clar1v (3)  Linux Man Pages
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 computes the (scaled) rth column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT  λI.
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 computes the (scaled) rth column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT  λI.
Purpose:

CLAR1V 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. 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) 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.
Parameters:

N
N is INTEGER The order of the matrix L D L**T.
B1B1 is INTEGER First index of the submatrix of L D L**T.
BNBN is INTEGER Last index of the submatrix of L D L**T.
LAMBDALAMBDA 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.
LL is REAL array, dimension (N1) The (n1) subdiagonal elements of the unit bidiagonal matrix L, in elements 1 to N1.
DD is REAL array, dimension (N) The n diagonal elements of the diagonal matrix D.
LDLD is REAL array, dimension (N1) The n1 elements L(i)*D(i).
LLDLLD is REAL array, dimension (N1) The n1 elements L(i)*L(i)*D(i).
PIVMINPIVMIN is REAL The minimum pivot in the Sturm sequence.
GAPTOLGAPTOL is REAL Tolerance that indicates when eigenvector entries are negligible w.r.t. their contribution to the residual.
ZZ is COMPLEX array, dimension (N) On input, all entries of Z must be set to 0. On output, Z contains the (scaled) rth column of the inverse. The scaling is such that Z(R) equals 1.
WANTNCWANTNC is LOGICAL Specifies whether NEGCNT has to be computed.
NEGCNTNEGCNT 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.
ZTZZTZ is REAL The square of the 2norm of Z.
MINGMAMINGMA is REAL The reciprocal of the largest (in magnitude) diagonal element of the inverse of L D L**T  sigma I.
RR 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.
ISUPPZISUPPZ 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 ).
NRMINVNRMINV is REAL NRMINV = 1/SQRT( ZTZ )
RESIDRESID is REAL The residual of the FP vector. RESID = ABS( MINGMA )/SQRT( ZTZ )
RQCORRRQCORR is REAL The Rayleigh Quotient correction to LAMBDA. RQCORR = MINGMA*TMP
WORKWORK is REAL 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 clar1v.f.
Author
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