Inheritance diagram for python.uq.dists.Dist.Dist:

Public Member Functions
	cdf (self, p, args, *kws)

	corrcoeff (self, covMatrix=None)

	cov (self)

	crossEntropy (self, samples)

	fromJson (cls, jsonObject)

	getBounds (self)

	getDim (self)

	klDivergence (self, dist, testSamplesUnit=None, testSamplesProb=None, n=1e4)

	l2error (self, dist, testSamplesUnit=None, testSamplesProb=None, n=1e4, dtype=SampleType.ACTIVEPROBABILISTIC)

	mean (self)

	pdf (self, p, args, *kws)

	ppf (self, p, args, *kws)

	rvs (self, n=1)

	std (self)

	var (self)

Detailed Description

The Dist class, which is the super class for all
distributions of this package

Member Function Documentation

◆ cdf()

python.uq.dists.Dist.Dist.cdf	(		self,
			p,
		*	args,
		**	kws
	)

Cumulative distribution function
@param p: (tuple) of floats
@return: cumulative distribution value

◆ corrcoeff()

python.uq.dists.Dist.Dist.corrcoeff	(	self,
		covMatrix = `None`
	)

References sgpp::datadriven::KernelDensityEstimator.cov(), sgpp::datadriven::LearnerSGDE.cov(), sgpp::datadriven::SparseGridDensityEstimator.cov(), sgpp::datadriven::DensityEstimator.cov(), python.uq.dists.Dist.Dist.cov(), python.uq.dists.KDEDist.KDEDist.cov(), python.uq.dists.NatafDist.NatafDist.cov(), and python.uq.dists.SGDEdist.SGDEdist.cov().

◆ cov()

python.uq.dists.Dist.Dist.cov ( self )

Get covariance matrix

Referenced by python.uq.dists.Dist.Dist.corrcoeff().

◆ crossEntropy()

python.uq.dists.Dist.Dist.crossEntropy	(	self,
		samples
	)

this measure computes the cross entropy with respect
to some unknown probability distribution from which only samples
are available. This measure is known to minimize the kl divergence.

@param samples: numpy array

◆ fromJson()

python.uq.dists.Dist.Dist.fromJson	(	cls,
		jsonObject
	)

Referenced by python.learner.Learner.Learner.setMemento(), python.uq.analysis.asgc.ASGCKnowledge.ASGCKnowledge.setMemento(), python.uq.learner.Learner.Learner.setMemento(), python.uq.sampler.asgc.ASGCSampler.ASGCSampler.setMemento(), and python.uq.uq_setting.UQSetting.UQSetting.setMemento().

◆ getBounds()

python.uq.dists.Dist.Dist.getBounds ( self )

Get the distribution's intervals
@return: numpy array [dim, 2]

Referenced by python.uq.dists.J.J.discretize(), and python.uq.dists.Dist.Dist.l2error().

◆ getDim()

python.uq.dists.Dist.Dist.getDim ( self )

Get number of marginal distributions
@return: int number of marginal distributions

Referenced by python.uq.dists.SGDEdist.SGDEdist.__str__(), python.uq.dists.Dist.Dist.cov(), python.uq.parameters.ParameterSet.ParameterSet.extractActiveSubset(), python.uq.dists.KDEDist.KDEDist.getBandwidths(), python.uq.dists.EstimatedDist.EstimatedDist.getBounds(), and python.uq.uq_setting.UQSetting.UQSetting.getDim().

◆ klDivergence()

python.uq.dists.Dist.Dist.klDivergence	(	self,
		dist,
		testSamplesUnit = `None`,
		testSamplesProb = `None`,
		n = `1e4`
	)

computes the KL-divergence from this distribution with respect to dist

\approx \frac{1}{n} \sum_{i = 1}^{n} p(x_i) log_2 (p(x_i) / q(x_i))

and for samples obtained via importance sampling it holds

\approx \frac{1}{n} \sum_{i = 1}^{n} log_2 (p(y_i) / q(y_i))
= \frac{1}{n} \sum_{i = 1}^{n} log_2 p(y_i) - log_2 q(y_i))
= [\frac{1}{n} \sum_{i = 1}^{n} log_2 p(y_i)] - [\frac{1}{n} \sum_{i = 1}^{n} log_2 q(y_i)]
= mean(log_2 p(y_i)) - mean(log_2 q(y_i))

@param dist: Dist
@param testSamplesUnit: numpy array
@param testSamplesProb: numpy array

◆ l2error()

python.uq.dists.Dist.Dist.l2error	(	self,
		dist,
		testSamplesUnit = `None`,
		testSamplesProb = `None`,
		n = `1e4`,
		dtype = `SampleType.ACTIVEPROBABILISTIC`
	)

mean squared error, defined as

|| p - p_n ||^2 = \int (p(x) - p_n(x))^2 * p(x) dx
                ~ 1/n \sum_i (p(x_i) - p_n(x_i)^2
for x_i drawn from p.
@param dist: Dist
@param testSamplesUnit: numpy array
@param testSamplesProb: numpy array
@param n: int, if no test samples are given, just select them
          uniformly within he range of the distribution

◆ mean()

python.uq.dists.Dist.Dist.mean ( self )

@return: expectation value

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis.computeMoments(), python.uq.analysis.mc.MCAnalysis.MCAnalysis.computeMoments(), python.uq.dists.LibAGFDist.LibAGFDist.var(), and python.uq.dists.SGDEdist.SGDEdist.var().

◆ pdf()

python.uq.dists.Dist.Dist.pdf	(		self,
			p,
		*	args,
		**	kws
	)

Probability distribution function
@param p: (tuple) of floats
@return: probability distribution value

Referenced by python.uq.dists.Dist.Dist.crossEntropy(), python.uq.dists.J.J.discretize(), python.uq.dists.Dist.Dist.klDivergence(), and python.uq.dists.Dist.Dist.l2error().

◆ ppf()

python.uq.dists.Dist.Dist.ppf	(		self,
			p,
		*	args,
		**	kws
	)

Point percentile function
@param p: (tuple) of floats
@return: point percentile value

Referenced by python.uq.dists.EstimatedDist.EstimatedDist.rvs(), python.uq.dists.NatafDist.NatafDist.rvs(), python.uq.dists.KDEDist.KDEDist.rvs(), and python.uq.dists.SGDEdist.SGDEdist.rvs().

◆ rvs()

python.uq.dists.Dist.Dist.rvs	(	self,
		n = `1`
	)

Generates n random numbers w.r.t. the marginal distributions
@param n: int number of random values
@return: numpy array [n, dim]

◆ std()

python.uq.dists.Dist.Dist.std ( self )

@return: standard deviation

◆ var()

python.uq.dists.Dist.Dist.var ( self )

@return: variance

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis.computeMoments(), python.uq.analysis.mc.MCAnalysis.MCAnalysis.computeMoments(), python.uq.dists.Dist.Dist.cov(), python.uq.dists.DataDist.DataDist.std(), python.uq.dists.Dist.Dist.std(), and python.uq.dists.J.J.std().

The documentation for this class was generated from the following file:

datadriven/python/uq/dists/Dist.py

Public Member Functions