NAME

       cstedc.f -

SYNOPSIS

   Functions/Subroutines
       subroutine cstedc (COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK,
           INFO)
           CSTEDC

Function/Subroutine Documentation

   subroutine cstedc (characterCOMPZ, integerN, real, dimension( * )D, real, dimension( * )E,
       complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( * )WORK, integerLWORK,
       real, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerLIWORK,
       integerINFO)
       CSTEDC

       Purpose:

            CSTEDC computes all eigenvalues and, optionally, eigenvectors of a
            symmetric tridiagonal matrix using the divide and conquer method.
            The eigenvectors of a full or band complex Hermitian matrix can also
            be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this
            matrix to tridiagonal form.

            This code 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.  See SLAED3 for details.

       Parameters:
           COMPZ

                     COMPZ is CHARACTER*1
                     = 'N':  Compute eigenvalues only.
                     = 'I':  Compute eigenvectors of tridiagonal matrix also.
                     = 'V':  Compute eigenvectors of original Hermitian matrix
                             also.  On entry, Z contains the unitary matrix used
                             to reduce the original matrix to tridiagonal form.

           N

                     N is INTEGER
                     The dimension of the symmetric tridiagonal matrix.  N >= 0.

           D

                     D is REAL array, dimension (N)
                     On entry, the diagonal elements of the tridiagonal matrix.
                     On exit, if INFO = 0, the eigenvalues in ascending order.

           E

                     E is REAL array, dimension (N-1)
                     On entry, the subdiagonal elements of the tridiagonal matrix.
                     On exit, E has been destroyed.

           Z

                     Z is COMPLEX array, dimension (LDZ,N)
                     On entry, if COMPZ = 'V', then Z contains the unitary
                     matrix used in the reduction to tridiagonal form.
                     On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
                     orthonormal eigenvectors of the original Hermitian matrix,
                     and if COMPZ = 'I', Z contains the orthonormal eigenvectors
                     of the symmetric tridiagonal matrix.
                     If  COMPZ = 'N', then Z is not referenced.

           LDZ

                     LDZ is INTEGER
                     The leading dimension of the array Z.  LDZ >= 1.
                     If eigenvectors are desired, then LDZ >= max(1,N).

           WORK

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

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.
                     If COMPZ = 'V' and N > 1, LWORK must be at least N*N.
                     Note that for COMPZ = 'V', then if N is less than or
                     equal to the minimum divide size, usually 25, then LWORK need
                     only be 1.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal 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 optimal LRWORK.

           LRWORK

                     LRWORK is INTEGER
                     The dimension of the array RWORK.
                     If COMPZ = 'N' or N <= 1, LRWORK must be at least 1.
                     If COMPZ = 'V' and N > 1, LRWORK must be at least
                                    1 + 3*N + 2*N*lg N + 4*N**2 ,
                                    where lg( N ) = smallest integer k such
                                    that 2**k >= N.
                     If COMPZ = 'I' and N > 1, LRWORK must be at least
                                    1 + 4*N + 2*N**2 .
                     Note that for COMPZ = 'I' or 'V', then if N is less than or
                     equal to the minimum divide size, usually 25, then LRWORK
                     need only be max(1,2*(N-1)).

                     If LRWORK = -1, then a workspace query is assumed; the
                     routine only calculates the optimal 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 optimal LIWORK.

           LIWORK

                     LIWORK is INTEGER
                     The dimension of the array IWORK.
                     If COMPZ = 'N' or N <= 1, LIWORK must be at least 1.
                     If COMPZ = 'V' or N > 1,  LIWORK must be at least
                                               6 + 6*N + 5*N*lg N.
                     If COMPZ = 'I' or N > 1,  LIWORK must be at least
                                               3 + 5*N .
                     Note that for COMPZ = 'I' or 'V', then if N is less than or
                     equal to the minimum divide size, usually 25, then LIWORK
                     need only be 1.

                     If LIWORK = -1, then a workspace query is assumed; the
                     routine only calculates the optimal 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:  The algorithm failed to compute an eigenvalue while
                           working on the submatrix lying in rows and columns
                           INFO/(N+1) through mod(INFO,N+1).

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Contributors:
           Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

       Definition at line 212 of file cstedc.f.

Author

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