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DSTEQR(l)			       )			     DSTEQR(l)

NAME
       DSTEQR  -  compute  all	eigenvalues and, optionally, eigenvectors of a
       symmetric tridiagonal matrix using the implicit QL or QR method

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

	   CHARACTER	  COMPZ

	   INTEGER	  INFO, LDZ, N

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

PURPOSE
       DSTEQR computes all eigenvalues and, optionally, eigenvectors of a sym‐
       metric  tridiagonal  matrix  using  the	implicit  QL or QR method. The
       eigenvectors of a full or band symmetric matrix can also	 be  found  if
       DSYTRD  or  DSPTRD  or  DSBTRD  has  been used to reduce this matrix to
       tridiagonal form.

ARGUMENTS
       COMPZ   (input) CHARACTER*1
	       = 'N':  Compute eigenvalues only.
	       = 'V':  Compute eigenvalues and eigenvectors  of	 the  original
	       symmetric  matrix.   On	entry,	Z  must contain the orthogonal
	       matrix used to reduce the original matrix to tridiagonal	 form.
	       = 'I':  Compute eigenvalues and eigenvectors of the tridiagonal
	       matrix.	Z is initialized to the identity matrix.

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

       D       (input/output) DOUBLE PRECISION array, dimension (N)
	       On entry, the diagonal elements of the tridiagonal matrix.   On
	       exit, if INFO = 0, the eigenvalues in ascending 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',  then  Z  contains  the  orthogonal
	       matrix  used in the reduction to tridiagonal form.  On exit, if
	       INFO = 0, then if  COMPZ =  'V',	 Z  contains  the  orthonormal
	       eigenvectors  of	 the original symmetric matrix, and if COMPZ =
	       'I', Z contains the orthonormal eigenvectors of	the  symmetric
	       tridiagonal matrix.  If COMPZ = 'N', then Z is not referenced.

       LDZ     (input) INTEGER
	       The  leading dimension of the array Z.  LDZ >= 1, and if eigen‐
	       vectors are desired, then  LDZ >= max(1,N).

       WORK    (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2))
	       If COMPZ = 'N', then WORK is not referenced.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       > 0:  the algorithm has failed to find all the eigenvalues in a
	       total  of  30*N	iterations;  if INFO = i, then i elements of E
	       have not converged to zero; on exit, D and E contain  the  ele‐
	       ments  of  a symmetric tridiagonal matrix which is orthogonally
	       similar to the original matrix.

LAPACK version 3.0		 15 June 2000			     DSTEQR(l)
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