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dstevr.f(3)				      LAPACK				      dstevr.f(3)

NAME
       dstevr.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dstevr (JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ,
	   WORK, LWORK, IWORK, LIWORK, INFO)
	    DSTEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors
	   for OTHER matrices

Function/Subroutine Documentation
   subroutine dstevr (characterJOBZ, characterRANGE, integerN, double precision, dimension( * )D,
       double precision, dimension( * )E, double precisionVL, double precisionVU, integerIL,
       integerIU, double precisionABSTOL, integerM, double precision, dimension( * )W, double
       precision, dimension( ldz, * )Z, integerLDZ, integer, dimension( * )ISUPPZ, double
       precision, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerLIWORK,
       integerINFO)
	DSTEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for
       OTHER matrices

       Purpose:

	    DSTEVR computes selected eigenvalues and, optionally, eigenvectors
	    of a real symmetric tridiagonal matrix T.  Eigenvalues and
	    eigenvectors can be selected by specifying either a range of values
	    or a range of indices for the desired eigenvalues.

	    Whenever possible, DSTEVR calls DSTEMR to compute the
	    eigenspectrum using Relatively Robust Representations.  DSTEMR
	    computes eigenvalues by the dqds algorithm, while orthogonal
	    eigenvectors are computed from various "good" L D L^T representations
	    (also known as Relatively Robust Representations). Gram-Schmidt
	    orthogonalization is avoided as far as possible. More specifically,
	    the various steps of the algorithm are as follows. For the i-th
	    unreduced block of T,
	       (a) Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T
		    is a relatively robust representation,
	       (b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high
		   relative accuracy by the dqds algorithm,
	       (c) If there is a cluster of close eigenvalues, "choose" sigma_i
		   close to the cluster, and go to step (a),
	       (d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T,
		   compute the corresponding eigenvector by forming a
		   rank-revealing twisted factorization.
	    The desired accuracy of the output can be specified by the input
	    parameter ABSTOL.

	    For more details, see "A new O(n^2) algorithm for the symmetric
	    tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon,
	    Computer Science Division Technical Report No. UCB//CSD-97-971,
	    UC Berkeley, May 1997.

	    Note 1 : DSTEVR calls DSTEMR when the full spectrum is requested
	    on machines which conform to the ieee-754 floating point standard.
	    DSTEVR calls DSTEBZ and DSTEIN on non-ieee machines and
	    when partial spectrum requests are made.

	    Normal execution of DSTEMR may create NaNs and infinities and
	    hence may abort due to a floating point exception in environments
	    which do not handle NaNs and infinities in the ieee standard default
	    manner.

       Parameters:
	   JOBZ

		     JOBZ is CHARACTER*1
		     = 'N':  Compute eigenvalues only;
		     = 'V':  Compute eigenvalues and eigenvectors.

	   RANGE

		     RANGE is CHARACTER*1
		     = 'A': all eigenvalues will be found.
		     = 'V': all eigenvalues in the half-open interval (VL,VU]
			    will be found.
		     = 'I': the IL-th through IU-th eigenvalues will be found.
		     For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and
		     DSTEIN are called

	   N

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

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		     On entry, the n diagonal elements of the tridiagonal matrix
		     A.
		     On exit, D may be multiplied by a constant factor chosen
		     to avoid over/underflow in computing the eigenvalues.

	   E

		     E is DOUBLE PRECISION array, dimension (max(1,N-1))
		     On entry, the (n-1) subdiagonal elements of the tridiagonal
		     matrix A in elements 1 to N-1 of E.
		     On exit, E may be multiplied by a constant factor chosen
		     to avoid over/underflow in computing the eigenvalues.

	   VL

		     VL is DOUBLE PRECISION

	   VU

		     VU is DOUBLE PRECISION
		     If RANGE='V', the lower and upper bounds of the interval to
		     be searched for eigenvalues. VL < VU.
		     Not referenced if RANGE = 'A' or 'I'.

	   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, if N > 0; IL = 1 and IU = 0 if N = 0.
		     Not referenced if RANGE = 'A' or 'V'.

	   ABSTOL

		     ABSTOL is DOUBLE PRECISION
		     The absolute error tolerance for the eigenvalues.
		     An approximate eigenvalue is accepted as converged
		     when it is determined to lie in an interval [a,b]
		     of width less than or equal to

			     ABSTOL + EPS *   max( |a|,|b| ) ,

		     where EPS is the machine precision.  If ABSTOL is less than
		     or equal to zero, then  EPS*|T|  will be used in its place,
		     where |T| is the 1-norm of the tridiagonal matrix obtained
		     by reducing A to tridiagonal form.

		     See "Computing Small Singular Values of Bidiagonal Matrices
		     with Guaranteed High Relative Accuracy," by Demmel and
		     Kahan, LAPACK Working Note #3.

		     If high relative accuracy is important, set ABSTOL to
		     DLAMCH( 'Safe minimum' ).	Doing so will guarantee that
		     eigenvalues are computed to high relative accuracy when
		     possible in future releases.  The current code does not
		     make any guarantees about high relative accuracy, but
		     future releases will. See J. Barlow and J. Demmel,
		     "Computing Accurate Eigensystems of Scaled Diagonally
		     Dominant Matrices", LAPACK Working Note #7, for a discussion
		     of which matrices define their eigenvalues to high relative
		     accuracy.

	   M

		     M is INTEGER
		     The total number of eigenvalues found.  0 <= M <= N.
		     If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

	   W

		     W is DOUBLE PRECISION array, dimension (N)
		     The first M elements contain the selected eigenvalues in
		     ascending order.

	   Z

		     Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M) )
		     If JOBZ = 'V', then if INFO = 0, the first M columns of Z
		     contain the orthonormal eigenvectors of the matrix A
		     corresponding to the selected eigenvalues, with the i-th
		     column of Z holding the eigenvector associated with W(i).
		     Note: the user must ensure that at least max(1,M) columns are
		     supplied in the array Z; if RANGE = 'V', the exact value of M
		     is not known in advance and an upper bound must be used.

	   LDZ

		     LDZ is INTEGER
		     The leading dimension of the array Z.  LDZ >= 1, and if
		     JOBZ = 'V', LDZ >= max(1,N).

	   ISUPPZ

		     ISUPPZ is INTEGER array, dimension ( 2*max(1,M) )
		     The support of the eigenvectors in Z, i.e., the indices
		     indicating the nonzero elements in Z. The i-th eigenvector
		     is nonzero only in elements ISUPPZ( 2*i-1 ) through
		     ISUPPZ( 2*i ).
		     Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal (and
		     minimal) LWORK.

	   LWORK

		     LWORK is INTEGER
		     The dimension of the array WORK.  LWORK >= max(1,20*N).

		     If LWORK = -1, then a workspace query is assumed; the routine
		     only calculates the optimal sizes of the WORK and IWORK
		     arrays, returns these values as the first entries of the WORK
		     and IWORK arrays, and no error message related to LWORK or
		     LIWORK is issued by XERBLA.

	   IWORK

		     IWORK is INTEGER array, dimension (MAX(1,LIWORK))
		     On exit, if INFO = 0, IWORK(1) returns the optimal (and
		     minimal) LIWORK.

	   LIWORK

		     LIWORK is INTEGER
		     The dimension of the array IWORK.	LIWORK >= max(1,10*N).

		     If LIWORK = -1, then a workspace query is assumed; the
		     routine only calculates the optimal sizes of the WORK and
		     IWORK arrays, returns these values as the first entries of
		     the WORK and IWORK arrays, and no error message related to
		     LWORK or LIWORK is issued by XERBLA.

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value
		     > 0:  Internal error

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Contributors:
	   Inderjit Dhillon, IBM Almaden, USA
	    Osni Marques, LBNL/NERSC, USA
	    Ken Stanley, Computer Science Division, University of California at Berkeley, USA

       Definition at line 296 of file dstevr.f.

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

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