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.

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
                    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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

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