# zgees.f man page

zgees.f —

## Synopsis

### Functions/Subroutines

subroutinezgees(JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS, LDVS, WORK, LWORK, RWORK, BWORK, INFO)ZGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices

## Function/Subroutine Documentation

### subroutine zgees (characterJOBVS, characterSORT, logical, externalSELECT, integerN, complex*16, dimension( lda, * )A, integerLDA, integerSDIM, complex*16, dimension( * )W, complex*16, dimension( ldvs, * )VS, integerLDVS, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, logical, dimension( * )BWORK, integerINFO)

**ZGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices**

**Purpose:**

```
ZGEES 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.
```

**Parameters:**

*JOBVS*

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

*SORT*

```
SORT is 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*

```
SELECT is a 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.
The eigenvalue W(j) is selected if SELECT(W(j)) is true.
```

*N*

```
N is INTEGER
The order of the matrix A. N >= 0.
```

*A*

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

*LDA*

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

*SDIM*

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

*W*

```
W is 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*

```
VS is 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*

```
LDVS is INTEGER
The leading dimension of the array VS. LDVS >= 1; if
JOBVS = 'V', LDVS >= N.
```

*WORK*

```
WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
```

*LWORK*

```
LWORK is INTEGER
The dimension of the array WORK. LWORK >= max(1,2*N).
For good performance, LWORK must generally be larger.
If LWORK = -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 LWORK is issued by XERBLA.
```

*RWORK*

`RWORK is DOUBLE PRECISION array, dimension (N)`

*BWORK*

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

*INFO*

```
INFO is 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 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.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 197 of file zgees.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zgees(3) is an alias of zgees.f(3).