Polynomial.C

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    Copyright (C) 2020 OpenCFD Ltd.
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#include "Polynomial.H"
 
// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
template<int PolySize>
Foam::Polynomial<PolySize>::Polynomial()
:
    VectorSpace<Polynomial<PolySize>, scalar, PolySize>(Zero),
    logActive_(false),
    logCoeff_(0)
{}
 
 
template<int PolySize>
Foam::Polynomial<PolySize>::Polynomial(std::initializer_list<scalar> coeffs)
:
    VectorSpace<Polynomial<PolySize>, scalar, PolySize>(),
    logActive_(false),
    logCoeff_(0)
{
    if (coeffs.size() != PolySize)
    {
        FatalErrorInFunction
            << "Size mismatch: Needed " << PolySize
            << " but given " << label(coeffs.size())
            << nl << exit(FatalError);
    }
 
    auto iter = coeffs.begin();
    for (int i=0; i<PolySize; ++i)
    {
        this->v_[i] = *iter;
        ++iter;
    }
}
 
 
template<int PolySize>
Foam::Polynomial<PolySize>::Polynomial(const scalar coeffs[PolySize])
:
    VectorSpace<Polynomial<PolySize>, scalar, PolySize>(),
    logActive_(false),
    logCoeff_(0)
{
    for (int i=0; i<PolySize; ++i)
    {
        this->v_[i] = coeffs[i];
    }
}
 
 
template<int PolySize>
Foam::Polynomial<PolySize>::Polynomial(const UList<scalar>& coeffs)
:
    VectorSpace<Polynomial<PolySize>, scalar, PolySize>(),
    logActive_(false),
    logCoeff_(0)
{
    if (coeffs.size() != PolySize)
    {
        FatalErrorInFunction
            << "Size mismatch: Needed " << PolySize
            << " but given " << coeffs.size()
            << nl << exit(FatalError);
    }
 
    for (int i = 0; i < PolySize; ++i)
    {
        this->v_[i] = coeffs[i];
    }
}
 
 
template<int PolySize>
Foam::Polynomial<PolySize>::Polynomial(Istream& is)
:
    VectorSpace<Polynomial<PolySize>, scalar, PolySize>(is),
    logActive_(false),
    logCoeff_(0)
{}
 
 
template<int PolySize>
Foam::Polynomial<PolySize>::Polynomial(const word& name, Istream& is)
:
    VectorSpace<Polynomial<PolySize>, scalar, PolySize>(),
    logActive_(false),
    logCoeff_(0)
{
    const word isName(is);
 
    if (isName != name)
    {
        FatalErrorInFunction
            << "Expected polynomial name " << name << " but read " << isName
            << nl << exit(FatalError);
    }
 
    is >>
        static_cast
        <
            VectorSpace<Polynomial<PolySize>, scalar, PolySize>&
        >(*this);
}
 
 
// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
template<int PolySize>
bool Foam::Polynomial<PolySize>::logActive() const
{
    return logActive_;
}
 
 
template<int PolySize>
Foam::scalar Foam::Polynomial<PolySize>::logCoeff() const
{
    return logCoeff_;
}
 
 
template<int PolySize>
Foam::scalar Foam::Polynomial<PolySize>::value(const scalar x) const
{
    scalar val = this->v_[0];
 
    // Avoid costly pow() in calculation
    scalar powX = x;
    for (label i=1; i<PolySize; ++i)
    {
        val += this->v_[i]*powX;
        powX *= x;
    }
 
    if (logActive_)
    {
        val += logCoeff_*log(x);
    }
 
    return val;
}
 
 
template<int PolySize>
Foam::scalar Foam::Polynomial<PolySize>::derivative(const scalar x) const
{
    scalar deriv = 0;
 
    if (PolySize > 1)
    {
        // Avoid costly pow() in calculation
        deriv += this->v_[1];
 
        scalar powX = x;
        for (label i=2; i<PolySize; ++i)
        {
            deriv += i*this->v_[i]*powX;
            powX *= x;
        }
    }
 
    if (logActive_)
    {
        deriv += logCoeff_/x;
    }
 
    return deriv;
}
 
 
template<int PolySize>
Foam::scalar Foam::Polynomial<PolySize>::integral
(
    const scalar x1,
    const scalar x2
) const
{
    // Avoid costly pow() in calculation
    scalar powX1 = x1;
    scalar powX2 = x2;
 
    scalar integ = this->v_[0]*(powX2 - powX1);
    for (label i=1; i<PolySize; ++i)
    {
        powX1 *= x1;
        powX2 *= x2;
        integ += this->v_[i]/(i + 1)*(powX2 - powX1);
    }
 
    if (logActive_)
    {
        integ += logCoeff_*((x2*log(x2) - x2) - (x1*log(x1) - x1));
    }
 
    return integ;
}
 
 
template<int PolySize>
typename Foam::Polynomial<PolySize>::intPolyType
Foam::Polynomial<PolySize>::integral(const scalar intConstant) const
{
    intPolyType newCoeffs;
 
    newCoeffs[0] = intConstant;
    forAll(*this, i)
    {
        newCoeffs[i+1] = this->v_[i]/(i + 1);
    }
 
    return newCoeffs;
}
 
 
template<int PolySize>
typename Foam::Polynomial<PolySize>::polyType
Foam::Polynomial<PolySize>::integralMinus1(const scalar intConstant) const
{
    polyType newCoeffs;
 
    if (this->v_[0] > VSMALL)
    {
        newCoeffs.logActive_ = true;
        newCoeffs.logCoeff_ = this->v_[0];
    }
 
    newCoeffs[0] = intConstant;
    for (label i=1; i<PolySize; ++i)
    {
        newCoeffs[i] = this->v_[i]/i;
    }
 
    return newCoeffs;
}
 
 
// ************************************************************************* //