## Copyright (C) 1993, 1998, 1999 A. Scottedward Hodel
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by the
## Free Software Foundation; either version 2, or (at your option) any
## later version.
##
## Octave is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
## for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, write to the Free
## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## function [U, Ucols] = krylovb (A, V, k ,eps1, pflg);
## construct orthogonal basis U of block Krylov subspace;
## [V AV A^2*V ... A^(k+1)*V];
## method used: householder reflections to guard against loss of
## orthogonality
## eps1: threshhold for 0 (optional, default: 1e-12)
## pflg: permutation flag (optional)
## outputs:
## returned basis U is orthogonal matrix; due to "zeroed"
## columns of product, may not satisfy A U = U H identity
## Ucols: dimension of span of krylov subspace (based on eps1)
## if k > m-1, krylov returns the Hessenberg decompostion of A.
##
## Note: krylovb directly calls and is superseded by krylov.

function [Uret, Ucols] = krylovb (A, V, k, eps1, pflg)

  switch (nargin)
    case (3)
      [Uret, H, Ucols] = krylov (A, V, k);
    case (4)
      [Uret, H, Ucols] = krylov (A, V, k, eps1);
    case (5)
      [Uret, H, Ucols] = krylov (A, V, k, eps1, pflg);
    otherwise
      usage ("[Uret, Ucols] = krylovb (A, V, k ,eps1, pflg));
  endswitch

endfunction