NAME

SYNOPSIS

  SUBROUTINE ZGEES( JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, W, Z, LDZ, 
 *      WORK, LDWORK, WORK2, WORK3, INFO)
  CHARACTER * 1 JOBZ, SORTEV
  DOUBLE COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
  INTEGER N, LDA, NOUT, LDZ, LDWORK, INFO
  LOGICAL SELECT
  LOGICAL WORK3(*)
  DOUBLE PRECISION WORK2(*)
 
  SUBROUTINE ZGEES_64( JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, W, Z, 
 *      LDZ, WORK, LDWORK, WORK2, WORK3, INFO)
  CHARACTER * 1 JOBZ, SORTEV
  DOUBLE COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
  INTEGER*8 N, LDA, NOUT, LDZ, LDWORK, INFO
  LOGICAL*8 SELECT
  LOGICAL*8 WORK3(*)
  DOUBLE PRECISION 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(8), DIMENSION(:) :: W, WORK
  COMPLEX(8), DIMENSION(:,:) :: A, Z
  INTEGER :: N, LDA, NOUT, LDZ, LDWORK, INFO
  LOGICAL :: SELECT
  LOGICAL, DIMENSION(:) :: WORK3
  REAL(8), 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(8), DIMENSION(:) :: W, WORK
  COMPLEX(8), DIMENSION(:,:) :: A, Z
  INTEGER(8) :: N, LDA, NOUT, LDZ, LDWORK, INFO
  LOGICAL(8) :: SELECT
  LOGICAL(8), DIMENSION(:) :: WORK3
  REAL(8), DIMENSION(:) :: WORK2
 

C INTERFACE

void zgees(char jobz, char sortev, logical(*select)(COMPLEX*16), int n, doublecomplex *a, int lda, int *nout, doublecomplex *w, doublecomplex *z, int ldz, int *info);

void zgees_64(char jobz, char sortev, logical(*select)(COMPLEX*16), long n, doublecomplex *a, long lda, long *nout, doublecomplex *w, doublecomplex *z, long ldz, long *info);

PURPOSE

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)

* SORTEV (input)

Specifies whether or not to order the eigenvalues on the diagonal of the Schur form.

* 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)

* WORK3 (workspace)

Not referenced if SORTEV = 'N'.

* INFO (output)