
DLAR1V(l) ) DLAR1V(l)
NAME
DLAR1V  compute the (scaled) rth 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) rth 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) rth 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 (N1)
The (n1) subdiagonal elements of the unit bidiagonal matrix L, in elements 1 to
N1.
D (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D.
LD (input) DOUBLE PRECISION array, dimension (N1)
The n1 elements L(i)*D(i).
LLD (input) DOUBLE PRECISION array, dimension (N1)
The n1 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) rth 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
LAPACK version 3.0 15 June 2000 DLAR1V(l) 
