ZHPEVX(l)								 )								 ZHPEVX(l)

NAME

       ZHPEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage

SYNOPSIS

       SUBROUTINE ZHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO )

	   CHARACTER	  JOBZ, RANGE, UPLO

	   INTEGER	  IL, INFO, IU, LDZ, M, N

	   DOUBLE	  PRECISION ABSTOL, VL, VU

	   INTEGER	  IFAIL( * ), IWORK( * )

	   DOUBLE	  PRECISION RWORK( * ), W( * )

	   COMPLEX*16	  AP( * ), WORK( * ), Z( LDZ, * )

PURPOSE

       ZHPEVX  computes  selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage. Eigenvalues/vectors
       can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

ARGUMENTS

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

       RANGE   (input) 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    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
	       On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array.  The  j-th  column  of  A	is
	       stored  in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) =
	       A(i,j) for j<=i<=n.

	       On exit, AP is overwritten by values generated during the reduction to tridiagonal form.  If UPLO = 'U',  the  diagonal	and  first
	       superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first sub-
	       diagonal of T overwrite the corresponding elements of A.

       VL      (input) DOUBLE PRECISION
	       VU      (input) 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      (input) INTEGER
	       IU	(input)  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  (input) 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 AP to tridiagonal form.

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

       W       (output) DOUBLE PRECISION array, dimension (N)
	       If INFO = 0, the selected eigenvalues in ascending order.

       Z       (output) COMPLEX*16 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     (input) INTEGER
	       The leading dimension of the array Z.  LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).

       WORK    (workspace) COMPLEX*16 array, dimension (2*N)

       RWORK   (workspace) DOUBLE PRECISION array, dimension (7*N)

       IWORK   (workspace) INTEGER array, dimension (5*N)

       IFAIL   (output) 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    (output) 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.

LAPACK version 3.0						   15 June 2000 							 ZHPEVX(l)