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

```
SSTEDC(3F)							    SSTEDC(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

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

CHARACTER	COMPZ

INTEGER	INFO, LDZ, LIWORK, LWORK, N

INTEGER	IWORK( * )

REAL		D( * ),	E( * ),	WORK( *	), Z( LDZ, * )
```

### PURPOSE[Toc][Back]

```     SSTEDC computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using	the divide and conquer method.	The
eigenvectors of a full or band real symmetric matrix can also be found if
SSYTRD or SSPTRD or SSBTRD	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	SLAED3 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 dense symmetric matrix
also.  On entry, Z	contains the orthogonal	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) REAL 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) REAL array,	dimension (N-1)
On	entry, the subdiagonal elements	of the tridiagonal matrix.  On
exit, E has been destroyed.

Page 1

SSTEDC(3F)							    SSTEDC(3F)

Z	     (input/output) REAL array,	dimension (LDZ,N)
On	entry, if COMPZ	= 'V', then Z contains the orthogonal 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 symmetric 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)	REAL 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 N <= 1	then
LWORK must	be at least 1.	If COMPZ = 'V' and N > 1 then LWORK
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
then LWORK	must be	at least ( 1 + 3*N + 2*N*lg N +	2*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 then
LIWORK must be at least 1.	 If COMPZ = 'V'	and N >	1 then LIWORK
must be at	least (	6 + 6*N	+ 5*N*lg N ).  If COMPZ	= 'I' and N >
1 then 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).
SSTEDC(3F)							    SSTEDC(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

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

CHARACTER	COMPZ

INTEGER	INFO, LDZ, LIWORK, LWORK, N

INTEGER	IWORK( * )

REAL		D( * ),	E( * ),	WORK( *	), Z( LDZ, * )
```

### PURPOSE[Toc][Back]

```     SSTEDC computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using	the divide and conquer method.	The
eigenvectors of a full or band real symmetric matrix can also be found if
SSYTRD or SSPTRD or SSBTRD	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	SLAED3 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 dense symmetric matrix
also.  On entry, Z	contains the orthogonal	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) REAL 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) REAL array,	dimension (N-1)
On	entry, the subdiagonal elements	of the tridiagonal matrix.  On
exit, E has been destroyed.

Page 1

SSTEDC(3F)							    SSTEDC(3F)

Z	     (input/output) REAL array,	dimension (LDZ,N)
On	entry, if COMPZ	= 'V', then Z contains the orthogonal 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 symmetric 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)	REAL 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 N <= 1	then
LWORK must	be at least 1.	If COMPZ = 'V' and N > 1 then LWORK
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
then LWORK	must be	at least ( 1 + 3*N + 2*N*lg N +	2*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 then
LIWORK must be at least 1.	 If COMPZ = 'V'	and N >	1 then LIWORK
must be at	least (	6 + 6*N	+ 5*N*lg N ).  If COMPZ	= 'I' and N >
1 then 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).

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