functionhouseholderReflection

Reflect a vector a on a plane with orthogonal vector u

Extends from Modelica.Icons.Function (Icon for functions), Modelica.Icons.ObsoleteModel (Icon for classes that are obsolete and will be removed in later versions).

Information

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

Inputs

TypeNameDefaultDescription
Real[:]aReal vector a to be reflected
Real[size(a, 1)]uHouseholder vector

Outputs

TypeNameDefaultDescription
Real[size(u, 1)]raReflection of a

Revisions

  • 2010/04/30 by Marcus Baur, DLR-RM