lagrange_interpolation.hpp

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//---------------------------------------------------------------------------//
// Copyright (c) 2020-2021 Mikhail Komarov <nemo@nil.foundation>
// Copyright (c) 2020-2021 Nikita Kaskov <nbering@nil.foundation>
// Copyright (c) 2021 Ilias Khairullin <ilias@nil.foundation>
//
// MIT License
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#ifndef CRYPTO3_MATH_LAGRANGE_INTERPOLATION_HPP
#define CRYPTO3_MATH_LAGRANGE_INTERPOLATION_HPP
 
#include <nil/crypto3/math/polynomial/polynomial.hpp>
#include <nil/crypto3/math/domains/evaluation_domain.hpp>
#include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
 
namespace nil {
    namespace crypto3 {
        namespace math {
            // Default implementation according to Wikipedia
            // https://en.wikipedia.org/wiki/Lagrange_polynomial
            template<typename InputRange,
                     typename FieldValueType =
                         typename std::iterator_traits<typename InputRange::iterator>::value_type::first_type>
            typename std::enable_if<
                std::is_same<std::pair<FieldValueType, FieldValueType>,
                             typename std::iterator_traits<typename InputRange::iterator>::value_type>::value,
                polynomial<FieldValueType>>::type
                lagrange_interpolation(const InputRange &points) {
 
                std::size_t k = std::size(points);
 
                polynomial<FieldValueType> result;
                for (std::size_t j = 0; j < k; ++j) {
                    polynomial<FieldValueType> term({points[j].second});
                    for (std::size_t m = 0; m < k; ++m) {
                        if (m != j) {
                            term = term * (polynomial<FieldValueType>({-points[m].first, FieldValueType::one()}) /
                                           polynomial<FieldValueType>({points[j].first - points[m].first}));
                        }
                    }
                    result = result + term;
                }
                return result;
            }
        }    // namespace math
    }        // namespace crypto3
}    // namespace nil
 
#endif    // CRYPTO3_MATH_LAGRANGE_INTERPOLATION_HPP