clar1v.f(3) LAPACK clar1v.f(3)
NAME
clar1v.f -
SYNOPSIS
Functions/Subroutines
subroutine clar1v (N, B1, BN, LAMBDA, D, L, LD, LLD, PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, R, ISUPPZ, NRMINV, RESID, RQCORR,
WORK)
CLAR1V
Function/Subroutine Documentation
subroutine clar1v (integerN, integerB1, integerBN, realLAMBDA, real, dimension( * )D, real, dimension( * )L, real, dimension( * )LD, real,
dimension( * )LLD, realPIVMIN, realGAPTOL, complex, dimension( * )Z, logicalWANTNC, integerNEGCNT, realZTZ, realMINGMA, integerR, integer,
dimension( * )ISUPPZ, realNRMINV, realRESID, realRQCORR, real, dimension( * )WORK)
CLAR1V
Purpose:
CLAR1V 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 REAL
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 REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the unit bidiagonal matrix
L, in elements 1 to N-1.
D
D is REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D.
LD
LD is REAL array, dimension (N-1)
The n-1 elements L(i)*D(i).
LLD
LLD is REAL array, dimension (N-1)
The n-1 elements L(i)*L(i)*D(i).
PIVMIN
PIVMIN is REAL
The minimum pivot in the Sturm sequence.
GAPTOL
GAPTOL is REAL
Tolerance that indicates when eigenvector entries are negligible
w.r.t. their contribution to the residual.
Z
Z is COMPLEX 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 REAL
The square of the 2-norm of Z.
MINGMA
MINGMA is REAL
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 REAL
NRMINV = 1/SQRT( ZTZ )
RESID
RESID is REAL
The residual of the FP vector.
RESID = ABS( MINGMA )/SQRT( ZTZ )
RQCORR
RQCORR is REAL
The Rayleigh Quotient correction to LAMBDA.
RQCORR = MINGMA*TMP
WORK
WORK is REAL array, dimension (4*N)
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
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 clar1v.f.
Author
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Version 3.4.1 Sun May 26 2013 clar1v.f(3)