zgees zgees_r zgeesx zgeesx_r zgeev zgeevx

zgeesx() void zgeesx ( char  jobvs, char  sort, int(*)(doublecomplex)  select, char  sense, int  n, int  lda, doublecomplex  a[], int *  sdim, doublecomplex  w[], int  ldvs, doublecomplex  vs[], double *  rconde, double *  rcondv, doublecomplex  work[], int  lwork, double  rwork[], int  bwork[], int *  info  ) (Expert driver) Schur factorization of a complex matrix Purpose zgeesx 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; computes a reciprocal condition number for the average of the selected eigenvalues (rconde); and computes a reciprocal condition number for the right invariant subspace corresponding to the selected eigenvalues (rcondv). The leading columns of Z form an orthonormal basis for this invariant subspace. For further explanation of the reciprocal condition numbers rconde and rcondv, see Section 4.8.1 of the LAPACK Users' Guide Third Edition (where these quantities are called s and sep respectively). 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.   An eigenvalue w[j] is selected if select(w[j]) is true (= 1). sort = 'N': select is not referenced. [in] sense Determines which reciprocal condition numbers are computed. = 'N': None are computed. = 'E': Computed for average of selected eigenvalues only. = 'V': Computed for selected right invariant subspace only. = 'B': Computed for both. If sense = 'E', 'V' or 'B', sort must equal 'S'. [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[][] is overwritten by its Schur form T. [in] 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] rconde sense = 'E' or 'B': rconde contains the reciprocal condition number for the average of the selected eigenvalues. sense = 'N' or 'V': Not referenced. [out] rcondv sense = 'V' or 'B': rcondv contains the reciprocal condition number for the selected right invariant subspace. sense = 'N' or 'E': Not referenced. [out] work[] Array work[lwork] Complex work array. On exit, if info = 0, work[0] returns the optimal lwork. [in] lwork The dimension of the array work[]. (lwork >= max(1, 2*n) if sense = 'N', lwork >= max(1, 2*sdim*(n-sdim)) if sense = 'E', 'V' or 'B', where sdim is the number of selected eigenvalues computed by this routine. Note that 2*sdim*(n-sdim) <= n*n/2. Note also that an error is only returned if lwork < max(1, 2*n), but if sense = 'E' or 'V' or 'B', this may not be large enough) For good performance, lwork must generally be larger. If lwork = -1, then a workspace query is assumed. The routine only calculates upper bounds on the optimal size of the array work[], returns this 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 sense had an illegal value (sense != 'E', 'V', 'B' nor 'N') = -5: The argument n had an illegal value (n < 0) = -6: The argument lda had an illegal value (lda < max(1, n)) = -10: The argument ldvs had an illegal value (ldvs too small) = -15: 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