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/**
* @file EllipticalDistribution.hxx
* @brief Abstract top-level class for elliptical distributions
*
* Copyright 2005-2015 Airbus-EDF-IMACS-Phimeca
*
* This library is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* along with this library. If not, see <http://www.gnu.org/licenses/>.
*
* @author schueller
* @date 2012-04-18 17:56:46 +0200 (Wed, 18 Apr 2012)
*/
#ifndef OPENTURNS_ELLIPTICALDISTRIBUTIONIMPLEMENTATION_HXX
#define OPENTURNS_ELLIPTICALDISTRIBUTIONIMPLEMENTATION_HXX
#include "ContinuousDistribution.hxx"
#include "CorrelationMatrix.hxx"
BEGIN_NAMESPACE_OPENTURNS
/**
* @class EllipticalDistribution
*
* A subclass for elliptical usual distributions.
*/
class OT_API EllipticalDistribution
: public ContinuousDistribution
{
CLASSNAME;
public:
// Numerical precision for computing the quantile
/** Default constructor */
EllipticalDistribution();
/** Parameter constructor */
EllipticalDistribution(const NumericalPoint & mean,
const NumericalPoint & sigma,
const CorrelationMatrix & R,
const NumericalScalar covarianceNormalizationFactor);
/** Virtual copy constructor */
virtual EllipticalDistribution * clone() const;
/** Comparison operator */
Bool operator ==(const EllipticalDistribution & other) const;
/** String converter */
String __repr__() const;
/** Tell if the distribution is elliptical */
Bool isElliptical() const;
/** Tell if the distribution has elliptical copula */
Bool hasEllipticalCopula() const;
/** Get the DDF of the distribution */
using ContinuousDistribution::computeDDF;
NumericalPoint computeDDF(const NumericalPoint & point) const;
/** Get the PDF of the distribution */
using ContinuousDistribution::computePDF;
NumericalScalar computePDF(const NumericalPoint & point) const;
/** Get the PDF gradient of the distribution */
using ContinuousDistribution::computePDFGradient;
NumericalPoint computePDFGradient(const NumericalPoint & point) const;
/** Compute the density generator of the elliptical distribution, i.e.
* the function phi such that the density of the distribution can
* be written as p(x) = phi(t(x-mu)R^{-1}(x-mu)) */
virtual NumericalScalar computeDensityGenerator(const NumericalScalar betaSquare) const;
virtual NumericalScalar computeLogDensityGenerator(const NumericalScalar betaSquare) const;
/** Compute the derivative of the density generator */
virtual NumericalScalar computeDensityGeneratorDerivative(const NumericalScalar betaSquare) const;
/** Compute the second derivative of the density generator */
virtual NumericalScalar computeDensityGeneratorSecondDerivative(const NumericalScalar betaSquare) const;
/** Compute the survival function */
using ContinuousDistribution::computeSurvivalFunction;
virtual NumericalScalar computeSurvivalFunction(const NumericalPoint & point) const;
/** Mean point accessor */
void setMean(const NumericalPoint & mean);
/** Sigma vector accessor */
void setSigma(const NumericalPoint & sigma);
/** Sigma vector accessor */
NumericalPoint getSigma() const;
/** Get the standard deviation of the distribution */
NumericalPoint getStandardDeviation() const;
/** Correlation matrix accessor */
void setCorrelation(const CorrelationMatrix & R);
/** Correlation matrix accessor */
CorrelationMatrix getCorrelation() const;
protected:
/** Compute the mean of the distribution */
void computeMean() const;
/** Compute the covariance of the distribution */
void computeCovariance() const;
public:
/** Normalize the given point u_i = (x_i - mu_i) / sigma_i */
NumericalPoint normalize(const NumericalPoint & x) const;
/** Denormalize the given point x_i = mu_i + sigma_i * x_i */
NumericalPoint denormalize(const NumericalPoint & u) const;
/** Inverse correlation matrix accessor */
SquareMatrix getInverseCorrelation() const;
/** Cholesky factor of the correlation matrix accessor */
TriangularMatrix getCholesky() const;
/** Inverse of the Cholesky factor of the correlation matrix accessor */
TriangularMatrix getInverseCholesky() const;
/** Get the isoprobabilist transformation */
IsoProbabilisticTransformation getIsoProbabilisticTransformation() const;
/** Get the inverse isoprobabilist transformation */
InverseIsoProbabilisticTransformation getInverseIsoProbabilisticTransformation() const;
/** Get the standard distribution, i.e. a distribution of the same kind but with zero mean,
* unit marginal standard distribution and identity correlation */
Implementation getStandardDistribution() const;
/** Parameters value and description accessor */
NumericalPointWithDescriptionCollection getParametersCollection() const;
using ContinuousDistribution::setParametersCollection;
void setParametersCollection(const NumericalPointCollection & parametersCollection);
void setParametersCollection(const NumericalPoint & flattenCollection);
/** Method save() stores the object through the StorageManager */
void save(Advocate & adv) const;
/** Method load() reloads the object from the StorageManager */
void load(Advocate & adv);
protected:
/** The sigma vector of the distribution */
mutable NumericalPoint sigma_;
/** The correlation matrix (Rij) of the distribution */
mutable CorrelationMatrix R_;
/** The shape matrix of the distribution = Diag(sigma_) * R_ * Diag(sigma_) */
mutable CovarianceMatrix shape_;
/** The inverse of the correlation matrix of the distribution */
SymmetricMatrix inverseR_;
/** The Cholesky factor of the shape matrix shape_ = cholesky_ * cholesky_.transpose() */
TriangularMatrix cholesky_;
/** The inverse Cholesky factor of the covariance matrix */
TriangularMatrix inverseCholesky_;
/** The normalization factor of the distribution */
NumericalScalar normalizationFactor_;
/** The scaling factor of the covariance matrix covariance = covarianceScalingFactor_ * shape_*/
NumericalScalar covarianceScalingFactor_;
private:
/** Compute the value of the auxiliary attributes */
void update();
}; /* class EllipticalDistribution */
END_NAMESPACE_OPENTURNS
#endif /* OPENTURNS_ELLIPTICALDISTRIBUTIONIMPLEMENTATION_HXX */
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