Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  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

SYNOPSIS

       SUBROUTINE ZHPGVD( ITYPE,  JOBZ,  UPLO,  N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK,
                          IWORK, LIWORK, INFO )

           CHARACTER      JOBZ, UPLO

           INTEGER        INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N

           INTEGER        IWORK( * )

           DOUBLE         PRECISION RWORK( * ), W( * )

           COMPLEX*16     AP( * ), BP( * ), WORK( * ), Z( LDZ, * )

PURPOSE

       ZHPGVD 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, stored in packed format, and B is also
        positive definite.
        If eigenvectors are desired, it uses a divide and conquer algorithm.
        The divide and conquer algorithm makes very mild assumptions about
        floating point arithmetic. It will work on machines with a guard
        digit in add/subtract, or on those binary machines without guard
        digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
        Cray-2. It could conceivably fail on hexadecimal or decimal machines
        without guard digits, but we know of none.

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.

        AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
                On entry, the upper or lower triangle of the Hermitian matrix
                A, packed columnwise in a linear array.  The j-th column of A
                is stored in the array AP as follows:
                if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
                if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
                On exit, the contents of AP are destroyed.

        BP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
                On entry, the upper or lower triangle of the Hermitian matrix
                B, packed columnwise in a linear array.  The j-th column of B
                is stored in the array BP as follows:
                if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
                if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
                On exit, the triangular factor U or L from the Cholesky
                factorization B = U**H*U or B = L*L**H, in the same storage
                format as B.

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

        Z       (output) COMPLEX*16 array, dimension (LDZ, N)
                If JOBZ = 'V', then if INFO = 0, Z 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 Z is not referenced.

        LDZ     (input) INTEGER
                The leading dimension of the array Z.  LDZ >= 1, and if
                JOBZ = 'V', LDZ >= max(1,N).

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

        LWORK   (input) INTEGER
                The dimension of the array WORK.
                If N <= 1,               LWORK >= 1.
                If JOBZ = 'N' and N > 1, LWORK >= N.
                If JOBZ = 'V' and N > 1, LWORK >= 2*N.
                If LWORK = -1, then a workspace query is assumed; the routine
                only calculates the required sizes of the WORK, RWORK and
                IWORK arrays, returns these values as the first entries of
                the WORK, RWORK and IWORK arrays, and no error message
                related to LWORK or LRWORK or LIWORK is issued by XERBLA.

        RWORK   (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
                On exit, if INFO = 0, RWORK(1) returns the required LRWORK.

        LRWORK  (input) INTEGER
                The dimension of array RWORK.
                If N <= 1,               LRWORK >= 1.
                If JOBZ = 'N' and N > 1, LRWORK >= N.
                If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
                If LRWORK = -1, then a workspace query is assumed; the
                routine only calculates the required sizes of the WORK, RWORK
                and IWORK arrays, returns these values as the first entries
                of the WORK, RWORK and IWORK arrays, and no error message
                related to LWORK or LRWORK or LIWORK is issued by XERBLA.

        IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
                On exit, if INFO = 0, IWORK(1) returns the required LIWORK.

        LIWORK  (input) INTEGER
                The dimension of array IWORK.
                If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
                If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
                If LIWORK = -1, then a workspace query is assumed; the
                routine only calculates the required sizes of the WORK, RWORK
                and IWORK arrays, returns these values as the first entries
                of the WORK, RWORK and IWORK arrays, and no error message
                related to LWORK or LRWORK or LIWORK is issued by XERBLA.

        INFO    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value
                > 0:  ZPPTRF or ZHPEVD returned an error code:
                <= N:  if INFO = i, ZHPEVD failed to converge;
                i off-diagonal elements of an intermediate
                tridiagonal form did not convergeto 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.

FURTHER DETAILS

        Based on contributions by
           Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

 LAPACK driver routine (version 3.3.1)      April 2011                            ZHPGVD(3lapack)