theoretica::taylor Namespace Reference

Taylor series expansions. More...

Functions
template<typename DualFunction >
polynomial< real >	expand_linear (DualFunction f, real x0=0)
	Computes the first order Taylor expansion of a generic function around x0, computed using dual numbers. More...
template<typename Dual2Function >
polynomial< real >	expand_quadratic (Dual2Function f, real x0=0)
	Computes the second order Taylor expansion of a generic function around x0, computed using dual numbers (of second order). More...

Detailed Description

Taylor series expansions.

Function Documentation

expand_linear()

template<typename DualFunction >

polynomial<real> theoretica::taylor::expand_linear ( DualFunction  f, real  x0 = 0  )

inline

Computes the first order Taylor expansion of a generic function around x0, computed using dual numbers.

Automatic differentiation is used to compute the exact values of the function and its derivatives at x0.

Parameters

f	A function taking and returning a dual number, representing the function to expand in series.
x0	The center of the Taylor expansion

Returns

The Taylor series expansion of the function to first degree

expand_quadratic()

template<typename Dual2Function >

polynomial<real> theoretica::taylor::expand_quadratic ( Dual2Function  f, real  x0 = 0  )

inline

Computes the second order Taylor expansion of a generic function around x0, computed using dual numbers (of second order).

Automatic differentiation is used to compute the exact values of the function and its derivatives at x0.

Parameters

f	A function taking and returning a dual2 number, representing the function to expand in series.
x0	The center of the Taylor expansion

Returns

The Taylor series expansion of the function to second degree