sgees
sgees - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z
SUBROUTINE SGEES( 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(*)
REAL A(LDA,*), WR(*), WI(*), Z(LDZ,*), WORK(*)
SUBROUTINE SGEES_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(*)
REAL A(LDA,*), WR(*), WI(*), Z(LDZ,*), WORK(*)
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, DIMENSION(:) :: WR, WI, WORK
REAL, 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, DIMENSION(:) :: WR, WI, WORK
REAL, DIMENSION(:,:) :: A, Z
#include <sunperf.h>
void sgees(char jobz, char sortev, logical(*select)(float,float), int n, float *a, int lda, int *nout, float *wr, float *wi, float *z, int ldz, int *info);
void sgees_64(char jobz, char sortev, logical(*select)(float,float), long n, float *a, long lda, long *nout, float *wr, float *wi, float *z, long ldz, long *info);
sgees computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues, the real Schur form T, and, optionally, the matrix of
Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T).
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).
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* JOBZ (input)
-
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* SORTEV (input)
-
Specifies whether or not to order the eigenvalues on the
diagonal of the Schur form.
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* SELECT (input)
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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).
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* N (input)
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The order of the matrix A. N >= 0.
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* A (input/output)
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On entry, the N-by-N matrix A.
On exit, A has been overwritten by its real Schur form T.
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* LDA (input)
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The leading dimension of the array A. LDA >= max(1,N).
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* NOUT (output)
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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.)
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* WR (output)
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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.
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* WI (output)
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See the description for WR.
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* Z (output)
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If JOBZ = 'V', Z contains the orthogonal matrix Z of Schur
vectors.
If JOBZ = 'N', Z is not referenced.
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* LDZ (input)
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The leading dimension of the array Z. LDZ >= 1; if
JOBZ = 'V', LDZ >= N.
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* WORK (workspace)
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On exit, if INFO = 0, WORK(1) contains the optimal LDWORK.
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* LDWORK (input)
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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.
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* WORK3 (workspace)
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Not referenced if SORTEV = 'N'.
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* INFO (output)
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