61 lines
1.5 KiB
C++
61 lines
1.5 KiB
C++
#pragma once
|
|
|
|
#include <array>
|
|
|
|
#include "autoopt/dual.hpp"
|
|
|
|
namespace autoopt {
|
|
|
|
template <typename T, class Func>
|
|
T derivative(Func&& f, const T& x) {
|
|
dual<T> a(x, T(1));
|
|
dual<T> b = f(a);
|
|
return b._dx;
|
|
}
|
|
|
|
template <typename T, std::size_t N, class Func>
|
|
std::array<T, N> gradient(Func&& f, const std::array<T, N>& x) {
|
|
std::array<T, N> grad{};
|
|
std::array<dual<T>, N> dual_x{};
|
|
for (std::size_t i = 0; i < N; ++i) {
|
|
dual_x[i] = dual<T>(x[i], T(0));
|
|
}
|
|
for (std::size_t i = 0; i < N; ++i) {
|
|
dual_x[i]._dx = T(1);
|
|
dual<T> dual_y = f(dual_x);
|
|
grad[i] = dual_y._dx;
|
|
dual_x[i]._dx = T(0);
|
|
}
|
|
return grad;
|
|
}
|
|
|
|
template <typename T, std::size_t N, std::size_t M>
|
|
using matrix_t = std::array<std::array<T, M>, N>;
|
|
|
|
template <typename T, std::size_t N, std::size_t M, class Func>
|
|
matrix_t<T, M, N> jacobian(Func&& f, const std::array<T, N>& x) {
|
|
matrix_t<T, M, N> jacob{};
|
|
std::array<dual<T>, N> dual_x{};
|
|
for (std::size_t i = 0; i < N; ++i) {
|
|
dual_x[i] = dual<T>(x[i], T(0));
|
|
}
|
|
for (std::size_t i = 0; i < N; ++i) {
|
|
dual_x[i]._dx = T(1);
|
|
std::array<dual<T>, M> dual_y = f(dual_x);
|
|
for (std::size_t j = 0; j < M; ++j) {
|
|
jacob[j][i] = dual_y[j]._dx;
|
|
}
|
|
dual_x[i]._dx = T(0);
|
|
}
|
|
return jacob;
|
|
}
|
|
|
|
template <typename T, std::size_t N, class Func>
|
|
matrix_t<T, N, N> hessian(Func&& f, const std::array<T, N>& x) {
|
|
auto helper_func = [&f]<typename U>(const std::array<U, N>& y) {
|
|
return gradient<U, N>(f, y);
|
|
};
|
|
return jacobian<T, N, N>(helper_func, x);
|
|
}
|
|
|
|
} // namespace autoopt
|