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#!/usr/bin/env python
import openturns as ot
import openturns.testing
import persalys
ot.RandomGenerator.SetSeed(0)
myStudy = persalys.Study("myStudy")
persalys.Study.Add(myStudy)
# Models
x1 = persalys.Input("x1", 0.2)
x2 = persalys.Input("x2", 1.2)
x3 = persalys.Input("x3", 1.0)
fake_var = persalys.Output("fake_var")
fake_var.setIsSelected(False)
y0 = persalys.Output("y0")
fake_y0 = persalys.Output("fake_y0")
y1 = persalys.Output("y1")
# symboilc model ##
formula_fake_var = "x1"
formula_y0 = "cos(0.5*x1) + sin(x2)"
formula_y1 = "cos(0.5*x1) + sin(x2) + x3"
symbolicModel = persalys.SymbolicPhysicalModel(
"symbolicModel",
[x1, x2, x3],
[fake_var, y0, fake_y0, y1],
[formula_fake_var, formula_y0, formula_y0, formula_y1],
)
myStudy.add(symbolicModel)
# python model ##
code = "from math import cos, sin, sqrt\n\ndef _exec(x1, x2, x3):\n y0 = cos(0.5*x1) + sin(x2) + sqrt(x3)\n return y0\n"
pythonModel = persalys.PythonPhysicalModel("pythonModel", [x1, x2, x3], [y0], code)
myStudy.add(pythonModel)
# coupling model ##
E = persalys.Input("E", 0, "")
F = persalys.Input("F", 0, "")
II = persalys.Input("I", 0, "")
L = persalys.Input("L", 0, "")
deviation = persalys.Output("deviation", "")
deviation.setValue(1.26262626263)
inputs = [E, F, II, L]
outputs = [deviation]
steps = []
input_files = []
input_file0 = persalys.CouplingInputFile(
"../python/test/coupling_model/beam_input_template.xml"
)
input_file0.setConfiguredPath("beam_input.xml")
input_file0.setVariables(
["E", "F", "I", "L"], ["@E", "@F", "@I", "@L"], ["{}", "{}", "{}", "{}"]
)
input_files.append(input_file0)
resource_files = []
resource_file0 = persalys.CouplingResourceFile("../python/test/coupling_model/beam.py")
resource_files.append(resource_file0)
output_files = []
output_file0 = persalys.CouplingOutputFile("beam_output.txt")
output_file0.setVariables(["deviation"], ["deviation="], [0], [0], [0])
output_files.append(output_file0)
step0 = persalys.CouplingStep(
"python3 beam.py", input_files, resource_files, output_files
)
step0.setIsShell(False)
steps.append(step0)
couplingModel = persalys.CouplingPhysicalModel("couplingModel", inputs, outputs, steps)
couplingModel.setCleanupWorkDirectory(True)
couplingModel.setCacheFiles("", "")
myStudy.add(couplingModel)
filename = "data_da.csv"
cDist = ot.JointDistribution(
[ot.Normal(), ot.Gumbel(), ot.Normal(), ot.Uniform()],
ot.BlockIndependentCopula([ot.IndependentCopula(2), ot.GumbelCopula()]),
)
sample = cDist.getSample(200)
sample.add([float("nan"), float("inf"), 0.0, 0.0])
sample.exportToCSVFile(filename, " ")
# Designs of Experiment ##
# fixed design ##
ot.RandomGenerator.SetSeed(0)
fixedDesign = persalys.FixedDesignOfExperiment("fixedDesign", symbolicModel)
inputSample = ot.LHSExperiment(
ot.JointDistribution([ot.Uniform(0.0, 10.0), ot.Uniform(0.0, 10.0)]), 10
).generate()
inputSample.stack(ot.Sample(10, [0.5]))
fixedDesign.setOriginalInputSample(inputSample)
fixedDesign.run()
myStudy.add(fixedDesign)
# grid ##
values = [[0.5 + i * 1.5 for i in range(7)], [0.5 + i * 1.5 for i in range(7)], [1]]
grid = persalys.GridDesignOfExperiment("grid", symbolicModel, values)
myStudy.add(grid)
# importDesign ##
importDesign = persalys.ImportedDesignOfExperiment(
"importDesign", symbolicModel, filename, [0, 2, 3]
)
importDesign.run()
myStudy.add(importDesign)
# onePointDesign ##
onePointDesign = persalys.GridDesignOfExperiment("onePointDesign", pythonModel)
myStudy.add(onePointDesign)
# twoPointsDesign ##
twoPointsDesign = persalys.GridDesignOfExperiment(
"twoPointsDesign", pythonModel, [[0.2], [1.2], [-0.2, 1.0]]
)
myStudy.add(twoPointsDesign)
# fixed DataModel ##
fixedDataModel = persalys.DataModel(
"fixedDataModel",
fixedDesign.getOriginalInputSample(),
fixedDesign.getResult().getDesignOfExperiment().getOutputSample(),
)
myStudy.add(fixedDataModel)
# imported DataModel ##
importDataModel = persalys.DataModel(
"importDataModel", filename, [0, 2, 3], [1], ["x_0", "x_2", "x_3"], ["x_1"]
)
myStudy.add(importDataModel)
# model evaluation
evaluation1 = persalys.ModelEvaluation("evaluation1", symbolicModel)
myStudy.add(evaluation1)
# morris ##
try:
morris = persalys.MorrisAnalysis("aMorris", symbolicModel)
morris.setInterestVariables(["y0"])
morris.setLevel(4)
morris.setTrajectoriesNumber(10)
morris.setSeed(2)
myStudy.add(morris)
except Exception:
print("No Morris")
# optimization ##
optim = persalys.OptimizationAnalysis("optim", symbolicModel, "TNC")
optim.setInterestVariables(["y1"])
optim.setVariableInputs(["x1", "x2"])
optim.setMaximumCallsNumber(150)
optim.setMaximumAbsoluteError(1e-6)
optim.setMaximumRelativeError(1e-6)
optim.setMaximumResidualError(1e-6)
optim.setMaximumConstraintError(1e-6)
myStudy.add(optim)
# multi-objective optimization
if ot.PlatformInfo.HasFeature("pagmo"):
mooptim = persalys.MultiObjectiveOptimizationAnalysis(
"mooptim", symbolicModel, "nsga2"
)
mooptim.setInterestVariables(["y0", "y1"])
mooptim.addConstraint("y0 > 2")
mooptim.setPopulationSize(60)
mooptim.setGenerationNumber(12)
mooptim.setVariableInputs(["x1", "x2", "x3"])
myStudy.add(mooptim)
# calibration ##
# a- observations
nbObs = 100
inObs = ot.Uniform(0.0, 10.0).getSample(nbObs)
inObs.setDescription(["x1"])
y0Noise = ot.Normal(0, 0.1).getSample(nbObs)
y0Sample = ot.ParametricFunction(symbolicModel.getFunction("y0"), [1, 2], [1.2, 1.0])(
inObs
)
y0Obs = y0Sample + y0Noise
y0Obs.setDescription(["y0"])
obs = persalys.Observations("observations", symbolicModel, inObs, y0Obs)
myStudy.add(obs)
# b- calibrationAnalysis
calibration = persalys.CalibrationAnalysis("calibration", obs)
calibration.setCalibratedInputs(["x2"], ot.Dirac([1.2]), ["x3"], [1.1])
calibration.setMethodName("GaussianNonlinear")
sigma = 0.15
errorCovariance = ot.CovarianceMatrix(1)
errorCovariance[0, 0] = sigma**2
calibration.setErrorCovariance(errorCovariance)
calibration.setBootStrapSize(25)
calibration.setConfidenceIntervalLength(0.99)
optimAlgo = calibration.getOptimizationAlgorithm()
optimAlgo.setMaximumCallsNumber(50)
optimAlgo.setMaximumAbsoluteError(1e-6)
optimAlgo.setMaximumRelativeError(1e-6)
optimAlgo.setMaximumResidualError(1e-6)
optimAlgo.setMaximumConstraintError(1e-6)
calibration.setOptimizationAlgorithm(optimAlgo)
myStudy.add(calibration)
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