This is a Function_ subclass whose output value y=f(x) is smoothly stepped from y=y0 to y1 as its input argument goes from x=x0 to x1. More...

Inheritance diagram for SimTK::Function_< T >::Step:

Public Member Functions
	Step (const T &y0, const T &y1, Real x0, Real x1)
	Create a Function_::Step object that smoothly interpolates its output through a given range as its input moves through its range. More...

T	calcValue (const Vector &xin) const
	Calculate the value of this function at a particular point. More...

T	calcDerivative (const Array_< int > &derivComponents, const Vector &xin) const
	Calculate a partial derivative of this function at a particular point. More...

virtual int	getArgumentSize () const
	Get the number of components expected in the input vector. More...

int	getMaxDerivativeOrder () const
	Get the maximum derivative order this Function_ object can calculate. More...

T	calcDerivative (const std::vector< int > &derivComponents, const Vector &x) const
	This provides compatibility with std::vector without requiring any copying. More...

Public Member Functions inherited from SimTK::Function_< T >
virtual	~Function_ ()

T	calcDerivative (const std::vector< int > &derivComponents, const Vector &x) const
	This provides compatibility with std::vector without requiring any copying. More...

Detailed Description

template<class T>
class SimTK::Function_< T >::Step

This is a Function_ subclass whose output value y=f(x) is smoothly stepped from y=y0 to y1 as its input argument goes from x=x0 to x1.

This is an S-shaped function with first and second derivatives y'(x0)=y'(x1)=0 and y''(x0)=y''(x1)==0. The third derivative y''' exists and is continuous but we cannot guarantee anything about it at the end points.

Constructor & Destructor Documentation

template<class T>

SimTK::Function_< T >::Step::Step	(	const T &	y0,
		const T &	y1,
		Real	x0,
		Real	x1
	)

inline

Create a Function_::Step object that smoothly interpolates its output through a given range as its input moves through its range.

Parameters

y0	Output value when (x-x0)*sign(x1-x0) <= 0.
y1	Output value when (x-x1)*sign(x1-x0) >= 0.
x0	Start of switching interval.
x1	End of switching interval.

Template Parameters

T	The template type is the type of y0 and y1. This must be a type that supports subtraction and scalar multiplication by a Real so that we can compute an expression like y=y0 + f*(y1-y0) for some Real scalar f.

Note that the numerical values of x0 and x1 can be in either order x0 < x1 or x0 > x1.

Member Function Documentation

template<class T>

T SimTK::Function_< T >::Step::calcValue ( const Vector & x ) const

inlinevirtual

Calculate the value of this function at a particular point.

Parameters

x	the Vector of input arguments. Its size must equal the value returned by getArgumentSize().

Implements SimTK::Function_< T >.

template<class T>

T SimTK::Function_< T >::Step::calcDerivative	(	const Array_< int > &	derivComponents,
		const Vector &	x
	)		const

inlinevirtual

Calculate a partial derivative of this function at a particular point.

Which derivative to take is specified by listing the input components with which to take it. For example, if derivComponents=={0}, that indicates a first derivative with respective to component 0. If derivComponents=={0, 0, 0}, that indicates a third derivative with respective to component 0. If derivComponents=={4, 7}, that indicates a partial second derivative with respect to components 4 and 7.

Parameters

derivComponents	The input components with respect to which the derivative should be taken. Its size must be less than or equal to the value returned by getMaxDerivativeOrder().
x	The Vector of input arguments. Its size must equal the value returned by getArgumentSize().