SSPEV(3)              LAPACK driver routine (version 3.1)             SSPEV(3)



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

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


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.

       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 +
               (j-1)*j/2) =  A(i,j)  for  1<=i<=j;  if  UPLO  =  'L',  AP(i  +
               (j-1)*(2*n-j)/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.

       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  off-
               diagonal  elements  of an intermediate tridiagonal form did not
               converge to zero.



 LAPACK driver routine (version 3.N1o)vember 2006                        SSPEV(3)