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The subroutine Xgetv0  is responsible for generating starting vectors. It is called upon to construct the initial Arnoldi/Lanczos vector   when this option is requested. Xgetv0 is also called upon to generate a new basis vector when the re-orthogonalization scheme of XYaitr calls for this, i.e. when an invariant subspace is encountered early during the construction of the Arnoldi factorization. In the latter case, the vector that is returned by Xgetv0 is already orthogonalized against the existing set of basis vectors. In either case, if the (shift-invert) computational mode calls for it, the vector is also forced to be in the range  of OP. The LAPACK subroutine Xlarnv is used to generate the random vectors. Subroutine Xgetv0 is called by XYaup2 and XYaitr.

Chao Yang