AD: Automatic differentiation

This library allows you to take the exact derivative of any function at compile time.

Examples

The library is most easily described by the following two examples.

One-dimensional

// Define a variable name
constexpr auto x = ad::_0;

// Define the function
constexpr auto f = (x + 1) * (x - 1);

// Take the first two derivatives
constexpr auto df  = f.derive();
constexpr auto d2f = df.derive();

std::cout << d2f(5) << '\n';

It is also possible to use the functions

• ad::cos
• ad::exp
• ad::pow
• ad::sin
• ad::sqrt
• ad::tan
• ad::log
• ad::sinh
• ad::cosh
• ad::tanh
• ad::asin
• ad::acos
• ad::atan
• ad::asinh
• ad::acosh
• ad::atanh

Multidimensional

// Define variable names
constexpr auto x = ad::_0;
constexpr auto y = ad::_1;

// Define the function
constexpr auto f = x * x * y;

// Take the first derivatives
constexpr auto dxf = f.derive(x);
constexpr auto dyf = f.derive(y); // Alternatively f.derive<1>()

// Take the second derivatives
constexpr auto dxxf = f.derive(x, x);
constexpr auto dyyf = f.derive(y, y);
constexpr auto dxyf = f.derive(x, y);