Flashnux

GNU/Linux man pages

Livre :
Expressions régulières,
Syntaxe et mise en oeuvre :

ISBN : 978-2-7460-9712-4
EAN : 9782746097124
(Editions ENI)

GNU/Linux

CentOS 4.8

 i386

zlar1v(l)
ZLAR1V

ZLAR1V

NAME
SYNOPSIS
PURPOSE
ARGUMENTS
FURTHER DETAILS

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 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) 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

zlar1v(l)