.Modelica.Math.Vectors.norm

Information

Syntax

Vectors.norm(v);
Vectors.norm(v,p=2);   // 1 ≤ p ≤ ∞

Description

The function call "Vectors.norm(v)" returns the Euclidean norm "sqrt(v*v)" of vector v. With the optional second argument "p", any other p-norm can be computed:

$function Vectors.norm$

Besides the Euclidean norm (p=2), also the 1-norm and the infinity-norm are sometimes used:

1-norm	= sum(abs(v))	norm(v,1)
2-norm	= sqrt(v*v)	norm(v) or norm(v,2)
infinity-norm	= max(abs(v))	norm(v,Modelica.Constants.inf)

Note, for any vector norm the following inequality holds:

norm(v1+v2,p) ≤ norm(v1,p) + norm(v2,p)

Example

  v = {2, -4, -2, -1};
  norm(v,1);    // = 9
  norm(v,2);    // = 5
  norm(v);      // = 5
  norm(v,10.5); // = 4.00052597412635
  norm(v,Modelica.Constants.inf);  // = 4

Interface

function norm
  extends Modelica.Icons.Function;
  input Real v[:] "Real vector";
  input Real p(min = 1) = 2 "Type of p-norm (often used: 1, 2, or Modelica.Constants.inf)";
  output Real result = 0.0 "p-norm of vector v";
end norm;