AutoDiffScalar.hpp File Reference

A forward-mode automatic-differentiation scalar: carries a value and its derivatives. More...

Classes
class	mundy::AutoDiffScalar< T, N >
	A forward-mode autodiff scalar over passive real type T with N tracked derivatives. More...
struct	mundy::NumTraits< AutoDiffScalar< T, N > >
	Numeric traits for AutoDiffScalar. Numeric values come from the passive type; the related types remain differentiable. More...
struct	mundy::ScalarBinaryOpTraits< AutoDiffScalar< T, N >, T, Op >
	An AutoDiffScalar combined with its passive type yields an AutoDiffScalar (either order). More...
struct	mundy::ScalarBinaryOpTraits< T, AutoDiffScalar< T, N >, Op >

Namespaces
namespace	mundy

Functions
Passive-value arithmetic (passive op AutoDiffScalar)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::operator+ (const T &s, const AutoDiffScalar< T, N > &a)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::operator- (const T &s, const AutoDiffScalar< T, N > &a)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::operator* (const T &s, const AutoDiffScalar< T, N > &a)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::operator/ (const T &s, const AutoDiffScalar< T, N > &a)
Comparisons (by value)
template<typename T, size_t N>
constexpr bool	mundy::operator== (const AutoDiffScalar< T, N > &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr bool	mundy::operator!= (const AutoDiffScalar< T, N > &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr bool	mundy::operator< (const AutoDiffScalar< T, N > &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr bool	mundy::operator<= (const AutoDiffScalar< T, N > &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr bool	mundy::operator> (const AutoDiffScalar< T, N > &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr bool	mundy::operator>= (const AutoDiffScalar< T, N > &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr bool	mundy::operator== (const AutoDiffScalar< T, N > &a, const T &b)
template<typename T, size_t N>
constexpr bool	mundy::operator!= (const AutoDiffScalar< T, N > &a, const T &b)
template<typename T, size_t N>
constexpr bool	mundy::operator< (const AutoDiffScalar< T, N > &a, const T &b)
template<typename T, size_t N>
constexpr bool	mundy::operator<= (const AutoDiffScalar< T, N > &a, const T &b)
template<typename T, size_t N>
constexpr bool	mundy::operator> (const AutoDiffScalar< T, N > &a, const T &b)
template<typename T, size_t N>
constexpr bool	mundy::operator>= (const AutoDiffScalar< T, N > &a, const T &b)
template<typename T, size_t N>
constexpr bool	mundy::operator== (const T &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr bool	mundy::operator!= (const T &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr bool	mundy::operator< (const T &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr bool	mundy::operator<= (const T &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr bool	mundy::operator> (const T &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr bool	mundy::operator>= (const T &a, const AutoDiffScalar< T, N > &b)
Math overloads (value via the mundy:: dispatch, derivative via the chain rule)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::sqrt (const AutoDiffScalar< T, N > &x)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::exp (const AutoDiffScalar< T, N > &x)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::log (const AutoDiffScalar< T, N > &x)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::sin (const AutoDiffScalar< T, N > &x)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::cos (const AutoDiffScalar< T, N > &x)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::acos (const AutoDiffScalar< T, N > &x)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::abs (const AutoDiffScalar< T, N > &x)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::pow (const AutoDiffScalar< T, N > &x, const T &p)
	Power with a passive exponent: d/dx x^p = p x^(p-1).
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::atan2 (const AutoDiffScalar< T, N > &y, const AutoDiffScalar< T, N > &x)
	Two-argument arctangent: d atan2(y,x) = (x dy - y dx) / (x^2 + y^2).
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::copysign (const AutoDiffScalar< T, N > &x, const T &s)
	Copy the sign of a passive value onto x; scales the derivative by the resulting sign flip.
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::copysign (const AutoDiffScalar< T, N > &x, const AutoDiffScalar< T, N > &s)
	Copy the sign of another AutoDiffScalar onto x; the sign source contributes no derivative.
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::min (const AutoDiffScalar< T, N > &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::max (const AutoDiffScalar< T, N > &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::min (const AutoDiffScalar< T, N > &a, const T &b)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::max (const AutoDiffScalar< T, N > &a, const T &b)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::min (const T &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
constexpr AutoDiffScalar< T, N >	mundy::max (const T &a, const AutoDiffScalar< T, N > &b)
template<typename T, size_t N>
std::ostream &	mundy::operator<< (std::ostream &os, const AutoDiffScalar< T, N > &a)
	Stream as "value [d0, d1, ...]".

Detailed Description

AutoDiffScalar is a drop-in scalar that propagates first derivatives by the chain rule. It satisfies the MundyMath custom-scalar contract — NumTraits, ScalarBinaryOpTraits, and ADL math overloads — so it can stand in for a primitive scalar throughout the library.

AutoDiffScalar<double, 2> x(3.0, 0);   // independent variable, d/dx seeded at slot 0
AutoDiffScalar<double, 2> y(4.0, 1);   // independent variable, d/dy seeded at slot 1
auto f = x * y + sqrt(x);              // f.value() == 12 + sqrt(3)
f.derivatives()[0];                    // df/dx == y + 0.5/sqrt(x)
f.derivatives()[1];                    // df/dy == x