Polynomial.H

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/*---------------------------------------------------------------------------*\
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    \\  /    A nd           | www.openfoam.com
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-------------------------------------------------------------------------------
    Copyright (C) 2011-2016 OpenFOAM Foundation
    Copyright (C) 2020 OpenCFD Ltd.
-------------------------------------------------------------------------------
License
    This file is part of OpenFOAM.
 
    OpenFOAM is free software: you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
    OpenFOAM 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 General Public License
    for more details.
 
    You should have received a copy of the GNU General Public License
    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
Class
    Foam::Polynomial
 
Description
    Polynomial templated on size (order):
 
    \verbatim
        poly = sum(coeffs[i]*x^i) + logCoeff*log(x)
    \endverbatim
 
    where <tt> 0 <= i <= N </tt>
 
    - integer powers, starting at zero
    - \c value(x) to evaluate the poly for a given value
    - \c derivative(x) returns derivative at value
    - \c integral(x1, x2) returns integral between two scalar values
    - \c integral() to return a new, integral coeff polynomial
      - increases the size (order)
    - \c integralMinus1() to return a new, integral coeff polynomial where
      the base poly starts at order -1
 
SourceFiles
    Polynomial.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef Foam_Polynomial_H
#define Foam_Polynomial_H
 
#include "word.H"
#include "scalar.H"
#include "Ostream.H"
#include "VectorSpace.H"
#include <initializer_list>
#include <type_traits>
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
// Forward Declarations
template<int PolySize> class Polynomial;
 
/*---------------------------------------------------------------------------*\
                        Class Polynomial Declaration
\*---------------------------------------------------------------------------*/
 
template<int PolySize>
class Polynomial
:
    public VectorSpace<Polynomial<PolySize>, scalar, PolySize>
{
    static_assert(PolySize > 0, "Size must be positive (non-zero)");
 
    // Private Data
 
        //- Include the log term? - only activated using integralMinus1()
        bool logActive_;
 
        //- Log coefficient - only activated using integralMinus1()
        scalar logCoeff_;
 
 
public:
 
    // Public Typedefs
 
        typedef Polynomial<PolySize> polyType;
        typedef Polynomial<PolySize+1> intPolyType;
 
 
    // Generated Methods: copy construct, copy assignment
 
 
    // Constructors
 
        //- Default construct, with all coefficients = 0
        Polynomial();
 
        //- Construct from an initializer list of coefficients
        Polynomial(std::initializer_list<scalar> coeffs);
 
        //- Construct from C-array of coefficients
        explicit Polynomial(const scalar coeffs[PolySize]);
 
        //- Construct from a list of coefficients
        explicit Polynomial(const UList<scalar>& coeffs);
 
        //- Construct from Istream
        explicit Polynomial(Istream& is);
 
        //- Construct from name and Istream
        Polynomial(const word& name, Istream& is);
 
 
    // Member Functions
 
        // Access
 
            //- Return true if the log term is active
            bool logActive() const noexcept;
 
            //- Return the log coefficient
            scalar logCoeff() const noexcept;
 
 
        // Evaluation
 
            //- Return polynomial value
            scalar value(const scalar x) const;
 
            //- Return derivative of the polynomial at the given x
            scalar derivative(const scalar x) const;
 
            //- Return integral between two values
            scalar integral(const scalar x1, const scalar x2) const;
 
            //- Return integral coefficients.
            //  Argument becomes zero'th element (constant of integration)
            intPolyType integral(const scalar intConstant = 0.0) const;
 
            //- Return integral coefficients when lowest order is -1.
            //  Argument becomes zero'th element (constant of integration)
            polyType integralMinus1(const scalar intConstant = 0.0) const;
 
 
    // IOstream Operators - uses VectorSpace operators
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#ifdef NoRepository
    #include "Polynomial.C"
#endif
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //