NAME

cgees - 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 CGEES( JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, W, Z, LDZ, 
 *      WORK, LDWORK, WORK2, WORK3, INFO)
  CHARACTER * 1 JOBZ, SORTEV
  COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
  INTEGER N, LDA, NOUT, LDZ, LDWORK, INFO
  LOGICAL SELECT
  LOGICAL WORK3(*)
  REAL WORK2(*)

  SUBROUTINE CGEES_64( JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, W, Z, 
 *      LDZ, WORK, LDWORK, WORK2, WORK3, INFO)
  CHARACTER * 1 JOBZ, SORTEV
  COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
  INTEGER*8 N, LDA, NOUT, LDZ, LDWORK, INFO
  LOGICAL*8 SELECT
  LOGICAL*8 WORK3(*)
  REAL WORK2(*)

F95 INTERFACE

  SUBROUTINE GEES( JOBZ, SORTEV, SELECT, [N], A, [LDA], NOUT, W, Z, 
 *       [LDZ], [WORK], [LDWORK], [WORK2], [WORK3], [INFO])
  CHARACTER(LEN=1) :: JOBZ, SORTEV
  COMPLEX, DIMENSION(:) :: W, WORK
  COMPLEX, DIMENSION(:,:) :: A, Z
  INTEGER :: N, LDA, NOUT, LDZ, LDWORK, INFO
  LOGICAL :: SELECT
  LOGICAL, DIMENSION(:) :: WORK3
  REAL, DIMENSION(:) :: WORK2

  SUBROUTINE GEES_64( JOBZ, SORTEV, SELECT, [N], A, [LDA], NOUT, W, Z, 
 *       [LDZ], [WORK], [LDWORK], [WORK2], [WORK3], [INFO])
  CHARACTER(LEN=1) :: JOBZ, SORTEV
  COMPLEX, DIMENSION(:) :: W, WORK
  COMPLEX, DIMENSION(:,:) :: A, Z
  INTEGER(8) :: N, LDA, NOUT, LDZ, LDWORK, INFO
  LOGICAL(8) :: SELECT
  LOGICAL(8), DIMENSION(:) :: WORK3
  REAL, DIMENSION(:) :: WORK2

C INTERFACE

#include <sunperf.h>

void cgees(char jobz, char sortev, logical(*select)(complex), int n, complex *a, int lda, int *nout, complex *w, complex *z, int ldz, int *info);

void cgees_64(char jobz, char sortev, logical(*select)(complex), long n, complex *a, long lda, long *nout, complex *w, complex *z, long ldz, long *info);

PURPOSE

cgees 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 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.

ARGUMENTS

JOBZ (input)

 = 'N': Schur vectors are not computed;

 = 'V': Schur vectors are computed.

SORTEV (input)
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)
SELECT must be declared EXTERNAL in the calling subroutine. If SORTEV = 'S', SELECT is used to select eigenvalues to order to the top left of the Schur form. If SORTEV = 'N', SELECT is not referenced. The eigenvalue W(j) is selected if SELECT(W(j)) is true.
N (input)
The order of the matrix A. N > = 0.
A (input/output)
On entry, the N-by-N matrix A. On exit, A has been overwritten by its Schur form T.
LDA (input)
The leading dimension of the array A. LDA > = max(1,N).
NOUT (output)
If SORTEV = 'N', NOUT = 0. If SORTEV = 'S', NOUT = number of eigenvalues for which SELECT is true.
W (output)
W contains the computed eigenvalues, in the same order that they appear on the diagonal of the output Schur form T.
Z (output)
If JOBZ = 'V', Z contains the unitary matrix Z of Schur vectors. If JOBZ = 'N', Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ > = 1; if JOBZ = 'V', LDZ > = N.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK > = max(1,2*N). For good performance, LDWORK must generally be larger.
If LDWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LDWORK is issued by XERBLA.
WORK2 (workspace)
dimension(N)
WORK3 (workspace)
dimension(N) Not referenced if SORTEV = 'N'.
INFO (output)
```
 = 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 JOBZ = 'V', Z 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.