def testProductCopula(self):
U = dists.J([dists.Uniform(0, 1), dists.Uniform(0, 1)])
self.assertEqual(U.mean(), 0.25)
self.assertEqual(U.var(), 1./9 - 1./16)
U = dists.J([dists.TNormal(0, 2, -5, 5)])
self.assertEqual(U.mean(), 0)
self.assertEqual(U.var(), 4)
U = dists.J([dists.TNormal(1, 2, -4, 6), dists.TNormal(2, 3, -3, 7)])
self.assertEqual(U.mean(), 2)
self.assertEqual(U.var(), 5. * 13. - 1. * 4.)
def test2DPPF(self):
# prepare data
C = np.array([[0.1, 0.08], [0.08, 0.1]]) / 10.
U = dists.MultivariateNormal([0.5, 0.5], C, 0, 1)
train_samples = U.rvs(1000)
fig = plt.figure()
plotDensity2d(U)
plt.title('true density')
fig.show()
dist = SGDEdist.byLearnerSGDEConfig(train_samples,
config={
"grid_level": 5,
"grid_type": "linear",
"refinement_numSteps": 0,
"refinement_numPoints": 10,
"regularization_type":
"Laplace",
"crossValidation_lambda":
0.000562341,
"crossValidation_enable":
False,
"crossValidation_kfold": 5,
"crossValidation_silent": True
},
bounds=U.getBounds())
fig = plt.figure()
plotDensity2d(dist)
plt.title('estimated SGDE density')
fig.show()
samples = dists.J([dists.Uniform(0, 1), dists.Uniform(0, 1)]).rvs(1000)
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('uniformly drawn samples')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
transformed_samples = dist.ppf(samples)
fig = plt.figure()
plt.plot(transformed_samples[:, 0], transformed_samples[:, 1], "o ")
plt.title('transformed samples')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
plt.show()
def testDiscretization(self):
epsilon = 1e-14
U = dists.J([dists.Uniform(-1, 2), dists.Uniform(0, 3)])
_, error = U.discretize(level=1, hasBorder=True)
assert error < epsilon
epsilon = 1e-3
U = dists.J([dists.TNormal(0.5, 0.1, 0, 1)])
sgde, error = U.discretize(level=10)
assert error < epsilon
epsilon = 1e-1
U = dists.J([dists.TNormal(0.5, 0.1, 0, 1), dists.Beta(5, 10)])
_, error = U.discretize(10)
assert error < epsilon
def test2DCDFandPPF(self):
# prepare data
C = np.array([[0.1, 0.08], [0.08, 0.1]]) / 10.
U = dists.MultivariateNormal([0.5, 0.5], C, 0, 1)
train_samples = U.rvs(1000)
fig = plt.figure()
plotDensity2d(U)
plt.title('true density')
fig.show()
dist = KDEDist(train_samples, bounds=U.getBounds())
fig = plt.figure()
plotDensity2d(dist)
plt.title('estimated KDE density')
fig.show()
samples = dists.J([dists.Uniform(0, 1),
dists.Uniform(0, 1)]).rvs(1000)
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('u space')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
transformed_samples = dist.ppf(samples)
fig = plt.figure()
plt.plot(transformed_samples[:, 0], transformed_samples[:, 1], "o ")
plt.title('x space (transformed)')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
samples = dist.cdf(transformed_samples)
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('u space (transformed)')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
plt.show()
def tesst2DPPF(self):
# prepare data
numDims = 2
mean = 0.5
C = np.array([[0.1, 0.08], [0.08, 0.1]]) / 10.
stddev = np.sqrt(C[0, 0])
U = dists.MultivariateNormal(np.ones(numDims) * mean, C, 0, 1)
dist = NatafDist.normal_marginals(mean,
stddev,
C,
bounds=U.getBounds())
fig = plt.figure()
plotDensity2d(U)
plt.title('true density')
fig.show()
fig = plt.figure()
plotDensity2d(dist)
plt.title('estimated Nataf density')
fig.show()
samples = dists.J([dists.Uniform(0, 1), dists.Uniform(0, 1)]).rvs(1000)
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('uniformly drawn samples')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
transformed_samples = dist.ppf(samples)
fig = plt.figure()
plt.plot(transformed_samples[:, 0], transformed_samples[:, 1], "o ")
plt.title('transformed samples')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
plt.show()
def test2DPPF(self):
# prepare data
C = np.array([[0.1, 0.08], [0.08, 0.1]]) / 10.
U = dists.MultivariateNormal([0.5, 0.5], C, 0, 1)
fig = plt.figure()
plotDensity2d(U)
plt.title('true density')
fig.show()
dist = KDEDist(U.rvs(1000),
kernelType=KernelType_EPANECHNIKOV,
bounds=U.getBounds())
fig = plt.figure()
plotDensity2d(dist)
plt.title('estimated KDE density')
fig.show()
samples = dists.J([dists.Uniform(0, 1),
dists.Uniform(0, 1)]).rvs(1000)
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('uniformly drawn samples')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
transformed_samples = dist.ppf(samples)
fig = plt.figure()
plt.plot(transformed_samples[:, 0], transformed_samples[:, 1], "o ")
plt.title('transformed samples')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
plt.show()
def test2DCDFandPPF(self, plot=True):
# prepare data
C = np.array([[0.1, 0.08], [0.08, 0.1]]) / 10.
U = dists.MultivariateNormal([0.5, 0.5], C, 0, 1)
train_samples = U.rvs(1000)
if plot:
fig = plt.figure()
plotDensity2d(U)
plt.title('true density')
fig.show()
dist = SGDEdist.byLearnerSGDEConfig(train_samples,
config={
"grid_level": 5,
"grid_type":
"polyClenshawCurtis",
"refinement_numSteps": 0,
"refinement_numPoints": 10,
"regularization_type":
"Laplace",
"crossValidation_lambda":
0.000562341,
"crossValidation_enable":
False,
"crossValidation_kfold": 5,
"crossValidation_silent": True,
"sgde_makePositive": False
},
bounds=U.getBounds())
if plot:
fig = plt.figure()
plotDensity2d(dist)
plt.title('estimated SGDE density')
fig.show()
samples = dists.J([dists.Uniform(0, 1), dists.Uniform(0, 1)]).rvs(500)
if plot:
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('u space')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
else:
print("-" * 80)
print(samples)
transformed_samples = dist.ppf(samples, shuffle=False)
if plot:
fig = plt.figure()
plt.plot(transformed_samples[:, 0], transformed_samples[:, 1],
"o ")
plt.title('x space (transformed)')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
else:
print("-" * 80)
print(transformed_samples)
samples = dist.cdf(transformed_samples, shuffle=False)
if plot:
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('u space (transformed)')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
plt.show()
else:
print("-" * 80)
print(samples)
