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

Syntax

Vectors.Utilities.householderReflection(a,u);

Description

Function "householderReflection(a, u)" performs the reflection of vector a about a plane orthogonal to vector u (Householder vector). Algebraically the operation is defined by

b=Q*a

with

Q = I - 2*u*u',

where Q is an orthogonal matrix, i.e.

Q = inv(Q) = Q'

Example

  a = {2, -4, -2, -1};
  u = {0.837, -0.478, -0.239, -0.119};

  householderReflection(a,u);    //  = {-5.0, -0.001, -0.0005, -0.0044}

See also

Utilities.householderVector
Matrices.Utilities.householderReflection
Matrices.Utilities.householderSimilarityTransformation

ra = householderReflection(a, u)

a	Type: Real[:] Description: Real vector a to be reflected
u	Type: Real[size(a, 1)] Description: householder vector

ra	Type: Real[size(u, 1)] Description: reflexion of a