Doc: Add reliability problems

doc/conf.py

@@ -48,6 +48,7 @@
     'examples_dirs': ['examples'],
     'gallery_dirs': ['auto_examples'],
     'show_signature': False,
+    'ignore_pattern': 'rp8.py|rp33'
 }
 
 if Version(sphinx_gallery.__version__) >= Version("0.17.0"):

doc/examples/reliability_problems/README.txt

@@ -0,0 +1,2 @@
+Reliability examples
+====================

doc/examples/reliability_problems/plot_case_rs.py

@@ -0,0 +1,122 @@
+"""
+R-S analysis and 2D graphics
+============================
+"""
+
+# %%
+# The objective of this example is to present the R-S problem.
+# We also present graphic elements for the visualization of the limit state surface in 2 dimensions.
+
+# %%
+import openturns as ot
+import openturns.viewer as otv
+import otbenchmark as otb
+
+# %%
+problem = otb.RminusSReliability()
+
+
+# %%
+event = problem.getEvent()
+g = event.getFunction()
+
+
+# %%
+problem.getProbability()
+
+# %%
+# Create the Monte-Carlo algorithm
+algoProb = ot.ProbabilitySimulationAlgorithm(event)
+algoProb.setMaximumOuterSampling(1000)
+algoProb.setMaximumCoefficientOfVariation(0.01)
+algoProb.run()
+
+
+# %%
+# Get the results
+resultAlgo = algoProb.getResult()
+neval = g.getEvaluationCallsNumber()
+print("Number of function calls = %d" % (neval))
+pf = resultAlgo.getProbabilityEstimate()
+print("Failure Probability = %.4f" % (pf))
+level = 0.95
+c95 = resultAlgo.getConfidenceLength(level)
+pmin = pf - 0.5 * c95
+pmax = pf + 0.5 * c95
+print("%.1f %% confidence interval :[%.4f,%.4f] " % (level * 100, pmin, pmax))
+
+# %%
+# ## Plot the contours of the function
+
+# %%
+inputVector = event.getAntecedent()
+distribution = inputVector.getDistribution()
+
+# %%
+R = distribution.getMarginal(0)
+S = distribution.getMarginal(1)
+
+# %%
+alphaMin = 0.001
+alphaMax = 1 - alphaMin
+lowerBound = ot.Point([R.computeQuantile(alphaMin)[0], S.computeQuantile(alphaMin)[0]])
+upperBound = ot.Point([R.computeQuantile(alphaMax)[0], S.computeQuantile(alphaMax)[0]])
+
+# %%
+nbPoints = [100, 100]
+_ = otv.View(g.draw(lowerBound, upperBound, nbPoints))
+
+# %%
+Y = R - S
+Y
+
+# %%
+_ = otv.View(Y.drawPDF())
+
+# %%
+# Print the iso-values of the distribution
+# ----------------------------------------
+
+# %%
+_ = otv.View(distribution.drawPDF())
+
+# %%
+# ## Visualise the safe and unsafe regions on a sample
+
+# %%
+sampleSize = 500
+
+# %%
+drawEvent = otb.DrawEvent(event)
+
+# %%
+cloud = drawEvent.drawSampleCrossCut(sampleSize)
+cloud
+
+# %%
+# ## Draw the limit state surface
+
+# %%
+bounds = ot.Interval(lowerBound, upperBound)
+bounds
+
+
+# %%
+graph = drawEvent.drawLimitStateCrossCut(bounds)
+graph.add(cloud)
+graph
+
+# %%
+# ## Fill the event domain with a color
+
+# %%
+domain = drawEvent.fillEventCrossCut(bounds)
+_ = otv.View(domain)
+
+# %%
+domain.setLegends(["", ""])
+domain.add(cloud)
+_ = otv.View(domain)
+
+# %%
+otv.View.ShowAll()