Derivatives.h File Reference

#include "AlgebraicTraits.h"
#include "Matrix.h"

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Functions
template<class FunctionType, class ArgumentType>
ArgumentType	fastDerivative (FunctionType function, ArgumentType value)
template<class SingleArgumentFunctionType, class ValueType>
ValueType	derivative (SingleArgumentFunctionType function, ValueType value)
template<class T>
T	partialDerivative (typename math_types< T >::MultipleArgFunction fun, typename math_types< T >::vector_type argv, int index)
template<class T>
const math_types< T >::vector_type	differential (typename math_types< T >::MultipleArgFunction function, const typename math_types< T >::vector_type &value)

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Detailed Description

Contains functions to compute the derivative, partial derivative or differential of functions.

Definition in file Derivatives.h.

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Function Documentation

template<class SingleArgumentFunctionType, class ValueType>

ValueType derivative	(	SingleArgumentFunctionType	function,
		ValueType	value
	)

Compute the derivative of function at point val.

Computes the derivative of func using "Richardson's deffered approach to the limit" Returns the derivative of a function func at a point x by Ridders' method of polynomial extrapolation. The value h is input as an estimated initial stepsize; it need not be small, but rather should be an increment in x over which func changes substantially. An estimate of the error in the derivative is returned as err.

Parameters:

	function	pointer to function whose derivative we want to evaluate
	value	point in which we evaluate the derivative

Returns:

the value of the derivative

Definition at line 80 of file Derivatives.h.

References AlgebraicTraits< T >::one(), and AlgebraicTraits< T >::zero().

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template<class T>

const math_types<T>::vector_type differential	(	typename math_types< T >::MultipleArgFunction	function,
		const typename math_types< T >::vector_type &	value
	)

Compute the differential of a multi-variable function

Parameters:

	function	multiple variable function whose differential we want to determine
	value	a vector containing the point in which to evaluate the differential

Returns:

the value of the differential (a vector)

Definition at line 241 of file Derivatives.h.

References partialDerivative().

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template<class FunctionType, class ArgumentType>

ArgumentType fastDerivative	(	FunctionType	function,
		ArgumentType	value
	)

Compute the derivative of function at point value. This function is fast but not so accurate for more accuracy use Richardson's deferred approach to the limit implemented in the function derivative(...)

Parameters:

	function	pointer to function whose derivative we want to evaluate. It must be a single argument function pointer or a functional object that declares operator() with one argument of type ArgumentType
	value	the point in which we evaluate the derivative

Returns:

the derivative value

See also:

derivative

Definition at line 36 of file Derivatives.h.

References AlgebraicTraits< T >::one().

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template<class T>

T partialDerivative	(	typename math_types< T >::MultipleArgFunction	fun,
		typename math_types< T >::vector_type	argv,
		int	index
	)

Compute the partial derivative of fun with respect to argument index

Computes the derivative of func using "Richardson's deffered approach to the limit" Returns the derivative of a function func at a point x by Ridders' method of polynomial extrapolation. The value h is input as an estimated initial stepsize; it need not be small, but rather should be an increment in x over which func changes substantially. An estimate of the error in the derivative is returned as err.

Parameters:

	fun	pointer to function whose derivative we want to evaluate
	argv	vector of arguments
	index	index in the arguments vector that tells with respect to which variable to compute the derivative

Returns:

derivative value

Definition at line 158 of file Derivatives.h.

References AlgebraicTraits< T >::one(), and AlgebraicTraits< T >::zero().

Referenced by differential().

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