CHPEVD(3)      LAPACK routine of NEC Numeric Library Collection      CHPEVD(3)



NAME
       CHPEVD

SYNOPSIS
       SUBROUTINE CHPEVD (JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
           LRWORK, IWORK, LIWORK, INFO)



PURPOSE
            CHPEVD computes all the eigenvalues and, optionally, eigenvectors of
            a complex Hermitian matrix A in packed storage.  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
           JOBZ      (input)
                     JOBZ is CHARACTER*1
                     = 'N':  Compute eigenvalues only;
                     = 'V':  Compute eigenvalues and eigenvectors.

           UPLO      (input)
                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N         (input)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           AP        (input/output)
                     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, AP is overwritten by values generated during the
                     reduction to tridiagonal form.  If UPLO = 'U', the diagonal
                     and first superdiagonal of the tridiagonal matrix T overwrite
                     the corresponding elements of A, and if UPLO = 'L', the
                     diagonal and first subdiagonal of T overwrite the
                     corresponding elements of A.

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

           Z         (output)
                     Z is COMPLEX array, dimension (LDZ, N)
                     If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
                     eigenvectors of the matrix A, with the i-th column of Z
                     holding the eigenvector associated with W(i).
                     If JOBZ = 'N', then Z is not referenced.

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

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

           LWORK     (input)
                     LWORK is INTEGER
                     The dimension of array WORK.
                     If N <= 1,               LWORK must be at least 1.
                     If JOBZ = 'N' and N > 1, LWORK must be at least N.
                     If JOBZ = 'V' and N > 1, LWORK must be at least 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     (output)
                     RWORK is REAL array, dimension (MAX(1,LRWORK))
                     On exit, if INFO = 0, RWORK(1) returns the required LRWORK.

           LRWORK    (input)
                     LRWORK is INTEGER
                     The dimension of array RWORK.
                     If N <= 1,               LRWORK must be at least 1.
                     If JOBZ = 'N' and N > 1, LRWORK must be at least N.
                     If JOBZ = 'V' and N > 1, LRWORK must be at least
                               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     (output)
                     IWORK is INTEGER array, dimension (MAX(1,LIWORK))
                     On exit, if INFO = 0, IWORK(1) returns the required LIWORK.

           LIWORK    (input)
                     LIWORK is INTEGER
                     The dimension of array IWORK.
                     If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
                     If JOBZ  = 'V' and N > 1, LIWORK must be at least 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)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value.
                     > 0:  if INFO = i, the algorithm failed to converge; i
                           off-diagonal elements of an intermediate tridiagonal
                           form did not converge to zero.



LAPACK routine                  31 October 2017                      CHPEVD(3)