SLAED0 (3lapack)

compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method

SYNOPSIS

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

      INTEGER        ICOMPQ, INFO, LDQ, LDQS, N, QSIZ

      INTEGER        IWORK( * )

      REAL           D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), WORK( *
                     )

PURPOSE

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

ARGUMENTS

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

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

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

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

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

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

  WORK   (workspace) REAL array,
         dimension (1 + 3*N + 2*N*lg N + 2*N**2) ( lg( N ) = smallest integer
         k such that 2^k >= N )

  IWORK  (workspace) 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 2 + 5*N.

  INFO   (output) 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).