def test_MultivariateNormalQMCNonPD(self):
# try with non-pd but psd cov; should work
engine = qmc.MultivariateNormalQMC(
[0, 0, 0],
[[1, 0, 1], [0, 1, 1], [1, 1, 2]],
)
assert engine._corr_matrix is not None
def test_MultivariateNormalQMCDim(self):
# incompatible dimension of mean/cov
with pytest.raises(ValueError,
match=r"Dimension mismatch between "
r"mean and covariance."):
seed = np.random.RandomState(123456)
qmc.MultivariateNormalQMC([0], [[1, 0], [0, 1]], seed=seed)
def test_NormalQMCInvTransform(self):
# d = 1
seed = np.random.RandomState(123456)
engine = qmc.MultivariateNormalQMC(
mean=np.zeros(1), inv_transform=True, seed=seed)
samples = engine.random()
assert_equal(samples.shape, (1, 1))
samples = engine.random(n=5)
assert_equal(samples.shape, (5, 1))
# d = 2
engine = qmc.MultivariateNormalQMC(
mean=np.zeros(2), inv_transform=True, seed=seed)
samples = engine.random()
assert_equal(samples.shape, (1, 2))
samples = engine.random(n=5)
assert_equal(samples.shape, (5, 2))
def test_MultivariateNormalQMCSymmetric(self):
# try with non-symmetric cov and expect an error
with pytest.raises(ValueError,
match=r"Covariance matrix is not "
r"symmetric."):
seed = np.random.RandomState(123456)
qmc.MultivariateNormalQMC([0, 0], [[1, 0], [2, 1]], seed=seed)
def test_MultivariateNormalQMCNonPD(self):
# try with non-pd but psd cov; should work
seed = np.random.RandomState(123456)
engine = qmc.MultivariateNormalQMC([0, 0, 0],
[[1, 0, 1], [0, 1, 1], [1, 1, 2]],
seed=seed)
assert_(engine._corr_matrix is not None)
def test_reset(self):
seed = np.random.RandomState(12345)
engine = qmc.MultivariateNormalQMC(mean=np.zeros(1), seed=seed)
samples = engine.random(2)
engine.reset()
samples_reset = engine.random(2)
assert_array_equal(samples, samples_reset)
def test_other_engine(self):
base_engine = qmc.Sobol(d=2, scramble=False)
engine = qmc.MultivariateNormalQMC(mean=np.zeros(2),
engine=base_engine,
inv_transform=True)
samples = engine.random()
assert_equal(samples.shape, (1, 2))
def test_NormalQMCSeeded(self):
# test even dimension
seed = np.random.default_rng(274600237797326520096085022671371676017)
engine = qmc.MultivariateNormalQMC(
mean=np.zeros(2), inv_transform=False, seed=seed)
samples = engine.random(n=2)
samples_expected = np.array([[0.446961, -1.243236],
[-0.230754, 0.21354]])
assert_array_almost_equal(samples, samples_expected)
# test odd dimension
seed = np.random.default_rng(274600237797326520096085022671371676017)
engine = qmc.MultivariateNormalQMC(
mean=np.zeros(3), inv_transform=False, seed=seed)
samples = engine.random(n=2)
samples_expected = np.array([[0.446961, -1.243236, 0.324827],
[-0.997875, 0.399134, 1.032234]])
assert_array_almost_equal(samples, samples_expected)
def test_NormalQMCSeededInvTransform(self):
# test even dimension
seed = np.random.default_rng(288527772707286126646493545351112463929)
engine = qmc.MultivariateNormalQMC(
mean=np.zeros(2), seed=seed, inv_transform=True)
samples = engine.random(n=2)
samples_expected = np.array([[-0.804472, 0.384649],
[0.396424, -0.117676]])
assert_array_almost_equal(samples, samples_expected)
# test odd dimension
seed = np.random.default_rng(288527772707286126646493545351112463929)
engine = qmc.MultivariateNormalQMC(
mean=np.zeros(3), seed=seed, inv_transform=True)
samples = engine.random(n=2)
samples_expected = np.array([[-0.804472, 0.384649, 1.583568],
[0.165333, -2.266828, -1.655572]])
assert_array_almost_equal(samples, samples_expected)
def test_validations(self):
message = r"Dimension of `engine` must be consistent"
with pytest.raises(ValueError, match=message):
qmc.MultivariateNormalQMC([0], engine=qmc.Sobol(d=2))
message = r"`engine` must be an instance of..."
with pytest.raises(ValueError, match=message):
qmc.MultivariateNormalQMC([0, 0], engine=np.random.default_rng())
message = r"Covariance matrix not PSD."
with pytest.raises(ValueError, match=message):
qmc.MultivariateNormalQMC([0, 0], [[1, 2], [2, 1]])
message = r"Covariance matrix is not symmetric."
with pytest.raises(ValueError, match=message):
qmc.MultivariateNormalQMC([0, 0], [[1, 0], [2, 1]])
message = r"Dimension mismatch between mean and covariance."
with pytest.raises(ValueError, match=message):
qmc.MultivariateNormalQMC([0], [[1, 0], [0, 1]])
def test_NormalQMCShapiro(self):
rng = np.random.default_rng(13242)
engine = qmc.MultivariateNormalQMC(mean=np.zeros(2), seed=rng)
samples = engine.random(n=256)
assert all(np.abs(samples.mean(axis=0)) < 1e-2)
assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
# perform Shapiro-Wilk test for normality
for i in (0, 1):
_, pval = shapiro(samples[:, i])
assert pval > 0.9
# make sure samples are uncorrelated
cov = np.cov(samples.transpose())
assert np.abs(cov[0, 1]) < 1e-2
def test_MultivariateNormalQMCSeeded(self):
# test even dimension
rng = np.random.default_rng(180182791534511062935571481899241825000)
a = rng.standard_normal((2, 2))
A = a @ a.transpose() + np.diag(rng.random(2))
engine = qmc.MultivariateNormalQMC(np.array([0, 0]), A,
inv_transform=False, seed=rng)
samples = engine.random(n=2)
samples_expected = np.array([[0.479575, 0.934723],
[1.712571, 0.172699]])
assert_array_almost_equal(samples, samples_expected)
# test odd dimension
rng = np.random.default_rng(180182791534511062935571481899241825000)
a = rng.standard_normal((3, 3))
A = a @ a.transpose() + np.diag(rng.random(3))
engine = qmc.MultivariateNormalQMC(np.array([0, 0, 0]), A,
inv_transform=False, seed=rng)
samples = engine.random(n=2)
samples_expected = np.array([[2.463393, 2.252826, -0.886809],
[1.252468, 0.029449, -1.126328]])
assert_array_almost_equal(samples, samples_expected)
def test_NormalQMCShapiro(self):
seed = np.random.RandomState(12345)
engine = qmc.MultivariateNormalQMC(mean=np.zeros(2), seed=seed)
samples = engine.random(n=256)
assert_(all(np.abs(samples.mean(axis=0)) < 1e-2))
assert_(all(np.abs(samples.std(axis=0) - 1) < 1e-2))
# perform Shapiro-Wilk test for normality
for i in (0, 1):
_, pval = shapiro(samples[:, i])
assert_(pval > 0.9)
# make sure samples are uncorrelated
cov = np.cov(samples.transpose())
assert_(np.abs(cov[0, 1]) < 1e-2)
def test_NormalQMCSeededInvTransform(self):
# test even dimension
seed = np.random.RandomState(12345)
engine = qmc.MultivariateNormalQMC(mean=np.zeros(2),
seed=seed,
inv_transform=True)
samples = engine.random(n=2)
samples_expected = np.array([[0.228309, -0.162516],
[-0.41622922, 0.46622792]])
assert_array_almost_equal(samples, samples_expected)
# test odd dimension
seed = np.random.RandomState(12345)
engine = qmc.MultivariateNormalQMC(mean=np.zeros(3),
seed=seed,
inv_transform=True)
samples = engine.random(n=2)
samples_expected = np.array([
[0.228309, -0.162516, 0.167352],
[-1.40525266, 1.37652443, -0.8519666],
])
assert_array_almost_equal(samples, samples_expected)
def test_NormalQMCSeeded(self):
# test even dimension
seed = np.random.RandomState(12345)
engine = qmc.MultivariateNormalQMC(mean=np.zeros(2),
inv_transform=False,
seed=seed)
samples = engine.random(n=2)
samples_expected = np.array([[-0.943472, 0.405116],
[-0.63099602, -1.32950772]])
assert_array_almost_equal(samples, samples_expected)
# test odd dimension
seed = np.random.RandomState(12345)
engine = qmc.MultivariateNormalQMC(mean=np.zeros(3),
inv_transform=False,
seed=seed)
samples = engine.random(n=2)
samples_expected = np.array([
[-0.943472, 0.405116, 0.268828],
[1.83169884, -1.40473647, 0.24334828],
])
assert_array_almost_equal(samples, samples_expected)
def test_MultivariateNormalQMC(self):
# d = 1 scalar
engine = qmc.MultivariateNormalQMC(mean=0, cov=5)
samples = engine.random()
assert_equal(samples.shape, (1, 1))
samples = engine.random(n=5)
assert_equal(samples.shape, (5, 1))
# d = 2 list
engine = qmc.MultivariateNormalQMC(mean=[0, 1], cov=[[1, 0], [0, 1]])
samples = engine.random()
assert_equal(samples.shape, (1, 2))
samples = engine.random(n=5)
assert_equal(samples.shape, (5, 2))
# d = 3 np.array
mean = np.array([0, 1, 2])
cov = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
engine = qmc.MultivariateNormalQMC(mean, cov)
samples = engine.random()
assert_equal(samples.shape, (1, 3))
samples = engine.random(n=5)
assert_equal(samples.shape, (5, 3))
def test_MultivariateNormalQMCSeededInvTransform(self):
# test even dimension
rng = np.random.default_rng(224125808928297329711992996940871155974)
a = rng.standard_normal((2, 2))
A = a @ a.transpose() + np.diag(rng.random(2))
engine = qmc.MultivariateNormalQMC(
np.array([0, 0]), A, seed=rng, inv_transform=True
)
samples = engine.random(n=2)
samples_expected = np.array([[-3.095968, -0.566545],
[0.603154, 0.222434]])
assert_array_almost_equal(samples, samples_expected)
# test odd dimension
rng = np.random.default_rng(224125808928297329711992996940871155974)
a = rng.standard_normal((3, 3))
A = a @ a.transpose() + np.diag(rng.random(3))
engine = qmc.MultivariateNormalQMC(
np.array([0, 0, 0]), A, seed=rng, inv_transform=True
)
samples = engine.random(n=2)
samples_expected = np.array([[1.427248, -0.338187, -1.560687],
[-0.357026, 1.662937, -0.29769]])
assert_array_almost_equal(samples, samples_expected)
def test_MultivariateNormalQMCShapiroInvTransform(self):
# test the standard case
seed = np.random.RandomState(12345)
engine = qmc.MultivariateNormalQMC(mean=[0, 0],
cov=[[1, 0], [0, 1]],
seed=seed,
inv_transform=True)
samples = engine.random(n=256)
assert_(all(np.abs(samples.mean(axis=0)) < 1e-2))
assert_(all(np.abs(samples.std(axis=0) - 1) < 1e-2))
# perform Shapiro-Wilk test for normality
for i in (0, 1):
_, pval = shapiro(samples[:, i])
assert_(pval > 0.9)
# make sure samples are uncorrelated
cov = np.cov(samples.transpose())
assert_(np.abs(cov[0, 1]) < 1e-2)
# test the correlated, non-zero mean case
seed = np.random.RandomState(12345)
engine = qmc.MultivariateNormalQMC(
mean=[1.0, 2.0],
cov=[[1.5, 0.5], [0.5, 1.5]],
seed=seed,
inv_transform=True,
)
samples = engine.random(n=256)
assert_(all(np.abs(samples.mean(axis=0) - [1, 2]) < 1e-2))
assert_(all(np.abs(samples.std(axis=0) - np.sqrt(1.5)) < 1e-2))
# perform Shapiro-Wilk test for normality
for i in (0, 1):
_, pval = shapiro(samples[:, i])
assert_(pval > 0.9)
# check covariance
cov = np.cov(samples.transpose())
assert_(np.abs(cov[0, 1] - 0.5) < 1e-2)
def test_MultivariateNormalQMCDegenerate(self):
# X, Y iid standard Normal and Z = X + Y, random vector (X, Y, Z)
seed = np.random.default_rng(163206374175814483578698216542904486209)
engine = qmc.MultivariateNormalQMC(
mean=[0.0, 0.0, 0.0],
cov=[[1.0, 0.0, 1.0], [0.0, 1.0, 1.0], [1.0, 1.0, 2.0]],
seed=seed,
)
samples = engine.random(n=512)
assert all(np.abs(samples.mean(axis=0)) < 1e-2)
assert np.abs(np.std(samples[:, 0]) - 1) < 1e-2
assert np.abs(np.std(samples[:, 1]) - 1) < 1e-2
assert np.abs(np.std(samples[:, 2]) - np.sqrt(2)) < 1e-2
for i in (0, 1, 2):
_, pval = shapiro(samples[:, i])
assert pval > 0.8
cov = np.cov(samples.transpose())
assert np.abs(cov[0, 1]) < 1e-2
assert np.abs(cov[0, 2] - 1) < 1e-2
# check to see if X + Y = Z almost exactly
assert all(np.abs(samples[:, 0] + samples[:, 1] - samples[:, 2])
< 1e-5)
def test_MultivariateNormalQMCDegenerate(self):
# X, Y iid standard Normal and Z = X + Y, random vector (X, Y, Z)
seed = np.random.RandomState(12345)
engine = qmc.MultivariateNormalQMC(
mean=[0.0, 0.0, 0.0],
cov=[[1.0, 0.0, 1.0], [0.0, 1.0, 1.0], [1.0, 1.0, 2.0]],
seed=seed,
)
samples = engine.random(n=512)
assert_(all(np.abs(samples.mean(axis=0)) < 1e-2))
assert_(np.abs(np.std(samples[:, 0]) - 1) < 1e-2)
assert_(np.abs(np.std(samples[:, 1]) - 1) < 1e-2)
assert_(np.abs(np.std(samples[:, 2]) - np.sqrt(2)) < 1e-2)
for i in (0, 1, 2):
_, pval = shapiro(samples[:, i])
assert_(pval > 0.8)
cov = np.cov(samples.transpose())
assert_(np.abs(cov[0, 1]) < 1e-2)
assert_(np.abs(cov[0, 2] - 1) < 1e-2)
# check to see if X + Y = Z almost exactly
assert_(
all(np.abs(samples[:, 0] + samples[:, 1] - samples[:, 2]) < 1e-5))
def test_MultivariateNormalQMCNonPSD(self):
# try with non-psd, non-pd cov and expect an assertion error
with pytest.raises(ValueError, match=r"Covariance matrix not PSD."):
seed = np.random.RandomState(123456)
qmc.MultivariateNormalQMC([0, 0], [[1, 2], [2, 1]], seed=seed)
def _wrapper_mv_qmc(*args, **kwargs):
d = kwargs.pop("d")
return qmc.MultivariateNormalQMC(mean=np.zeros(d), **kwargs)
