zhpevd(3S)

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

SYNOPSIS
     SUBROUTINE ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
                        LRWORK, IWORK, LIWORK, INFO )

         CHARACTER      JOBZ, UPLO

         INTEGER        INFO, LDZ, LIWORK, LRWORK, LWORK, N

         INTEGER        IWORK( * )

         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
     ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of a
     complex Hermitian matrix A in packed storage. If eigenvectors are
     desired, it uses a divide and conquer algorithm.

     The divide and conquer algorithm makes very mild assumptions about
     floating point arithmetic. It will work on machines with a guard digit in
     add/subtract, or on those binary machines without guard digits which
     subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
     conceivably fail on hexadecimal or decimal machines without guard digits,
     but we know of none.


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/output) COMPLEX*16 array, dimension (LWORK)
             On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
             The dimension of array WORK.  If N <= 1,               LWORK must
             be at least 1.  If JOBZ = 'N' and N > 1, LWORK must be at least
             N.  If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.

             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   (workspace/output) DOUBLE PRECISION array,
             dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the
             optimal LRWORK.

     LRWORK  (input) INTEGER
             The dimension of array RWORK.  If N <= 1,               LRWORK
             must be at least 1.  If JOBZ = 'N' and N > 1, LRWORK must be at
             least N.  If JOBZ = 'V' and N > 1, LRWORK must be at least 1 +
             5*N + 2*N**2.

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

     IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
             On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

     LIWORK  (input) INTEGER
             The dimension of array IWORK.  If JOBZ  = 'N' or N <= 1, LIWORK
             must be at least 1.  If JOBZ  = 'V' and N > 1, LIWORK must be at
             least 3 + 5*N.

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

     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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