dpteqr(l) [redhat man page]

DPTEQR(l)								 )								 DPTEQR(l)

NAME

       DPTEQR  -  compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the
       matrix using DPTTRF, and then calling DBDSQR to compute the singular values of the bidiagonal factor

SYNOPSIS

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

	   CHARACTER	  COMPZ

	   INTEGER	  INFO, LDZ, N

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

PURPOSE

       DPTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by  first  factoring  the
       matrix  using DPTTRF, and then calling DBDSQR to compute the singular values of the bidiagonal factor.  This routine computes the eigenval-
       ues 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 DSYTRD, DSPTRD,  or  DSBTRD  has  been  used	to
       reduce  this  matrix to tridiagonal form. (The reduction to tridiagonal form, however, may preclude the possibility of obtaining high rela-
       tive 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N-1)
	       On entry, the (n-1) subdiagonal elements of the tridiagonal matrix.  On exit, E has been destroyed.

       Z       (input/output) DOUBLE PRECISION 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 orthonor-
	       mal 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) DOUBLE PRECISION 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.

LAPACK version 3.0						   15 June 2000 							 DPTEQR(l)