quadrature.hpp

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/*
 * Copyright (C) 2023  Christopher J. Howard
 *
 * This file is part of Antkeeper source code.
 *
 * Antkeeper source code 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.
 *
 * Antkeeper source code 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 Antkeeper source code.  If not, see <http://www.gnu.org/licenses/>.
 */
 
#ifndef ANTKEEPER_MATH_QUADRATURE_HPP
#define ANTKEEPER_MATH_QUADRATURE_HPP
 
#include <iterator>
#include <type_traits>
 
namespace math {
 
namespace quadrature {
 
template<class UnaryOp, class InputIt>
[[nodiscard]] typename std::invoke_result<UnaryOp, typename std::iterator_traits<InputIt>::value_type>::type
    simpson(UnaryOp f, InputIt first, InputIt last)
{
    typedef typename std::iterator_traits<InputIt>::value_type input_type;
    typedef typename std::invoke_result<UnaryOp, input_type>::type output_type;
    typedef decltype(*last - *first) difference_type;
    
    if (first == last)
        return output_type{0};
    
    output_type f_a = f(*first);
    
    InputIt second = first;
    ++second;
    
    if (second == last)
        return f_a;
    
    difference_type h = *second - *first;
    output_type f_b = f(*first + h / difference_type(2));
    output_type f_c = f(*second);
    
    output_type sum = (f_a + f_b * difference_type(4) + f_c) * h;
    
    for (first = second++; second != last; first = second++)
    {
        h = *second - *first;
        
        f_a = f_c;
        f_c = f(*second);
        f_b = f(*first + h / difference_type(2));
        
        sum += (f_a + f_b * difference_type(4) + f_c) * h;
    }
    
    return sum / difference_type(6);
}
 
template<class UnaryOp, class InputIt>
[[nodiscard]] typename std::invoke_result<UnaryOp, typename std::iterator_traits<InputIt>::value_type>::type
    trapezoid(UnaryOp f, InputIt first, InputIt last)
{
    typedef typename std::iterator_traits<InputIt>::value_type input_type;
    typedef typename std::invoke_result<UnaryOp, input_type>::type output_type;
    typedef decltype(*last - *first) difference_type;
    
    if (first == last)
        return output_type{0};
    
    output_type f_a = f(*first);
    
    InputIt second = first;
    ++second;
    
    if (second == last)
        return f_a;
    
    output_type f_b = f(*second);
    output_type sum = (f_a + f_b) * (*second - *first);
    
    for (first = second++; second != last; first = second++)
    {
        f_a = f_b;
        f_b = f(*second);
        sum += (f_a + f_b) * (*second - *first);
    }
    
    return sum / difference_type(2);
}
 
} // namespace quadrature
 
} // namespace math
 
#endif // ANTKEEPER_MATH_QUADRATURE_HPP