Complex¶

Overview¶

XAD implements specialisations of std::complex for the XAD active data types AReal and FReal. They are are provided in the header XAD/Complex.hpp, along with all the mathematical operations defined in the standard.

Note that the complex header is not automatically included with XAD/XAD.hpp. Users must include it as needed.

template <typename T> class std::complex<AReal<T>>¶: Specialisation for adjoint mode data type (in std namespace).

template <typename T> class std::complex<FReal<T>>¶: Specialisation for forward mode data type (in std namespace).

Members¶

All standard complex members are implemented.

Below are the non-standard additions and changes of the interface only, using the placeholder AReal<T> as a placeholder inner type. The same functions are also defined for FReal<T>.

XReal<T> &real()¶: This function returns a reference rather than a copy of the real part, to allow for easy access and adjusting of derivatives using derivative().

XReal<T> &imag()¶: Returns a reference rather than a copy.

const XReal<T> &real() const¶: Returns a reference rather than a copy.

const XReal<T> &imag() const¶: Returns a reference rather than a copy.

void setDerivative(const T &real_derivative, const T &imag_derivative = T())¶: Sets the derivatives (either $\dot{x}$ or $\bar{x}$ ) for both the real and imaginary parts.

void setAdjoint(const T &real_derivative, const T &imag_derivative = T())¶: Alias for setDerivative()

std::complex<T> getDerivative() const¶: Gets the derivatives (either $\dot{x}$ or $\bar{x}$ ) for both the real and imaginary parts, represented as a complex of the underlying (double) type.

std::complex<T> getAdjoint() const¶: Alias for getDerivative()

Non-Member Functions¶

template <typename T> std::complex<T> derivative(const std::complex<AReal<T>> &z)¶

Returns the adjoints of the z variable, represented as a complex number of the underlying double type.

Note that since the return type is not a reference, setting derivatives should be done by using the member function template <typename T> std::complex<AReal<T> >::setDerivative() or using the real and imag member functions instead.

template <typename T> std::complex<T> derivative(const std::complex<FReal<T>> &z)¶

Returns the derivatives of the z variable, represented as a complex number of the underlying double type.

Note that since the return type is not a reference, setting derivatives should be done by using the member function template <typename T> std::complex<FReal<T> >::setDerivative() or using the real and imag member functions instead.

template <typename T> std::complex<T> value(const std::complex<AReal<T>> &z)¶: Returns the value of the z variable (underlying double type), represented as a complex number.

template <typename T> std::complex<T> value(const std::complex<FReal<T>> &z)¶: Returns the value of the z variable (underlying double type), represented as a complex number.

template <typename T> AReal<T> &real(std::complex<AReal<T>> &z)¶: Access to the real part by reference.

template <typename T> FReal<T> &real(std::complex<FReal<T>> &z)¶: Access to the real part by reference.

template <typename T> AReal<T> &imag(std::complex<AReal<T>> &z)¶: Access to the imaginary part by reference.

template <typename T> FReal<T> &imag(std::complex<FReal<T>> &z)¶: Access to the imaginary part by reference.

Math Operations¶

All arithmetic operators and mathematical functions in the C++11 standard have been specialised with the XAD complex data types as well. This also includes the stream read and write operations.

Last update: January 2023