ZHEGV (3lapack)

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( * )

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 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.

  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.