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



NAME
       SSTEVD

SYNOPSIS
       SUBROUTINE SSTEVD (JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
           INFO)



PURPOSE
            SSTEVD computes all eigenvalues and, optionally, eigenvectors of a
            real symmetric tridiagonal matrix. 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.

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

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

           E         (input/output)
                     E is REAL array, dimension (N-1)
                     On entry, the (n-1) subdiagonal elements of the tridiagonal
                     matrix A, stored in elements 1 to N-1 of E.
                     On exit, the contents of E are destroyed.

           Z         (output)
                     Z is REAL 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 D(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 REAL array,
                                                    dimension (LWORK)
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK     (input)
                     LWORK is INTEGER
                     The dimension of the array WORK.
                     If JOBZ  = 'N' or N <= 1 then LWORK must be at least 1.
                     If JOBZ  = 'V' and N > 1 then LWORK must be at least
                                    ( 1 + 4*N + N**2 ).

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal sizes of the WORK and IWORK
                     arrays, returns these values as the first entries of the WORK
                     and IWORK arrays, and no error message related to LWORK 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 optimal LIWORK.

           LIWORK    (input)
                     LIWORK is INTEGER
                     The dimension of the array IWORK.
                     If JOBZ  = 'N' or N <= 1 then LIWORK must be at least 1.
                     If JOBZ  = 'V' and N > 1 then LIWORK must be at least 3+5*N.

                     If LIWORK = -1, then a workspace query is assumed; the
                     routine only calculates the optimal sizes of the WORK and
                     IWORK arrays, returns these values as the first entries of
                     the WORK and IWORK arrays, and no error message related to
                     LWORK 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 E did not converge to zero.



LAPACK routine                  31 October 2017                      SSTEVD(3)