zhpev(3S)

NAME
     ZHPEV - compute all the eigenvalues and, optionally, eigenvectors of a
     complex Hermitian matrix in packed storage

SYNOPSIS
     SUBROUTINE ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO )

         CHARACTER     JOBZ, UPLO

         INTEGER       INFO, LDZ, N

         DOUBLE        PRECISION RWORK( * ), W( * )

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

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a
     complex Hermitian matrix in packed storage.

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

     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 subdiagonal of T overwrite the corresponding elements of A.

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

     Z       (output) COMPLEX*16 array, dimension (LDZ, N)
             If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
             eigenvectors of the matrix A, with the i-th column of Z holding
             the eigenvector associated with W(i).  If JOBZ = 'N', then Z is
             not referenced.

     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 (max(1, 2*N-1))

     RWORK   (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))

     INFO    (output) INTEGER
             = 0:  successful exit.
             < 0:  if INFO = -i, the i-th argument had an illegal value.
             > 0:  if INFO = i, the algorithm failed to converge; i off-
             diagonal elements of an intermediate tridiagonal form did not
             converge to zero.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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