spteqr(3F)

NAME
     SPTEQR - compute all eigenvalues and, optionally, eigenvectors 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 factor

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

         CHARACTER      COMPZ

         INTEGER        INFO, LDZ, N

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

PURPOSE
     SPTEQR computes all eigenvalues and, optionally, eigenvectors 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 factor.

     This routine computes the eigenvalues of the positive definite
     tridiagonal matrix to high relative accuracy.  This means that if the
     eigenvalues range over many orders of magnitude 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 definite 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 eigenvalues 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 tridiagonal matrix.  On
             normal exit, D contains the eigenvalues, 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 destroyed.

     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 illegal 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 converge; if INFO = N+i, i off-diagonal elements of the
             bidiagonal factor did not converge to zero.