CXML
        	    
LAPACK version 3.0
spteqr(3)

PURPOSE
  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

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

      CHARACTER	     COMPZ

      INTEGER	     INFO, LDZ, N

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

DESCRIPTION
  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 (4*N)

  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.