# cggev3.f man page

cggev3.f

## Synopsis

### Functions/Subroutines

subroutine cggev3 (JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
CGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm)

## Function/Subroutine Documentation

### subroutine cggev3 (character JOBVL, character JOBVR, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( * ) ALPHA, complex, dimension( * ) BETA, complex, dimension( ldvl, * ) VL, integer LDVL, complex, dimension( ldvr, * ) VR, integer LDVR, complex, dimension( * ) WORK, integer LWORK, real, dimension( * ) RWORK, integer INFO)

CGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm)

Purpose:

``` CGGEV3 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 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 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 array, dimension (N)`

BETA

```          BETA is COMPLEX 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 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 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 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.

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 REAL 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 SHGEQZ,
=N+2: error return from STGEVC.```
Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

January 2015

Definition at line 218 of file cggev3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cggev3(3) is an alias of cggev3.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK