WOLFRAM SYSTEM MODELER

# toUpperHessenberg

Transform a real square matrix A to upper Hessenberg form H by orthogonal similarity transformation: Q' * A * Q = H # Wolfram Language

In:= `SystemModel["Modelica.Math.Matrices.Utilities.toUpperHessenberg"]`
Out:= # Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

#### Syntax

```         H = Matrices.Utilities.toUpperHessenberg(A);
(H, V, tau, info) = Matrices.Utilities.toUpperHessenberg(A,ilo, ihi);
```

#### Description

Function toUpperHessenberg computes a upper Hessenberg form H of a matrix A by orthogonal similarity transformation: Q' * A * Q = H. With the optional inputs ilo and ihi, also partial transformation is possible. The function calls LAPACK function DGEHRD. See Matrices.LAPACK.dgehrd for more information about the additional outputs V, tau, info and inputs ilo, ihi.

#### Example

``` A  = [1, 2, 3;
6, 5, 4;
1, 0, 0];

H = toUpperHessenberg(A);

results in:

H = [1.0,  -2.466,  2.630;
-6.083, 5.514, -3.081;
0.0,   0.919, -0.514]

```

Matrices.hessenberg

# Syntax

(H, V, tau, info) = toUpperHessenberg(A, ilo, ihi)

# Inputs (3)

A Type: Real[:,size(A, 1)] Description: Square matrix A Default Value: 1 Type: Integer Description: Lowest index where the original matrix had been Hessenbergform Default Value: size(A, 1) Type: Integer Description: Highest index where the original matrix had been Hessenbergform

# Outputs (4)

H Type: Real[size(A, 1),size(A, 2)] Description: Upper Hessenberg form Type: Real[size(A, 1),size(A, 2)] Description: V=[v1,v2,..vn-1,0] with vi are vectors which define the elementary reflectors Type: Real[max(0, size(A, 1) - 1)] Description: Scalar factors of the elementary reflectors Type: Integer Description: Information of successful function call

# Revisions

• 2010/04/30 by Marcus Baur, DLR-RM