zgees zgees_r zgeesx zgeesx_r zgeev zgeevx

zgees() void zgees ( char  jobvs, char  sort, int(*)(doublecomplex)  select, int  n, int  lda, doublecomplex  a[], int *  sdim, doublecomplex  w[], int  ldvs, doublecomplex  vs[], doublecomplex  work[], int  lwork, double  rwork[], int  bwork[], int *  info  ) (Simple driver) Schur factorization of a complex matrix Purpose This routine computes for an n x n complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z. This gives the Schur factorization 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. The matrix A is reduced to upper Hessenberg form first. Then the eigenvalues and the Schur factorization are computed by QR method. Parameters [in] jobvs = 'N': Schur vectors are not computed. = 'V': Schur vectors are computed. [in] sort 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). [in] select sort = 'S': select is used to select eigenvalues to order to the top left of the Schur form.   The eigenvalue w[j] is selected if select(w[j]) is true (= 1). sort = 'N': select is not referenced. [in] n Order of the matrix A. (n >= 0) (If n = 0, returns without computation) [in] lda Leading dimension of the two dimensional array a[][]. (lda >= max(1, n)) [in,out] a[][] Array a[la][lda] (la >= n) [in] n x n matrix A. [out] a[][] has been overwritten by its Schur form T. [out] sdim sort = 'N': sdim = 0. sort = 'S': sdim = number of eigenvalues for which select is true. [out] w[] Array w[lw] (lw >= n) w[] contains the computed eigenvalues, in the same order that they appear on the diagonal of the output Schur form T. [in] ldvs Leading dimension of the two dimensional array vs[][]. (ldvs >= 1 if jobvs = 'N', ldvs >= n if jobvs = 'V') [out] vs[][] Array vs[lvs][ldvs] (lvs >= n) jobvs = 'V': vs[][] contains the unitary matrix Z of Schur vectors. jobvs = 'N': vs[][] is not referenced. [out] work[] Array work[lwork] Complex work array. On exit, if info = 0, work[0] returns the optimal lwork. [in] lwork The length of work[] (lwork >= max(1, 2*n)). For good performance, lwork must generally be larger. If lwork = -1, then a workspace query is assumed. The routine only calculates the optimal size of the work[] array, and returns the value in work[0]. [out] rwork[] Array rwork[lrwork] (lrwork >= n) Work array. [out] bwork[] Array bwork[lbwork] (lbwork >= n) Logical type (integer) work array. Not referenced if sort = 'N'. [out] info = 0: Successful exit = -1: The argument jobvs had an illegal value (jobvs != 'V' nor 'N') = -2: The argument sort had an illegal value (sort != 'S' nor 'N') = -4: The argument n had an illegal value (n < 0) = -5: The argument lda had an illegal value (lda < max(1, n)) = -9: The argument ldvs had an illegal value (ldvs too small) = -12: The argument lwork had an illegal value (lwork too small) = i (0 < i <= n): The QR algorithm failed to compute all the eigenvalues. Elements 0 to ilo-2 and i to n-1 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 eigenvalues could not be reordered because some eigenvalues 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. Reference LAPACK