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NAME ZGEES - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z SYNOPSIS SUBROUTINE ZGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS, LDVS, WORK, LWORK, RWORK, BWORK, INFO ) CHARACTER JOBVS, SORT INTEGER INFO, LDA, LDVS, LWORK, N, SDIM LOGICAL BWORK( * ) DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * ) LOGICAL SELECT EXTERNAL SELECT PURPOSE ZGEES computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z. This gives the Schur factoriza- tion A = Z*T*(Z**H). Optionally, it also orders the eigenvalues on the diagonal of the Schur form so that selected eigenvalues are at the top left. The leading columns of Z then form an orthonormal basis for the invariant subspace corresponding to the selected eigenvalues. A complex matrix is in Schur form if it is upper triangular. ARGUMENTS JOBVS (input) CHARACTER*1 = 'N': Schur vectors are not computed; = 'V': Schur vectors are computed. SORT (input) CHARACTER*1 Specifies whether or not to order the eigenvalues on the diagonal of the Schur form. = 'N': Eigenvalues are not ordered: = 'S': Eigenvalues are ordered (see SELECT). SELECT (input) LOGICAL FUNCTION of one COMPLEX*16 variable SELECT must be declared EXTERNAL in the calling sub- routine. If SORT = 'S', SELECT is used to select eigenvalues to order to the top left of the Schur form. IF SORT = 'N', SELECT is not referenced. The eigenvalue W(j) is selected if SELECT(W(j)) is true. N (input) INTEGER The order of the matrix A. N >= 0. A (input/output) COMPLEX*16 array, dimension (LDA,N) On entry the N-by-N matrix A. On exit, A has been overwritten by its Schur form T. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). SDIM (output) INTEGER If SORT = 'N', SDIM = 0. If SORT = 'S', SDIM = number of eigenvalues for which SELECT is true. W (output) COMPLEX*16 array, dimension (N) W contains the computed eigenvalues, in the same order that they appear on the diagonal of the output Schur form T. VS (output) COMPLEX*16 array, dimension (LDVS,N) If JOBVS = 'V', VS contains the unitary matrix Z of Schur vectors. If JOBVS = 'N', VS is not refer- enced. LDVS (input) INTEGER The leading dimension of the array VS. LDVS >= 1; if JOBVS = 'V', LDVS >= N. WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= max(1,2*N). For good performance, LWORK must gen- erally be larger. RWORK (workspace) DOUBLE PRECISION array, dimension (N) BWORK (workspace) LOGICAL array, dimension (N) Not referenced if SORT = 'N'. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, and i is <= N: the QR algorithm failed to compute all the eigenvalues; elements 1:ILO-1 and i+1:N of W contain those eigenvalues which have converged; if JOBVS = 'V', VS contains the matrix which reduces A to its partially converged Schur form. = N+1: the eigen- values could not be reordered because some eigen- values were too close to separate (the problem is very ill-conditioned); = N+2: after reordering, roundoff changed values of some complex eigenvalues so that leading eigenvalues in the Schur form no longer satisfy SELECT = .TRUE.. This could also be caused by underflow due to scaling.