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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, * )



     #include <sunperf.h>

     void zhpevx(char jobz, char range, char uplo, int  n,  doub-
               lecomplex  *zap, double vl, double vu, int il, int
               iu, double abstol, int *m, double  *w,  doublecom-
               plex *zz, int ldz, int *ifail, int *info) ;

PURPOSE
     ZHPEVX computes selected eigenvalues and, optionally, eigen-
     vectors  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 eigen-
     values.


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  Her-
               mitian  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 subdiagonal 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 refer-
               enced 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 tri-
               diagonal 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 eigenvec-
               tor  fails to converge, then that column of Z con-
               tains 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  ele-
               ments  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 ille-
               gal value
               > 0:  if INFO = i, then i eigenvectors  failed  to
               converge.   Their  indices  are  stored  in  array
               IFAIL.

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