Note
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Exploitation of simulation algorithm resultsΒΆ
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
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.
distribution_R = ot.LogNormalMuSigma(300.0, 30.0, 0.0).getDistribution()
distribution_F = ot.Normal(75e3, 5e3)
marginals = [distribution_R, distribution_F]
distribution = ot.JointDistribution(marginals)
Create the model.
model = ot.SymbolicFunction(["R", "F"], ["R-F/(pi_*100.0)"])
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.
model = ot.MemoizeFunction(model)
Remove all the values stored in the history mechanism. Care : it is done regardless the status of the History mechanism.
model.clearHistory()
Create the event whose probability we want to estimate.
vect = ot.RandomVector(distribution)
G = ot.CompositeRandomVector(model, vect)
event = ot.ThresholdEvent(G, ot.Less(), 0.0)
Create a Monte Carlo algorithm.
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 and used ot draw the convergence graph. Compact strategy : N points
N = 1000
algo.setConvergenceStrategy(ot.Compact(N))
algo.run()
Retrieve result structure.
result = algo.getResult()
Display the simulation event probability.
result.getProbabilityEstimate()
0.030618686868686892
Criteria 3 : Display the Standard Deviation of the estimator
result.getStandardDeviation()
0.0030608920682558276
Display the variance of the simulation probability estimator.
result.getVarianceEstimate()
9.369060253511439e-06
Criteria 2 : Display the number of iterations of the simulation
result.getOuterSampling()
3168
Display the total number of evaluations of the model
result.getOuterSampling() * result.getBlockSize()
3168
Save the number of calls to the model, its gradient and hessian done so far.
modelCallNumberAfter = model.getEvaluationCallsNumber()
modelGradientCallNumberAfter = model.getGradientCallsNumber()
modelHessianCallNumberAfter = model.getHessianCallsNumber()
Display the number of iterations executed and the number of evaluations of the model.
modelCallNumberAfter - modelCallNumberBefore
3168
Get the mean point in event domain care : only for Monte Carlo and LHS sampling methods.
result.getMeanPointInEventDomain()
Get the associated importance factors care : only for Monte Carlo and LHS sampling methods.
result.getImportanceFactors()
graph = result.drawImportanceFactors()
view = viewer.View(graph)
Display the confidence interval length centered around the MonteCarlo probability. The confidence interval is
with level 0.95, where is the estimated probability and is the confidence interval length.
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,
"]",
)
0.95 Confidence Interval length = 0.011998476428691476
IC at 0.95 = [ 0.024619448654341153 ; 0.03661792508303263 ]
Draw the convergence graph and the confidence interval of level alpha. By default, alpha = 0.95.
alpha = 0.90
graph = algo.drawProbabilityConvergence(alpha)
view = viewer.View(graph)
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.
inputSampleStored = model.getInputHistory()
outputSampleStored = model.getOutputHistory()
inputSampleStored
Get the values of the estimator and its variance stored according to the History Strategy specified and used to draw the convergence graph.
estimator_probability_sample = algo.getConvergenceStrategy().getSample()[0]
estimator_variance_sample = algo.getConvergenceStrategy().getSample()[1]
print(estimator_probability_sample, estimator_variance_sample)
plt.show()
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