.Modelica_LinearSystems2.Math.Matrices.Internal.householderSimilarityTransformation2

Information

It is assumed that the input vector u is a Housholder vector of the shape

u = (u1, u2, ..., ur,0, ..., 0)

where r is an integer input. From

S = I - 2*u*u'/u'*u = [P, 0; 0, I]

with

dim(P) = r x r,   dim(I) = n-r x n-r

results

S*A*S = [P*A11*P, P*A12; A21*P, A22]

Interface

function householderSimilarityTransformation2
  extends Modelica.Icons.Function;
  import Modelica.Math.Vectors.length;
  input Real A[:, size(A, 1)];
  input Real u[size(A, 1)] "householder vector";
  input Integer r;
  output Real SAS[size(A, 1), size(A, 1)];
end householderSimilarityTransformation2;