zhegv.f(3)

NAME
zhegv.f -

SYNOPSIS

  Functions/Subroutines
subroutine ZHEGV (ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, RWORK, INFO)
ZHEGST

Function/Subroutine Documentation

  subroutine ZHEGV (INTEGERITYPE, CHARACTERJOBZ, CHARACTERUPLO, INTEGERN, COMPLEX*16, dimension( lda, * )A, INTEGERLDA, COMPLEX*16, dimension( ldb, * )B, INTEGERLDB, DOUBLE PRECISION, dimension( * )W, COMPLEX*16, dimension( * )WORK, INTEGERLWORK, DOUBLE PRECISION, dimension( * )RWORK, INTEGERINFO)

ZHEGST

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.

Parameters:
    ITYPE

              ITYPE is 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

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

    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangles of A and B are stored;
              = 'L':  Lower triangles of A and B are stored.

    N

              N is INTEGER
              The order of the matrices A and B.  N >= 0.

    A

              A is 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

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

    B

              B is 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

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).

    W

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

    WORK

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

    LWORK

              LWORK is 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

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

    INFO

              INFO is 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.

Author:
    Univ'. of Tennessee

    Univ'. of California Berkeley

    Univ'. of Colorado Denver

    NAG Ltd'.

Date:
    November 2011

Definition at line 181 of file zhegv.f'.

Author

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