# %% # The following statement create the calibrated function from the model. The calibrated parameters :math:`K_s`, :math:`Z_v`, :math:`Z_m` are at indices 1, 2, 3 in the inputs arguments of the model. # %% calibratedIndices = [1,2,3] mycf = ot.ParametricFunction(g, calibratedIndices, thetaPrior) # %% # Calibration with linear least squares # ------------------------------------- # %% # The `LinearLeastSquaresCalibration` class performs the linear least squares calibration by linearizing the model in the neighbourhood of the reference point. # %% algo = ot.LinearLeastSquaresCalibration(mycf, Qobs, Hobs, thetaPrior, "SVD") # %% # The `run` method computes the solution of the problem. # %% algo.run() # %% calibrationResult = algo.getResult() # %% # The `getParameterMAP` method returns the maximum of the posterior distribution of :math:`\theta`. # %% thetaStar = calibrationResult.getParameterMAP()
#! /usr/bin/env python import openturns as ot ot.TESTPREAMBLE() ot.PlatformInfo.SetNumericalPrecision(5) m = 10 x = [[0.5 + i] for i in range(m)] inVars = ["a", "b", "c", "x"] formulas = ["a + b * exp(c * x)", "(a * x^2 + b) / (c + x^2)"] g = ot.SymbolicFunction(inVars, formulas) trueParameter = [2.8, 1.2, 0.5] params = [0, 1, 2] model = ot.ParametricFunction(g, params, trueParameter) y = model(x) y += ot.Normal([0.0] * 2, [0.05] * 2, ot.IdentityMatrix(2)).getSample(m) candidate = [1.0] * 3 methods = ["SVD", "QR", "Cholesky"] for method in methods: print("method=", method) algo = ot.LinearLeastSquaresCalibration(model, x, y, candidate, method) algo.run() print("result=", algo.getResult())
# %% logisticParametric = ot.ParametricFunction(logisticModelPy,[22,23],thetaPrior) # %% # Check that we can evaluate the parametric function. # %% populationPredicted = logisticParametric(timeObservationsVector) populationPredicted[0:10] # %% # Calibration # ------------ # %% algo = ot.LinearLeastSquaresCalibration(logisticParametric, timeObservationsVector, populationObservationsVector, thetaPrior) # %% algo.run() # %% calibrationResult = algo.getResult() # %% thetaMAP = calibrationResult.getParameterMAP() thetaMAP # %% thetaPosterior = calibrationResult.getParameterPosterior() thetaPosterior.computeBilateralConfidenceIntervalWithMarginalProbability(0.95)[0]
model = ot.ParametricFunction(g, calibratedIndices, candidate) outputObservationNoiseSigma = 2. # (Pa) observationOutputNoise = ot.Normal(0., outputObservationNoiseSigma) size = 1000 # Generate exact outputs inputSample = inputRandomVector.getSample(size) outputStress = g(inputSample) # Add noise sampleNoiseH = observationOutputNoise.getSample(size) outputObservations = outputStress + sampleNoiseH # Calibrate inputObservations = inputSample[:, 0] algo = ot.LinearLeastSquaresCalibration(model, inputObservations, outputObservations, candidate, "SVD") algo.run() calibrationResult = algo.getResult() # Check residual distribution residualDistribution = calibrationResult.getObservationsError() meanResidual = residualDistribution.getMean()[0] assert meanResidual == 0. sigmaResidual = residualDistribution.getStandardDeviation()[0] rtol = 0. atol = 5.e-2 ott.assert_almost_equal(sigmaResidual, outputObservationNoiseSigma, rtol, atol) # Check other fields print("result=", calibrationResult)
# %% # The following statement create the calibrated function from the model. The calibrated parameters `R`, `C`, `Gamma` are at indices 1, 2, 3 in the inputs arguments of the model. # %% calibratedIndices = [1, 2, 3] mycf = ot.ParametricFunction(g, calibratedIndices, thetaPrior) # %% # Calibration with linear least squares # ------------------------------------- # %% # The `LinearLeastSquaresCalibration` class performs the linear least squares calibration by linearizing the model in the neighbourhood of the reference point. # %% algo = ot.LinearLeastSquaresCalibration(mycf, observedStrain, observedStress, thetaPrior, "SVD") # %% # The `run` method computes the solution of the problem. # %% algo.run() # %% calibrationResult = algo.getResult() # %% # Analysis of the results # ----------------------- # %%