AffFunction

Purpose

Representation of affine functions in the form F*x + g

Syntax

L = AffFunction(F,g)
L = AffFunction(F)
L = AffFunction(F,g,Data)

Description

The AffFunction class represents affine functions of the form ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction1.png where ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction2.png is a real matrix and ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction3.png is a real column vector. Dimensions of ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction4.png and ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction5.png must coincide such that the output is a vector or scalar.

Input Arguments

F

Real matrix representing the coefficients in the linear term ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction6.png in ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction7.png.

Class: double

g

Real vector representing the affine terms ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction8.png in ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction9.png.

Class: double

Data

Any data related to the function.

Output Arguments

L

AffFunction object.

Example(s)

Example 1

Construct affine function ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction10.png
L = AffFunction(3,1)
Affine Function: R^1 -> R^1
Construct linear function ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction11.png
k = AffFunction(2*pi)
Affine Function: R^1 -> R^1

Example 2

Construct vectorized affine function ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction12.png with respect to vector ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction13.png with two elements
 F = AffFunction([1 2;3 4],[1; -1]) 
Affine Function: R^2 -> R^2

Example 3

Construct affine function ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction14.png where ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction15.png and ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction16.png are regression coefficients from the data ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction17.png and ../../../../../../fig/mpt/modules/geometry/functions/@AffFunction/afffunction18.png. The data we want to store
 data.x = 0:0.01:0.5;

 data.y = sin(data.x);

 data.file= 'DSCa001';
 Compute the regression coefficients and store them in h
      
 h = polyfit(data.x,data.y,1); 
 We can store the data from which the function was obtained under Data property 
 A=AffFunction(h(1),h(2),data)
Affine Function: R^1 -> R^1

See Also

function, quadfunction


© 2010-2013 Martin Herceg: ETH Zurich, herceg@control.ee.ethz.ch