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RedHat 9 (Linux i386) - man page for zlar1v (redhat section l)

ZLAR1V(l)					)					ZLAR1V(l)

NAME
       ZLAR1V  -  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 ZLAR1V( 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( * )

	   COMPLEX*16	  Z( * )

PURPOSE
       ZLAR1V  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 ei-
		genvalue 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) COMPLEX*16 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  magnitude.  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
	  Ken Stanley, Computer Science Division, University of
	    California at Berkeley, USA

LAPACK version 3.0			   15 June 2000 				ZLAR1V(l)


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