# %% # 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
# -----------------------
# %%
