zhpgvd.f(3)

NAME
zhpgvd.f -

SYNOPSIS

  Functions/Subroutines
subroutine ZHPGVD (ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
ZHPGST

Function/Subroutine Documentation

  subroutine ZHPGVD (INTEGERITYPE, CHARACTERJOBZ, CHARACTERUPLO, INTEGERN, COMPLEX*16, dimension( * )AP, COMPLEX*16, dimension( * )BP, DOUBLE PRECISION, dimension( * )W, COMPLEX*16, dimension( ldz, * )Z, INTEGERLDZ, COMPLEX*16, dimension( * )WORK, INTEGERLWORK, DOUBLE PRECISION, dimension( * )RWORK, INTEGERLRWORK, INTEGER, dimension( * )IWORK, INTEGERLIWORK, INTEGERINFO)

ZHPGST

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.

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.

    AP

              AP is 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

              BP is 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

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

    Z

              Z is 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

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

    WORK

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

    LWORK

              LWORK is 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

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

    LRWORK

              LRWORK is 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

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

    LIWORK

              LIWORK is 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

              INFO is 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.

Author:
    Univ'. of Tennessee

    Univ'. of California Berkeley

    Univ'. of Colorado Denver

    NAG Ltd'.

Date:
    November 2011

Contributors:
    Mark Fahey, Department of Mathematics, Univ'. of Kentucky, USA

Definition at line 231 of file zhpgvd.f'.

Author

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