SSPEVD  -  compute  all  the  eigenvalues and, optionally,
       eigenvectors of a real symmetric matrix A in packed  stor­
       age


SYNOPSIS

       SUBROUTINE SSPEVD( JOBZ,  UPLO,  N,  AP,  W, Z, LDZ, WORK,
                          LWORK, IWORK, LIWORK, INFO )

           CHARACTER      JOBZ, UPLO

           INTEGER        INFO, LDZ, LIWORK, LWORK, N

           INTEGER        IWORK( * )

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


PURPOSE

       SSPEVD  computes  all  the  eigenvalues  and,  optionally,
       eigenvectors of a real symmetric matrix A in packed  stor­
       age.  If  eigenvectors  are  desired, it uses a divide and
       conquer algorithm.

       The divide and conquer algorithm makes very  mild  assump­
       tions  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 with­
       out guard digits, but we know of none.


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  sym­
               metric  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

               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 associ­
               ated with W(i).  If JOBZ = 'N', then Z is not ref­
               erenced.

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

       WORK    (workspace/output) REAL array,
               dimension (LWORK) On exit, if INFO  =  0,  WORK(1)
               returns the optimal LWORK.

       LWORK   (input) INTEGER
               The  dimension  of  the  array  WORK.   If N <= 1,
               LWORK must be at least 1.  If JOBZ = 'N' and  N  >
               1,  LWORK must be at least 2*N.  If JOBZ = 'V' and
               N > 1, LWORK must be at least 1 + 6*N + N**2.

               If LWORK = -1, then a workspace query is  assumed;
               the  routine  only  calculates the optimal size of
               the WORK array, returns this value  as  the  first
               entry  of  the  WORK  array,  and no error message
               related to LWORK is issued by XERBLA.

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

       LIWORK  (input) INTEGER
               The dimension of the array IWORK.  If JOBZ  =  'N'
               or  N <= 1, LIWORK must be at least 1.  If JOBZ  =
               'V' and N > 1, LIWORK must be at least 3 + 5*N.

               If LIWORK = -1, then a workspace query is assumed;
               the  routine  only  calculates the optimal size of
               the IWORK array, returns this value as  the  first
               entry  of  the  IWORK  array, and no error message
               related to LIWORK is issued by XERBLA.

       INFO    (output) INTEGER
               = 0:  successful exit

               gal value.
               >  0:   if  INFO = i, the algorithm failed to con­
               verge; i off-diagonal elements of an  intermediate
               tridiagonal form did not converge to zero.


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