LAPACK  3.4.0
LAPACK: Linear Algebra PACKage
Functions/Subroutines
clar1v.f File Reference

Go to the source code of this file.

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 ( INTEGER  N,
INTEGER  B1,
INTEGER  BN,
REAL  LAMBDA,
REAL, dimension( * )  D,
REAL, dimension( * )  L,
REAL, dimension( * )  LD,
REAL, dimension( * )  LLD,
REAL  PIVMIN,
REAL  GAPTOL,
COMPLEX, dimension( * )  Z,
LOGICAL  WANTNC,
INTEGER  NEGCNT,
REAL  ZTZ,
REAL  MINGMA,
INTEGER  R,
INTEGER, dimension( * )  ISUPPZ,
REAL  NRMINV,
REAL  RESID,
REAL  RQCORR,
REAL, dimension( * )  WORK 
)

CLAR1V

Download CLAR1V + dependencies [TGZ] [ZIP] [TXT]
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:
[in]N
          N is INTEGER
           The order of the matrix L D L**T.
[in]B1
          B1 is INTEGER
           First index of the submatrix of L D L**T.
[in]BN
          BN is INTEGER
           Last index of the submatrix of L D L**T.
[in]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.
[in]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.
[in]D
          D is REAL array, dimension (N)
           The n diagonal elements of the diagonal matrix D.
[in]LD
          LD is REAL array, dimension (N-1)
           The n-1 elements L(i)*D(i).
[in]LLD
          LLD is REAL array, dimension (N-1)
           The n-1 elements L(i)*L(i)*D(i).
[in]PIVMIN
          PIVMIN is REAL
           The minimum pivot in the Sturm sequence.
[in]GAPTOL
          GAPTOL is REAL
           Tolerance that indicates when eigenvector entries are negligible
           w.r.t. their contribution to the residual.
[in,out]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.
[in]WANTNC
          WANTNC is LOGICAL
           Specifies whether NEGCNT has to be computed.
[out]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.
[out]ZTZ
          ZTZ is REAL
           The square of the 2-norm of Z.
[out]MINGMA
          MINGMA is REAL
           The reciprocal of the largest (in magnitude) diagonal
           element of the inverse of L D L**T - sigma I.
[in,out]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.
[out]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 ).
[out]NRMINV
          NRMINV is REAL
           NRMINV = 1/SQRT( ZTZ )
[out]RESID
          RESID is REAL
           The residual of the FP vector.
           RESID = ABS( MINGMA )/SQRT( ZTZ )
[out]RQCORR
          RQCORR is REAL
           The Rayleigh Quotient correction to LAMBDA.
           RQCORR = MINGMA*TMP
[out]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.

Here is the caller graph for this function:

 All Files Functions