functionnorm
Return the p-norm of a matrix
Extends from Modelica.Icons.Function (Icon for functions).
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)
See also
Inputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real[:,:] | A | Input matrix | |
| Real | p | 2 | Type of p-norm (only allowed: 1, 2 or Modelica.Constants.inf) |
Outputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real | result | 0.0 | p-norm of matrix A |