def test_cond_mvn_exception_given():
"""Test cond_mvn raises exceptions when invalid `given_ind` or `given_value` is passed."""
mean, cov, dependent_ind, given_ind, given_value = get_strategies(
"cond_mvn_exception_given",
)
n = cov.shape[0]
if n % 3 != 0:
# Valid case: only `given_ind` is empty or both `given_ind` and `given_value` are empty
cond_mvn(mean, cov, dependent_ind, given_ind, given_value)
else:
# `given_value` is empty or does not align with `given_ind`
with pytest.raises(ValueError) as e:
cond_mvn(mean, cov, dependent_ind, given_ind, given_value)
assert "lengths of given_value and given_ind must be the same" in str(e.value)
def test_cond_mvn():
"""Test cond_mvn against the original from R package cond_mvnorm."""
request = get_strategies("cond_mvn")
r_cond_mean, r_cond_cov = r_cond_mvn(*request)
cond_mean, cond_cov = cond_mvn(*request)
np.testing.assert_allclose(cond_mean, r_cond_mean)
np.testing.assert_allclose(cond_cov, r_cond_cov)
def test_gaussian_copula_mvn():
"""
The results from a Gaussian copula with normal marginal distributions
should be identical to the direct use of a multivariate normal
distribution.
"""
dim = rng.integers(2, 10)
means = rng.uniform(-100, 100, dim)
sigma = rng.normal(size=(dim, dim))
cov = sigma @ sigma.T
marginals = list()
for i in range(dim):
mean, sigma = means[i], np.sqrt(cov[i, i])
marginals.append(cp.Normal(mu=mean, sigma=sigma))
distribution = cp.J(*marginals)
sample = distribution.sample(1).T[0]
full = list(range(0, dim))
dependent_ind = [rng.choice(full)]
given_ind = full[:]
# TODO: This test always treats the first element as given.
# We need it to be more flexible and select random subsets.
given_ind.remove(dependent_ind[0])
given_value = sample[given_ind]
np.testing.assert_almost_equal(np.linalg.inv(np.linalg.inv(cov)), cov)
np.random.seed(seed)
given_value_u = [
distribution[ind].cdf(given_value[i])
for i, ind in enumerate(given_ind)
]
condi_value_u = cond_gaussian_copula(cov, dependent_ind, given_ind,
given_value_u)
gc_value = distribution[int(dependent_ind[0])].inv(condi_value_u)
np.random.seed(seed)
cond_mean, cond_cov = cond_mvn(means, cov, dependent_ind, given_ind,
given_value)
cond_dist = multivariate_norm(cond_mean, cond_cov)
cn_value = np.atleast_1d(cond_dist.rvs())
np.testing.assert_almost_equal(cn_value, gc_value)
def cond_gaussian_copula(cov, dependent_ind, given_ind, given_value_u):
given_value_u = np.atleast_1d(given_value_u)
assert np.all((given_value_u >= 0)
& (given_value_u <= 1)), "sanitize your inputs!"
given_value_y = norm().ppf(given_value_u)
means = np.zeros(cov.shape[0])
cond_mean, cond_cov = cond_mvn(means, _cov2corr(cov), dependent_ind,
given_ind, given_value_y)
cond_dist = multivariate_norm(cond_mean, cond_cov)
cond_draw = np.atleast_1d(cond_dist.rvs())
cond_quan = norm.cdf(cond_draw)
return np.atleast_1d(cond_quan)
def test_cond_gaussian_copula():
"""
The results from a Gaussian copula with normal marginal distributions
should be identical to the direct use of a multivariate normal
distribution.
"""
args_gc, args_cn = get_strategies("test_cond_gaussian_copula")
cov, dependent_ind, given_ind, given_value_u, distribution = args_gc
np.random.seed(123)
condi_value_u = cond_gaussian_copula(cov, dependent_ind, given_ind, given_value_u)
dist_subset = list()
for ind in dependent_ind:
dist_subset.append(distribution[int(ind)])
dist_subset = cp.J(*dist_subset)
gc_value = dist_subset.inv(condi_value_u)
np.random.seed(123)
cond_mean, cond_cov = cond_mvn(*args_cn)
cond_dist = multivariate_norm(cond_mean, cond_cov)
cn_value = np.atleast_1d(cond_dist.rvs())
np.testing.assert_almost_equal(cn_value, gc_value)
def _r_condmvn(
n,
mean,
cov,
dependent_ind,
given_ind,
x_given,
):
"""Function to generate conditional law.
Function to simulate conditional gaussian distribution of x[dependent.ind]
| x[given.ind] = x.given where x is multivariateNormal(mean = mean, covariance = cov)
"""
cond_mean, cond_var = cond_mvn(
mean,
cov,
dependent_ind=dependent_ind,
given_ind=given_ind,
given_value=x_given,
)
distribution = cp.MvNormal(cond_mean, cond_var)
return distribution.sample(n)
def test_cond_mvn_exception_cov():
"""Test cond_mvn raises exceptions when invalid `cov` is passed."""
mean, cov, dependent_ind, given_ind, given_value = get_strategies(
"test_cond_mvn_exception_cov",
)
n = cov.shape[0]
if n % 3 != 0 and n % 2 != 0:
# `cov` is negative definite matrix
with pytest.raises(ValueError) as e:
cond_mvn(mean, cov, dependent_ind, given_ind, given_value)
assert "cov is not positive-definite" in str(e.value)
elif n % 2 != 0:
# `cov` is not symmetric
with pytest.raises(ValueError) as e:
cond_mvn(mean, cov, dependent_ind, given_ind, given_value)
assert "cov is not a symmetric matrix" in str(e.value)
else:
cond_mvn(mean, cov, dependent_ind, given_ind, given_value)
sample = distribution.sample(1).T[0]
full = list(range(0, dim))
dependent_ind = [np.random.choice(full)]
given_ind = full[:]
# TODO: This test always treats the first element as given. We need it to be more
# flexible and select random subets.
given_ind.remove(dependent_ind[0])
given_value = sample[given_ind]
np.random.seed(123)
given_value_u = [
distribution[ind].cdf(given_value[i])
for i, ind in enumerate(given_ind)
]
condi_value_u = cond_gaussian_copula(cov, dependent_ind, given_ind,
given_value_u)
gc_value = distribution[int(dependent_ind[0])].inv(condi_value_u)
np.random.seed(123)
cond_mean, cond_cov = cond_mvn(means, cov, dependent_ind, given_ind,
given_value)
cond_dist = multivariate_norm(cond_mean, cond_cov)
cn_value = np.atleast_1d(cond_dist.rvs())
print(dim)
np.testing.assert_allclose(cn_value, gc_value, rtol=1e-4)
def cond_gaussian_copula(cov, dependent_ind, given_ind, given_value_u, size=1):
r"""Conditional sampling from Gaussian copula.
This function provides the probability distribution of conditional sample
drawn from a Gaussian copula, given covariance matrix and a uniform random vector.
Parameters
----------
cov : array_like
Covariance matrix of the desired sample.
dependent_ind : int or array_like
The indices of dependent variables.
given_ind : array_like
The indices of independent variables.
given_value_u : array_like
The given random vector (:math:`u`) that is uniformly distributed between 0 and 1.
size : int
Number of draws from the conditional distribution. (default value is `1`)
Returns
-------
cond_quan : numpy.ndarray
The conditional sample (:math:`G(u)`) that is between 0 and 1,
and has the same length as ``dependent_ind``.
Examples
--------
>>> np.random.seed(123)
>>> cov = np.array([[ 3.290887, 0.465004, -3.411841],
... [ 0.465004, 3.962172, -0.574745],
... [-3.411841, -0.574745, 4.063252]])
>>> dependent_ind = 2
>>> given_ind = [0, 1]
>>> given_value_u = [0.0596779, 0.39804426]
>>> condi_value_u = cond_gaussian_copula(cov, dependent_ind, given_ind, given_value_u)
>>> np.testing.assert_almost_equal(condi_value_u[0], 0.856504, decimal=6)
"""
given_value_u = np.atleast_1d(given_value_u)
# Check `given_value_u` are between 0 and 1
if not np.all((given_value_u >= 0) & (given_value_u <= 1)):
raise ValueError("given_value_u must be between 0 and 1")
# F^{−1}(u)
given_value_y = norm().ppf(given_value_u)
mean = np.zeros(cov.shape[0])
cond_mean, cond_cov = cond_mvn(
mean,
_cov2corr(cov),
dependent_ind,
given_ind,
given_value_y,
)
# C(u, Sigma)
cond_dist = multivariate_norm(cond_mean, cond_cov)
cond_draw = np.atleast_1d(cond_dist.rvs(size=size))
cond_quan = np.atleast_1d(norm.cdf(cond_draw))
return cond_quan