dlar1v.f man page

dlar1v.f —

Synopsis

Functions/Subroutines

subroutine dlar1v (N, B1, BN, LAMBDA, D, L, LD, LLD, PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, R, ISUPPZ, NRMINV, RESID, RQCORR, WORK)
DLAR1V computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI.

Function/Subroutine Documentation

subroutine dlar1v (integerN, integerB1, integerBN, double precisionLAMBDA, double precision, dimension( * )D, double precision, dimension( * )L, double precision, dimension( * )LD, double precision, dimension( * )LLD, double precisionPIVMIN, double precisionGAPTOL, double precision, dimension( * )Z, logicalWANTNC, integerNEGCNT, double precisionZTZ, double precisionMINGMA, integerR, integer, dimension( * )ISUPPZ, double precisionNRMINV, double precisionRESID, double precisionRQCORR, double precision, dimension( * )WORK)

DLAR1V computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI.

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. When sigma is close to an eigenvalue, the
computed vector is an accurate eigenvector. Usually, r corresponds
to the index where the eigenvector is largest in magnitude.
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.

Parameters:

N

N is INTEGER
 The order of the matrix L D L**T.

B1

B1 is INTEGER
 First index of the submatrix of L D L**T.

BN

BN is INTEGER
 Last index of the submatrix of L D L**T.

LAMBDA

LAMBDA is DOUBLE PRECISION
 The shift. In order to compute an accurate eigenvector,
 LAMBDA should be a good approximation to an eigenvalue
 of L D L**T.

L

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

D

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

LD

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

LLD

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

PIVMIN

PIVMIN is DOUBLE PRECISION
 The minimum pivot in the Sturm sequence.

GAPTOL

GAPTOL is DOUBLE PRECISION
 Tolerance that indicates when eigenvector entries are negligible
 w.r.t. their contribution to the residual.

Z

Z is DOUBLE PRECISION array, dimension (N)
 On input, all entries of Z must be set to 0.
 On output, Z contains the (scaled) r-th column of the
 inverse. The scaling is such that Z(R) equals 1.

WANTNC

WANTNC is LOGICAL
 Specifies whether NEGCNT has to be computed.

NEGCNT

NEGCNT is INTEGER
 If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin
 in the  matrix factorization L D L**T, and NEGCNT = -1 otherwise.

ZTZ

ZTZ is DOUBLE PRECISION
 The square of the 2-norm of Z.

MINGMA

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

R

R is INTEGER
 The twist index for the twisted factorization used to
 compute Z.
 On input, 0 <= R <= N. If R is input as 0, R is set to
 the index where (L D L**T - sigma I)^{-1} is largest
 in magnitude. If 1 <= R <= N, R is unchanged.
 On output, R contains the twist index used to compute Z.
 Ideally, R designates the position of the maximum entry in the
 eigenvector.

ISUPPZ

ISUPPZ is 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 ).

NRMINV

NRMINV is DOUBLE PRECISION
 NRMINV = 1/SQRT( ZTZ )

RESID

RESID is DOUBLE PRECISION
 The residual of the FP vector.
 RESID = ABS( MINGMA )/SQRT( ZTZ )

RQCORR

RQCORR is DOUBLE PRECISION
 The Rayleigh Quotient correction to LAMBDA.
 RQCORR = MINGMA*TMP

WORK

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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Contributors:

Beresford Parlett, University of California, Berkeley, USA
Jim Demmel, University of California, Berkeley, USA
Inderjit Dhillon, University of Texas, Austin, USA
Osni Marques, LBNL/NERSC, USA
Christof Voemel, University of California, Berkeley, USA

Definition at line 229 of file dlar1v.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

dlar1v(3) is an alias of dlar1v.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK