def ot_drawcontour(ot_draw):
ot.ResourceMap_SetAsUnsignedInteger("Contour-DefaultLevelsNumber", 7)
drawables = ot_draw.getDrawables()
levels = []
for i in range(len(drawables)):
contours = drawables[i]
levels.append(contours.getLevels()[0])
ot.ResourceMap.SetAsUnsignedInteger('Drawable-DefaultPalettePhase',
len(levels)) #Colors
palette = ot.Drawable.BuildDefaultPalette(len(levels)) #Colors
newcontour = ot_draw.getDrawable(0)
drawables = list()
for i in range(len(levels)):
newcontour.setLevels([levels[i]]) # Inline the level values
newcontour.setDrawLabels(True)
newcontour.setLabels([str("{:.3e}".format(levels[i]))])
# We have to copy the drawable because a Python list stores only pointers
drawables.append(ot.Drawable(newcontour))
graphFineTune = ot.Graph("", "", "", True, '')
graphFineTune.setDrawables(drawables)
graphFineTune.setColors(palette) # Add colors
return graphFineTune
# %%
# The two distributions are very different, with a spiky posterior distribution. This shows that the calibration is very sensible to the observations.
# %%
# Tuning the posterior distribution estimation
# --------------------------------------------
#
# The "GaussianNonLinearCalibration-BootstrapSize" key controls the posterior distribution estimation.
#
# * If "GaussianNonLinearCalibration-BootstrapSize" > 0 (by default it is equal to 100), then a bootstrap resample algorithm is used to see the dispersion of the MAP estimator. This allows to see the variability of the estimator with respect to the finite observation sample.
# * If "GaussianNonLinearCalibration-BootstrapSize" is zero, then the Gaussian linear calibration estimator is used (i.e. the `GaussianLinearCalibration` class) at the optimum. This is called the Laplace approximation.
#
# We must configure the key before creating the object (otherwise changing the parameter does not change the result).
# %%
ot.ResourceMap_SetAsUnsignedInteger("GaussianNonLinearCalibration-BootstrapSize",0)
# %%
algo = ot.GaussianNonLinearCalibration(mycf, Qobs, Hobs, thetaPrior, sigma, errorCovariance)
# %%
algo.run()
# %%
calibrationResult = algo.getResult()
# %%
graph = calibrationResult.drawParameterDistributions()
plt.show()
# %%
# We consider a bivariate random vector :math:`X = (X_1, X_2)` with the following independent marginals :
#
# - an exponential distribution with parameter :math:`\lambda=1`, :math:`X_1 \sim \mathcal{E}(1.0)` ;
# - a standard unit gaussian :math:`X_2 \sim \mathcal{N}(0,1)`.
#
# The support of the input vector is :math:`[0, +\infty[ \times \mathbb{R}`
#
# %%
distX1 = ot.Exponential(1.0)
distX2 = ot.Normal()
distX = ot.ComposedDistribution([distX1, distX2])
# %%
# We can draw the bidimensional PDF of the distribution `distX` over :math:`[0,-10] \times [10,10]` :
ot.ResourceMap_SetAsUnsignedInteger("Contour-DefaultLevelsNumber", 8)
graphPDF = distX.drawPDF([0, -10], [10, 10])
graphPDF.setTitle(r'2D-PDF of the input variables $(X_1, X_2)$')
graphPDF.setXTitle(r'$x_1$')
graphPDF.setYTitle(r'$x_2$')
graphPDF.setLegendPosition("bottomright")
view = otv.View(graphPDF)
# %%
# We consider the model :math:`f : (x_1, x_2) \mapsto x_1 x_2` which maps the random input vector :math:`X` to the output variable :math:`Y=f(X) \in \mathbb{R}`. We also draw the isolines of the model `f`.
#
f = ot.SymbolicFunction(['x1', 'x2'], ['x1 * x2'])
graphModel = f.draw([0.0, -10.0], [10.0, 10.0])
graphModel.setXTitle(r'$x_1$')
graphModel.setXTitle(r'$x_2$')
graphModel.setTitle(r'Isolines of the model : $Y = f(X)$')