Hi Phil,
First of all, thank you for using OpenTURNS. Here is my input concerning your
questions:
1. It is very easy to flip/translate (and even scale) an univariate
distribution in OpenTURNS using the arithmetic of random variables, see
flip_distribution.py.
2. There is currently no way to truncate multivariate distributions in
OpenTURNS, but a quick and dirty (ie mathematically correct but not optimized)
way to get it is given in truncated_nd_distribution.py
3. I have no idea on what is going on. I added the relevant guys to the
discussion, but keep in mind that Denis and Julien are on holidays and Sofiane
has a terrible workload, so you may have to wait a little bit for their input
For this kind of questions, it is better to use the users mailing list, see
http://openturns.org/mailman/listinfo/users to subscribe to the list.
Best regards,
Régis
De :Phil Fernandes [mailto:[email protected]]
Envoyé : mardi 25 juillet 2017 00:29
À : LEBRUN, Regis; [email protected]
Objet : OpenTurns inquiry
Hello Regis, Denis,
I am an engineer with Enbridge Pipelines and we have recently begun using
OpenTurns for reliability analysis of our infrastructure. So far I am finding
it to be an excellent and very comprehensive software library – thank you for
helping develop it.
I have run into a few of issues when using OpenTurns and was wondering if you
might be able to provide some help:
1. Is there a way of mirroring skewed distributions, for example flipping
a Weibull distribution so that instead of a lower limit it has an upper limit?
2. Is it possible to truncate a multivariate kernel density
distributions? We can truncate univariate parametric distributions using the
syntax
truncdist = ot.TruncatedDistribution(mydist, lower, upper)
but is there something analogous for multivariate KDEs where we can define
bounds for each dimension?
3. There is a conflict between the Python library PyMC3 and Theano and
OpenTurns. If Theano is imported first, OpenTurns fails to import with the
following error
Traceback (most recent call last):
File "<ipython-input-3-704e69d30dff>", line 1, in <module>
import openturns as ot
File "C:\Anaconda3\lib\site-packages\openturns\__init__.py", line 61, in
<module>
from .common import *
File "C:\Anaconda3\lib\site-packages\openturns\common.py", line 20, in
<module>
_common = swig_import_helper()
File "C:\Anaconda3\lib\site-packages\openturns\common.py", line 19, in
swig_import_helper
return importlib.import_module('_common')
File "C:\Anaconda3\lib\importlib\__init__.py", line 126, in import_module
return _bootstrap._gcd_import(name[level:], package, level)
ModuleNotFoundError: No module named '_common'
If I reverse the import order (i.e., OpenTurns first, then PyMC3 or Theano),
then PymC3/Theano fails to import with
Traceback (most recent call last):
File "<ipython-input-2-e9f7838173a6>", line 5, in <module>
import pymc3 as pm
File "C:\Anaconda3\lib\site-packages\pymc3\__init__.py", line 5, in <module>
from .distributions import *
File "C:\Anaconda3\lib\site-packages\pymc3\distributions\__init__.py", line
1, in <module>
from . import timeseries
File "C:\Anaconda3\lib\site-packages\pymc3\distributions\timeseries.py", line
1, in <module>
import theano.tensor as tt
File "C:\Anaconda3\lib\site-packages\theano\__init__.py", line 80, in <module>
from theano.scan_module import (scan, map, reduce, foldl, foldr, clone,
File "C:\Anaconda3\lib\site-packages\theano\scan_module\__init__.py", line
41, in <module>
from theano.scan_module import scan_opt
File "C:\Anaconda3\lib\site-packages\theano\scan_module\scan_opt.py", line
60, in <module>
from theano import tensor, scalar
File "C:\Anaconda3\lib\site-packages\theano\tensor\__init__.py", line 9, in
<module>
from theano.tensor.subtensor import *
File "C:\Anaconda3\lib\site-packages\theano\tensor\subtensor.py", line 26, in
<module>
import theano.gof.cutils # needed to import cutils_ext
File "C:\Anaconda3\lib\site-packages\theano\gof\cutils.py", line 320, in
<module>
compile_cutils()
File "C:\Anaconda3\lib\site-packages\theano\gof\cutils.py", line 285, in
compile_cutils
preargs=args)
File "C:\Anaconda3\lib\site-packages\theano\gof\cmodule.py", line 2325, in
compile_str
return dlimport(lib_filename)
File "C:\Anaconda3\lib\site-packages\theano\gof\cmodule.py", line 302, in
dlimport
rval = __import__(module_name, {}, {}, [module_name])
ImportError: DLL load failed: The specified procedure could not be found.
Your help would be very much appreciated.
Thank you.
Phil Fernandes P.Eng, MASc
Engineer, Reliability Assessment
—
ENBRIDGE PIPELINES INC.
TEL: 780-420-8210 | FAX: 780-420-5234
7045 Enbridge Centre, 10175 101 Street NW, Edmonton, AB, T5J 0H3
www.enbridge.com
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appropriate to ensure that this message and any attachments are virus free. import openturns as ot
distribution = ot.Weibull(2.0, 1.5)
flipped_distribution = 3.0 - distribution
xMin = -5.0
xMax = 7.0
graph = distribution.drawPDF(xMin, xMax)
graph.add(flipped_distribution.drawPDF(xMin, xMax))
graph.setTitle("")
graph.setColors(["red", "blue"])
graph.setLegends(["initial", "flipped"])
ot.Show(graph)
import openturns as ot
class TruncatedNDDistribution(ot.PythonDistribution):
def __init__(self, distribution, bounds):
super(TruncatedNDDistribution, self).__init__(distribution.getDimension())
if distribution.getDimension() != bounds.getDimension():
raise ValueError('Distribution and bounds have incompatible dimension')
bounds = bounds.intersect(distribution.getRange())
self.distribution_ = distribution
self.bounds_ = bounds
self.lowerBound_ = bounds.getLowerBound()
self.upperBound_ = bounds.getUpperBound()
self.normalization_ = distribution.computeProbability(bounds)
if self.normalization_ == 0.0:
raise ValueError('The truncation bounds have a zero probability')
def getRange(self):
return self.bounds_
def computePDF(self, X):
if not self.bounds_.numericallyContains(X):
return False
return self.distribution_.computePDF(X) / self.normalization_
def computeCDF(self, X):
interval = self.bounds_.intersect(ot.Interval([-ot.SpecFunc.MaxScalar]*self.distribution_.getDimension(), X))
return self.distribution_.computeProbability(interval) / self.normalization_
def getRealization(self):
stop = False
while not stop:
X = self.distribution_.getRealization()
stop = self.bounds_.contains(X)
return X
dimension = 2
size = 70
sample = ot.Normal(dimension).getSample(size)
ks = ot.KernelSmoothing().build(sample)
truncatedKS = ot.Distribution(TruncatedNDDistribution(ks, ot.Interval([-2.0]*dimension, [2.0]*dimension)))
graph = truncatedKS.drawPDF([-2.5]*dimension, [2.5]*dimension, [256]*dimension)
graph.add(ot.Cloud(truncatedKS.getSample(200)))
graph.setColors(["blue", "red"])
ot.Show(graph)
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