.Modelica_LinearSystems2.WorkInProgress.Math.Complex.Matrices.norm

Information

Syntax

Matrices.norm(A);
Matrices.norm(A, p=2);

Description

The function call "Matrices.norm(A)" returns the 2-norm of matrix A, i.e., the largest singular value of A.
The function call "Matrices.norm(A, p)" returns the p-norm of matrix A. The only allowed values for p are

• "p=1": the largest column sum of A
• "p=2": the largest singular value of A
• "p=Modelica.Constants.inf": the largest row sum of A

Note, for any matrices A1, A2 the following inequality holds:

Matrices.norm(A1+A2,p) ≤ Matrices.norm(A1,p) + Matrices.norm(A2,p)

Note, for any matrix A and vector v the following inequality holds:

Vectors.norm(A*v,p) ≤ Matrices.norm(A,p)*Vectors.norm(A,p)

Interface

function norm
  extends Modelica.Icons.Function;
  import Modelica.ComplexMath;
  import Complex;
  import Modelica_LinearSystems2;
  input Complex A[:, :] "Input matrix";
  input Real p(min = 1) = 2 "Type of p-norm (only allowed: 1, 2 or Modelica.Constants.inf)";
  output Real result = 0.0 "p-norm of matrix A";
end norm;