.Modelica.Math.Matrices.Utilities.toUpperHessenberg

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]

See also

Interface

function toUpperHessenberg
  extends Modelica.Icons.Function;
  import Modelica.Math.Matrices;
  import Modelica.Math.Matrices.LAPACK;
  input Real A[:, size(A, 1)] "Square matrix A";
  input Integer ilo = 1 "Lowest index where the original matrix is not in upper triangular form";
  input Integer ihi = size(A, 1) "Highest index where the original matrix is not in upper triangular form";
  output Real H[size(A, 1), size(A, 2)] "Upper Hessenberg form";
  output Real V[size(A, 1), size(A, 2)] "V=[v1,v2,..vn-1,0] with vi are vectors which define the elementary reflectors";
  output Real tau[max(0, size(A, 1) - 1)] "Scalar factors of the elementary reflectors";
  output Integer info "Information of successful function call";
end toUpperHessenberg;

Revisions

• 2010/04/30 by Marcus Baur, DLR-RM