.. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_results.py: Exploitation of simulation algorithm results ============================================ In this example we are going to retrieve all the results proposed by probability simulation algorithms: - the probability estimate - the estimator variance - the confidence interval - the convergence graph of the estimator - the stored input and output numerical samples - importance factors .. code-block:: default from __future__ import print_function import openturns as ot import openturns.viewer as viewer from matplotlib import pylab as plt ot.Log.Show(ot.Log.NONE) Create the joint distribution of the parameters. .. code-block:: default distribution_R = ot.LogNormalMuSigma(300.0, 30.0, 0.0).getDistribution() distribution_F = ot.Normal(75e3, 5e3) marginals = [distribution_R, distribution_F] distribution = ot.ComposedDistribution(marginals) Create the model. .. code-block:: default model = ot.SymbolicFunction(['R', 'F'], ['R-F/(pi_*100.0)']) .. code-block:: default modelCallNumberBefore = model.getEvaluationCallsNumber() modelGradientCallNumberBefore = model.getGradientCallsNumber() modelHessianCallNumberBefore = model.getHessianCallsNumber() To have access to the input and output samples after the simulation, activate the History mechanism. .. code-block:: default model = ot.MemoizeFunction(model) Remove all the values stored in the history mechanism. Care : it is done regardless the status of the History mechanism. .. code-block:: default model.clearHistory() Create the event whose probability we want to estimate. .. code-block:: default vect = ot.RandomVector(distribution) G = ot.CompositeRandomVector(model, vect) event = ot.ThresholdEvent(G, ot.Less(), 0.0) Create a Monte Carlo algorithm. .. code-block:: default experiment = ot.MonteCarloExperiment() algo = ot.ProbabilitySimulationAlgorithm(event, experiment) algo.setMaximumCoefficientOfVariation(0.1) algo.setMaximumStandardDeviation(0.001) algo.setMaximumOuterSampling(int(1e4)) Define the HistoryStrategy to store the values of :math:`P_n` and :math:`\sigma_n` used ot draw the convergence graph. Compact strategy : N points .. code-block:: default N = 1000 algo.setConvergenceStrategy(ot.Compact(N)) algo.run() Retrieve result structure. .. code-block:: default result = algo.getResult() Display the simulation event probability. .. code-block:: default result.getProbabilityEstimate() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none 0.02892561983471075 Criteria 3 : Display the Standard Deviation of the estimator .. code-block:: default result.getStandardDeviation() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none 0.0028793594509308627 Display the variance of the simulation probability estimator. .. code-block:: default result.getVarianceEstimate() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none 8.290710847664879e-06 Criteria 2 : Display the number of iterations of the simulation .. code-block:: default result.getOuterSampling() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none 3388 Display the total number of evaluations of the model .. code-block:: default result.getOuterSampling() * result.getBlockSize() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none 3388 Save the number of calls to the model, its gradient and hessian done so far. .. code-block:: default modelCallNumberAfter = model.getEvaluationCallsNumber() modelGradientCallNumberAfter = model.getGradientCallsNumber() modelHessianCallNumberAfter = model.getHessianCallsNumber() Display the number of iterations executed and the number of evaluations of the model. .. code-block:: default modelCallNumberAfter - modelCallNumberBefore .. rst-class:: sphx-glr-script-out Out: .. code-block:: none 3388 Get the mean point in event domain care : only for Monte Carlo and LHS sampling methods. .. code-block:: default result.getMeanPointInEventDomain() .. raw:: html

[245.234,80683.9]



Get the associated importance factors care : only for Monte Carlo and LHS sampling methods. .. code-block:: default result.getImportanceFactors() .. raw:: html

[X0 : 0.750364, X1 : 0.249636]



.. code-block:: default graph = result.drawImportanceFactors() view = viewer.View(graph) .. image:: /auto_reliability_sensitivity/reliability/images/sphx_glr_plot_probability_simulation_results_001.png :alt: Importance Factors from Simulation - v0 :class: sphx-glr-single-img Display the confidence interval length centered around the MonteCarlo probability. The confidence interval is .. math:: IC = [\tilde{p} - 0.5 \ell, \tilde{p} + 0.5 \ell] with level 0.95, where :math:`\tilde{p}` is the estimated probability and :math:`\ell` is the confidence interval length. .. code-block:: default probability = result.getProbabilityEstimate() length95 = result.getConfidenceLength(0.95) print("0.95 Confidence Interval length = ", length95) print("IC at 0.95 = [", probability - 0.5*length95, "; ", probability + 0.5*length95, "]") .. rst-class:: sphx-glr-script-out Out: .. code-block:: none 0.95 Confidence Interval length = 0.01128688164473903 IC at 0.95 = [ 0.023282179012341236 ; 0.034569060657080264 ] Draw the convergence graph and the confidence interval of level alpha. By default, alpha = 0.95. .. code-block:: default alpha = 0.90 graph = algo.drawProbabilityConvergence(alpha) view = viewer.View(graph) .. image:: /auto_reliability_sensitivity/reliability/images/sphx_glr_plot_probability_simulation_results_002.png :alt: ProbabilitySimulationAlgorithm convergence graph at level 0.9 :class: sphx-glr-single-img Get the numerical samples of the input and output random vectors stored according to the History Strategy specified and used to evaluate the probability estimator and its variance. .. code-block:: default inputSampleStored = model.getInputHistory() outputSampleStored = model.getOutputHistory() inputSampleStored .. raw:: html
v0v1
0337.303173381.5
1332.122767377.29
2303.613765820.79
...
3385297.622772351.49
3386284.235976613.42
3387242.507176285.83


Get the values of the estimator and its variance stored according to the History Strategy specified and used to draw the convergence graph. .. code-block:: default estimator_probability_sample = algo.getConvergenceStrategy().getSample()[0] estimator_variance_sample = algo.getConvergenceStrategy().getSample()[1] print(estimator_probability_sample, estimator_variance_sample) plt.show() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none [0,-1] [0,-1] .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.159 seconds) .. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_probability_simulation_results.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_probability_simulation_results.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_probability_simulation_results.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_