# zggev.f man page

zggev.f —

## Synopsis

### Functions/Subroutines

subroutinezggev(JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)ZGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

## Function/Subroutine Documentation

### subroutine zggev (characterJOBVL, characterJOBVR, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( * )ALPHA, complex*16, dimension( * )BETA, complex*16, dimension( ldvl, * )VL, integerLDVL, complex*16, dimension( ldvr, * )VR, integerLDVR, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)

**ZGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices**

**Purpose:**

```
ZGGEV computes for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, and optionally, the left and/or
right generalized eigenvectors.
A generalized eigenvalue for a pair of matrices (A,B) is a scalar
lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
singular. It is usually represented as the pair (alpha,beta), as
there is a reasonable interpretation for beta=0, and even for both
being zero.
The right generalized eigenvector v(j) corresponding to the
generalized eigenvalue lambda(j) of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j).
The left generalized eigenvector u(j) corresponding to the
generalized eigenvalues lambda(j) of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B
where u(j)**H is the conjugate-transpose of u(j).
```

**Parameters:**

*JOBVL*

```
JOBVL is CHARACTER*1
= 'N': do not compute the left generalized eigenvectors;
= 'V': compute the left generalized eigenvectors.
```

*JOBVR*

```
JOBVR is CHARACTER*1
= 'N': do not compute the right generalized eigenvectors;
= 'V': compute the right generalized eigenvectors.
```

*N*

```
N is INTEGER
The order of the matrices A, B, VL, and VR. N >= 0.
```

*A*

```
A is COMPLEX*16 array, dimension (LDA, N)
On entry, the matrix A in the pair (A,B).
On exit, A has been overwritten.
```

*LDA*

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

*B*

```
B is COMPLEX*16 array, dimension (LDB, N)
On entry, the matrix B in the pair (A,B).
On exit, B has been overwritten.
```

*LDB*

```
LDB is INTEGER
The leading dimension of B. LDB >= max(1,N).
```

*ALPHA*

`ALPHA is COMPLEX*16 array, dimension (N)`

*BETA*

```
BETA is COMPLEX*16 array, dimension (N)
On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
generalized eigenvalues.
Note: the quotients ALPHA(j)/BETA(j) may easily over- or
underflow, and BETA(j) may even be zero. Thus, the user
should avoid naively computing the ratio alpha/beta.
However, ALPHA will be always less than and usually
comparable with norm(A) in magnitude, and BETA always less
than and usually comparable with norm(B).
```

*VL*

```
VL is COMPLEX*16 array, dimension (LDVL,N)
If JOBVL = 'V', the left generalized eigenvectors u(j) are
stored one after another in the columns of VL, in the same
order as their eigenvalues.
Each eigenvector is scaled so the largest component has
abs(real part) + abs(imag. part) = 1.
Not referenced if JOBVL = 'N'.
```

*LDVL*

```
LDVL is INTEGER
The leading dimension of the matrix VL. LDVL >= 1, and
if JOBVL = 'V', LDVL >= N.
```

*VR*

```
VR is COMPLEX*16 array, dimension (LDVR,N)
If JOBVR = 'V', the right generalized eigenvectors v(j) are
stored one after another in the columns of VR, in the same
order as their eigenvalues.
Each eigenvector is scaled so the largest component has
abs(real part) + abs(imag. part) = 1.
Not referenced if JOBVR = 'N'.
```

*LDVR*

```
LDVR is INTEGER
The leading dimension of the matrix VR. LDVR >= 1, and
if JOBVR = 'V', LDVR >= 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 (8*N)`

*INFO*

```
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
=1,...,N:
The QZ iteration failed. No eigenvectors have been
calculated, but ALPHA(j) and BETA(j) should be
correct for j=INFO+1,...,N.
> N: =N+1: other then QZ iteration failed in DHGEQZ,
=N+2: error return from DTGEVC.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

April 2012

Definition at line 217 of file zggev.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK