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SPTEQR(l)					)					SPTEQR(l)

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 def-
       inite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBD-
       SQR  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 tridiago-
	       nal 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.

LAPACK version 3.0			   15 June 2000 				SPTEQR(l)
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