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

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

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:: 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.

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Functions/Subroutines

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