/usr/include/openturns/Normal.hxx is in libopenturns-dev 0.15-2.
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/**
* @file Normal.hxx
* @brief The Normal distribution
*
* (C) Copyright 2005-2011 EDF-EADS-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 2.1 of the License.
*
* 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
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
* @author: $LastChangedBy: souchaud $
* @date: $LastChangedDate: 2011-07-01 10:34:36 +0200 (Fri, 01 Jul 2011) $
* Id: $Id: Normal.hxx 1981 2011-07-01 08:34:36Z souchaud $
*/
#ifndef OPENTURNS_NORMAL_HXX
#define OPENTURNS_NORMAL_HXX
#include "OTprivate.hxx"
#include "EllipticalDistribution.hxx"
namespace OpenTURNS {
namespace Uncertainty {
namespace Distribution {
/**
* @class Normal
*
* The Normal (gaussian) distribution.
*/
class Normal
: public Model::EllipticalDistribution
{
// Maximum number of samples in the evaluation of the CDF
static const UnsignedLong MaximumNumberOfPoints; // 10000000
// Minimum number of samples in the evaluation of the CDF
static const UnsignedLong MinimumNumberOfPoints; // 1000000
// Maximum precision required for the CDF in the multidimensional case (dim > 3)
static const NumericalScalar MaximumCDFEpsilon; // 5.0e-6
// Minimum precision required for the CDF in the multidimensional case (dim > 3)
static const NumericalScalar MinimumCDFEpsilon; // 5.0e-2
CLASSNAME;
public:
typedef Model::EllipticalDistribution EllipticalDistribution; // required by SWIG
typedef EllipticalDistribution::Implementation Implementation;
typedef EllipticalDistribution::InvalidArgumentException InvalidArgumentException;
typedef EllipticalDistribution::InvalidDimensionException InvalidDimensionException;
typedef EllipticalDistribution::NotDefinedException NotDefinedException;
typedef EllipticalDistribution::NumericalPoint NumericalPoint;
typedef EllipticalDistribution::NumericalSample NumericalSample;
typedef EllipticalDistribution::CovarianceMatrix CovarianceMatrix;
typedef EllipticalDistribution::Indices Indices;
typedef EllipticalDistribution::Interval Interval;
typedef EllipticalDistribution::IsoProbabilisticTransformation IsoProbabilisticTransformation;
typedef EllipticalDistribution::InverseIsoProbabilisticTransformation InverseIsoProbabilisticTransformation;
typedef EllipticalDistribution::CorrelationMatrix CorrelationMatrix;
typedef EllipticalDistribution::SymmetricMatrix SymmetricMatrix;
typedef EllipticalDistribution::SquareMatrix SquareMatrix;
typedef EllipticalDistribution::StorageManager StorageManager;
/** Default constructor */
explicit Normal(const UnsignedLong dimension = 1)
/* throw(InvalidArgumentException) */;
/** Dimension 1 constructor */
explicit Normal(const NumericalScalar mu, const NumericalScalar sd)
/* throw(InvalidArgumentException) */;
/** Constructor for multiD normal distribution */
explicit Normal(const NumericalPoint & mean,
const NumericalPoint & sigma,
const CorrelationMatrix & R)
/* throw(InvalidArgumentException) */;
explicit Normal(const NumericalPoint & mean,
const CovarianceMatrix & C)
/* throw(InvalidArgumentException) */;
/** String converter */
String __repr__() const;
String __str__(const String & offset = "") const;
/* Interface inherited from Distribution */
/** Virtual constructor */
Normal * clone() const;
/** Compute the density generator of the ellipticalal generator, 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)) */
NumericalScalar computeDensityGenerator(const NumericalScalar betaSquare) const;
/** Compute the derivative of the density generator */
NumericalScalar computeDensityGeneratorDerivative(const NumericalScalar betaSquare) const;
/** Compute the seconde derivative of the density generator */
NumericalScalar computeDensityGeneratorSecondDerivative(const NumericalScalar betaSquare) const;
/** Get one realization of the Normal distribution */
NumericalPoint getRealization() const;
/** Get the CDF of the Normal distribution */
using EllipticalDistribution::computeCDF;
NumericalScalar computeCDF(const NumericalPoint & point, const Bool tail = false) const;
/** Get the probability content of an interval */
NumericalScalar computeProbability(const Interval & interval) const;
/** Get the characteristic function of the distribution, i.e. phi(u) = E(exp(I*u*X)) */
NumericalComplex computeCharacteristicFunction(const NumericalScalar x,
const Bool logScale = false) const;
/** Get the CDF gradient of the distribution */
NumericalPoint computeCDFGradient(const NumericalPoint & point) const;
/** Compute the radial distribution CDF */
NumericalScalar computeRadialDistributionCDF(const NumericalScalar radius,
const Bool tail = false) const;
/** Compute the PDF of Xi | X1, ..., Xi-1. x = Xi, y = (X1,...,Xi-1) */
NumericalScalar computeConditionalPDF(const NumericalScalar x, const NumericalPoint & y) const;
/** Compute the CDF of Xi | X1, ..., Xi-1. x = Xi, y = (X1,...,Xi-1) */
NumericalScalar computeConditionalCDF(const NumericalScalar x, const NumericalPoint & y) const;
/** Compute the quantile of Xi | X1, ..., Xi-1, i.e. x such that CDF(x|y) = q with x = Xi, y = (X1,...,Xi-1) */
NumericalScalar computeConditionalQuantile(const NumericalScalar q, const NumericalPoint & y) const;
/** Get the i-th marginal distribution */
Normal * getMarginal(const UnsignedLong i) const /* throw(InvalidArgumentException) */;
/** Get the distribution of the marginal distribution corresponding to indices dimensions */
Normal * getMarginal(const Indices & indices) const /* throw(InvalidArgumentException) */;
/** Get the roughness, i.e. the L2-norm of the PDF */
NumericalScalar getRoughness() const;
/** Get the skewness of the distribution */
NumericalPoint getSkewness() const /* throw(NotDefinedException) */;
/** Get the kurtosis of the distribution */
NumericalPoint getKurtosis() const /* throw(NotDefinedException) */;
/** Get the raw moments of the standardized distribution */
NumericalPoint getStandardMoment(const UnsignedLong n) const;
/** Sigma vector accessor */
void setSigma(const NumericalPoint & sigma)
/* throw(InvalidArgumentException) */;
/** Correlation matrix accessor */
void setCorrelation(const CorrelationMatrix & R)
/* throw(InvalidArgumentException) */;
/** Get the copula of a distribution */
Implementation getCopula() const;
/* Interface specific to Normal */
/** Tell if the distribution has independent copula */
Bool hasIndependentCopula() const;
/** Method save() stores the object through the StorageManager */
void save(StorageManager::Advocate & adv) const;
/** Method load() reloads the object from the StorageManager */
void load(StorageManager::Advocate & adv);
protected:
private:
/** Quantile computation for dimension=1 */
NumericalScalar computeScalarQuantile(const NumericalScalar prob,
const Bool tail = false,
const NumericalScalar precision = DefaultQuantileEpsilon) const;
/** Check if the distribution has independent copula */
void checkIndependentCopula();
/** The normalization factor of the Normal distribution */
NumericalScalar normalizationFactor_;
/** Store the independence status */
Bool hasIndependentCopula_;
}; /* class Normal */
} /* namespace Distribution */
} /* namespace Uncertainty */
} /* namespace OpenTURNS */
#endif /* OPENTURNS_NORMAL_HXX */
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