·  Home
+   man pages
 -> Linux -> FreeBSD -> OpenBSD -> NetBSD -> Tru64 Unix -> HP-UX 11i -> IRIX
·  Linux HOWTOs
·  FreeBSD Tips
·  *niX Forums

man pages->IRIX man pages -> complib/zstedc (3)
 Title
 Content
 Arch
 Section All Sections 1 - General Commands 2 - System Calls 3 - Subroutines 4 - Special Files 5 - File Formats 6 - Games 7 - Macros and Conventions 8 - Maintenance Commands 9 - Kernel Interface n - New Commands

Contents

```
ZSTEDC(3F)							    ZSTEDC(3F)

```

NAME[Toc][Back]

```     ZSTEDC - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using	the divide and conquer method
```

SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZSTEDC(	COMPZ, N, D, E,	Z, LDZ,	WORK, LWORK, RWORK, LRWORK,
IWORK, LIWORK, INFO )

CHARACTER	COMPZ

INTEGER	INFO, LDZ, LIWORK, LRWORK, LWORK, N

INTEGER	IWORK( * )

DOUBLE		PRECISION D( * ), E( * ), RWORK( * )

COMPLEX*16	WORK( *	), Z( LDZ, * )
```

PURPOSE[Toc][Back]

```     ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using	the divide and conquer method.	The
eigenvectors of a full or band complex Hermitian matrix can also be found
if	ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this	matrix to
tridiagonal form.

This code makes very mild assumptions about floating point	arithmetic. It
will work on machines with	a guard	digit in add/subtract, or on those
binary machines without guard digits which	subtract like the Cray X-MP,
Cray Y-MP,	Cray C-90, or Cray-2.  It could	conceivably fail on
hexadecimal or decimal machines without guard digits, but we know of
none.  See	DLAED3 for details.

```

ARGUMENTS[Toc][Back]

```     COMPZ   (input) CHARACTER*1
= 'N':  Compute eigenvalues only.
= 'I':  Compute eigenvectors of tridiagonal matrix	also.
= 'V':  Compute eigenvectors of original Hermitian	matrix also.
On	entry, Z contains the unitary matrix used to reduce the
original matrix to	tridiagonal form.

N	     (input) INTEGER
The dimension of the symmetric tridiagonal	matrix.	 N >= 0.

D	     (input/output) DOUBLE PRECISION array, dimension (N)
On	entry, the diagonal elements of	the tridiagonal	matrix.	 On
exit, if INFO = 0,	the eigenvalues	in ascending order.

E	     (input/output) DOUBLE PRECISION array, dimension (N-1)
On	entry, the subdiagonal elements	of the tridiagonal matrix.  On
exit, E has been destroyed.

Page 1

ZSTEDC(3F)							    ZSTEDC(3F)

Z	     (input/output) COMPLEX*16 array, dimension	(LDZ,N)
On	entry, if COMPZ	= 'V', then Z contains the unitary matrix used
in	the reduction to tridiagonal form.  On exit, if	INFO = 0, then
if	COMPZ =	'V', Z contains	the orthonormal	eigenvectors of	the
original Hermitian	matrix,	and if COMPZ = 'I', Z contains the
orthonormal eigenvectors of the symmetric tridiagonal matrix.  If
COMPZ = 'N', then Z is not	referenced.

LDZ     (input) INTEGER
The leading dimension of the array	Z.  LDZ	>= 1.  If eigenvectors
are desired, then LDZ >= max(1,N).

WORK    (workspace/output)	COMPLEX*16 array, dimension (LWORK)
On	exit, if LWORK > 0, WORK(1) returns the	optimal	LWORK.

LWORK   (input) INTEGER
The dimension of the array	WORK.  If COMPZ	= 'N' or 'I', or N <=
1,	LWORK must be at least 1.  If COMPZ = 'V' and N	> 1, LWORK
must be at	least N*N.

RWORK   (workspace/output)	DOUBLE PRECISION array,
dimension (LRWORK)	On exit, if LRWORK > 0,	RWORK(1) returns the
optimal LRWORK.

LRWORK  (input) INTEGER
The dimension of the array	RWORK.	If COMPZ = 'N' or N <= 1,
LRWORK must be at least 1.	 If COMPZ = 'V'	and N >	1, LRWORK must
be	at least 1 + 3*N + 2*N*lg N + 3*N**2 , where lg( N ) =
smallest integer k	such that 2**k >= N.  If COMPZ = 'I' and N >
1,	LRWORK must be at least	1 + 3*N	+ 2*N*lg N + 3*N**2 .

IWORK   (workspace/output)	INTEGER	array, dimension (LIWORK)
On	exit, if LIWORK	> 0, IWORK(1) returns the optimal LIWORK.

LIWORK  (input) INTEGER
The dimension of the array	IWORK.	If COMPZ = 'N' or N <= 1,
LIWORK must be at least 1.	 If COMPZ = 'V'	or N > 1,  LIWORK must
be	at least 6 + 6*N + 5*N*lg N.  If COMPZ = 'I' or	N > 1,	LIWORK
must be at	least 2	+ 5*N .

INFO    (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  The algorithm failed	to compute an eigenvalue while working
on	the submatrix lying in rows and	columns	INFO/(N+1) through
mod(INFO,N+1).
ZSTEDC(3F)							    ZSTEDC(3F)

```

NAME[Toc][Back]

```     ZSTEDC - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using	the divide and conquer method
```

SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZSTEDC(	COMPZ, N, D, E,	Z, LDZ,	WORK, LWORK, RWORK, LRWORK,
IWORK, LIWORK, INFO )

CHARACTER	COMPZ

INTEGER	INFO, LDZ, LIWORK, LRWORK, LWORK, N

INTEGER	IWORK( * )

DOUBLE		PRECISION D( * ), E( * ), RWORK( * )

COMPLEX*16	WORK( *	), Z( LDZ, * )
```

PURPOSE[Toc][Back]

```     ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using	the divide and conquer method.	The
eigenvectors of a full or band complex Hermitian matrix can also be found
if	ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this	matrix to
tridiagonal form.

This code makes very mild assumptions about floating point	arithmetic. It
will work on machines with	a guard	digit in add/subtract, or on those
binary machines without guard digits which	subtract like the Cray X-MP,
Cray Y-MP,	Cray C-90, or Cray-2.  It could	conceivably fail on
hexadecimal or decimal machines without guard digits, but we know of
none.  See	DLAED3 for details.

```

ARGUMENTS[Toc][Back]

```     COMPZ   (input) CHARACTER*1
= 'N':  Compute eigenvalues only.
= 'I':  Compute eigenvectors of tridiagonal matrix	also.
= 'V':  Compute eigenvectors of original Hermitian	matrix also.
On	entry, Z contains the unitary matrix used to reduce the
original matrix to	tridiagonal form.

N	     (input) INTEGER
The dimension of the symmetric tridiagonal	matrix.	 N >= 0.

D	     (input/output) DOUBLE PRECISION array, dimension (N)
On	entry, the diagonal elements of	the tridiagonal	matrix.	 On
exit, if INFO = 0,	the eigenvalues	in ascending order.

E	     (input/output) DOUBLE PRECISION array, dimension (N-1)
On	entry, the subdiagonal elements	of the tridiagonal matrix.  On
exit, E has been destroyed.

Page 1

ZSTEDC(3F)							    ZSTEDC(3F)

Z	     (input/output) COMPLEX*16 array, dimension	(LDZ,N)
On	entry, if COMPZ	= 'V', then Z contains the unitary matrix used
in	the reduction to tridiagonal form.  On exit, if	INFO = 0, then
if	COMPZ =	'V', Z contains	the orthonormal	eigenvectors of	the
original Hermitian	matrix,	and if COMPZ = 'I', Z contains the
orthonormal eigenvectors of the symmetric tridiagonal matrix.  If
COMPZ = 'N', then Z is not	referenced.

LDZ     (input) INTEGER
The leading dimension of the array	Z.  LDZ	>= 1.  If eigenvectors
are desired, then LDZ >= max(1,N).

WORK    (workspace/output)	COMPLEX*16 array, dimension (LWORK)
On	exit, if LWORK > 0, WORK(1) returns the	optimal	LWORK.

LWORK   (input) INTEGER
The dimension of the array	WORK.  If COMPZ	= 'N' or 'I', or N <=
1,	LWORK must be at least 1.  If COMPZ = 'V' and N	> 1, LWORK
must be at	least N*N.

RWORK   (workspace/output)	DOUBLE PRECISION array,
dimension (LRWORK)	On exit, if LRWORK > 0,	RWORK(1) returns the
optimal LRWORK.

LRWORK  (input) INTEGER
The dimension of the array	RWORK.	If COMPZ = 'N' or N <= 1,
LRWORK must be at least 1.	 If COMPZ = 'V'	and N >	1, LRWORK must
be	at least 1 + 3*N + 2*N*lg N + 3*N**2 , where lg( N ) =
smallest integer k	such that 2**k >= N.  If COMPZ = 'I' and N >
1,	LRWORK must be at least	1 + 3*N	+ 2*N*lg N + 3*N**2 .

IWORK   (workspace/output)	INTEGER	array, dimension (LIWORK)
On	exit, if LIWORK	> 0, IWORK(1) returns the optimal LIWORK.

LIWORK  (input) INTEGER
The dimension of the array	IWORK.	If COMPZ = 'N' or N <= 1,
LIWORK must be at least 1.	 If COMPZ = 'V'	or N > 1,  LIWORK must
be	at least 6 + 6*N + 5*N*lg N.  If COMPZ = 'I' or	N > 1,	LIWORK
must be at	least 2	+ 5*N .

INFO    (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  The algorithm failed	to compute an eigenvalue while working
on	the submatrix lying in rows and	columns	INFO/(N+1) through
mod(INFO,N+1).

PPPPaaaaggggeeee 2222```
[ Back ]
Similar pages