SRC/chpgvd.f(3)            Library Functions Manual            SRC/chpgvd.f(3)

NAME
       SRC/chpgvd.f

SYNOPSIS
   Functions/Subroutines
       subroutine chpgvd (itype, jobz, uplo, n, ap, bp, w, z, ldz, work,
           lwork, rwork, lrwork, iwork, liwork, info)
           CHPGVD

Function/Subroutine Documentation
   subroutine chpgvd (integer itype, character jobz, character uplo, integer
       n, complex, dimension( * ) ap, complex, dimension( * ) bp, real,
       dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex,
       dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer
       lrwork, integer, dimension( * ) iwork, integer liwork, integer info)
       CHPGVD

       Purpose:


           !>
           !> CHPGVD 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.
           !>
           !>

       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 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 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 REAL array, dimension (N)
           !>          If INFO = 0, the eigenvalues in ascending order.
           !>

           Z

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

           LWORK

           !>          LWORK is INTEGER
           !>          The dimension of 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 REAL 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:  CPPTRF or CHPEVD returned an error code:
           !>             <= N:  if INFO = i, CHPEVD 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
           !>                    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.

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

       Definition at line 223 of file chpgvd.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/chpgvd.f(3)