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NAME
     dsteqr - compute all eigenvalues and, optionally,  eigenvec-
     tors of a symmetric tridiagonal matrix using the implicit QL
     or QR method

SYNOPSIS
     SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )

     CHARACTER COMPZ

     INTEGER INFO, LDZ, N

     DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )



     #include <sunperf.h>

     void dsteqr(char compz, int n, double *d, double *e,  double
               *dz, int ldz, int *info) ;

PURPOSE
     DSTEQR computes all eigenvalues and,  optionally,  eigenvec-
     tors of a symmetric tridiagonal matrix using the implicit QL
     or QR method.  The eigenvectors of a full or band  symmetric
     matrix  can  also be found if DSYTRD or DSPTRD or DSBTRD has
     been used to reduce this matrix to tridiagonal form.


ARGUMENTS
     COMPZ     (input) CHARACTER*1
               = 'N':  Compute eigenvalues only.
               = 'V':  Compute eigenvalues  and  eigenvectors  of
               the  original  symmetric matrix.  On entry, Z must
               contain the orthogonal matrix used to  reduce  the
               original matrix to tridiagonal form.  = 'I':  Com-
               pute eigenvalues and eigenvectors of the tridiago-
               nal  matrix.   Z  is  initialized  to the identity
               matrix.

     N         (input) INTEGER
               The order of the matrix.  N >= 0.

     D         (input/output) DOUBLE PRECISION  array,  dimension
               (N)
               On entry, the diagonal elements of the tridiagonal
               matrix.   On exit, if INFO = 0, the eigenvalues in
               ascending order.

     E         (input/output) DOUBLE PRECISION  array,  dimension
               (N-1)
               On entry, the (n-1) subdiagonal  elements  of  the
               tridiagonal  matrix.   On  exit,  E  has been des-
               troyed.

     Z         (input/output) DOUBLE PRECISION  array,  dimension
               (LDZ, N)
               On entry, if  COMPZ = 'V',  then  Z  contains  the
               orthogonal  matrix used in the reduction to tridi-
               agonal form.  On exit, if INFO = 0, then if  COMPZ
               =  'V', Z contains the orthonormal eigenvectors of
               the original symmetric matrix, and if COMPZ = 'I',
               Z  contains  the  orthonormal  eigenvectors of the
               symmetric tridiagonal matrix.   If  COMPZ  =  'N',
               then Z is not referenced.

     LDZ       (input) INTEGER
               The leading dimension of the array Z.  LDZ  >=  1,
               and  if  eigenvectors  are  desired,  then  LDZ >=
               max(1,N).

     WORK      (workspace)  DOUBLE  PRECISION  array,   dimension
               (max(1,2*N-2))
               If COMPZ = 'N', then WORK is not referenced.

     INFO      (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value
               > 0:  the algorithm has failed  to  find  all  the
               eigenvalues in a total of 30*N iterations; if INFO
               = i, then i elements of E have  not  converged  to
               zero;  on  exit, D and E contain the elements of a
               symmetric tridiagonal matrix which is orthogonally
               similar to the original matrix.

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