SLAED0(3)      LAPACK routine of NEC Numeric Library Collection      SLAED0(3)



NAME
       SLAED0

SYNOPSIS
       SUBROUTINE SLAED0 (ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK,
           IWORK, INFO)



PURPOSE
            SLAED0 computes all eigenvalues and corresponding eigenvectors of a
            symmetric tridiagonal matrix using the divide and conquer method.




ARGUMENTS
           ICOMPQ    (input)
                     ICOMPQ is INTEGER
                     = 0:  Compute eigenvalues only.
                     = 1:  Compute eigenvectors of original dense symmetric matrix
                           also.  On entry, Q contains the orthogonal matrix used
                           to reduce the original matrix to tridiagonal form.
                     = 2:  Compute eigenvalues and eigenvectors of tridiagonal
                           matrix.

           QSIZ      (input)
                     QSIZ is INTEGER
                    The dimension of the orthogonal matrix used to reduce
                    the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

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

           D         (input/output)
                     D is REAL array, dimension (N)
                    On entry, the main diagonal of the tridiagonal matrix.
                    On exit, its eigenvalues.

           E         (input)
                     E is REAL array, dimension (N-1)
                    The off-diagonal elements of the tridiagonal matrix.
                    On exit, E has been destroyed.

           Q         (input/output)
                     Q is REAL array, dimension (LDQ, N)
                    On entry, Q must contain an N-by-N orthogonal matrix.
                    If ICOMPQ = 0    Q is not referenced.
                    If ICOMPQ = 1    On entry, Q is a subset of the columns of the
                                     orthogonal matrix used to reduce the full
                                     matrix to tridiagonal form corresponding to
                                     the subset of the full matrix which is being
                                     decomposed at this time.
                    If ICOMPQ = 2    On entry, Q will be the identity matrix.
                                     On exit, Q contains the eigenvectors of the
                                     tridiagonal matrix.

           LDQ       (input)
                     LDQ is INTEGER
                    The leading dimension of the array Q.  If eigenvectors are
                    desired, then  LDQ >= max(1,N).  In any case,  LDQ >= 1.

           QSTORE    (output)
                     QSTORE is REAL array, dimension (LDQS, N)
                    Referenced only when ICOMPQ = 1.  Used to store parts of
                    the eigenvector matrix when the updating matrix multiplies
                    take place.

           LDQS      (input)
                     LDQS is INTEGER
                    The leading dimension of the array QSTORE.  If ICOMPQ = 1,
                    then  LDQS >= max(1,N).  In any case,  LDQS >= 1.

           WORK      (output)
                     WORK is REAL array,
                    If ICOMPQ = 0 or 1, the dimension of WORK must be at least
                                1 + 3*N + 2*N*lg N + 3*N**2
                                ( lg( N ) = smallest integer k
                                            such that 2^k >= N )
                    If ICOMPQ = 2, the dimension of WORK must be at least
                                4*N + N**2.

           IWORK     (output)
                     IWORK is INTEGER array,
                    If ICOMPQ = 0 or 1, the dimension of IWORK must be at least
                                   6 + 6*N + 5*N*lg N.
                                   ( lg( N ) = smallest integer k
                                               such that 2^k >= N )
                    If ICOMPQ = 2, the dimension of IWORK must be at least
                                   3 + 5*N.

           INFO      (output)
                     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).



LAPACK routine                  31 October 2017                      SLAED0(3)