def test_samples_z2():
dist1 = Uniform(loc=0.0, scale=5.0)
dist2 = Uniform(loc=0.0, scale=3.0)
ntf_obj = Nataf(distributions=[dist1, dist2])
samples_z = np.array([[0.3, 1.2], [0.2, 2.4]]).T
ntf_obj.run(samples_z=samples_z, jacobian=True)
g = []
for i in range(2):
if i == 0:
g.append((ntf_obj.samples_x[i] == np.array(
[3.089557110944763, 1.737779128317309])).all())
elif i == 1:
g.append((ntf_obj.samples_x[i] == np.array(
[4.424651648891459, 2.9754073922262116])).all())
assert np.all(g)
def test_samples_x1():
dist1 = Uniform(loc=0.0, scale=5.0)
dist2 = Uniform(loc=0.0, scale=3.0)
ntf_obj = Nataf(distributions=[dist1, dist2])
samples_x = np.array([[0.3, 1.2, 3.5], [0.2, 2.4, 0.9]]).T
ntf_obj.run(samples_x=samples_x, jacobian=True)
g = []
for i in range(3):
if i == 0:
g.append((ntf_obj.samples_z[i] == np.array(
[-1.5547735945968535, -1.501085946044025])).all())
elif i == 1:
g.append((ntf_obj.samples_z[i] == np.array(
[-0.7063025628400874, 0.841621233572914])).all())
else:
g.append((ntf_obj.samples_z[i] == np.array(
[0.5244005127080407, -0.5244005127080409])).all())
assert np.all(g)
def test_samples_z_jzx2():
dist1 = Uniform(loc=0.0, scale=5.0)
dist2 = Uniform(loc=0.0, scale=3.0)
ntf_obj = Nataf(distributions=[dist1, dist2])
samples_z = np.array([[0.3, 1.2], [0.2, 2.4]]).T
ntf_obj.run(samples_z=samples_z, jacobian=True)
g = []
for i in range(2):
if i == 0:
g.append(
(ntf_obj.jzx[i] == np.array([[0.524400601939789, 0.0],
[0.0,
0.8524218415758338]])).all())
else:
g.append(
(ntf_obj.jzx[i] == np.array([[1.0299400748281828, 0.0],
[0.0,
14.884586948005541]])).all())
assert np.all(g)
def test_samples_x_jxz2():
dist1 = Uniform(loc=0.0, scale=5.0)
dist2 = Uniform(loc=0.0, scale=3.0)
ntf_obj = Nataf(distributions=[dist1, dist2])
samples_x = np.array([[0.3, 1.2, 3.5], [0.2, 2.4, 0.9]]).T
ntf_obj.run(samples_x=samples_x, jacobian=True)
g = []
for i in range(3):
if i == 0:
g.append((ntf_obj.jxz[i] == np.array([[1.6789373877365803, 0.0],
[0.0,
2.577850090371836]])).all())
elif i == 1:
g.append(
(ntf_obj.jxz[i] == np.array([[0.6433491348614259, 0.0],
[0.0,
1.1906381155257868]])).all())
else:
g.append((ntf_obj.jxz[i] == np.array([[0.5752207318528584, 0.0],
[0.0,
0.958701219754764]])).all())
assert np.all(g)
plt.scatter(samples_x[:, 0], samples_x[:, 1])
plt.grid(True)
plt.xlabel('$X_1$')
plt.ylabel('$X_2$')
plt.show()
# %% md
#
# We can invoke the :code:`run` method of the :code:`nataf_obj` object to transform the non-Gaussian random variables
# from space :code:`X`to the correlated standard normal space :code:`Z`. Here, we provide as :code:`boolean (True)` an
# optional attribute :code:`jacobian` to calculate the Jacobian of the transformation. The distorted correlation matrix
# can be accessed in the attribute :code:`corr_z`
# %%
nataf_obj.run(samples_x=samples_x, jacobian=True)
print(nataf_obj.corr_z)
# %% md
#
# We can visualize the correlated (standard normal) samples by plotting them on axes of each distribution's range.
# %%
plt.figure()
plt.title('Correlated standard normal samples')
plt.scatter(nataf_obj.samples_z[:, 0], nataf_obj.samples_z[:, 1])
plt.grid(True)
plt.xlabel('$Z_1$')
plt.ylabel('$Z_2$')
plt.show()
def test_samples_z_jzx1():
dist1 = Normal(loc=0.0, scale=5.0)
ntf_obj = Nataf(distributions=[dist1])
samples_z = np.array([0.3, 1.2, 3.5])
ntf_obj.run(samples_z=samples_z, jacobian=False)
assert ntf_obj.jzx is None
def test_samples_z_shape():
dist1 = Normal(loc=0.0, scale=5.0)
ntf_obj = Nataf(distributions=[dist1])
samples_z = np.array([0.3, 1.2, 3.5])
ntf_obj.run(samples_z)
assert ntf_obj.samples_z.shape == (3, 1)