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NAME
     sspevd - compute all the eigenvalues and, optionally, eigen-
     vectors of a real symmetric matrix A in packed storage

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, * )



     #include <sunperf.h>

     void sspevd(char jobz, char uplo, int n, float  *sap,  float
               *w, float *sz, int ldz, int *info) ;

PURPOSE
     SSPEVD computes all the eigenvalues and, optionally,  eigen-
     vectors  of  a real symmetric matrix A in packed storage. If
     eigenvectors are desired, it uses a divide and conquer algo-
     rithm.

     The divide and conquer algorithm makes very mild assumptions
     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  without  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
               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  associ-
               ated  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/output) REAL array,
               dimension (LWORK) On exit, if LWORK >  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 + 5*N + 2*N*lg N
               + 2*N**2 ), where lg( N )  =  smallest  integer  k
               such that 2**k >= N.

     IWORK     (workspace/output)   INTEGER   array,    dimension
               (LIWORK)
               On exit, if  LIWORK  >  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 2 + 5*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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