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

```
DGEEV(3F)							     DGEEV(3F)

```

### NAME[Toc][Back]

```     DGEEV - compute for an N-by-N real	nonsymmetric matrix A, the eigenvalues
and, optionally, the left and/or right eigenvectors
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DGEEV( JOBVL, JOBVR, N,	A, LDA,	WR, WI,	VL, LDVL, VR, LDVR,
WORK, LWORK, INFO )

CHARACTER     JOBVL, JOBVR

INTEGER       INFO, LDA, LDVL,	LDVR, LWORK, N

DOUBLE	       PRECISION A( LDA, * ), VL( LDVL,	* ), VR( LDVR, * ),
WI( * ),	WORK( *	), WR( * )
```

### PURPOSE[Toc][Back]

```     DGEEV computes for	an N-by-N real nonsymmetric matrix A, the eigenvalues
and, optionally, the left and/or right eigenvectors.

The right eigenvector v(j)	of A satisfies
A	* v(j) = lambda(j) * v(j)
where lambda(j) is	its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).

The computed eigenvectors are normalized to have Euclidean	norm equal to
1 and largest component real.

```

### ARGUMENTS[Toc][Back]

```     JOBVL   (input) CHARACTER*1
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of A are computed.

JOBVR   (input) CHARACTER*1
= 'N': right eigenvectors of A are	not computed;
= 'V': right eigenvectors of A are	computed.

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

A	     (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On	entry, the N-by-N matrix A.  On	exit, A	has been overwritten.

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

WR	     (output) DOUBLE PRECISION array, dimension	(N)
WI	     (output) DOUBLE PRECISION array, dimension	(N) WR and WI
contain the real and imaginary parts, respectively, of the
computed eigenvalues.  Complex conjugate pairs of eigenvalues

Page 1

DGEEV(3F)							     DGEEV(3F)

appear consecutively with the eigenvalue having the positive
imaginary part first.

VL	     (output) DOUBLE PRECISION array, dimension	(LDVL,N)
If	JOBVL =	'V', the left eigenvectors u(j)	are stored one after
another in	the columns of VL, in the same order as	their
eigenvalues.  If JOBVL = 'N', VL is not referenced.  If the j-th
eigenvalue	is real, then u(j) = VL(:,j), the j-th column of VL.
If	the j-th and (j+1)-st eigenvalues form a complex conjugate
pair, then	u(j) = VL(:,j) + i*VL(:,j+1) and
u(j+1) = VL(:,j) -	i*VL(:,j+1).

LDVL    (input) INTEGER
The leading dimension of the array	VL.  LDVL >= 1;	if JOBVL =
'V', LDVL >= N.

VR	     (output) DOUBLE PRECISION array, dimension	(LDVR,N)
If	JOBVR =	'V', the right eigenvectors v(j) are stored one	after
another in	the columns of VR, in the same order as	their
eigenvalues.  If JOBVR = 'N', VR is not referenced.  If the j-th
eigenvalue	is real, then v(j) = VR(:,j), the j-th column of VR.
If	the j-th and (j+1)-st eigenvalues form a complex conjugate
pair, then	v(j) = VR(:,j) + i*VR(:,j+1) and
v(j+1) = VR(:,j) -	i*VR(:,j+1).

LDVR    (input) INTEGER
The leading dimension of the array	VR.  LDVR >= 1;	if JOBVR =
'V', LDVR >= N.

WORK    (workspace/output)	DOUBLE PRECISION 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(1,3*N), and	if
JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*N.	For good performance,
LWORK must	generally be larger.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  if INFO = i,	the QR algorithm failed	to compute all the
eigenvalues, and no eigenvectors have been	computed; elements
i+1:N of WR and WI	contain	eigenvalues which have converged.
DGEEV(3F)							     DGEEV(3F)

```

### NAME[Toc][Back]

```     DGEEV - compute for an N-by-N real	nonsymmetric matrix A, the eigenvalues
and, optionally, the left and/or right eigenvectors
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DGEEV( JOBVL, JOBVR, N,	A, LDA,	WR, WI,	VL, LDVL, VR, LDVR,
WORK, LWORK, INFO )

CHARACTER     JOBVL, JOBVR

INTEGER       INFO, LDA, LDVL,	LDVR, LWORK, N

DOUBLE	       PRECISION A( LDA, * ), VL( LDVL,	* ), VR( LDVR, * ),
WI( * ),	WORK( *	), WR( * )
```

### PURPOSE[Toc][Back]

```     DGEEV computes for	an N-by-N real nonsymmetric matrix A, the eigenvalues
and, optionally, the left and/or right eigenvectors.

The right eigenvector v(j)	of A satisfies
A	* v(j) = lambda(j) * v(j)
where lambda(j) is	its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).

The computed eigenvectors are normalized to have Euclidean	norm equal to
1 and largest component real.

```

### ARGUMENTS[Toc][Back]

```     JOBVL   (input) CHARACTER*1
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of A are computed.

JOBVR   (input) CHARACTER*1
= 'N': right eigenvectors of A are	not computed;
= 'V': right eigenvectors of A are	computed.

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

A	     (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On	entry, the N-by-N matrix A.  On	exit, A	has been overwritten.

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

WR	     (output) DOUBLE PRECISION array, dimension	(N)
WI	     (output) DOUBLE PRECISION array, dimension	(N) WR and WI
contain the real and imaginary parts, respectively, of the
computed eigenvalues.  Complex conjugate pairs of eigenvalues

Page 1

DGEEV(3F)							     DGEEV(3F)

appear consecutively with the eigenvalue having the positive
imaginary part first.

VL	     (output) DOUBLE PRECISION array, dimension	(LDVL,N)
If	JOBVL =	'V', the left eigenvectors u(j)	are stored one after
another in	the columns of VL, in the same order as	their
eigenvalues.  If JOBVL = 'N', VL is not referenced.  If the j-th
eigenvalue	is real, then u(j) = VL(:,j), the j-th column of VL.
If	the j-th and (j+1)-st eigenvalues form a complex conjugate
pair, then	u(j) = VL(:,j) + i*VL(:,j+1) and
u(j+1) = VL(:,j) -	i*VL(:,j+1).

LDVL    (input) INTEGER
The leading dimension of the array	VL.  LDVL >= 1;	if JOBVL =
'V', LDVL >= N.

VR	     (output) DOUBLE PRECISION array, dimension	(LDVR,N)
If	JOBVR =	'V', the right eigenvectors v(j) are stored one	after
another in	the columns of VR, in the same order as	their
eigenvalues.  If JOBVR = 'N', VR is not referenced.  If the j-th
eigenvalue	is real, then v(j) = VR(:,j), the j-th column of VR.
If	the j-th and (j+1)-st eigenvalues form a complex conjugate
pair, then	v(j) = VR(:,j) + i*VR(:,j+1) and
v(j+1) = VR(:,j) -	i*VR(:,j+1).

LDVR    (input) INTEGER
The leading dimension of the array	VR.  LDVR >= 1;	if JOBVR =
'V', LDVR >= N.

WORK    (workspace/output)	DOUBLE PRECISION 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(1,3*N), and	if
JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*N.	For good performance,
LWORK must	generally be larger.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  if INFO = i,	the QR algorithm failed	to compute all the
eigenvalues, and no eigenvectors have been	computed; elements
i+1:N of WR and WI	contain	eigenvalues which have converged.

PPPPaaaaggggeeee 2222```
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