Hi Michael,
Have a look
here:https://github.com/openturns/www/blob/master/_images/scripts/plot_kriging.py
I will check your script next rainy day!
Cheers
Régis
Le vendredi 10 août 2018 à 14:22:58 UTC+2, BAUDIN Michael
<[email protected]> a écrit :
Hi !
I am currently working on kriging and try to reproduce the graphics which is
printed in the carrousel of openturns.org :
https://www.qwant.com/?q=openturns%20kriging&t=images&o=0:1e0b94f86add70a402dfc53f500aa057&size=all&license=all&freshness=all&color=all&imagetype=all&source=web
More precisely, I would like to compute the 95% confidence bounds of the
kriging predictions. However, I could not find the Python script corresponding
to the figure neither on openturns.org nor in the doc (nor in the Slides of the
User’s days, nor in the Use Cases Guide). Is this Python script available ?
I also tried to produce the script by myself, and failed.... In PS, I put a
Python script which tries to reproduce the figure. The confidence bounds
produced by the script are extremely tight compared to what I expected. My
guess is that the issue is related to the estimate of the covariance model : in
OpenTURNS, the SquaredExponential is anisotropic while the figure might be
produced with an isotropic covariance. I also tried to prevent the optimization
algorithm from tuning the theta parameter with the setOptimizeParameters
method, but I wasn’t able to use correctly (the parameters still change,
however with a different value). What is the explanation for these tight bounds
?
Best regards,
Michaël
PS
# coding: utf-8
#
# # Références
#
# Metamodeling with Gaussian processes, Bertrand Iooss, EDF R&D, 2014,
www.gdr-mascotnum.fr/media/sssamo14_iooss.pdf
#
import numpy as np
import openturns as ot
import pylab as pl
#
n_test = 100
x_test_coord = np.linspace(0,12,n_test)
x_test = ot.Sample(x_test_coord,1)
y_test = np.sin(x_test)
# Base d'apprentissage de 7 points.
#
x_train_coord = [1.,3.,4.,6.,7.9,11., 11.5]
x_train = ot.Sample(x_train_coord,1)
y_train = np.sin(x_train)
n_train = len(x_train)
n_train
#
dimension = 1
basis = ot.ConstantBasisFactory(dimension).build()
covarianceModel = ot.SquaredExponential([1.]*dimension, [5.0])
algo = ot.KrigingAlgorithm(x_train, y_train, covarianceModel, basis)
algo.setOptimizeParameters(False)
algo.run()
result = algo.getResult()
krigeageMM = result.getMetaModel()
#
krigeageMM = result.getMetaModel()
y_test_MM = krigeageMM(x_test)
#
level = 0.95
alpha = (1-level)/2
sampleQinf = ot.Sample(n_test,1)
sampleQsup = ot.Sample(n_test,1)
for i in range(n_test):
xi = x_test[i]
var = result.getConditionalCovariance(xi)[0,0]
yi = y_test_MM[i][0]
N = ot.Normal(yi,np.sqrt(var))
q025 = N.computeQuantile(alpha)[0]
sampleQinf[i,0] = q025
q975 = N.computeQuantile(1-alpha)[0]
sampleQsup[i,0] = q975
#
pl.plot(x_test,y_test,"k-",label="Exact")
pl.plot(x_test,y_test_MM,"b--",label="Krigeage")
pl.plot(x_train,y_train,"ro",label="Apprentissage")
pl.plot(x_test,sampleQinf,"g-",label="%.2f%%" % (100*level))
pl.plot(x_test,sampleQsup,"g-")
pl.title("sin")
pl.xlabel("X")
pl.ylabel("Y")
pl.legend()
Ce message et toutes les pièces jointes (ci-après le 'Message') sont établis à
l'intention exclusive des destinataires et les informations qui y figurent sont
strictement confidentielles. Toute utilisation de ce Message non conforme à sa
destination, toute diffusion ou toute publication totale ou partielle, est
interdite sauf autorisation expresse.
Si vous n'êtes pas le destinataire de ce Message, il vous est interdit de le
copier, de le faire suivre, de le divulguer ou d'en utiliser tout ou partie. Si
vous avez reçu ce Message par erreur, merci de le supprimer de votre système,
ainsi que toutes ses copies, et de n'en garder aucune trace sur quelque support
que ce soit. Nous vous remercions également d'en avertir immédiatement
l'expéditeur par retour du message.
Il est impossible de garantir que les communications par messagerie
électronique arrivent en temps utile, sont sécurisées ou dénuées de toute
erreur ou virus.
____________________________________________________
This message and any attachments (the 'Message') are intended solely for the
addressees. The information contained in this Message is confidential. Any use
of information contained in this Message not in accord with its purpose, any
dissemination or disclosure, either whole or partial, is prohibited except
formal approval.
If you are not the addressee, you may not copy, forward, disclose or use any
part of it. If you have received this message in error, please delete it and
all copies from your system and notify the sender immediately by return message.
E-mail communication cannot be guaranteed to be timely secure, error or
virus-free.
_______________________________________________
OpenTURNS users mailing list
[email protected]
http://openturns.org/mailman/listinfo/users
_______________________________________________
OpenTURNS users mailing list
[email protected]
http://openturns.org/mailman/listinfo/users
