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

```
SSPEV(3F)							     SSPEV(3F)

```

### NAME[Toc][Back]

```     SSPEV - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in	packed storage
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SSPEV( JOBZ, UPLO, N, AP, W, Z,	LDZ, WORK, INFO	)

CHARACTER     JOBZ, UPLO

INTEGER       INFO, LDZ, N

REAL	       AP( * ),	W( * ),	WORK( *	), Z( LDZ, * )
```

### PURPOSE[Toc][Back]

```     SSPEV computes all	the eigenvalues	and, optionally, eigenvectors of a
real symmetric matrix A in	packed storage.

```

### ARGUMENTS[Toc][Back]

```     JOBZ    (input) CHARACTER*1
= 'N':  Compute eigenvalues only;
= 'V':  Compute eigenvalues and eigenvectors.

UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

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

AP	     (input/output) REAL array,	dimension (N*(N+1)/2)
On	entry, the upper or lower triangle of the symmetric matrix A,
packed columnwise in a linear array.  The j-th column of A	is
stored in the array AP as follows:	 if UPLO = 'U',	AP(i + (j1)*j/2)
= A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*nj)/2)
= A(i,j) for	j<=i<=n.

On	exit, AP is overwritten	by values generated during the
reduction to tridiagonal form.  If	UPLO = 'U', the	diagonal and
first superdiagonal of the	tridiagonal matrix T overwrite the
corresponding elements of A, and if UPLO =	'L', the diagonal and
first subdiagonal of T overwrite the corresponding	elements of A.

W	     (output) REAL array, dimension (N)
If	INFO = 0, the eigenvalues in ascending order.

Z	     (output) REAL array, dimension (LDZ, N)
If	JOBZ = 'V', then if INFO = 0, Z	contains the orthonormal
eigenvectors of the matrix	A, with	the i-th column	of Z holding
the eigenvector associated	with W(i).  If JOBZ = 'N', then	Z is
not referenced.

Page 1

SSPEV(3F)							     SSPEV(3F)

LDZ     (input) INTEGER
The leading dimension of the array	Z.  LDZ	>= 1, and if JOBZ =
'V', LDZ >= max(1,N).

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.
> 0:  if INFO = i,	the algorithm failed to	converge; i offdiagonal
elements of an intermediate tridiagonal form did not
converge to zero.
SSPEV(3F)							     SSPEV(3F)

```

### NAME[Toc][Back]

```     SSPEV - compute all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in	packed storage
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SSPEV( JOBZ, UPLO, N, AP, W, Z,	LDZ, WORK, INFO	)

CHARACTER     JOBZ, UPLO

INTEGER       INFO, LDZ, N

REAL	       AP( * ),	W( * ),	WORK( *	), Z( LDZ, * )
```

### PURPOSE[Toc][Back]

```     SSPEV computes all	the eigenvalues	and, optionally, eigenvectors of a
real symmetric matrix A in	packed storage.

```

### ARGUMENTS[Toc][Back]

```     JOBZ    (input) CHARACTER*1
= 'N':  Compute eigenvalues only;
= 'V':  Compute eigenvalues and eigenvectors.

UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

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

AP	     (input/output) REAL array,	dimension (N*(N+1)/2)
On	entry, the upper or lower triangle of the symmetric matrix A,
packed columnwise in a linear array.  The j-th column of A	is
stored in the array AP as follows:	 if UPLO = 'U',	AP(i + (j1)*j/2)
= A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*nj)/2)
= A(i,j) for	j<=i<=n.

On	exit, AP is overwritten	by values generated during the
reduction to tridiagonal form.  If	UPLO = 'U', the	diagonal and
first superdiagonal of the	tridiagonal matrix T overwrite the
corresponding elements of A, and if UPLO =	'L', the diagonal and
first subdiagonal of T overwrite the corresponding	elements of A.

W	     (output) REAL array, dimension (N)
If	INFO = 0, the eigenvalues in ascending order.

Z	     (output) REAL array, dimension (LDZ, N)
If	JOBZ = 'V', then if INFO = 0, Z	contains the orthonormal
eigenvectors of the matrix	A, with	the i-th column	of Z holding
the eigenvector associated	with W(i).  If JOBZ = 'N', then	Z is
not referenced.

Page 1

SSPEV(3F)							     SSPEV(3F)

LDZ     (input) INTEGER
The leading dimension of the array	Z.  LDZ	>= 1, and if JOBZ =
'V', LDZ >= max(1,N).

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.
> 0:  if INFO = i,	the algorithm failed to	converge; i offdiagonal
elements of an intermediate tridiagonal form did not
converge to zero.

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