Functions group

Detailed Description

This group collects function types directly based on gsFunction.

Implementations of gsFunction must at the very least implement the evaluation function gsFunction::eval_into(). It is also recommended to specify the source and target dimensions by overriding gsFunction::domainDim() and gsFunction::targetDim().

The functions for the derivatives may either be overridden or left as the default implementations, which use finite differences.

Evaluation members

All evaluation functions take a matrix u as an argument which specifies where the function should be evaluated. This matrix should have d rows, and every column specifies one point of the domain at which the function should be evaluated.

Here is an overview over the different evaluation procedures available:

Name of procedure	Evaluate what
eval(u)	value
deriv(u)	first derivative(s)
deriv2(u)	second derivative(s)

All evaluation functions also provide a version suffixed with _into which takes a matrix reference as an additional output parameter into which the result will be stored.

Template Parameters

T	arithmetic type

Classes
class	gsAffineFunction< T >
	Representation of an affine function. More...
class	gsBasisFun< T >
	Represents an individual function in a function set, or a certain component of a vector-valued function. More...
class	gsConstantFunction< T >
	Class defining a globally constant function. More...
class	gsFuncCoordinate< T >
	Represents a certain component of a vector-valued function. More...
class	gsFunction< T >
	A function \(f:\mathbb{R}^n\rightarrow\mathbb{R}^m\) from a n-dimensional domain to an m-dimensional image. More...
class	gsFunctionExpr< T >
	Class defining a multivariate (real or vector) function given by a string mathematical expression. More...
class	gsFunctionSet< T >
	Interface for the set of functions defined on a domain (the total number of functions in the set equals to \(S\) ) More...
class	gsGeometry< T >
	Abstract base class representing a geometry map. More...
class	gsGeometryTransform< T >
	Representation of a transformed geometry. More...