.Modelica.ComplexMath.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

See also

Matrices.norm

Interface

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

Generated at 2020-06-05T07:38:22Z by OpenModelica 1.16.0~dev-420-gc007a39