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


SYNOPSIS

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

           CHARACTER      JOBZ, UPLO

           INTEGER        INFO, LDZ, LIWORK, LWORK, N

           INTEGER        IWORK( * )

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


PURPOSE

       DSPEVD  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)   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.

               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)
               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) DOUBLE PRECISION 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.

               = 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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