errorCovariance[i, i] = 2.0 + (1.0 + i) * (1.0 + i)
for j in range(i):
errorCovariance[i, j] = 1.0 / (1.0 + i + j)
globalErrorCovariance = ot.CovarianceMatrix(2 * m)
for i in range(2 * m):
globalErrorCovariance[i, i] = 2.0 + (1.0 + i) * (1.0 + i)
for j in range(i):
globalErrorCovariance[i, j] = 1.0 / (1.0 + i + j)
methods = ["SVD", "QR", "Cholesky"]
for method in methods:
print("method=", method)
# 1. Check with local error covariance
print("Local error covariance")
algo = ot.GaussianLinearCalibration(modelX, x, y, candidate,
priorCovariance, errorCovariance,
method)
algo.run()
calibrationResult = algo.getResult()
# Analysis of the results
# Maximum A Posteriori estimator
thetaMAP = calibrationResult.getParameterMAP()
exactTheta = ot.Point([5.69186, 0.0832132, 0.992301])
rtol = 1.e-2
assert_almost_equal(thetaMAP, exactTheta, rtol)
# Covariance matrix of theta
thetaPosterior = calibrationResult.getParameterPosterior()
covarianceThetaStar = matrixToSample(thetaPosterior.getCovariance())
exactCovarianceTheta = ot.Sample(
# %%
sigma = ot.CovarianceMatrix(3)
sigma[0, 0] = sigmaR**2
sigma[1, 1] = sigmaC**2
sigma[2, 2] = sigmaGamma**2
sigma
# %%
# Gaussian linear calibration
# ---------------------------
# %%
# The `GaussianLinearCalibration` class performs the gaussian linear calibration by linearizing the model in the neighbourhood of the prior.
# %%
algo = ot.GaussianLinearCalibration(mycf, observedStrain, observedStress,
thetaPrior, sigma, errorCovariance)
# %%
# The `run` method computes the solution of the problem.
# %%
algo.run()
# %%
calibrationResult = algo.getResult()
# %%
# Analysis of the results
# -----------------------
# %%
sigmaKs = 5.
sigmaZv = 1.
sigmaZm = 1.
# %%
sigma = ot.CovarianceMatrix(3)
sigma[0, 0] = sigmaKs**2
sigma[1, 1] = sigmaZv**2
sigma[2, 2] = sigmaZm**2
print(sigma)
# %%
# The `GaussianLinearCalibration` class performs Gaussian linear calibration by linearizing the model in the neighbourhood of the prior.
# %%
algo = ot.GaussianLinearCalibration(mycf, Qobs, Hobs, thetaPrior, sigma,
errorCovariance, "SVD")
# %%
# The `run` method computes the solution of the problem.
# %%
algo.run()
# %%
calibrationResult = algo.getResult()
# %%
# Analysis of the results
# -----------------------
# %%
sigmaR = 0.1 * R
sigmaC = 0.1 * C
sigmaGamma = 0.1 * Gamma
priorCovariance = ot.CovarianceMatrix(3)
priorCovariance[0, 0] = sigmaR**2
priorCovariance[1, 1] = sigmaC**2
priorCovariance[2, 2] = sigmaGamma**2
methods = ["SVD", "QR", "Cholesky"]
for method in methods:
print("method=", method)
# 1. Local calibration
# The `GaussianLinearCalibration` class performs the gaussian linear
# calibration by linearizing the model in the neighbourhood of the prior.
algo = ot.GaussianLinearCalibration(mycf, observedStrain, observedStress, \
thetaPrior, priorCovariance, localErrorCovariance, method)
# The `run` method computes the solution of the problem.
algo.run()
calibrationResult = algo.getResult()
# Analysis of the results
# Maximum A Posteriori estimator
thetaMAP = calibrationResult.getParameterMAP()
exactTheta = ot.Point([762.661, 3056.59, 8.52781])
assert_almost_equal(thetaMAP, exactTheta)
# Covariance matrix of theta
thetaPosterior = calibrationResult.getParameterPosterior()
covarianceThetaStar = matrixToSample(thetaPosterior.getCovariance())
errorCovariance[i, i] = 2.0 + (1.0 + i) * (1.0 + i)
for j in range(i):
errorCovariance[i, j] = 1.0 / (1.0 + i + j)
globalErrorCovariance = ot.CovarianceMatrix(outputDimension * size)
for i in range(outputDimension * size):
globalErrorCovariance[i, i] = 0.1 * (2.0 + (1.0 + i) * (1.0 + i))
for j in range(i):
globalErrorCovariance[i, j] = 0.1 / (1.0 + i + j)
methods = ["SVD", "QR", "Cholesky"]
for method in methods:
print("method=", method)
# 1. Check with local error covariance
print("Local error covariance")
algo = ot.GaussianLinearCalibration(
model, inputObservations, outputObservations, candidate, priorCovariance, errorCovariance, method
)
algo.run()
calibrationResult = algo.getResult()
# Analysis of the results
# Maximum A Posteriori estimator
parameterMAP = calibrationResult.getParameterMAP()
print("MAP=", repr(parameterMAP))
rtol = 0.0
atol = 1.0
ott.assert_almost_equal(parameterMAP, trueParameter, rtol, atol)
# 2. Check with global error covariance
print("Global error covariance")
algo = ot.GaussianLinearCalibration(