# ztgevc.f (3) - Linux Manuals

ztgevc.f -

## SYNOPSIS

### Functions/Subroutines

subroutine ztgevc (SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO)
ZTGEVC

## Function/Subroutine Documentation

### subroutine ztgevc (characterSIDE, characterHOWMNY, logical, dimension( * )SELECT, integerN, complex*16, dimension( lds, * )S, integerLDS, complex*16, dimension( ldp, * )P, integerLDP, complex*16, dimension( ldvl, * )VL, integerLDVL, complex*16, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)

ZTGEVC

Purpose:

``` ZTGEVC computes some or all of the right and/or left eigenvectors of
a pair of complex matrices (S,P), where S and P are upper triangular.
Matrix pairs of this type are produced by the generalized Schur
factorization of a complex matrix pair (A,B):

A = Q*S*Z**H,  B = Q*P*Z**H

as computed by ZGGHRD + ZHGEQZ.

The right eigenvector x and the left eigenvector y of (S,P)
corresponding to an eigenvalue w are defined by:

S*x = w*P*x,  (y**H)*S = w*(y**H)*P,

where y**H denotes the conjugate tranpose of y.
The eigenvalues are not input to this routine, but are computed
directly from the diagonal elements of S and P.

This routine returns the matrices X and/or Y of right and left
eigenvectors of (S,P), or the products Z*X and/or Q*Y,
where Z and Q are input matrices.
If Q and Z are the unitary factors from the generalized Schur
factorization of a matrix pair (A,B), then Z*X and Q*Y
are the matrices of right and left eigenvectors of (A,B).
```

Parameters:

SIDE

```          SIDE is CHARACTER*1
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
```

HOWMNY

```          HOWMNY is CHARACTER*1
= 'A': compute all right and/or left eigenvectors;
= 'B': compute all right and/or left eigenvectors,
backtransformed by the matrices in VR and/or VL;
= 'S': compute selected right and/or left eigenvectors,
specified by the logical array SELECT.
```

SELECT

```          SELECT is LOGICAL array, dimension (N)
If HOWMNY='S', SELECT specifies the eigenvectors to be
computed.  The eigenvector corresponding to the j-th
eigenvalue is computed if SELECT(j) = .TRUE..
Not referenced if HOWMNY = 'A' or 'B'.
```

N

```          N is INTEGER
The order of the matrices S and P.  N >= 0.
```

S

```          S is COMPLEX*16 array, dimension (LDS,N)
The upper triangular matrix S from a generalized Schur
factorization, as computed by ZHGEQZ.
```

LDS

```          LDS is INTEGER
The leading dimension of array S.  LDS >= max(1,N).
```

P

```          P is COMPLEX*16 array, dimension (LDP,N)
The upper triangular matrix P from a generalized Schur
factorization, as computed by ZHGEQZ.  P must have real
diagonal elements.
```

LDP

```          LDP is INTEGER
The leading dimension of array P.  LDP >= max(1,N).
```

VL

```          VL is COMPLEX*16 array, dimension (LDVL,MM)
On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
contain an N-by-N matrix Q (usually the unitary matrix Q
of left Schur vectors returned by ZHGEQZ).
On exit, if SIDE = 'L' or 'B', VL contains:
if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);
if HOWMNY = 'B', the matrix Q*Y;
if HOWMNY = 'S', the left eigenvectors of (S,P) specified by
SELECT, stored consecutively in the columns of
VL, in the same order as their eigenvalues.
Not referenced if SIDE = 'R'.
```

LDVL

```          LDVL is INTEGER
The leading dimension of array VL.  LDVL >= 1, and if
SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N.
```

VR

```          VR is COMPLEX*16 array, dimension (LDVR,MM)
On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
contain an N-by-N matrix Q (usually the unitary matrix Z
of right Schur vectors returned by ZHGEQZ).
On exit, if SIDE = 'R' or 'B', VR contains:
if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);
if HOWMNY = 'B', the matrix Z*X;
if HOWMNY = 'S', the right eigenvectors of (S,P) specified by
SELECT, stored consecutively in the columns of
VR, in the same order as their eigenvalues.
Not referenced if SIDE = 'L'.
```

LDVR

```          LDVR is INTEGER
The leading dimension of the array VR.  LDVR >= 1, and if
SIDE = 'R' or 'B', LDVR >= N.
```

MM

```          MM is INTEGER
The number of columns in the arrays VL and/or VR. MM >= M.
```

M

```          M is INTEGER
The number of columns in the arrays VL and/or VR actually
used to store the eigenvectors.  If HOWMNY = 'A' or 'B', M
is set to N.  Each selected eigenvector occupies one column.
```

WORK

```          WORK is COMPLEX*16 array, dimension (2*N)
```

RWORK

```          RWORK is DOUBLE PRECISION array, dimension (2*N)
```

INFO

```          INFO is INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 219 of file ztgevc.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.