chud computes Q such that: $$Q^T Q = R^T R + x x^T$$
chdd computes Q such that: $$Q^T Q = R^T R - x x^T$$
chdd reports an error if \(R^T R - x x^T\) is not positive
definite. The two functions use LINPACK's dchud and
dchdd routines respectively, two of the few routines from
LINPACK without analogues in LAPACK.
References
Dongarra, J. J., Moler, C. B., Bunch, J. R., Stewart, G. W. (1979)
LINPACK User's Guide.