functiontoUpperHessenberg

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

Extends from Modelica.Icons.Function (Icon for functions).

Information

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. The optional inputs ilo and ihi improve efficiency if the matrix is already partially converted to Hessenberg form; it is assumed that matrix A is already upper Hessenberg for rows and columns 1:(ilo-1) and (ihi+1):size(A, 1). The function calls LAPACK.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]

Inputs

Type	Name	Default	Description
Real[:,size(A, 1)]	A		Square matrix A
Integer	ilo	1	Lowest index where the original matrix is not in upper triangular form
Integer	ihi	size(A, 1)	Highest index where the original matrix is not in upper triangular form

Outputs

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

Revisions

2010/04/30 by Marcus Baur, DLR-RM