zheev(3S)

NAME
     ZHEEV - compute all eigenvalues and, optionally, eigenvectors of a
     complex Hermitian matrix A

SYNOPSIS
     SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO )

         CHARACTER     JOBZ, UPLO

         INTEGER       INFO, LDA, LWORK, N

         DOUBLE        PRECISION RWORK( * ), W( * )

         COMPLEX*16    A( LDA, * ), WORK( * )

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
     ZHEEV computes all eigenvalues and, optionally, eigenvectors of a complex
     Hermitian matrix A.

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.

     A       (input/output) COMPLEX*16 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, if JOBZ = 'V', then if INFO = 0, A contains
             the orthonormal eigenvectors of the matrix A.  If JOBZ = 'N',
             then on exit the lower triangle (if UPLO='L') or the upper
             triangle (if UPLO='U') of A, including the diagonal, is
             destroyed.

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

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

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

     LWORK   (input) INTEGER
             The length of the array WORK.  LWORK >= max(1,2*N-1).  For
             optimal efficiency, LWORK >= (NB+1)*N, where NB is the blocksize
             for ZHETRD 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   (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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