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NAME
     spteqr - compute all eigenvalues and, optionally,  eigenvec-
     tors  of a symmetric positive definite tridiagonal matrix by
     first factoring the matrix using SPTTRF,  and  then  calling
     SBDSQR to compute the singular values of the bidiagonal fac-
     tor

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

     CHARACTER COMPZ

     INTEGER INFO, LDZ, N

     REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )



     #include <sunperf.h>

     void spteqr(char compz, int n, float  *d,  float  *e,  float
               *sz, int ldz, int *info) ;

PURPOSE
     SPTEQR computes all eigenvalues and,  optionally,  eigenvec-
     tors  of a symmetric positive definite tridiagonal matrix by
     first factoring the matrix using SPTTRF,  and  then  calling
     SBDSQR to compute the singular values of the bidiagonal fac-
     tor.

     This routine computes the eigenvalues of the positive defin-
     ite  tridiagonal  matrix  to  high  relative accuracy.  This
     means that if the eigenvalues range over many orders of mag-
     nitude in size, then the small eigenvalues and corresponding
     eigenvectors will be  computed  more  accurately  than,  for
     example, with the standard QR method.

     The eigenvectors of a full or band symmetric positive defin-
     ite  matrix  can  also be found if SSYTRD, SSPTRD, or SSBTRD
     has been used to reduce this  matrix  to  tridiagonal  form.
     (The  reduction  to  tridiagonal form, however, may preclude
     the possibility of obtaining high relative accuracy  in  the
     small  eigenvalues  of  the original matrix, if these eigen-
     values range over many orders of magnitude.)


ARGUMENTS
     COMPZ     (input) CHARACTER*1
               = 'N':  Compute eigenvalues only.
               = 'V':  Compute eigenvectors of original symmetric
               matrix  also.   Array  Z  contains  the orthogonal
               matrix used  to  reduce  the  original  matrix  to
               tridiagonal form.  = 'I':  Compute eigenvectors of
               tridiagonal matrix also.

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

     D         (input/output) REAL array, dimension (N)
               On entry, the n diagonal elements of the tridiago-
               nal matrix.  On normal exit, D contains the eigen-
               values, in descending order.

     E         (input/output) REAL 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) REAL array, dimension (LDZ, N)
               On entry, if COMPZ = 'V',  the  orthogonal  matrix
               used  in  the  reduction  to tridiagonal form.  On
               exit, if COMPZ = 'V', the orthonormal eigenvectors
               of  the original symmetric matrix; if COMPZ = 'I',
               the orthonormal eigenvectors  of  the  tridiagonal
               matrix.   If  INFO  >  0  on  exit, Z contains the
               eigenvectors  associated  with  only  the   stored
               eigenvalues.   If   COMPZ  =  'N',  then  Z is not
               referenced.

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

     WORK      (workspace) REAL array, dimension (LWORK)
               If  COMPZ = 'N', then LWORK = 2*N If  COMPZ =  'V'
               or 'I', then LWORK = MAX(1,4*N-4)

     INFO      (output) INTEGER
               = 0:  successful exit.
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value.
               > 0:  if INFO = i, and i is:  <= N   the  Cholesky
               factorization of the matrix could not be performed
               because the i-th principal minor was not  positive
               definite.   > N   the SVD algorithm failed to con-
               verge; if INFO = N+i, i off-diagonal  elements  of
               the bidiagonal factor did not converge to zero.

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