scalation.linalgebra

Householder

object Householder

The Householder object provides methods to compute Householder vectors and reflector matrices.

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  11. def house(x: VectorD): (VectorD, Double)

    Compute a Householder vector v and its corresponding scalar b, where P = I - b * v * v.

    Compute a Householder vector v and its corresponding scalar b, where P = I - b * v * v.t is an orthogonal matrix and Px = ||x|| * e_1.

    x

    the vector to create the Householder vector from

    See also

    Algorithm 5.1.1 in Matrix Computations.

  12. def houseR(x: VectorD): MatrixD

    Compute the Householder reflector matrix h = I - 2*u*u.

    Compute the Householder reflector matrix h = I - 2*u*u.t.

    x

    the vector to create the Householder reflector from

    See also

    www.math.siu.edu/matlab/tutorial4.pdf

  13. def houseV(x: VectorD): VectorD

    Compute the Householder unit vector u, where P = I - b * u * u.

    Compute the Householder unit vector u, where P = I - b * u * u.t is an orthogonal matrix.

    x

    the vector to create the unit Householder vector from

    See also

    www.math.siu.edu/matlab/tutorial4.pdf

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