JUCE/modules/juce_dsp/maths/juce_Polynomial.h

/*
  ==============================================================================

   This file is part of the JUCE 7 technical preview.
   Copyright (c) 2022 - Raw Material Software Limited

   You may use this code under the terms of the GPL v3
   (see www.gnu.org/licenses).

   For the technical preview this file cannot be licensed commercially.

   JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
   EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
   DISCLAIMED.

  ==============================================================================
*/

namespace juce
{
namespace dsp
{

/**
    A class representing a polynomial

    @tags{DSP}
*/
template <typename FloatingType>
class Polynomial
{
public:
    //==============================================================================
    /** Creates a new polynomial which will always evaluate to zero. */
    Polynomial()
    {
        coeffs.add (0);
    }

    /** Creates a new polynomial with given coefficients.

        @param numCoefficients The number of coefficients stored in coefficients.
                               This is also the order of the returned polynomial.
        @param coefficients    The coefficients which will be used by the newly
                               created polynomial. The Polynomial class will keep
                               a private copy of the coefficients.
    */
    Polynomial (const FloatingType* coefficients, int numCoefficients)
        : coeffs (coefficients, numCoefficients)
    {
        jassert (! coeffs.isEmpty());
    }

    /** Creates a copy of another polynomial. */
    Polynomial (const Polynomial&) = default;

    /** Creates a copy of another polynomial. */
    Polynomial (Polynomial&&) = default;

    /** Creates a copy of another polynomial. */
    Polynomial& operator= (const Polynomial&) = default;

    /** Creates a copy of another polynomial. */
    Polynomial& operator= (Polynomial&&) = default;

    /** Creates a new polynomial with coefficients by a C++11 initializer list.
        This function can be used in the following way:
        Polynomial<float> p ({0.5f, -0.3f, 0.2f});
    */
    template <typename... Values>
    Polynomial (Values... items)  : coeffs (items...)
    {
        jassert (! coeffs.isEmpty());
    }

    //==============================================================================
    /** Returns a single coefficient of the receiver for reading */
    FloatingType operator[] (int index) const noexcept              { return coeffs.getUnchecked (index); }

    /** Returns a single coefficient of the receiver for modifying. */
    FloatingType& operator[] (int index) noexcept                   { return coeffs.getReference (index); }

    /** Evaluates the value of the polynomial at a single point x. */
    FloatingType operator() (FloatingType x) const noexcept
    {
        // Horner's method
        FloatingType y (0);

        for (int i = coeffs.size(); --i >= 0;)
            y = (x * y) + coeffs.getUnchecked(i);

        return y;
    }

    /** Returns the order of the polynomial. */
    int getOrder() noexcept
    {
        return coeffs.size() - 1;
    }

    //==============================================================================
    /** Returns the polynomial with all its coefficients multiplied with a gain factor */
    Polynomial<FloatingType> withGain (double gain) const
    {
        auto result = *this;

        for (auto& c : result.coeffs)
            c *= gain;

        return result;
    }

    /** Returns the sum of this polynomial with another */
    Polynomial<FloatingType> getSumWith (const Polynomial<FloatingType>& other) const
    {
        if (coeffs.size() < other.coeffs.size())
            return other.getSumWith (*this);

        auto result = *this;

        for (int i = 0; i < other.coeffs.size(); ++i)
            result[i] += other[i];

        return result;
    }

    /** computes the product of two polynomials and return the result */
    Polynomial<FloatingType> getProductWith (const Polynomial<FloatingType>& other) const
    {
        Polynomial<FloatingType> result;
        result.coeffs.clearQuick();

        auto N1 = coeffs.size();
        auto N2 = other.coeffs.size();
        auto Nmax = jmax (N1, N2);

        auto N = N1 + N2 - 1;

        for (int i = 0; i < N; ++i)
        {
            FloatingType value (0);

            for (int j = 0; j < Nmax; ++j)
                if (j >= 0 && j < N1 && i - j >= 0 && i - j < N2)
                    value = value + (*this)[j] * other[i - j];

            result.coeffs.add (value);
        }

        return result;
    }

private:
    //==============================================================================
    Array<FloatingType> coeffs;

    JUCE_LEAK_DETECTOR (Polynomial)
};

} // namespace dsp
} // namespace juce