unintegrable.H

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Class
    Foam::distributions::unintegrable
 
Description
    Base class for distributions that do not have a closed integral form for
    the cumulative density function (CDF) for some or all effective size
    exponents.
 
SourceFiles
    unintegrable.C
 
See also
    Foam::distribution
 
\*---------------------------------------------------------------------------*/
 
#ifndef unintegrable_H
#define unintegrable_H
 
#include "distribution.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
namespace distributions
{
 
/*---------------------------------------------------------------------------*\
                        Class unintegrable Declaration
\*---------------------------------------------------------------------------*/
 
class unintegrable
:
    public distribution
{
private:
 
    // Private Data
 
        //- Number of intervals to use over the range of the distribution
        const label n_;
 
        //- X-coordinates. These are spaced to contain equal increments of the
        //  CDF. Sampling is a inversion of the CDF; i.e., solve CDF(x) = s for
        //  x, where s is a random sample between 0 and 1. Uniform increments
        //  of CDF make this inversion trivial.
        mutable autoPtr<scalarField> xPtr_;
 
        //- Values of Phi (i.e., the un-normalised CDF) at the minimum and
        //  maximum x-coordinates
        mutable autoPtr<Pair<scalar>> Phi01Ptr_;
 
        //- Values of the PDF at the X-coordinates
        mutable autoPtr<scalarField> PDFPtr_;
 
 
    // Private Member Functions
 
        //- X-coordinates
        const scalarField& x() const;
 
        //- Values of the PDF at the X-coordinates
        const scalarField& PDF() const;
 
 
protected:
 
    // Protected Member Functions
 
        //- Return values of the un-normalised PDF for the given size exponent
        //  and x-coordinates. Must be provided by derivations.
        virtual tmp<scalarField> phi
        (
            const label q,
            const scalarField& x
        ) const = 0;
 
        //- Return values of the un-normalised CDF for the given size exponent
        //  and x-coordinates. Can be overloaded by derivations, for example, if
        //  there is a simpler analytic solution for certain effective size
        //  exponents (probably zero).
        virtual tmp<scalarField> Phi
        (
            const label q,
            const scalarField& x
        ) const;
 
        //- Return values of the un-normalised CDF at the minimum and maximum
        //  x-coordinates for the given size exponent. Can be overloaded by
        //  derivations, for example, if there is a simpler analytic solution
        //  for certain effective size exponents (probably zero).
        virtual Pair<scalar> Phi01(const label q) const;
 
        //- Access cached values of the un-normalised CDF at the minimum and
        //  maximum x-coordinates.
        const Pair<scalar>& Phi01() const;
 
 
public:
 
    // Static Member Functions
 
        //- Integrate the values y with respect to the coordinates x
        static tmp<scalarField> integrate
        (
            const scalarField& x,
            const scalarField& y
        );
 
        //- Integrate the values x*y with respect to the coordinates x
        static tmp<scalarField> integrateX
        (
            const scalarField& x,
            const scalarField& y
        );
 
        //- Sample an interval, given the interval's bounding x-coordinates,
        //  values Phi (the un-normalised CDF), and a random sample. First
        //  order interpolation.
        static scalar sampleInterval
        (
            const Pair<scalar>& x,
            const Pair<scalar>& Phi,
            const scalar s
        );
 
        //- Sample an interval, given the interval's bounding x-coordinates,
        //  values phi and Phi (the un-normalised PDF and CDF), and a random
        //  sample. Second order interpolation.
        static scalar sampleInterval
        (
            const Pair<scalar>& x,
            const Pair<scalar>& phi,
            const Pair<scalar>& Phi,
            const scalar s
        );
 
        //- Sample a discretised distribution, given the x-coordinates,
        //  values Phi (the un-normalised CDF), and a random sample. First
        //  order interpolation.
        static scalar sample
        (
            const scalarField& x,
            const scalarField& Phi,
            const scalar s
        );
 
        //- Sample a discretised distribution, given the x-coordinates, values
        //  phi and Phi (the un-normalised PDF and CDF), and a random sample.
        //  Second order interpolation.
        static scalar sample
        (
            const scalarField& x,
            const scalarField& phi,
            const scalarField& Phi,
            const scalar s
        );
 
 
 
    // Constructors
 
        //- Construct from a dictionary
        unintegrable
        (
            const word& name,
            const dictionary& dict,
            Random& rndGen,
            const label sampleQ
        );
 
        //- Construct from components
        unintegrable
        (
            Random& rndGen,
            const label Q,
            const label sampleQ,
            const label n
        );
 
        //- Construct copy
        unintegrable(const unintegrable& d, const label sampleQ);
 
 
    //- Destructor
    virtual ~unintegrable();
 
 
    // Member Functions
 
        //- Sample the distribution
        scalar sample() const;
 
        //- Sample the distribution
        using distribution::sample;
 
        //- Return the mean value
        virtual scalar mean() const;
 
        //- Return coordinates to plot across the range of the distribution
        using distribution::x;
 
        //- Return the distribution probability density function
        virtual tmp<scalarField> PDF(const scalarField& x) const;
};
 
 
/*---------------------------------------------------------------------------*\
                        Class unintegrable Declaration
\*---------------------------------------------------------------------------*/
 
class unintegrableForNonZeroQ
:
    public unintegrable
{
protected:
 
    // Protected Member Functions
 
        //- Return values of the un-normalised CDF at the minimum and maximum
        //  x-coordinates for the given size exponent.
        virtual Pair<scalar> Phi01(const label q) const;
 
        //- Access cached values of the un-normalised CDF at the minimum and
        //  maximum x-coordinates.
        using unintegrable::Phi01;
 
 
public:
 
    // Constructors
 
        //- Inherit constructors
        using unintegrable::unintegrable;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace distributions
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //