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

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

def	corrcoeff (self, covMatrix=None)

def	cov (self)

def	crossEntropy (self, samples)

def	fromJson (cls, jsonObject)

def	getBounds (self)

def	getDim (self)

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

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

def	mean (self)

def	pdf (self, p, args, kws)

def	ppf (self, p, args, kws)

def	rvs (self, n=1)

def	std (self)

def	var (self)

Detailed Description

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

Member Function Documentation

◆ cdf()

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

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

◆ corrcoeff()

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

References python.uq.dists.Dist.Dist.cov(), and python.uq.dists.Dist.Dist.klDivergence().

◆ cov()

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

Get covariance matrix

References sgpp::base::ForwardSelectorRefinement_refinement_key.getDim(), sgpp::base::ImpurityRefinement_refinement_key.getDim(), sgpp::base::PredictiveRefinement_refinement_key.getDim(), python.uq.analysis.asgc.ASGCAnalysisSpecification.ASGCAnalysisSpecification.getDim(), python.uq.dists.Beta.Beta.getDim(), python.uq.dists.Corr.Corr.getDim(), python.uq.dists.Dist.Dist.getDim(), python.uq.dists.DataDist.DataDist.getDim(), python.data.DataContainer.DataContainer.getDim(), python.uq.dists.Beta.Beta.var(), python.uq.dists.Dist.Dist.var(), sgpp::combigrid::BsplineStochasticCollocation.var, sgpp::combigrid::PolynomialStochasticCollocation.var, python.uq.dists.DataDist.DataDist.var(), and python.uq.analysis.Analysis.Analysis.var().

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

◆ crossEntropy()

def 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

References python.uq.dists.Dist.Dist.l2error(), python.uq.dists.CorrBeta.CorrBeta.pdf(), python.uq.dists.Dist.Dist.pdf(), python.uq.dists.Corr.Corr.pdf(), python.uq.dists.Beta.Beta.pdf(), python.uq.dists.DataDist.DataDist.pdf(), sgpp::combigrid::ProbabilityDensityFunction1D.pdf(), and sgpp::combigrid::OrthogonalPolynomialBasis1D.pdf().

◆ fromJson()

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

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

◆ getBounds()

def 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()

def 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()

def 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

References python.uq.dists.CorrBeta.CorrBeta.pdf(), python.uq.dists.Dist.Dist.pdf(), python.uq.dists.Corr.Corr.pdf(), python.uq.dists.Beta.Beta.pdf(), python.uq.dists.DataDist.DataDist.pdf(), sgpp::combigrid::ProbabilityDensityFunction1D.pdf(), and sgpp::combigrid::OrthogonalPolynomialBasis1D.pdf().

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

◆ l2error()

def 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

References python.uq.dists.CorrBeta.CorrBeta.getBounds(), sgpp::combigrid::AbstractLinearEvaluator< V >.getBounds(), python.uq.dists.Corr.Corr.getBounds(), python.uq.dists.Beta.Beta.getBounds(), python.uq.dists.Dist.Dist.getBounds(), python.uq.dists.DataDist.DataDist.getBounds(), sgpp::combigrid::BSplineScalarProductEvaluator.getBounds(), python.uq.dists.CorrBeta.CorrBeta.pdf(), python.uq.dists.Dist.Dist.pdf(), python.uq.dists.Corr.Corr.pdf(), python.uq.dists.Beta.Beta.pdf(), python.uq.dists.DataDist.DataDist.pdf(), sgpp::combigrid::ProbabilityDensityFunction1D.pdf(), and sgpp::combigrid::OrthogonalPolynomialBasis1D.pdf().

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

◆ mean()

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

@return: expectation value

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

◆ pdf()

def 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()

def 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.KDEDist.KDEDist.rvs(), python.uq.dists.NatafDist.NatafDist.rvs(), and python.uq.dists.SGDEdist.SGDEdist.rvs().

◆ rvs()

def 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()

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

@return: standard deviation

References python.uq.dists.Beta.Beta.var(), python.uq.dists.Dist.Dist.var(), sgpp::combigrid::BsplineStochasticCollocation.var, sgpp::combigrid::PolynomialStochasticCollocation.var, python.uq.dists.DataDist.DataDist.var(), and python.uq.analysis.Analysis.Analysis.var().

◆ var()

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

@return: variance

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