NormFunction

Purpose

Class representing 1- or infinity-norm function.

Syntax

f = NormFunction(flag)
f = NormFunction(flag, Q)

Description

The common object for representing 1- and infinity- norm functions given as ../../../../../../fig/mpt/modules/geometry/functions/@NormFunction/normfunction1.png where ../../../../../../fig/mpt/modules/geometry/functions/@NormFunction/normfunction2.png. The one norm is given as a sum of absolute values

../../../../../../fig/mpt/modules/geometry/functions/@NormFunction/normfunction8.png

and the infinity norm is given as the maximum over the absolute values

../../../../../../fig/mpt/modules/geometry/functions/@NormFunction/normfunction9.png

where ../../../../../../fig/mpt/modules/geometry/functions/@NormFunction/normfunction3.png is the dimension of the vector ../../../../../../fig/mpt/modules/geometry/functions/@NormFunction/normfunction4.png. If the weighing matrix Q is provided, then the product ../../../../../../fig/mpt/modules/geometry/functions/@NormFunction/normfunction5.png is considered. The weight Q does not need to be square. Function value is always scalar.

2-norms are not supported because they are neither quadratic, nor piecewise linear.

Do not use these objects in the user interface. Use OneNormFunction and InfNormFunction objects instead.

Input Arguments

1

Flag indicating the type of the norm. It can be either 1 or Inf.

Class: double

Allowed values:

  • 1
  • Inf

Q

Weighing matrix where the number of columns determines the dimension of the vector argument.

Class: double

Output Arguments

f

The NormFunction object.

Class: NormFunction

Example(s)

Example 1

Construct 1-norm function ../../../../../../fig/mpt/modules/geometry/functions/@NormFunction/normfunction6.png.
f1=NormFunction(1,diag([2,-3]))
1-norm function in R^2
Evaluate the function in the point [2;1].
 f1.feval([2;1]) 
ans =

     7

Construct infinity-norm function ../../../../../../fig/mpt/modules/geometry/functions/@NormFunction/normfunction7.png.
finf=NormFunction(Inf,diag([2,-3]))
Inf-norm function in R^2
Evaluate the function in the point [2;1].
 finf.feval([2;1]) 
ans =

     4

See Also

onenormfunction, infnormfunction, afffunction, quadfunction


© 2003-2013 Michal Kvasnica: STU Bratislava, michal.kvasnica@stuba.sk

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