NAME

       dstedc.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dstedc (COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)
           DSTEDC

Function/Subroutine Documentation

   subroutine dstedc (character COMPZ, integer N, double precision, dimension( * ) D, double
       precision, dimension( * ) E, double precision, dimension( ldz, * ) Z, integer LDZ, double
       precision, dimension( * ) WORK, integer LWORK, integer, dimension( * ) IWORK, integer
       LIWORK, integer INFO)
       DSTEDC

       Purpose:

            DSTEDC computes all eigenvalues and, optionally, eigenvectors of a
            symmetric tridiagonal matrix using the divide and conquer method.
            The eigenvectors of a full or band real symmetric matrix can also be
            found if DSYTRD or DSPTRD or DSBTRD 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 DLAED3 for details.

       Parameters:
           COMPZ

                     COMPZ is CHARACTER*1
                     = 'N':  Compute eigenvalues only.
                     = 'I':  Compute eigenvectors of tridiagonal matrix also.
                     = 'V':  Compute eigenvectors of original dense symmetric
                             matrix also.  On entry, Z contains the orthogonal
                             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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N-1)
                     On entry, the subdiagonal elements of the tridiagonal matrix.
                     On exit, E has been destroyed.

           Z

                     Z is DOUBLE PRECISION array, dimension (LDZ,N)
                     On entry, if COMPZ = 'V', then Z contains the orthogonal
                     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 symmetric 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 DOUBLE PRECISION array,
                                                    dimension (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 N <= 1 then LWORK must be at least 1.
                     If COMPZ = 'V' and N > 1 then LWORK 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 then LWORK must be at least
                                    ( 1 + 4*N + 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 LWORK need
                     only be max(1,2*(N-1)).

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK 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 then LIWORK must be at least 1.
                     If COMPZ = 'V' and N > 1 then LIWORK must be at least
                                    ( 6 + 6*N + 5*N*lg N ).
                     If COMPZ = 'I' and N > 1 then 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 size of the IWORK array,
                     returns this value as the first entry of the IWORK array, and
                     no error message related to 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 2015

       Contributors:
           Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
            Modified by Francoise Tisseur, University of Tennessee

Author

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