matrix/utility.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) 2020-2021 Ilias Khairullin <ilias@nil.foundation>
//
// MIT License
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
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//
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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//---------------------------------------------------------------------------//
 
#ifndef CRYPTO3_ALGEBRA_MATRIX_UTILITY_HPP
#define CRYPTO3_ALGEBRA_MATRIX_UTILITY_HPP
 
#include <nil/crypto3/algebra/matrix/matrix.hpp>
 
#include <tuple>
 
namespace nil {
    namespace crypto3 {
        namespace algebra {
 
            template<typename F, typename T, typename... Matrices,
                     typename U = std::invoke_result_t<F, T, typename Matrices::value_type...>,
                     std::size_t N = detail::all_same_value<std::size_t, Matrices::column_size...>::value,
                     std::size_t M = detail::all_same_value<std::size_t, Matrices::row_size...>::value>
            constexpr matrix<U, N, M> elementwise(F f, const matrix<T, N, M> &m, const Matrices &...matrices) {
                matrix<U, N, M> op_applied = {};
                for (std::size_t i = 0; i < N; ++i) {
                    for (std::size_t j = 0; j < M; ++j) {
                        op_applied[i][j] = std::apply(f, std::forward_as_tuple(m[i][j], matrices[i][j]...));
                    }
                }
                return op_applied;
            }
 
            template<typename T, typename U, std::size_t N, std::size_t M>
            constexpr matrix<T, N, M> cast(const matrix<U, N, M> &m) {
                return elementwise([](const U u) { return static_cast<T>(u); }, m);
            }
 
            template<std::size_t N, std::size_t M, typename F>
            constexpr decltype(auto) generate(F &&f) {
                matrix<std::invoke_result_t<F, std::size_t, std::size_t>, N, M> generated = {};
                for (std::size_t i = 0; i < N; ++i) {
                    for (std::size_t j = 0; j < M; ++j) {
                        generated[i][j] = std::apply(f, std::forward_as_tuple(i, j));
                    }
                }
                return generated;
            }
 
            template<std::size_t N, std::size_t M, typename T>
            constexpr matrix<T, N, M> fill(T value) {
                return generate<N, M>([value](std::size_t, std::size_t) { return value; });
            }
 
            template<typename T, std::size_t N>
            const /*expr*/ matrix<T, N, N> identity = generate<N, N>([](std::size_t i, std::size_t j) {
                return T(i == j ? 1 : 0);
            });
 
            template<typename T, std::size_t N>
            constexpr matrix<T, N, N> get_identity() {
                return generate<N, N>([](std::size_t i, std::size_t j) { return T(i == j ? 1 : 0); });
            }
 
            template<std::size_t Row, std::size_t Col, std::size_t M, std::size_t N, typename T>
            constexpr matrix<T, M * Row, N * Col> repmat(const matrix<T, M, N> &m) {
                return generate<M * Row, N * Col>([&m](std::size_t i, std::size_t j) { return m[i % M][j % N]; });
            }
 
            template<std::size_t M, std::size_t N, typename T>
            constexpr matrix<T, M, N> swaprow(matrix<T, M, N> m, std::size_t a, std::size_t b) {
                for (int i = 0; i < N; i++) {
                    T tmp = m[a][i];
                    m[a][i] = m[b][i];
                    m[b][i] = tmp;
                }
                return m;
            }
 
            template<std::size_t M, std::size_t N, typename T>
            constexpr matrix<T, M, N> swapcol(matrix<T, M, N> m, std::size_t a, std::size_t b) {
                for (int i = 0; i < N; i++) {
                    T tmp = m[i][a];
                    m[i][a] = m[i][b];
                    m[i][b] = tmp;
                }
                return m;
            }
 
            template<std::size_t M, std::size_t N, std::size_t P, typename T>
            constexpr matrix<T, M, N + P> horzcat(const matrix<T, M, N> &a, const matrix<T, M, P> &b) {
                return generate<M, N + P>(
                    [&a, &b](std::size_t i, std::size_t j) { return j < N ? a[i][j] : b[i][j - N]; });
            }
 
            template<std::size_t M, std::size_t N, std::size_t P, typename T>
            constexpr matrix<T, M + N, P> vertcat(const matrix<T, M, P> &a, const matrix<T, N, P> &b) {
                return generate<M + N, P>(
                    [&a, &b](std::size_t i, std::size_t j) { return i < M ? a[i][j] : b[i - M][j]; });
            }
 
            template<std::size_t P, std::size_t Q, std::size_t M, std::size_t N, typename T>
            constexpr matrix<T, P, Q> submat(const matrix<T, M, N> &m, std::size_t a, std::size_t b) {
                if ((a + P > M) || (b + Q > N))
                    throw "index out of range";
                return generate<P, Q>([&m, &a, &b](std::size_t i, std::size_t j) { return m[a + i][b + j]; });
            }
 
            template<std::size_t P, std::size_t Q, std::size_t M, std::size_t N, typename T>
            constexpr matrix<T, P, Q> reshape(const matrix<T, M, N> &m) {
                static_assert(P * Q == M * N, "Reshaped matrix must preserve size! P*Q != M*N");
                return generate<P, Q>(
                    [&m](std::size_t i, std::size_t j) { return m[(i * Q + j) / N][(i * Q + j) % N]; });
            }
 
            template<typename T, std::size_t N>
            constexpr matrix<T, N, 1> as_column(const vector<T, N> &v) {
                return generate<N, 1>([&v](auto i, auto) { return v[i]; });
            }
 
            template<typename T, std::size_t N>
            constexpr matrix<T, 1, N> as_row(const vector<T, N> &v) {
                return generate<1, N>([&v](auto, auto j) { return v[j]; });
            }
 
        }    // namespace algebra
    }        // namespace crypto3
}    // namespace nil
 
#endif    // CRYPTO3_ALGEBRA_MATRIX_UTILITY_HPP