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

```
STREVC(3F)							    STREVC(3F)

```

### NAME[Toc][Back]

```     STREVC - compute some or all of the right and/or left eigenvectors	of a
real upper	quasi-triangular matrix	T
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	STREVC(	SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR,
MM, M, WORK, INFO )

CHARACTER	HOWMNY,	SIDE

INTEGER	INFO, LDT, LDVL, LDVR, M, MM, N

LOGICAL	SELECT(	* )

REAL		T( LDT,	* ), VL( LDVL, * ), VR(	LDVR, *	), WORK( * )
```

### PURPOSE[Toc][Back]

```     STREVC computes some or all of the	right and/or left eigenvectors of a
real upper	quasi-triangular matrix	T.

The right eigenvector x and the left eigenvector y	of T corresponding to
an	eigenvalue w are defined by:

T*x =	w*x,	 y'*T =	w*y'

where y' denotes the conjugate transpose of the vector y.

If	all eigenvectors are requested,	the routine may	either return the
matrices X	and/or Y of right or left eigenvectors of T, or	the products
Q*X and/or	Q*Y, where Q is	an input orthogonal
matrix. If	T was obtained from the	real-Schur factorization of an
original matrix A = Q*T*Q', then Q*X and Q*Y are the matrices of right or
left eigenvectors of A.

T must be in Schur	canonical form (as returned by SHSEQR),	that is, block
upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2
diagonal block has	its diagonal elements equal and	its off-diagonal
elements of opposite sign.	 Corresponding to each 2-by-2 diagonal block
is	a complex conjugate pair of eigenvalues	and eigenvectors; only one
eigenvector of the	pair is	computed, namely the one corresponding to the
eigenvalue	with positive imaginary	part.

```

### ARGUMENTS[Toc][Back]

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

Page 1

STREVC(3F)							    STREVC(3F)

HOWMNY  (input) CHARACTER*1
= 'A':  compute all right and/or left eigenvectors;
= 'B':  compute all right and/or left eigenvectors, and
backtransform them	using the input	matrices supplied in VR	and/or
VL; = 'S':	 compute selected right	and/or left eigenvectors,
specified by the logical array SELECT.

SELECT  (input/output) LOGICAL array, dimension (N)
If	HOWMNY = 'S', SELECT specifies the eigenvectors	to be
computed.	If HOWMNY = 'A'	or 'B',	SELECT is not referenced.  To
select the	real eigenvector corresponding to a real eigenvalue
w(j), SELECT(j) must be set to .TRUE..  To	select the complex
eigenvector corresponding to a complex conjugate pair w(j)	and
w(j+1), either SELECT(j) or SELECT(j+1) must be set to .TRUE.;
then on exit SELECT(j) is .TRUE. and SELECT(j+1) is .FALSE..

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

T	     (input) REAL array, dimension (LDT,N)
The upper quasi-triangular	matrix T in Schur canonical form.

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

VL	     (input/output) REAL 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 orthogonal	matrix Q of Schur
vectors returned by SHSEQR).  On exit, if SIDE = 'L' or 'B', VL
contains:	if HOWMNY = 'A', the matrix Y of left eigenvectors of
T;	if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left
eigenvectors of T specified by SELECT, stored consecutively in
the columns of VL,	in the same order as their eigenvalues.	 A
complex eigenvector corresponding to a complex eigenvalue is
stored in two consecutive columns,	the first holding the real
part, and the second the imaginary	part.  If SIDE = 'R', VL is
not referenced.

LDVL    (input) INTEGER
The leading dimension of the array	VL.  LDVL >= max(1,N) if SIDE
= 'L' or 'B'; LDVL	>= 1 otherwise.

VR	     (input/output) REAL 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 orthogonal	matrix Q of Schur
vectors returned by SHSEQR).  On exit, if SIDE = 'R' or 'B', VR
contains:	if HOWMNY = 'A', the matrix X of right eigenvectors of
T;	if HOWMNY = 'B', the matrix Q*X; if HOWMNY = 'S', the right
eigenvectors of T specified by SELECT, stored consecutively in
the columns of VR,	in the same order as their eigenvalues.	 A
complex eigenvector corresponding to a complex eigenvalue is
stored in two consecutive columns,	the first holding the real

Page 2

STREVC(3F)							    STREVC(3F)

part and the second the imaginary part.  If SIDE =	'L', VR	is not
referenced.

LDVR    (input) INTEGER
The leading dimension of the array	VR.  LDVR >= max(1,N) if SIDE
= 'R' or 'B'; LDVR	>= 1 otherwise.

MM	     (input) INTEGER
The number	of columns in the arrays VL and/or VR. MM >= M.

M	     (output) 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 real	eigenvector occupies one column	and each
selected complex eigenvector occupies two columns.

WORK    (workspace) REAL array, dimension (3*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER	DETAILS
The algorithm used	in this	program	is basically backward (forward)
substitution, with	scaling	to make	the the	code robust against possible
overflow.

Each eigenvector is normalized so that the	element	of largest magnitude
has magnitude 1; here the magnitude of a complex number (x,y) is taken to
be	|x| + |y|.
STREVC(3F)							    STREVC(3F)

```

### NAME[Toc][Back]

```     STREVC - compute some or all of the right and/or left eigenvectors	of a
real upper	quasi-triangular matrix	T
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	STREVC(	SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR,
MM, M, WORK, INFO )

CHARACTER	HOWMNY,	SIDE

INTEGER	INFO, LDT, LDVL, LDVR, M, MM, N

LOGICAL	SELECT(	* )

REAL		T( LDT,	* ), VL( LDVL, * ), VR(	LDVR, *	), WORK( * )
```

### PURPOSE[Toc][Back]

```     STREVC computes some or all of the	right and/or left eigenvectors of a
real upper	quasi-triangular matrix	T.

The right eigenvector x and the left eigenvector y	of T corresponding to
an	eigenvalue w are defined by:

T*x =	w*x,	 y'*T =	w*y'

where y' denotes the conjugate transpose of the vector y.

If	all eigenvectors are requested,	the routine may	either return the
matrices X	and/or Y of right or left eigenvectors of T, or	the products
Q*X and/or	Q*Y, where Q is	an input orthogonal
matrix. If	T was obtained from the	real-Schur factorization of an
original matrix A = Q*T*Q', then Q*X and Q*Y are the matrices of right or
left eigenvectors of A.

T must be in Schur	canonical form (as returned by SHSEQR),	that is, block
upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2
diagonal block has	its diagonal elements equal and	its off-diagonal
elements of opposite sign.	 Corresponding to each 2-by-2 diagonal block
is	a complex conjugate pair of eigenvalues	and eigenvectors; only one
eigenvector of the	pair is	computed, namely the one corresponding to the
eigenvalue	with positive imaginary	part.

```

### ARGUMENTS[Toc][Back]

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

Page 1

STREVC(3F)							    STREVC(3F)

HOWMNY  (input) CHARACTER*1
= 'A':  compute all right and/or left eigenvectors;
= 'B':  compute all right and/or left eigenvectors, and
backtransform them	using the input	matrices supplied in VR	and/or
VL; = 'S':	 compute selected right	and/or left eigenvectors,
specified by the logical array SELECT.

SELECT  (input/output) LOGICAL array, dimension (N)
If	HOWMNY = 'S', SELECT specifies the eigenvectors	to be
computed.	If HOWMNY = 'A'	or 'B',	SELECT is not referenced.  To
select the	real eigenvector corresponding to a real eigenvalue
w(j), SELECT(j) must be set to .TRUE..  To	select the complex
eigenvector corresponding to a complex conjugate pair w(j)	and
w(j+1), either SELECT(j) or SELECT(j+1) must be set to .TRUE.;
then on exit SELECT(j) is .TRUE. and SELECT(j+1) is .FALSE..

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

T	     (input) REAL array, dimension (LDT,N)
The upper quasi-triangular	matrix T in Schur canonical form.

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

VL	     (input/output) REAL 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 orthogonal	matrix Q of Schur
vectors returned by SHSEQR).  On exit, if SIDE = 'L' or 'B', VL
contains:	if HOWMNY = 'A', the matrix Y of left eigenvectors of
T;	if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left
eigenvectors of T specified by SELECT, stored consecutively in
the columns of VL,	in the same order as their eigenvalues.	 A
complex eigenvector corresponding to a complex eigenvalue is
stored in two consecutive columns,	the first holding the real
part, and the second the imaginary	part.  If SIDE = 'R', VL is
not referenced.

LDVL    (input) INTEGER
The leading dimension of the array	VL.  LDVL >= max(1,N) if SIDE
= 'L' or 'B'; LDVL	>= 1 otherwise.

VR	     (input/output) REAL 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 orthogonal	matrix Q of Schur
vectors returned by SHSEQR).  On exit, if SIDE = 'R' or 'B', VR
contains:	if HOWMNY = 'A', the matrix X of right eigenvectors of
T;	if HOWMNY = 'B', the matrix Q*X; if HOWMNY = 'S', the right
eigenvectors of T specified by SELECT, stored consecutively in
the columns of VR,	in the same order as their eigenvalues.	 A
complex eigenvector corresponding to a complex eigenvalue is
stored in two consecutive columns,	the first holding the real

Page 2

STREVC(3F)							    STREVC(3F)

part and the second the imaginary part.  If SIDE =	'L', VR	is not
referenced.

LDVR    (input) INTEGER
The leading dimension of the array	VR.  LDVR >= max(1,N) if SIDE
= 'R' or 'B'; LDVR	>= 1 otherwise.

MM	     (input) INTEGER
The number	of columns in the arrays VL and/or VR. MM >= M.

M	     (output) 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 real	eigenvector occupies one column	and each
selected complex eigenvector occupies two columns.

WORK    (workspace) REAL array, dimension (3*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER	DETAILS
The algorithm used	in this	program	is basically backward (forward)
substitution, with	scaling	to make	the the	code robust against possible
overflow.

Each eigenvector is normalized so that the	element	of largest magnitude
has magnitude 1; here the magnitude of a complex number (x,y) is taken to
be	|x| + |y|.

PPPPaaaaggggeeee 3333```
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