zhegv(3S)

NAME
     ZHEGV - compute all the eigenvalues, and optionally, the eigenvectors of
     a complex generalized Hermitian-definite eigenproblem, of the form
     A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

SYNOPSIS
     SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK,
                       RWORK, INFO )

         CHARACTER     JOBZ, UPLO

         INTEGER       INFO, ITYPE, LDA, LDB, LWORK, N

         DOUBLE        PRECISION RWORK( * ), W( * )

         COMPLEX*16    A( LDA, * ), B( LDB, * ), 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
     ZHEGV computes all the eigenvalues, and optionally, the eigenvectors of a
     complex generalized Hermitian-definite eigenproblem, of the form
     A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are
     assumed to be Hermitian and B is also
     positive definite.


ARGUMENTS
     ITYPE   (input) INTEGER
             Specifies the problem type to be solved:
             = 1:  A*x = (lambda)*B*x
             = 2:  A*B*x = (lambda)*x
             = 3:  B*A*x = (lambda)*x

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

     UPLO    (input) CHARACTER*1
             = 'U':  Upper triangles of A and B are stored;
             = 'L':  Lower triangles of A and B are stored.
     N       (input) INTEGER
             The order of the matrices A and B.  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 matrix Z
             of eigenvectors.  The eigenvectors are normalized as follows:  if
             ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I.
             If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or
             the lower triangle (if UPLO='L') of A, including the diagonal, is
             destroyed.

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

     B       (input/output) COMPLEX*16 array, dimension (LDB, N)
             On entry, the Hermitian positive definite matrix B.  If UPLO =
             'U', the leading N-by-N upper triangular part of B contains the
             upper triangular part of the matrix B.  If UPLO = 'L', the
             leading N-by-N lower triangular part of B contains the lower
             triangular part of the matrix B.

             On exit, if INFO <= N, the part of B containing the matrix is
             overwritten by the triangular factor U or L from the Cholesky
             factorization B = U**H*U or B = L*L**H.

     LDB     (input) INTEGER
             The leading dimension of the array B.  LDB >= 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:  ZPOTRF or ZHEEV returned an error code:
             <= N:  if INFO = i, ZHEEV failed to converge; i off-diagonal
             elements of an intermediate tridiagonal form did not converge to
             zero; > N:   if INFO = N + i, for 1 <= i <= N, then the leading
             minor of order i of B is not positive definite.  The
             factorization of B could not be completed and no eigenvalues or
             eigenvectors were computed.

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

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