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man pages->IRIX man pages -> complib/zgeesx (3)
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### Contents

```
ZGEESX(3F)							    ZGEESX(3F)

```

### NAME[Toc][Back]

```     ZGEESX - 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[Toc][Back]

```     SUBROUTINE	ZGEESX(	JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,	VS,
LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK, BWORK, INFO
)

CHARACTER	JOBVS, SENSE, SORT

INTEGER	INFO, LDA, LDVS, LWORK,	N, SDIM

DOUBLE		PRECISION RCONDE, RCONDV

LOGICAL	BWORK( * )

DOUBLE		PRECISION RWORK( * )

COMPLEX*16	A( LDA,	* ), VS( LDVS, * ), W( * ), WORK( * )

LOGICAL	SELECT

EXTERNAL	SELECT
```

### PURPOSE[Toc][Back]

```     ZGEESX 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; 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 4.10 of the LAPACK Users' Guide (where	these
quantities	are called s and sep respectively).

A complex matrix is in Schur form if it is	upper triangular.

```

### ARGUMENTS[Toc][Back]

```     JOBVS   (input) CHARACTER*1
= 'N': Schur vectors are not computed;
= 'V': Schur vectors are computed.

Page 1

ZGEESX(3F)							    ZGEESX(3F)

SORT    (input) CHARACTER*1
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) LOGICAL FUNCTION of one COMPLEX*16	argument
SELECT must be declared EXTERNAL in the calling subroutine.  If
SORT = 'S', SELECT	is used	to select eigenvalues to order to the
top left of the Schur form.  If SORT = 'N', SELECT	is not
referenced.  An eigenvalue	W(j) is	selected if SELECT(W(j)) is
true.

SENSE   (input) CHARACTER*1
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'.

N	     (input) INTEGER
The order of the matrix A.	N >= 0.

A	     (input/output) COMPLEX*16 array, dimension	(LDA, N)
On	entry, the N-by-N matrix A.  On	exit, A	is overwritten by its
Schur form	T.

LDA     (input) INTEGER
The leading dimension of the array	A.  LDA	>= max(1,N).

SDIM    (output) INTEGER
If	SORT = 'N', SDIM = 0.  If SORT = 'S', SDIM = number of
eigenvalues for which SELECT is true.

W	     (output) COMPLEX*16 array,	dimension (N)
W contains	the computed eigenvalues, in the same order that they
appear on the diagonal of the output Schur	form T.

VS	     (output) COMPLEX*16 array,	dimension (LDVS,N)
If	JOBVS =	'V', VS	contains the unitary matrix Z of Schur
vectors.  If JOBVS	= 'N', VS is not referenced.

LDVS    (input) INTEGER
The leading dimension of the array	VS.  LDVS >= 1,	and if JOBVS =
'V', LDVS >= N.

RCONDE  (output) DOUBLE PRECISION
If	SENSE =	'E' or 'B', RCONDE contains the	reciprocal condition
number for	the average of the selected eigenvalues.  Not
referenced	if SENSE = 'N' or 'V'.

Page 2

ZGEESX(3F)							    ZGEESX(3F)

RCONDV  (output) DOUBLE PRECISION
If	SENSE =	'V' or 'B', RCONDV contains the	reciprocal condition
number for	the selected right invariant subspace.	Not referenced
if	SENSE =	'N' or 'E'.

WORK    (workspace/output)	COMPLEX*16 array, dimension (LWORK)
On	exit, if INFO =	0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array	WORK.  LWORK >=	max(1,2*N).  Also, if
SENSE = 'E' or 'V'	or 'B',	LWORK >= 2*SDIM*(N-SDIM), where	SDIM
is	the number of selected eigenvalues computed by this routine.
Note that 2*SDIM*(N-SDIM) <= N*N/2.  For good performance,	LWORK
must generally be larger.

RWORK   (workspace) DOUBLE	PRECISION array, dimension (N)

BWORK   (workspace) LOGICAL array,	dimension (N)
Not referenced if SORT = 'N'.

INFO    (output) INTEGER
= 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 JOBVS	= 'V', VS contains the
transformation 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 illconditioned);
= 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.
ZGEESX(3F)							    ZGEESX(3F)

```

### NAME[Toc][Back]

```     ZGEESX - 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[Toc][Back]

```     SUBROUTINE	ZGEESX(	JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,	VS,
LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK, BWORK, INFO
)

CHARACTER	JOBVS, SENSE, SORT

INTEGER	INFO, LDA, LDVS, LWORK,	N, SDIM

DOUBLE		PRECISION RCONDE, RCONDV

LOGICAL	BWORK( * )

DOUBLE		PRECISION RWORK( * )

COMPLEX*16	A( LDA,	* ), VS( LDVS, * ), W( * ), WORK( * )

LOGICAL	SELECT

EXTERNAL	SELECT
```

### PURPOSE[Toc][Back]

```     ZGEESX 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; 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 4.10 of the LAPACK Users' Guide (where	these
quantities	are called s and sep respectively).

A complex matrix is in Schur form if it is	upper triangular.

```

### ARGUMENTS[Toc][Back]

```     JOBVS   (input) CHARACTER*1
= 'N': Schur vectors are not computed;
= 'V': Schur vectors are computed.

Page 1

ZGEESX(3F)							    ZGEESX(3F)

SORT    (input) CHARACTER*1
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) LOGICAL FUNCTION of one COMPLEX*16	argument
SELECT must be declared EXTERNAL in the calling subroutine.  If
SORT = 'S', SELECT	is used	to select eigenvalues to order to the
top left of the Schur form.  If SORT = 'N', SELECT	is not
referenced.  An eigenvalue	W(j) is	selected if SELECT(W(j)) is
true.

SENSE   (input) CHARACTER*1
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'.

N	     (input) INTEGER
The order of the matrix A.	N >= 0.

A	     (input/output) COMPLEX*16 array, dimension	(LDA, N)
On	entry, the N-by-N matrix A.  On	exit, A	is overwritten by its
Schur form	T.

LDA     (input) INTEGER
The leading dimension of the array	A.  LDA	>= max(1,N).

SDIM    (output) INTEGER
If	SORT = 'N', SDIM = 0.  If SORT = 'S', SDIM = number of
eigenvalues for which SELECT is true.

W	     (output) COMPLEX*16 array,	dimension (N)
W contains	the computed eigenvalues, in the same order that they
appear on the diagonal of the output Schur	form T.

VS	     (output) COMPLEX*16 array,	dimension (LDVS,N)
If	JOBVS =	'V', VS	contains the unitary matrix Z of Schur
vectors.  If JOBVS	= 'N', VS is not referenced.

LDVS    (input) INTEGER
The leading dimension of the array	VS.  LDVS >= 1,	and if JOBVS =
'V', LDVS >= N.

RCONDE  (output) DOUBLE PRECISION
If	SENSE =	'E' or 'B', RCONDE contains the	reciprocal condition
number for	the average of the selected eigenvalues.  Not
referenced	if SENSE = 'N' or 'V'.

Page 2

ZGEESX(3F)							    ZGEESX(3F)

RCONDV  (output) DOUBLE PRECISION
If	SENSE =	'V' or 'B', RCONDV contains the	reciprocal condition
number for	the selected right invariant subspace.	Not referenced
if	SENSE =	'N' or 'E'.

WORK    (workspace/output)	COMPLEX*16 array, dimension (LWORK)
On	exit, if INFO =	0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array	WORK.  LWORK >=	max(1,2*N).  Also, if
SENSE = 'E' or 'V'	or 'B',	LWORK >= 2*SDIM*(N-SDIM), where	SDIM
is	the number of selected eigenvalues computed by this routine.
Note that 2*SDIM*(N-SDIM) <= N*N/2.  For good performance,	LWORK
must generally be larger.

RWORK   (workspace) DOUBLE	PRECISION array, dimension (N)

BWORK   (workspace) LOGICAL array,	dimension (N)
Not referenced if SORT = 'N'.

INFO    (output) INTEGER
= 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 JOBVS	= 'V', VS contains the
transformation 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 illconditioned);
= 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.

PPPPaaaaggggeeee 3333```
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