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krylovb.m
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1999-12-24
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# 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 [Uret,Ucols] = krylovb(A,V,k,eps1,pflg);
# 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 (default: 1e-12)
# pflg: permutation flag
# 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# Note: krylovb directly calls and is superseded by krylov.
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}); %d arguments passed", ...
nargin);
endswitch
endfunction