DLAR1V(l)								 )								 DLAR1V(l)

NAME

       DLAR1V  - compute the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma
       I

SYNOPSIS

       SUBROUTINE DLAR1V( N, B1, BN, SIGMA, D, L, LD, LLD, GERSCH, Z, ZTZ, MINGMA, R, ISUPPZ, WORK )

	   INTEGER	  B1, BN, N, R

	   DOUBLE	  PRECISION MINGMA, SIGMA, ZTZ

	   INTEGER	  ISUPPZ( * )

	   DOUBLE	  PRECISION D( * ), GERSCH( * ), L( * ), LD( * ), LLD( * ), WORK( * ), Z( * )

PURPOSE

       DLAR1V computes the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T  -  sigma
       I. The following steps accomplish this computation : (a) Stationary qd transform,  L D L^T - sigma I = L(+) D(+) L(+)^T, (b) Progressive qd
       transform, L D L^T - sigma I = U(-) D(-) U(-)^T, (c) Computation of the diagonal elements of the inverse of
	   L D L^T - sigma I by combining the above transforms, and choosing
	   r as the index where the diagonal of the inverse is (one of the)
	   largest in magnitude.
       (d) Computation of the (scaled) r-th column of the inverse using the
	   twisted factorization obtained by combining the top part of the
	   the stationary and the bottom part of the progressive transform.

ARGUMENTS

       N	(input) INTEGER
		The order of the matrix L D L^T.

       B1	(input) INTEGER
		First index of the submatrix of L D L^T.

       BN	(input) INTEGER
		Last index of the submatrix of L D L^T.

       SIGMA	(input) DOUBLE PRECISION
		The shift. Initially, when R = 0, SIGMA should be a good approximation to an eigenvalue of L D L^T.

       L	(input) DOUBLE PRECISION array, dimension (N-1)
		The (n-1) subdiagonal elements of the unit bidiagonal matrix L, in elements 1 to N-1.

       D	(input) DOUBLE PRECISION array, dimension (N)
		The n diagonal elements of the diagonal matrix D.

       LD	(input) DOUBLE PRECISION array, dimension (N-1)
		The n-1 elements L(i)*D(i).

       LLD	(input) DOUBLE PRECISION array, dimension (N-1)
		The n-1 elements L(i)*L(i)*D(i).

       GERSCH	(input) DOUBLE PRECISION array, dimension (2*N)
		The n Gerschgorin intervals. These are used to restrict the initial search for R, when R is input as 0.

       Z	(output) DOUBLE PRECISION array, dimension (N)
		The (scaled) r-th column of the inverse. Z(R) is returned to be 1.

       ZTZ	(output) DOUBLE PRECISION
		The square of the norm of Z.

       MINGMA	(output) DOUBLE PRECISION
		The reciprocal of the largest (in magnitude) diagonal element of the inverse of L D L^T - sigma I.

       R	(input/output) INTEGER
		Initially, R should be input to be 0 and is then output as the index where the diagonal element of the inverse is largest in  mag-
		nitude. In later iterations, this same value of R should be input.

       ISUPPZ	(output) INTEGER array, dimension (2)
		The support of the vector in Z, i.e., the vector Z is nonzero only in elements ISUPPZ(1) through ISUPPZ( 2 ).

       WORK	(workspace) DOUBLE PRECISION array, dimension (4*N)

FURTHER DETAILS

       Based on contributions by
	  Inderjit Dhillon, IBM Almaden, USA
	  Osni Marques, LBNL/NERSC, USA

LAPACK version 3.0						   15 June 2000 							 DLAR1V(l)