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cheevx.f(3)				      LAPACK				      cheevx.f(3)

NAME
       cheevx.f -

SYNOPSIS
   Functions/Subroutines
       subroutine cheevx (JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ,
	   WORK, LWORK, RWORK, IWORK, IFAIL, INFO)
	    CHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors
	   for HE matrices

Function/Subroutine Documentation
   subroutine cheevx (characterJOBZ, characterRANGE, characterUPLO, integerN, complex, dimension(
       lda, * )A, integerLDA, realVL, realVU, integerIL, integerIU, realABSTOL, integerM, real,
       dimension( * )W, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( * )WORK,
       integerLWORK, real, dimension( * )RWORK, integer, dimension( * )IWORK, integer, dimension(
       * )IFAIL, integerINFO)
	CHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for
       HE matrices

       Purpose:

	    CHEEVX computes selected eigenvalues and, optionally, eigenvectors
	    of a complex Hermitian 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.

	   UPLO

		     UPLO is CHARACTER*1
		     = 'U':  Upper triangle of A is stored;
		     = 'L':  Lower triangle of A is stored.

	   N

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

	   A

		     A is COMPLEX array, dimension (LDA, N)
		     On entry, the Hermitian matrix A.	If UPLO = 'U', the
		     leading N-by-N upper triangular part of A contains the
		     upper triangular part of the matrix A.  If UPLO = 'L',
		     the leading N-by-N lower triangular part of A contains
		     the lower triangular part of the matrix A.
		     On exit, the lower triangle (if UPLO='L') or the upper
		     triangle (if UPLO='U') of A, including the diagonal, is
		     destroyed.

	   LDA

		     LDA is INTEGER
		     The leading dimension of the array A.  LDA >= max(1,N).

	   VL

		     VL is REAL

	   VU

		     VU is REAL
		     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 REAL
		     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.

		     Eigenvalues will be computed most accurately when ABSTOL is
		     set to twice the underflow threshold 2*SLAMCH('S'), not zero.
		     If this routine returns with INFO>0, indicating that some
		     eigenvectors did not converge, try setting ABSTOL to
		     2*SLAMCH('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 REAL array, dimension (N)
		     On normal exit, the first M elements contain the selected
		     eigenvalues in ascending order.

	   Z

		     Z is COMPLEX 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, 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 COMPLEX array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

		     LWORK is INTEGER
		     The length of the array WORK.  LWORK >= 1, when N <= 1;
		     otherwise 2*N.
		     For optimal efficiency, LWORK >= (NB+1)*N,
		     where NB is the max of the blocksize for CHETRD and for
		     CUNMTR as returned by ILAENV.

		     If LWORK = -1, then a workspace query is assumed; the routine
		     only calculates the optimal size of the WORK array, returns
		     this value as the first entry of the WORK array, and no error
		     message related to LWORK is issued by XERBLA.

	   RWORK

		     RWORK is REAL array, dimension (7*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 251 of file cheevx.f.

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

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