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dlar1v.f(3)				      LAPACK				      dlar1v.f(3)

NAME
       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 - \I.

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 - \I.

       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.

Version 3.4.2				 Tue Sep 25 2012			      dlar1v.f(3)
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