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dstevx.f(3)				      LAPACK				      dstevx.f(3)

NAME
       dstevx.f -

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

Function/Subroutine Documentation
   subroutine dstevx (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, double precision, dimension( * )WORK,
       integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)
	DSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for
       OTHER matrices

       Purpose:

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

       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.

	   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.

		     Eigenvalues will be computed most accurately when ABSTOL is
		     set to twice the underflow threshold 2*DLAMCH('S'), not zero.
		     If this routine returns with INFO>0, indicating that some
		     eigenvectors did not converge, try setting ABSTOL to
		     2*DLAMCH('S').

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

	   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).
		     If an eigenvector fails to converge (INFO > 0), then that
		     column of Z contains the latest approximation to the
		     eigenvector, and the index of the eigenvector is returned
		     in IFAIL.	If JOBZ = 'N', then Z is not referenced.
		     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).

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (5*N)

	   IWORK

		     IWORK is INTEGER array, dimension (5*N)

	   IFAIL

		     IFAIL is INTEGER array, dimension (N)
		     If JOBZ = 'V', then if INFO = 0, the first M elements of
		     IFAIL are zero.  If INFO > 0, then IFAIL contains the
		     indices of the eigenvectors that failed to converge.
		     If JOBZ = 'N', then IFAIL is not referenced.

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value
		     > 0:  if INFO = i, then i eigenvectors failed to converge.
			   Their indices are stored in array IFAIL.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 220 of file dstevx.f.

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

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