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


SYNOPSIS

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

           CHARACTER     JOBZ, UPLO

           INTEGER       INFO, LDZ, N

           DOUBLE        PRECISION AP( * ), W( * ), WORK( * ), Z(
                         LDZ, * )


PURPOSE

       DSPEV computes all the eigenvalues and, optionally, eigen­
       vectors 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)   DOUBLE   PRECISION   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
               = '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) DOUBLE PRECISION array, dimension (N)
               If INFO = 0, the eigenvalues in ascending order.

       Z       (output) DOUBLE PRECISION array, dimension (LDZ,
               N)

               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) DOUBLE PRECISION array, dimension
               (3*N)

       INFO    (output) INTEGER
               = 0:  successful exit.
               < 0:  if INFO = -i, the i-th argument had an ille­
               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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