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C++ API

: [housv, beta, zer] = housh (x, j, z)

Compute Householder reflection vector housv to reflect x to be the j-th column of identity, i.e.,

(I - beta*housv*housv')x =  norm (x)*e(j) if x(j) < 0,
(I - beta*housv*housv')x = -norm (x)*e(j) if x(j) >= 0

Inputs

x

vector

j

index into vector

z

threshold for zero (usually should be the number 0)

Outputs (see Golub and Van Loan):

beta

If beta = 0, then no reflection need be applied (zer set to 0)

housv

householder vector

Package: octave