def plotResultsPCE(self, pce, train_samples, expansion, sampling_strategy,
num_samples, degree_1d, out):
fig, ax, _ = plotFunction3d(lambda x: pce.evaluate(x), xlim=[-2, 1], ylim=[0, 1])
ax.scatter(train_samples[0, :],
train_samples[1, :],
np.zeros(num_samples))
if out:
filename = os.path.join(self.pathResults,
"%s_eval_pce_d%i_%s_%s_N%i_deg%i.pdf" % (self.radix,
self.numDims,
expansion,
sampling_strategy,
num_samples,
degree_1d))
plt.savefig(filename)
fig, ax, _ = plotError3d(lambda x: self.simulation(x),
lambda x: pce.evaluate(x),
xlim=[-2, 1], ylim=[0, 1])
if out:
filename = os.path.join(self.pathResults,
"%s_eval_pce_d%i_%s_%s_N%i_deg%i.pdf" % (self.radix,
self.numDims,
expansion,
sampling_strategy,
num_samples,
degree_1d))
plt.savefig(filename)
if not out:
plt.show()
def discretize2d_linear(self):
# discretize the product of both
grid1, alpha1 = self.interpolate(2, 3, 2)
grid2, alpha2 = self.interpolate(2, 3, 3)
jgrid, jalpha = discretizeProduct(grid1, alpha1, grid2, alpha2)
# get reference values
def f(x):
return evalSGFunction(grid1, alpha1, x) * evalSGFunction(
grid2, alpha2, x)
n = 50
fig, ax, y1 = plotFunction3d(f, n=n)
ax.set_title("product")
fig.show()
fig, ax, y2 = plotSG3d(jgrid, jalpha, n=n)
ax.set_title(
"(size=%i, maxlevel=%i, deg=%i), err = %g" %
(jgrid.getStorage().getSize(), jgrid.getStorage().getMaxLevel(),
getDegree(jgrid), np.max(abs(y1 - y2))))
fig.show()
assert np.max(np.abs(y1 - y2)) < 1e-13
plt.show()
fun = sin
# plot analytic function
if plot:
if numDims == 1:
fig = plt.figure()
plotFunction1d(fun)
plt.title("analytic")
fig.show()
elif numDims == 2:
fig = plt.figure()
plotFunction2d(fun)
plt.title("analytic")
fig.show()
fig, ax, _ = plotFunction3d(fun)
ax.set_title("analytic")
ax.set_zlim(-2, 2)
fig.show()
plt.savefig("sin_analytic.pdf")
# get a sparse grid approximation
grid = Grid.createLinearGrid(numDims)
grid.getGenerator().regular(level)
gs = grid.getStorage()
alpha = hierarchizeFun(fun)
print("l=%i: (gs=%i)" % (level, grid.getSize()))
print("-" * 80)
# plot the result
def __init__(self, numDims=2, rosenblatt=False):
self.radix = 'test_genz'
self.plot = False
self.pathResults = os.path.join("results")
self.rosenblatt = rosenblatt
self.numDims = numDims
self.correlation = 0.9
corrMatrix = np.ones((self.numDims, self.numDims)) * self.correlation
np.fill_diagonal(corrMatrix, 1.0)
self.dist = NatafDist.beta_marginals(0,
1,
5.0,
10.0,
corrMatrix=corrMatrix,
bounds=np.array([[0, 1], [0, 1]]))
# --------------------------------------------------------
# set distributions of the input parameters
# --------------------------------------------------------
builder = ParameterBuilder()
up = builder.defineUncertainParameters()
if rosenblatt:
up.new().isCalled("x,y").withDistribution(
self.dist).withRosenblattTransformation()
else:
up.new().isCalled("x,y").withDistribution(self.dist)
self.params = builder.andGetResult()
# --------------------------------------------------------
# simulation function: oscillatory genz function
# --------------------------------------------------------
self.c = 4.5 * (np.arange(0, self.numDims, 1) + 0.5) / self.numDims
def f(x, c=self.c, **kws):
return np.cos(np.sum(c * x))
self.simulation = f
# --------------------------------------------------------
def insert_labels(ax, zlabel):
ax.set_xticks([0, 0.5, 1])
ax.set_yticks([0, 0.5, 1])
ax.set_xlabel(r"$\xi_1$")
ax.set_ylabel(r"$\xi_2$")
ax.set_zlabel(zlabel)
ax.xaxis.labelpad = 13
ax.yaxis.labelpad = 13
ax.zaxis.labelpad = 10
if False:
fig = plt.figure()
plotFunction2d(self.dist.pdf,
color_bar_label=r'$f(\xi_1, \xi_2)$',
addContour=False)
plt.xlabel(r"$\xi_1$")
plt.ylabel(r"$\xi_2$")
savefig(fig, "plots/correlated_beta_2d", tikz=False)
fig = plt.figure()
fig, ax, _ = plotFunction3d(self.dist.pdf)
insert_labels(ax, r"$f(\xi_1, \xi_2)$")
savefig(fig, "plots/correlated_beta_3d", tikz=False)
# --------------------------------------------------------
if False:
fig = plt.figure()
plotFunction2d(self.simulation,
color_bar_label=r'$u(\xi_1, \xi_2)$',
addContour=False)
plt.xlabel(r"$\xi_1$")
plt.ylabel(r"$\xi_2$")
savefig(fig, "plots/oscillating_genz_2d", tikz=False)
fig, ax, _ = plotFunction3d(self.simulation)
insert_labels(ax, r"$u(\xi_1, \xi_2)$")
savefig(fig, "plots/oscillating_genz_3d", mpl3d=True)