Function Reference
— Function File: [housv, beta, zer] = housh (x, j, z)

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

          (I - beta*housv*housv')x =  norm(x)*e(j) if x(1) < 0,
          (I - beta*housv*housv')x = -norm(x)*e(j) if x(1) >= 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