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CLARRV(l)			       )			     CLARRV(l)

NAME
       CLARRV - compute the eigenvectors of the tridiagonal matrix T = L D L^T
       given L, D and the eigenvalues of L D L^T

SYNOPSIS
       SUBROUTINE CLARRV( N, D, L, ISPLIT, M, W, IBLOCK, GERSCH, TOL, Z,  LDZ,
			  ISUPPZ, WORK, IWORK, INFO )

	   INTEGER	  INFO, LDZ, M, N

	   REAL		  TOL

	   INTEGER	  IBLOCK( * ), ISPLIT( * ), ISUPPZ( * ), IWORK( * )

	   REAL		  D( * ), GERSCH( * ), L( * ), W( * ), WORK( * )

	   COMPLEX	  Z( LDZ, * )

PURPOSE
       CLARRV  computes the eigenvectors of the tridiagonal matrix T = L D L^T
       given L, D and the eigenvalues of L D L^T. The input eigenvalues should
       have high relative accuracy with respect to the entries of L and D. The
       desired accuracy of the output can be specified by the input  parameter
       TOL.

ARGUMENTS
       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 diagonal matrix D.  On
	       exit, D may be overwritten.

       L       (input/output) REAL array, dimension (N-1)
	       On entry, the (n-1) subdiagonal elements of the unit bidiagonal
	       matrix  L  in  elements 1 to N-1 of L. L(N) need not be set. On
	       exit, L is overwritten.

       ISPLIT  (input) INTEGER array, dimension (N)
	       The splitting points, at which T breaks	up  into  submatrices.
	       The  first submatrix consists of rows/columns 1 to ISPLIT( 1 ),
	       the second of rows/columns ISPLIT( 1 )+1 through ISPLIT(	 2  ),
	       etc.

       TOL     (input) REAL
	       The  absolute error tolerance for the eigenvalues/eigenvectors.
	       Errors in the input eigenvalues must be bounded	by  TOL.   The
	       eigenvectors output have residual norms bounded by TOL, and the
	       dot products between different eigenvectors are bounded by TOL.
	       TOL must be at least N*EPS*|T|, where EPS is the machine preci‐
	       sion and |T| is the 1-norm of the tridiagonal matrix.

       M       (input) INTEGER
	       The total number of eigenvalues found.  0 <= M <= N.  If	 RANGE
	       = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

       W       (input) REAL array, dimension (N)
	       The  first  M  elements	of W contain the eigenvalues for which
	       eigenvectors are to be computed.	  The  eigenvalues  should  be
	       grouped by split-off block and ordered from smallest to largest
	       within the block ( The output array W from SLARRE  is  expected
	       here ).	Errors in W must be bounded by TOL (see above).

       IBLOCK  (input) INTEGER array, dimension (N)
	       The  submatrix indices associated with the corresponding eigen‐
	       values in W; IBLOCK(i)=1 if  eigenvalue	W(i)  belongs  to  the
	       first  submatrix from the top, =2 if W(i) belongs to the second
	       submatrix, etc.

       Z       (output) COMPLEX array, dimension (LDZ, max(1,M) )
	       If JOBZ = 'V', then if INFO = 0, the first M columns of Z  con‐
	       tain the orthonormal eigenvectors of the matrix T corresponding
	       to the selected eigenvalues, with the i-th column of Z  holding
	       the eigenvector associated with W(i).  If JOBZ = 'N', then Z is
	       not referenced.	Note: the  user	 must  ensure  that  at	 least
	       max(1,M)	 columns  are supplied in the array Z; if RANGE = 'V',
	       the exact value of M is not known in advance and an upper bound
	       must be used.

       LDZ     (input) INTEGER
	       The  leading dimension of the array Z.  LDZ >= 1, and if JOBZ =
	       'V', LDZ >= max(1,N).

       ISUPPZ  (output) INTEGER ARRAY, dimension ( 2*max(1,M) )
	       The support of the eigenvectors in Z, i.e., the	indices	 indi‐
	       cating  the  nonzero  elements  in  Z.  The i-th eigenvector is
	       nonzero only in elements ISUPPZ( 2*i-1 ) through ISUPPZ( 2*i ).

       WORK    (workspace) REAL array, dimension (13*N)

       IWORK   (workspace) INTEGER array, dimension (6*N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       > 0:  if INFO = 1, internal error in SLARRB if INFO = 2, inter‐
	       nal error in CSTEIN

FURTHER DETAILS
       Based on contributions by
	  Inderjit Dhillon, IBM Almaden, USA
	  Osni Marques, LBNL/NERSC, USA
	  Ken Stanley, Computer Science Division, University of
	    California at Berkeley, USA

LAPACK version 3.0		 15 June 2000			     CLARRV(l)
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