💿🐜 Antkeeper source code
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126 lines
3.4 KiB
126 lines
3.4 KiB
/*
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* Copyright (C) 2023 Christopher J. Howard
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*
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* This file is part of Antkeeper source code.
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*
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* Antkeeper source code is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Antkeeper source code is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef ANTKEEPER_MATH_QUADRATURE_HPP
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#define ANTKEEPER_MATH_QUADRATURE_HPP
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#include <iterator>
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#include <type_traits>
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namespace math {
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/// Numerical integration functions.
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namespace quadrature {
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/**
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* Approximates the definite integral of a function using Simpson's 1/3 rule.
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*
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* @param f Unary function object to integrate.
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* @param first,last Range of sample points on `[first, last)`.
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*
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* @return Approximated integral of @p f.
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*
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* @see https://en.wikipedia.org/wiki/Simpson%27s_rule
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*/
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template<class UnaryOp, class InputIt>
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[[nodiscard]] typename std::invoke_result<UnaryOp, typename std::iterator_traits<InputIt>::value_type>::type
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simpson(UnaryOp f, InputIt first, InputIt last)
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{
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typedef typename std::iterator_traits<InputIt>::value_type input_type;
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typedef typename std::invoke_result<UnaryOp, input_type>::type output_type;
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typedef decltype(*last - *first) difference_type;
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if (first == last)
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return output_type{0};
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output_type f_a = f(*first);
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InputIt second = first;
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++second;
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if (second == last)
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return f_a;
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difference_type h = *second - *first;
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output_type f_b = f(*first + h / difference_type(2));
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output_type f_c = f(*second);
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output_type sum = (f_a + f_b * difference_type(4) + f_c) * h;
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for (first = second++; second != last; first = second++)
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{
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h = *second - *first;
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f_a = f_c;
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f_c = f(*second);
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f_b = f(*first + h / difference_type(2));
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sum += (f_a + f_b * difference_type(4) + f_c) * h;
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}
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return sum / difference_type(6);
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}
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/**
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* Approximates the definite integral of a function using the trapezoidal rule.
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*
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* @param f Unary function object to integrate.
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* @param first,last Range of sample points on `[first, last)`.
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*
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* @return Approximated integral of @p f.
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*
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* @see https://en.wikipedia.org/wiki/Trapezoidal_rule
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*/
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template<class UnaryOp, class InputIt>
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[[nodiscard]] typename std::invoke_result<UnaryOp, typename std::iterator_traits<InputIt>::value_type>::type
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trapezoid(UnaryOp f, InputIt first, InputIt last)
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{
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typedef typename std::iterator_traits<InputIt>::value_type input_type;
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typedef typename std::invoke_result<UnaryOp, input_type>::type output_type;
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typedef decltype(*last - *first) difference_type;
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if (first == last)
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return output_type{0};
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output_type f_a = f(*first);
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InputIt second = first;
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++second;
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if (second == last)
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return f_a;
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output_type f_b = f(*second);
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output_type sum = (f_a + f_b) * (*second - *first);
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for (first = second++; second != last; first = second++)
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{
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f_a = f_b;
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f_b = f(*second);
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sum += (f_a + f_b) * (*second - *first);
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}
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return sum / difference_type(2);
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}
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} // namespace quadrature
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} // namespace math
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#endif // ANTKEEPER_MATH_QUADRATURE_HPP
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