NAME

SYNOPSIS

  SUBROUTINE DGEES( JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, WR, WI, Z, 
 *      LDZ, WORK, LDWORK, WORK3, INFO)
  CHARACTER * 1 JOBZ, SORTEV
  INTEGER N, LDA, NOUT, LDZ, LDWORK, INFO
  LOGICAL SELECT
  LOGICAL WORK3(*)
  DOUBLE PRECISION A(LDA,*), WR(*), WI(*), Z(LDZ,*), WORK(*)
 
  SUBROUTINE DGEES_64( JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, WR, WI, 
 *      Z, LDZ, WORK, LDWORK, WORK3, INFO)
  CHARACTER * 1 JOBZ, SORTEV
  INTEGER*8 N, LDA, NOUT, LDZ, LDWORK, INFO
  LOGICAL*8 SELECT
  LOGICAL*8 WORK3(*)
  DOUBLE PRECISION A(LDA,*), WR(*), WI(*), Z(LDZ,*), WORK(*)
 

F95 INTERFACE

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

C INTERFACE

void dgees(char jobz, char sortev, logical(*select)(double,double), int n, double *a, int lda, int *nout, double *wr, double *wi, double *z, int ldz, int *info);

void dgees_64(char jobz, char sortev, logical(*select)(double,double), long n, double *a, long lda, long *nout, double *wr, double *wi, double *z, long ldz, long *info);

PURPOSE

Optionally, it also orders the eigenvalues on the diagonal of the real 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 matrix is in real Schur form if it is upper quasi-triangular with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the form

        [  a  b  ]
        [  c  a  ]

where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).

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 sort to the top left of the Schur form. If SORTEV = 'N', SELECT is not referenced. An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if SELECT(WR(j),WI(j)) is true; i.e., if either one of a complex conjugate pair of eigenvalues is selected, then both complex eigenvalues are selected. Note that a selected complex eigenvalue may no longer satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since ordering may change the value of complex eigenvalues (especially if the eigenvalue is ill-conditioned); in this case INFO is set to N+2 (see INFO below).

* 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 real 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 (after sorting) for which SELECT is true. (Complex conjugate pairs for which SELECT is true for either eigenvalue count as 2.)

* WR (output)

WR and WI contain the real and imaginary parts, respectively, of the computed eigenvalues in the same order that they appear on the diagonal of the output Schur form T. Complex conjugate pairs of eigenvalues will appear consecutively with the eigenvalue having the positive imaginary part first.

* WI (output)

See the description for WR.

* Z (output)

If JOBZ = 'V', Z contains the orthogonal 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) contains the optimal LDWORK.

* LDWORK (input)

The dimension of the array WORK. LDWORK >= max(1,3*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.

* WORK3 (workspace)

Not referenced if SORTEV = 'N'.

* INFO (output)