object Householder
The Householder object provides methods to compute Householder vectors and
reflector matrices.
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def
house(x: VectoD): (VectorD, Double)
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'.
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.
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def
houseR(x: VectorD): MatrixD
Compute the Householder reflector matrix 'h = I - 2*u*u.t'.
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
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def
houseV(x: VectorD): VectorD
Compute the Householder unit vector 'u', where 'P = I - b * u * u.t' is an orthogonal matrix.
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