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# ssbev

```
NAME
SSBEV - compute all the eigenvalues and, optionally, eigen-
vectors of a real symmetric band matrix A

SYNOPSIS
SUBROUTINE SSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
WORK, INFO )

CHARACTER     JOBZ, UPLO

INTEGER       INFO, KD, LDAB, LDZ, N

REAL          AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ,
* )

PURPOSE
SSBEV computes all the eigenvalues and, optionally, eigen-
vectors of a real symmetric band matrix A.

ARGUMENTS
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.

KD      (input) INTEGER
The number of superdiagonals of the matrix A if UPLO
= 'U', or the number of subdiagonals if UPLO = 'L'.
KD >= 0.

AB      (input/output) REAL array, dimension (LDAB, N)
On entry, the upper or lower triangle of the sym-
metric band matrix A, stored in the first KD+1 rows
of the array.  The j-th column of A is stored in the
j-th column of the array AB as follows: if UPLO =
'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for
j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated dur-
ing the reduction to tridiagonal form.  If UPLO =
'U', the first superdiagonal and the diagonal of the
tridiagonal matrix T are returned in rows KD and
KD+1 of AB, and if UPLO = 'L', the diagonal and
first subdiagonal of T are returned in the first two

rows of AB.

LDAB    (input) INTEGER
The leading dimension of the array AB.  LDAB >= KD +
1.

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.

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 (max(1,3*N-2))

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 off-diagonal elements of an intermediate tridiago-
nal form did not converge to zero.
```