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CentOS 7.0 - man page for dlarre.f (centos section 3)

dlarre.f(3)				      LAPACK				      dlarre.f(3)

NAME
       dlarre.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlarre (RANGE, N, VL, VU, IL, IU, D, E, E2, RTOL1, RTOL2, SPLTOL, NSPLIT,
	   ISPLIT, M, W, WERR, WGAP, IBLOCK, INDEXW, GERS, PIVMIN, WORK, IWORK, INFO)
	   DLARRE given the tridiagonal matrix T, sets small off-diagonal elements to zero and
	   for each unreduced block Ti, finds base representations and eigenvalues.

Function/Subroutine Documentation
   subroutine dlarre (characterRANGE, integerN, double precisionVL, double precisionVU,
       integerIL, integerIU, double precision, dimension( * )D, double precision, dimension( *
       )E, double precision, dimension( * )E2, double precisionRTOL1, double precisionRTOL2,
       double precisionSPLTOL, integerNSPLIT, integer, dimension( * )ISPLIT, integerM, double
       precision, dimension( * )W, double precision, dimension( * )WERR, double precision,
       dimension( * )WGAP, integer, dimension( * )IBLOCK, integer, dimension( * )INDEXW, double
       precision, dimension( * )GERS, double precisionPIVMIN, double precision, dimension( *
       )WORK, integer, dimension( * )IWORK, integerINFO)
       DLARRE given the tridiagonal matrix T, sets small off-diagonal elements to zero and for
       each unreduced block Ti, finds base representations and eigenvalues.

       Purpose:

	    To find the desired eigenvalues of a given real symmetric
	    tridiagonal matrix T, DLARRE sets any "small" off-diagonal
	    elements to zero, and for each unreduced block T_i, it finds
	    (a) a suitable shift at one end of the block's spectrum,
	    (b) the base representation, T_i - sigma_i I = L_i D_i L_i^T, and
	    (c) eigenvalues of each L_i D_i L_i^T.
	    The representations and eigenvalues found are then used by
	    DSTEMR to compute the eigenvectors of T.
	    The accuracy varies depending on whether bisection is used to
	    find a few eigenvalues or the dqds algorithm (subroutine DLASQ2) to
	    conpute all and then discard any unwanted one.
	    As an added benefit, DLARRE also outputs the n
	    Gerschgorin intervals for the matrices L_i D_i L_i^T.

       Parameters:
	   RANGE

		     RANGE is CHARACTER*1
		     = 'A': ("All")   all eigenvalues will be found.
		     = 'V': ("Value") all eigenvalues in the half-open interval
				      (VL, VU] will be found.
		     = 'I': ("Index") the IL-th through IU-th eigenvalues (of the
				      entire matrix) will be found.

	   N

		     N is INTEGER
		     The order of the matrix. N > 0.

	   VL

		     VL is DOUBLE PRECISION

	   VU

		     VU is DOUBLE PRECISION
		     If RANGE='V', the lower and upper bounds for the eigenvalues.
		     Eigenvalues less than or equal to VL, or greater than VU,
		     will not be returned.  VL < VU.
		     If RANGE='I' or ='A', DLARRE computes bounds on the desired
		     part of the spectrum.

	   IL

		     IL is INTEGER

	   IU

		     IU is INTEGER
		     If RANGE='I', the indices (in ascending order) of the
		     smallest and largest eigenvalues to be returned.
		     1 <= IL <= IU <= N.

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		     On entry, the N diagonal elements of the tridiagonal
		     matrix T.
		     On exit, the N diagonal elements of the diagonal
		     matrices D_i.

	   E

		     E is DOUBLE PRECISION array, dimension (N)
		     On entry, the first (N-1) entries contain the subdiagonal
		     elements of the tridiagonal matrix T; E(N) need not be set.
		     On exit, E contains the subdiagonal elements of the unit
		     bidiagonal matrices L_i. The entries E( ISPLIT( I ) ),
		     1 <= I <= NSPLIT, contain the base points sigma_i on output.

	   E2

		     E2 is DOUBLE PRECISION array, dimension (N)
		     On entry, the first (N-1) entries contain the SQUARES of the
		     subdiagonal elements of the tridiagonal matrix T;
		     E2(N) need not be set.
		     On exit, the entries E2( ISPLIT( I ) ),
		     1 <= I <= NSPLIT, have been set to zero

	   RTOL1

		     RTOL1 is DOUBLE PRECISION

	   RTOL2

		     RTOL2 is DOUBLE PRECISION
		      Parameters for bisection.
		      An interval [LEFT,RIGHT] has converged if
		      RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )

	   SPLTOL

		     SPLTOL is DOUBLE PRECISION
		     The threshold for splitting.

	   NSPLIT

		     NSPLIT is INTEGER
		     The number of blocks T splits into. 1 <= NSPLIT <= N.

	   ISPLIT

		     ISPLIT is INTEGER array, dimension (N)
		     The splitting points, at which T breaks up into blocks.
		     The first block consists of rows/columns 1 to ISPLIT(1),
		     the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
		     etc., and the NSPLIT-th consists of rows/columns
		     ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.

	   M

		     M is INTEGER
		     The total number of eigenvalues (of all L_i D_i L_i^T)
		     found.

	   W

		     W is DOUBLE PRECISION array, dimension (N)
		     The first M elements contain the eigenvalues. The
		     eigenvalues of each of the blocks, L_i D_i L_i^T, are
		     sorted in ascending order ( DLARRE may use the
		     remaining N-M elements as workspace).

	   WERR

		     WERR is DOUBLE PRECISION array, dimension (N)
		     The error bound on the corresponding eigenvalue in W.

	   WGAP

		     WGAP is DOUBLE PRECISION array, dimension (N)
		     The separation from the right neighbor eigenvalue in W.
		     The gap is only with respect to the eigenvalues of the same block
		     as each block has its own representation tree.
		     Exception: at the right end of a block we store the left gap

	   IBLOCK

		     IBLOCK is INTEGER array, dimension (N)
		     The indices of the blocks (submatrices) associated with the
		     corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue
		     W(i) belongs to the first block from the top, =2 if W(i)
		     belongs to the second block, etc.

	   INDEXW

		     INDEXW is INTEGER array, dimension (N)
		     The indices of the eigenvalues within each block (submatrix);
		     for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the
		     i-th eigenvalue W(i) is the 10-th eigenvalue in block 2

	   GERS

		     GERS is DOUBLE PRECISION array, dimension (2*N)
		     The N Gerschgorin intervals (the i-th Gerschgorin interval
		     is (GERS(2*i-1), GERS(2*i)).

	   PIVMIN

		     PIVMIN is DOUBLE PRECISION
		     The minimum pivot in the Sturm sequence for T.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (6*N)
		     Workspace.

	   IWORK

		     IWORK is INTEGER array, dimension (5*N)
		     Workspace.

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     > 0:  A problem occured in DLARRE.
		     < 0:  One of the called subroutines signaled an internal problem.
			   Needs inspection of the corresponding parameter IINFO
			   for further information.

		     =-1:  Problem in DLARRD.
		     = 2:  No base representation could be found in MAXTRY iterations.
			   Increasing MAXTRY and recompilation might be a remedy.
		     =-3:  Problem in DLARRB when computing the refined root
			   representation for DLASQ2.
		     =-4:  Problem in DLARRB when preforming bisection on the
			   desired part of the spectrum.
		     =-5:  Problem in DLASQ2.
		     =-6:  Problem in DLASQ2.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Further Details:

	     The base representations are required to suffer very little
	     element growth and consequently define all their eigenvalues to
	     high relative accuracy.

       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 295 of file dlarre.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

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


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