergeom.cov(m=[7, 9], n=[8, 12])
cov6 = [[[1.05, -1.05], [-1.05, 1.05]],
[[0.7875, -0.7875], [-0.7875, 0.7875]]]
assert_allclose(cov5, cov6, rtol=1e-8)
def test_var(self):
# test with hypergeom
var0 = multivariate_hypergeom.var(m=[10, 5], n=4)
var1 = hypergeom.var(M=15, n=4, N=10)
assert_allclose(var0, var1, rtol=1e-8)
def test_var_broadcasting(self):
var0 = multivariate_hypergeom.var(m=[10, 5], n=[4, 8])
var1 = multivariate_hypergeom.var(m=[10, 5], n=4)
var2 = multivariate_hypergeom.var(m=[10, 5], n=8)
assert_allclose(var0[0], var1, rtol=1e-8)
assert_allclose(var0[1], var2, rtol=1e-8)
var3 = multivariate_hypergeom.var(m=[[10, 5], [10, 14]], n=[4, 8])
var4 = [[0.6984127, 0.6984127], [1.352657, 1.352657]]
assert_allclose(var3, var4, rtol=1e-8)
var5 = multivariate_hypergeom.var(m=[[5], [10]], n=[5, 10])
var6 = [[0.], [0.]]
assert_allclose(var5, var6, rtol=1e-8)
def test_mean(self):
# test with hypergeom
mean0 = multivariate_hypergeom.mean(m=[10, 5], n=4)
mean1 = hypergeom.mean(M=15, n=4, N=10)
assert_allclose(mean0[0], mean1, rtol=1e-8)
mean2 = multivariate_hypergeom.mean(m=[12, 8], n=10)
mean3 = [12.*10./20., 8.*10./20.]
assert_allclose(mean2, mean3, rtol=1e-8)
def test_mean_broadcasting(self):
mean0 = multivariate_hypergeom.mean(m=[[3, 5], [10, 5]], n=[4, 8])
mean1 = [[3.*4./8., 5.*4./8.], [10.*8./15., 5.*8./15.]]
assert_allclose(mean0, mean1, rtol=1e-8)
def test_mean_edge_cases(self):
mean0 = multivariate_hypergeom.mean(m=[0, 0, 0], n=0)
assert_equal(mean0, [0., 0., 0.])
mean1 = multivariate_hypergeom.mean(m=[1, 0, 0], n=2)
assert_equal(mean1, [np.nan, np.nan, np.nan])
mean2 = multivariate_hypergeom.mean(m=[[1, 0, 0], [1, 0, 1]], n=2)
assert_allclose(mean2, [[np.nan, np.nan, np.nan], [1., 0., 1.]],
rtol=1e-17)
mean3 = multivariate_hypergeom.mean(m=np.array([], np.int_), n=0)
assert_equal(mean3, [])
assert_(mean3.shape == (0, ))
def test_var_edge_cases(self):
var0 = multivariate_hypergeom.var(m=[0, 0, 0], n=0)
assert_allclose(var0, [0., 0., 0.], rtol=1e-16)
var1 = multivariate_hypergeom.var(m=[1, 0, 0], n=2)
assert_equal(var1, [np.nan, np.nan, np.nan])
var2 = multivariate_hypergeom.var(m=[[1, 0, 0], [1, 0, 1]], n=2)
assert_allclose(var2, [[np.nan, np.nan, np.nan], [0., 0., 0.]],
rtol=1e-17)
var3 = multivariate_hypergeom.var(m=np.array([], np.int_), n=0)
assert_equal(var3, [])
assert_(var3.shape == (0, ))
def test_cov_edge_cases(self):
cov0 = multivariate_hypergeom.cov(m=[1, 0, 0], n=1)
cov1 = [[0., 0., 0.], [0., 0., 0.], [0., 0., 0.]]
assert_allclose(cov0, cov1, rtol=1e-17)
cov3 = multivariate_hypergeom.cov(m=[0, 0, 0], n=0)
cov4 = [[0., 0., 0.], [0., 0., 0.], [0., 0., 0.]]
assert_equal(cov3, cov4)
cov5 = multivariate_hypergeom.cov(m=np.array([], np.int_), n=0)
cov6 = np.array([], dtype=np.float_).reshape(0, 0)
assert_allclose(cov5, cov6, rtol=1e-17)
assert_(cov5.shape == (0, 0))
def test_frozen(self):
# The frozen distribution should agree with the regular one
np.random.seed(1234)
n = 12
m = [7, 9, 11, 13]
x = [[0, 0, 0, 12], [0, 0, 1, 11], [0, 1, 1, 10],
[1, 1, 1, 9], [1, 1, 2, 8]]
x = np.asarray(x, dtype=np.int_)
mhg_frozen = multivariate_hypergeom(m, n)
assert_allclose(mhg_frozen.pmf(x),
multivariate_hypergeom.pmf(x, m, n))
assert_allclose(mhg_frozen.logpmf(x),
multivariate_hypergeom.logpmf(x, m, n))
assert_allclose(mhg_frozen.var(), multivariate_hypergeom.var(m, n))
assert_allclose(mhg_frozen.cov(), multivariate_hypergeom.cov(m, n))
def test_invalid_params(self):
assert_raises(ValueError, multivariate_hypergeom.pmf, 5, 10, 5)
assert_raises(ValueError, multivariate_hypergeom.pmf, 5, [10], 5)
assert_raises(ValueError, multivariate_hypergeom.pmf, [5, 4], [10], 5)
assert_raises(TypeError, multivariate_hypergeom.pmf, [5.5, 4.5],
[10, 15], 5)
assert_raises(TypeError, multivariate_hypergeom.pmf, [5, 4],
[10.5, 15.5], 5)
assert_raises(TypeError, multivariate_hypergeom.pmf, [5, 4],
[10, 15], 5.5)
def check_pickling(distfn, args):
# check that a distribution instance pickles and unpickles
# pay special attention to the random_state property
# save the random_state (restore later)
rndm = distfn.random_state
distfn.random_state = 1234
distfn.rvs(*args, size=8)
s = pickle.dumps(distfn)
r0 = distfn.rvs(*args, size=8)
unpickled = pickle.loads(s)
r1 = unpickled.rvs(*args, size=8)
assert_equal(r0, r1)
# restore the random_state
distfn.random_state = rndm
def test_random_state_property():
scale = np.eye(3)
scale[0, 1] = 0.5
scale[1, 0] = 0.5
dists = [
[multivariate_normal, ()],
[dirichlet, (np.array([1.]), )],
[wishart, (10, scale)],
[invwishart, (10, scale)],
[multinomial, (5, [0.5, 0.4, 0.1])],
[ortho_group, (2,)],
[special_ortho_group, (2,)]
]
for distfn, args in dists:
check_random_state_property(distfn, args)
check_pickling(distfn, args)
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