normal.H

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    You should have received a copy of the GNU General Public License
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Class
    Foam::distributionModels::normal
 
Description
    Particle-size distribution model wherein random samples are drawn
    from the doubly-truncated univariate normal probability density function:
 
    \f[
        f(x; \mu, \sigma, A, B) =
            \frac{1}{\sigma}
            \frac{
                \phi \left( \frac{x - \mu}{\sigma} \right)
            }{
                \Phi \left( \frac{B - \mu}{\sigma} \right)
              - \Phi \left( \frac{A - \mu}{\sigma} \right)
            }
    \f]
    where
 
    \vartable
      f(x; \mu, \sigma, A, B) | Doubly-truncated univariate normal distribution
      \mu         | Mean of the parent general normal distribution
      \sigma      | Standard deviation of the parent general normal distribution
      \phi(\cdot) | General normal probability density function
      \Phi(\cdot) | General normal cumulative distribution function
      x           | Sample
      A           | Minimum of the distribution
      B           | Maximum of the distribution
    \endvartable
 
    Constraints:
    - \f$ \infty > B > A > 0 \f$
    - \f$ x \in [B,A] \f$
    - \f$ \sigma^2 > 0 \f$
 
    Random samples are generated by the inverse transform sampling technique
    by using the quantile function of the doubly-truncated univariate normal
    probability density function:
 
    \f[
        x = \mu + \sigma \sqrt{2} \, {erf}^{-1} \left( 2 p - 1 \right)
    \f]
    with
 
    \f[
        p = u \,
            \left(
                \Phi\left(
                    \frac{B - \mu}{\sigma}
                    \right)
              - \Phi\left(
                    \frac{A - \mu}{\sigma}
                    \right)
            \right)
          + \Phi\left( \frac{A - \mu}{\sigma} \right)
    \f]
 
    \f[
        \Phi(\xi) =
            \frac{1}{2}
            \left(
                1 + {erf}\left(\frac{\xi - \mu}{\sigma \sqrt{2} }\right)
            \right)
    \f]
    where \f$ u \f$ is sample drawn from the uniform probability
    density function on the unit interval \f$ (0, 1) \f$.
 
    Reference:
    \verbatim
        Governing expressions (tag:B):
            Burkardt, J. (2014).
            The truncated normal distribution.
            Department of Scientific Computing Website,
            Florida State University, 1-35.
            URL:people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf
            (Retrieved on: 19 Feb 2021)
    \endverbatim
 
Usage
    Minimal example by using \c constant/<CloudProperties>:
    \verbatim
    subModels
    {
        injectionModels
        {
            <name>
            {
                ...
 
                sizeDistribution
                {
                    type        normal;
                    normalDistribution
                    {
                        mu        <mean>;
                        sigma     <stardard deviation>;
                        minValue  <min>;
                        maxValue  <max>;
                    }
                }
            }
        }
    }
    \endverbatim
 
    where the entries mean:
    \table
      Property   | Description                       | Type | Reqd   | Deflt
      type       | Type name: normal                 | word | yes    | -
      normalDistribution | Distribution settings     | dict | yes    | -
      mu         | Mean of the parent general normal distribution <!--
                 -->                                 | scalar | yes  | -
      sigma      | Standard deviation of the parent general normal <!--
                 --> distribution                    | scalar | yes  | -
      minValue   | Minimum of the distribution       | scalar | yes  | -
      maxValue   | Maximum of the distribution       | scalar | yes  | -
    \endtable
 
Note
  - The mean and standard deviation of the parent general normal probability
  distribution function (i.e. input) are not the same with those of the
  truncated probability distribution function.
 
SourceFiles
    normal.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef distributionModels_normal_H
#define distributionModels_normal_H
 
#include "distributionModel.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
namespace distributionModels
{
 
/*---------------------------------------------------------------------------*\
                           Class normal Declaration
\*---------------------------------------------------------------------------*/
 
class normal
:
    public distributionModel
{
    // Private Data
 
        //- Mean of the parent general normal distribution
        scalar mu_;
 
        //- Standard deviation of the parent general normal distribution
        scalar sigma_;
 
 
public:
 
    //- Runtime type information
    TypeName("normal");
 
 
    // Constructors
 
        //- Construct from components
        normal(const dictionary& dict, Random& rndGen);
 
        //- Copy construct
        normal(const normal& p);
 
        //- Construct and return a clone
        virtual autoPtr<distributionModel> clone() const
        {
            return autoPtr<distributionModel>(new normal(*this));
        }
 
        //- No copy assignment
        void operator=(const normal&) = delete;
 
 
    //- Destructor
    virtual ~normal() = default;
 
 
    // Member Functions
 
        //- Sample the distribution
        virtual scalar sample() const;
 
        //- Return the theoretical mean of the distribution
        virtual scalar meanValue() const;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace distributionModels
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //