240 lines
7.2 KiB
C++
240 lines
7.2 KiB
C++
#ifndef MINI_ODEINT_H_
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#define MINI_ODEINT_H_
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#include <array>
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#include <cassert>
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#include <cmath>
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#include <iterator>
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#include <ranges>
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#include <span>
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namespace mini_odeint {
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template <typename T> struct DormandPrince {
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using value_type = T;
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static constexpr std::size_t stages = 7;
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static constexpr std::size_t order = 5;
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static constexpr std::size_t estimator_order = 4;
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static constexpr std::size_t dense_order = 5;
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static constexpr std::array<T, stages> c{
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0.0, 1.0 / 5.0, 3.0 / 10.0, 4.0 / 5.0, 8.0 / 9.0, 1.0, 1.0};
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static constexpr std::array<std::array<T, stages - 1>, stages> a{
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{{0.0, 0.0, 0.0, 0.0, 0.0},
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{1.0 / 5.0, 0.0, 0.0, 0.0, 0.0},
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{3.0 / 40.0, 9.0 / 40.0, 0.0, 0.0, 0.0},
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{44.0 / 45.0, -56.0 / 15.0, 32.0 / 9.0, 0.0, 0.0},
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{19372.0 / 6561.0, -25360.0 / 2187.0, 64448.0 / 6561.0, -212.0 / 729.0,
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0.0},
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{9017.0 / 3168.0, -355.0 / 33.0, 46732.0 / 5247.0, 49.0 / 176.0,
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-5103.0 / 18656.0},
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{35.0 / 384.0, 0.0, 500.0 / 1113.0, 125.0 / 192.0, -2187.0 / 6784.0,
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11.0 / 84.0}}};
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static constexpr std::array<T, stages> b_hat{
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35.0 / 384.0, 0.0, 500.0 / 1113.0, 125.0 / 192.0, -2187.0 / 6784.0,
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11.0 / 84.0, 0.0};
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static constexpr std::array<T, stages> b{5179.0 / 57600.0, 0.0,
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7571.0 / 16695.0, 393.0 / 640.0,
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-92097.0 / 339200.0, 187.0 / 2100.0,
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1.0 / 40.0};
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static constexpr std::array<std::array<T, dense_order>, stages> p{
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{{1.0, -32272833064.0 / 11282082432.0, 34969693132.0 / 11282082432.0,
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-13107642775.0 / 11282082432.0, 157015080.0 / 11282082432.0},
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{0.0, 0.0, 0.0, 0.0, 0.0},
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{0.0, 1323431896.0 * 100.0 / 32700410799.0,
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-2074956840.0 * 100.0 / 32700410799.0,
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914128567.0 * 100.0 / 32700410799.0,
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-15701508.0 * 100.0 / 32700410799.0},
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{0.0, -889289856.0 * 25.0 / 5641041216.0,
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2460397220.0 * 25.0 / 5641041216.0, -1518414297.0 * 25.0 / 5641041216.0,
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94209048.0 * 25.0 / 5641041216.0},
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{0.0, 259006536.0 * 2187.0 / 199316789632.0,
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-687873124.0 * 2187.0 / 199316789632.0,
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451824525.0 * 2187.0 / 199316789632.0,
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-52338360.0 * 2187.0 / 199316789632.0},
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{0.0, -361440756.0 * 11.0 / 2467955532.0,
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946554244.0 * 11.0 / 2467955532.0, -661884105.0 * 11.0 / 2467955532.0,
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106151040.0 * 11.0 / 2467955532.0},
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{0.0, 44764047.0 / 29380423.0, -127201567 / 29380423.0,
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90730570.0 / 29380423.0, -8293050.0 / 29380423.0}}};
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};
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template <typename E> struct Vec3 {
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using value_type = E;
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E x, y, z;
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constexpr Vec3() = default;
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constexpr Vec3(E x, E y, E z) : x(x), y(y), z(z) {}
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constexpr explicit Vec3(std::array<E, 3> v) : x(v[0]), y(v[1]), z(v[2]) {}
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friend constexpr Vec3 operator+(const Vec3 &lhs, const Vec3 &rhs) {
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return Vec3{lhs.x + rhs.x, lhs.y + rhs.y, lhs.z + rhs.z};
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}
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friend constexpr Vec3 operator*(const Vec3 &lhs, const value_type &rhs) {
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return Vec3{lhs.x * rhs, lhs.y * rhs, lhs.z * rhs};
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}
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friend constexpr Vec3 operator*(const value_type &lhs, const Vec3 &rhs) {
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return Vec3{lhs * rhs.x, lhs * rhs.y, lhs * rhs.z};
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}
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constexpr Vec3 &operator+=(const Vec3 &rhs) {
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x += rhs.x;
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y += rhs.y;
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z += rhs.z;
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return *this;
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}
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};
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namespace alg {
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template <typename T> inline auto inf_norm(const T &v) {
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std::ranges::max_element(v, {}, [](auto n) { return std::abs(n); });
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}
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inline float inf_norm(float v) { return std::abs(v); }
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inline double inf_norm(double v) { return std::abs(v); }
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template <typename E> inline E inf_norm(const Vec3<E> &v) {
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return std::max({std::abs(v.x), std::abs(v.y), std::abs(v.z)});
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}
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} // namespace alg
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template <typename Vector, typename Scalar = std::iter_value_t<Vector>,
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typename Tableau = DormandPrince<Scalar>>
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requires std::same_as<Scalar, std::iter_value_t<Tableau>>
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inline std::size_t explicitRungeKutta(std::span<Vector> ys,
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std::span<Scalar const> ts, Vector y0,
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Scalar tol, auto &&dydx)
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requires requires(decltype(dydx) f) {
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{ f(Vector{}, Scalar{}) } -> std::same_as<Vector>;
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}
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{
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const auto stages = Tableau::stages;
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const auto dense_order = Tableau::dense_order;
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const auto order = Tableau::order;
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const auto &a = Tableau::a;
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const auto &p = Tableau::p;
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const auto &c = Tableau::c;
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const auto &b = Tableau::b;
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const auto &b_hat = Tableau::b_hat;
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static_assert(Tableau::c.back() == 1.0, "last c value must be 1.0");
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auto y_hat_n = y0;
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ys[0] = y0;
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std::size_t it = 1;
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std::array<Vector, stages> k;
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const auto N = ts.size();
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if (!N) {
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return 0;
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}
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auto t_n = ts[0];
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auto h_n = ts[N - 1] - t_n;
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int step_count = 0;
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k[stages - 1] = dydx(y0, t_n);
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while (t_n < ts[N - 1]) {
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auto step_rejected = true;
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while (step_rejected) {
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// reuse last k (we have asserted that the last c value is 1.0)
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const auto last_k_store = k[stages - 1];
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k[0] = k[stages - 1];
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for (std::size_t i = 1; i < stages; ++i) {
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Vector sum_ak{};
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for (std::size_t j = 0; j < i; ++j) {
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sum_ak += a[i][j] * k[j];
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}
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k[i] = dydx(y_hat_n + h_n * sum_ak, t_n + c[i] * h_n);
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}
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// calculate final value and error
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Vector error{};
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Vector sum_bk{};
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for (std::size_t i = 0; i < stages; ++i) {
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sum_bk += b_hat[i] * k[i];
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error += (b_hat[i] - b[i]) * k[i];
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}
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const auto y_hat_np1 = y_hat_n + h_n * sum_bk;
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// check if step is successful, ie error is within tolerance
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const auto E_hp1 = alg::inf_norm(h_n * error);
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if (E_hp1 < tol) {
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// if moved over any requested times then interpolate their values
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const auto t_np1 = t_n + h_n;
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while (it < N && t_np1 >= ts[it]) {
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const auto sigma = (ts[it] - t_n) / h_n;
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Vector Phi{};
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for (std::size_t i = 0; i < stages; ++i) {
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auto term = sigma;
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auto b_i = term * p[i][0];
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for (std::size_t j = 1; j < dense_order; ++j) {
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term *= sigma;
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b_i += term * p[i][j];
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}
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Phi += b_i * k[i];
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}
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ys[it] = y_hat_n + h_n * Phi;
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++it;
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}
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// move to next step
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step_rejected = false;
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y_hat_n = y_hat_np1;
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t_n = t_np1;
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++step_count;
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} else {
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// failed step, reset last k back to stored value
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k[stages - 1] = last_k_store;
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}
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// adapt step size
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h_n *= 0.9 * std::pow(tol / E_hp1, 1.0 / (order + 1.0));
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}
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}
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assert(it == N);
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return it;
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}
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} // namespace mini_odeint
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#include <vector>
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#include <iostream>
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int main() {
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using namespace mini_odeint;
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// make vector of floats from 0.0 to 1.0 by 0.001
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std::vector<float> times;
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times.reserve(1001);
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for (int i = 0; i < 1000; ++i) {
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times.push_back(i / 1000.0);
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}
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std::vector<Vec3<float>> ys(times.size());
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explicitRungeKutta(
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std::span(ys), std::span<const float>(times), Vec3<float>{1.0, 1.0, 1.0},
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float(1e-6), [](auto y, auto t) { return Vec3<float>{-y.x, 0.0, 0.0}; });
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for (const auto &v : ys) {
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std::cout << v.x << '\n';
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}
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}
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#endif // MINI_ODEINT_H_
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