Expressions¶

Expression Template¶

template <typename T, typename Derived>
class Expression¶

Represents a mathematical expression in a type. Active data types, such as AReal and FReal, as well as all mathematical expressions inherit from this class. Therefore all mathematical operations are defined on this type, rather than any specific derived class.

The derived classes are typically created transparently to the user.

Note that this class uses the CRTP pattern, where Derived is the derived class itself, so that static polymorphism can be used.

All global arithmetic operations defined in C++ are specialized for Expression, so that double or float can be replaced seamlessly with a XAD data type. This also includes comparisons.

Expression Traits¶

XAD also defines expression traits to find out information about expressions in a templated context. This is typically only needed when custom functions dealing with the XAD expressions are added.

enum Direction¶

Enum to indicate the direction of algorithmic differentiation associated with a type.

enumerator DIR_NONE¶

Not an algorithmic differentiation type

enumerator DIR_FORWARD¶

Forward mode AD type

enumerator DIR_REVERSE¶

Reverse mode AD type

template <typename T>
class ExprTraits¶

Main traits class to find out information about an expression type.

static const bool isExpr¶

True if the type is in fact an expression (or any XAD active variable)

static const int numVariables¶

Number of variables that are port of the expression

static const bool isForward¶

Boolean to represent if forward-mode AD

static const bool isReverse¶

Boolean to represent if adjoint mode AD

static const bool isLiteral¶

True if type is an elementary AD type (e.g. AReal)

type nested_type¶

The underlying double type of the expression, e.g. double for AReal<double>, or AReal<FReal<double>> (unwrapping all layers)

type value_type¶

The underlying active type of the expression, e.g. AReal<double> for a complex expression involving reverse mode active variables.

type scalar_type¶

The scalar type of the expression, unwrapping one layer in case of higher-order derivatives. For example, returns double for AReal<double>, and FReal<double> for AReal<FReal<double>> .