def test_2DNormalDist_variance(self):
# prepare data
U = dists.J(
[dists.Normal(2.0, .5, -1, 4),
dists.Normal(1.0, .5, -1, 3)])
# U = dists.J([dists.Normal(0.5, .5, -1, 2),
# dists.Normal(0.5, .4, -1, 2)])
# define linear transformation
trans = JointTransformation()
for a, b in U.getBounds():
trans.add(LinearTransformation(a, b))
# get a sparse grid approximation
grid = Grid.createPolyGrid(U.getDim(), 10)
grid.getGenerator().regular(5)
gs = grid.getStorage()
# now refine adaptively 5 times
p = DataVector(gs.getDimension())
nodalValues = np.ndarray(gs.getSize())
# set function values in alpha
for i in range(gs.getSize()):
gs.getPoint(i).getStandardCoordinates(p)
nodalValues[i] = U.pdf(trans.unitToProbabilistic(p.array()))
# hierarchize
alpha = hierarchize(grid, nodalValues)
# # make positive
# alpha_vec = DataVector(alpha)
# createOperationMakePositive().makePositive(grid, alpha_vec)
# alpha = alpha_vec.array()
dist = SGDEdist(grid, alpha, bounds=U.getBounds())
fig = plt.figure()
plotDensity2d(U)
fig.show()
fig = plt.figure()
plotSG2d(dist.grid,
dist.alpha,
addContour=True,
show_negative=True,
show_grid_points=True)
fig.show()
print("2d: mean = %g ~ %g" % (U.mean(), dist.mean()))
print("2d: var = %g ~ %g" % (U.var(), dist.var()))
plt.show()
def test_1DNormalDist_variance(self):
# prepare data
U = dists.Normal(1, 2, -8, 8)
# U = dists.Normal(0.5, .2, 0, 1)
# define linear transformation
trans = JointTransformation()
a, b = U.getBounds()
trans.add(LinearTransformation(a, b))
# get a sparse grid approximation
grid = Grid.createPolyGrid(U.getDim(), 10)
grid.getGenerator().regular(5)
gs = grid.getStorage()
# now refine adaptively 5 times
p = DataVector(gs.getDimension())
nodalValues = np.ndarray(gs.getSize())
# set function values in alpha
for i in range(gs.getSize()):
gs.getPoint(i).getStandardCoordinates(p)
nodalValues[i] = U.pdf(trans.unitToProbabilistic(p.array()))
# hierarchize
alpha = hierarchize(grid, nodalValues)
dist = SGDEdist(grid, alpha, bounds=U.getBounds())
fig = plt.figure()
plotDensity1d(U,
alpha_value=0.1,
mean_label="$\mathbb{E}",
interval_label="$\alpha=0.1$")
fig.show()
fig = plt.figure()
plotDensity1d(dist,
alpha_value=0.1,
mean_label="$\mathbb{E}",
interval_label="$\alpha=0.1$")
fig.show()
print("1d: mean = %g ~ %g" % (U.mean(), dist.mean()))
print("1d: var = %g ~ %g" % (U.var(), dist.var()))
plt.show()