quadraticEqn.H

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    Copyright (C) 2020 OpenCFD Ltd.
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License
    This file is part of OpenFOAM.
 
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    under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
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Class
    Foam::quadraticEqn
 
Description
    Container to encapsulate various operations for
    quadratic equation of the forms with real coefficients:
 
    \f[
        a*x^2 + b*x + c = 0
          x^2 + B*x + C = 0
    \f]
 
    The expressions for the roots of \c quadraticEqn are as follows:
 
    \f[
        x1 = - (b + sign(b) sqrt(b^2 - 4ac)/(2*a))
 
        x2 = c/(a*x1)
    \f]
 
    where \c (b^2 - 4ac) is evaluated by fused multiply-adds to avoid
    detrimental cancellation.
 
    Reference:
    \verbatim
        Cancellation-avoiding quadratic formula (tag:F):
            Ford, W. (2014).
            Numerical linear algebra with applications: Using MATLAB.
            London: Elsevier/Academic Press.
            DOI:10.1016/C2011-0-07533-6
 
        Kahan's algo. to compute 'b^2-a*c' using fused multiply-adds (tag:JML):
            Jeannerod, C. P., Louvet, N., & Muller, J. M. (2013).
            Further analysis of Kahan's algorithm for the accurate
            computation of 2× 2 determinants.
            Mathematics of Computation, 82(284), 2245-2264.
            DOI:10.1090/S0025-5718-2013-02679-8
    \endverbatim
 
See also
    Test-quadraticEqn.C
 
SourceFiles
    quadraticEqnI.H
    quadraticEqn.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef Foam_quadraticEqn_H
#define Foam_quadraticEqn_H
 
#include "Roots.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
/*---------------------------------------------------------------------------*\
                         Class quadraticEqn Declaration
\*---------------------------------------------------------------------------*/
 
class quadraticEqn
:
    public VectorSpace<quadraticEqn, scalar, 3>
{
public:
 
    //- Component labeling enumeration
    enum components { A, B, C };
 
 
    // Constructors
 
        //- Default construct
        quadraticEqn() = default;
 
        //- Construct initialized to zero
        inline quadraticEqn(const Foam::zero);
 
        //- Construct from components
        inline quadraticEqn(const scalar a, const scalar b, const scalar c);
 
 
    // Member Functions
 
    // Access
 
        scalar a() const noexcept { return this->v_[A]; }
        scalar b() const noexcept { return this->v_[B]; }
        scalar c() const noexcept { return this->v_[C]; }
 
        scalar& a() noexcept { return this->v_[A]; }
        scalar& b() noexcept { return this->v_[B]; }
        scalar& c() noexcept { return this->v_[C]; }
 
 
    // Evaluate
 
        //- Evaluate the quadratic equation at x
        inline scalar value(const scalar x) const;
 
        //- Evaluate the derivative of the quadratic equation at x
        inline scalar derivative(const scalar x) const;
 
        //- Estimate the error of evaluation of the quadratic equation at x
        inline scalar error(const scalar x) const;
 
        //- Return the roots of the quadratic equation with no particular order
        //  if discriminant > 0: return two distinct real roots
        //  if discriminant < 0: return one of the complex conjugate-pair roots
        //  otherwise          : return two identical real roots
        Roots<2> roots() const;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#include "quadraticEqnI.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //