zhegv.f - Man Page

subroutine zhegv (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, rwork, info)
ZHEGV

ZHEGV  

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
                    principal minor of order i of B is not positive.
                    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.

Definition at line 179 of file zhegv.f.