theoretica::multidual< N > Class Template Reference

Multidual number algebra for functions of the form \(f: \mathbb{R}^n \rightarrow \mathbb{R}\). More...

#include <multidual.h>

Public Member Functions
	multidual ()
	Construct a multidual number as \((0 + \vec 0)\).
	multidual (real r, vec< real, N > u)
	Construct a multidual number from a real number and an N dimensional vector.
	multidual (real r)
	Construct a multidual number from a real number.
multidual &	operator= (real x)
	Initialize a multidual number from a real number.
real	Re () const
	Get the real part.
real &	Re ()
	Access the real part.
vec< real, N >	Dual () const
	Get the multidual part.
vec< real, N > &	Dual ()
	Access the multidual part.
real	Dual (unsigned int i) const
	Get the i-th element of the multidual part, corresponding to the i-th independent variable in automatic differentiation.
real &	Dual (unsigned int i)
	Access the i-th element of the multidual part, corresponding to the i-th independent variable in automatic differentiation.
multidual	conjugate () const
	Get the multidual conjugate.
multidual	inverse () const
	Get the inverse of a multidual number.
multidual	operator+ () const
	Identity (for consistency)
multidual	operator+ (const multidual &other) const
	Sum two multidual numbers.
multidual	operator+ (real r) const
	Sum a real number to a multidual number.
multidual	operator- () const
	Get the opposite of a multidual number.
multidual	operator- (const multidual &other) const
	Subtract two multidual numbers.
multidual	operator- (real r) const
	Subtract a real number from a multidual number.
multidual	operator* (const multidual &other) const
	Multiply two multidual numbers.
multidual	operator* (real r) const
	Multiply a multidual number by a real number.
multidual	operator/ (const multidual &other) const
	Dual division.
multidual	operator/ (real r) const
	Divide a multidual number by a real number.
multidual &	operator+= (const multidual &other)
	Sum a real number to this one.
multidual &	operator+= (real r)
	Sum a real number to this multidual number.
multidual &	operator-= (const multidual &other)
	Subtract a real number from this one.
multidual &	operator-= (real r)
	Subtract a real number from this multidual number.
multidual &	operator*= (const multidual &other)
	Multiply this multidual number by another one.
multidual &	operator*= (real r)
	Multiply this multidual number by a real number.
multidual &	operator/= (const multidual &other)
	Divide this multidual number by another one.
multidual &	operator/= (real r)
	Divide a multidual number by a real number.
bool	operator== (const multidual &other)
	Check whether two multidual numbers have the same real and multidual parts.
unsigned int	size () const
	Get the number of independent variables associated with the multidual number.
void	resize (unsigned int size)
	Change the size of the dual part of the number (only for dynamically allocated vectors)
std::string	to_string (const std::string &epsilon="e") const
	Convert the multidual number to string representation.
	operator std::string ()
	Convert the multidual number to string representation.

Static Public Member Functions
static vec< multidual< N >, N >	make_argument (const vec< real, N > &x)
	Construct an N-dimensional vector of multidual numbers to be passed as argument to a multidual function.
static vec< real, N >	extract_real (const vec< multidual< N >, N > &v)
	Extract the real vector from a vector of multidual numbers as a vec<real, N>
static mat< real, N, N >	extract_dual (const vec< multidual< N >, N > &v)
	Extract the dual matrix (Jacobian) from a vector of multidual numbers as a mat<N, N>
static void	extract (const vec< multidual< N >, N > &v, vec< real, N > &x, mat< real, N, N > &J)
	Extract the real vector and dual matrix from a vector of multidual numbers as a vec<real, N> and mat<real, N, N>

Public Attributes
real	a
	The real part of the multidimensional dual number.
vec< real, N >	v
	The dual part of the multidimensional dual number as a real vector.

Friends
std::ostream &	operator<< (std::ostream &out, const multidual &obj)
	Stream the multidual number in string representation to an output stream (std::ostream)

Detailed Description

template<unsigned int N = 0>
class theoretica::multidual< N >

Multidual number algebra for functions of the form \(f: \mathbb{R}^n \rightarrow \mathbb{R}\).

Member Function Documentation

make_argument()

template<unsigned int N = 0>

static vec< multidual< N >, N > theoretica::multidual< N >::make_argument ( const vec< real, N > &  x )

inlinestatic

Construct an N-dimensional vector of multidual numbers to be passed as argument to a multidual function.

Parameters

x	A vector of real numbers containing the variables to pass

to_string()

template<unsigned int N = 0>

std::string theoretica::multidual< N >::to_string ( const std::string &  epsilon = "e" ) const

inline

Convert the multidual number to string representation.

Parameters

epsilon

The character to use to represent epsilon

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The documentation for this class was generated from the following file:

• autodiff/multidual.h