# HG changeset patch
# User jwe
# Date 923511434 0
# Node ID 02259d65461a3d3c40af744af482fbf55995cb67
# Parent  2e74d8aa1a2018594d447dbe0050beaba312b655
[project @ 1999-04-07 18:57:14 by jwe]

diff -r 2e74d8aa1a20 -r 02259d65461a scripts/linear-algebra/krygetq.m
--- a/scripts/linear-algebra/krygetq.m	Wed Apr 07 18:34:20 1999 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,60 +0,0 @@
-# Copyright (C) 1993, 1998 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, 675 Mass Ave, Cambridge, MA 02139, USA.
-
-function QQ = krygetq(HH,alpha,kb)
-# function QQ = krygetq(HH,alpha,kb)
-# used internally by krylovb
-# construct last kb columns of orthogonal transform returned by qrhouse
-# Inputs:
-#   HH,alpha: set of nh Householder reflections set returned by qrhouse
-#   kb: desired number of columns
-# Outputs: 
-#   QQ: n x kb orthogonal matrix; basis of orthogonal subspace provided
-#      by final kb reflections in HH.
-#   Note: due to details in qrhouse and krylovb, QQ is *not* necessarily 
-#      the last kb columns defined by HH.  span(QQ) is orthogonal to the
-#      subspace spanned by the first (nh-kb) reflections in HH.
-
-# Written by A. S. Hodel 1993--1995
-# $Revision$
-# $Log$
-
-[n,m] = size(HH);
-kb1 = m+1-kb;
-
-# construct permuted identity on the right rows:
-# since qrhouse removes zero rows, we've got to check the rows to which
-# the current householder reflections actually reflected their columns
-Hs = HH(:,kb1:m);
-if(is_vector(Hs))
-  nzidx = find(Hs' != 0);
-else
-  nzidx = find(max(abs(Hs')) != 0);
-endif
-nzidx = nzidx(1:kb);
-QQ = zeros(n,kb);
-QQ(nzidx,1:kb) = eye(kb);
-
-# back out QQ matrix 
-for i=m:-1:1
- hv = HH(:,i);
- av = alpha(i);
- QQ = QQ-av*hv*(hv'*QQ);
-end;
-
-endfunction
diff -r 2e74d8aa1a20 -r 02259d65461a scripts/linear-algebra/qrhouse.m
--- a/scripts/linear-algebra/qrhouse.m	Wed Apr 07 18:34:20 1999 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,87 +0,0 @@
-# Copyright (C) 1992, 1998 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, 675 Mass Ave, Cambridge, MA 02139, USA.
-
-function [hv,alph,kb] = qrhouse(VV,eps1)
-# function [hv,alph,kb] = qrhouse(VV{,eps1})
-# construct orthogonal basis of span(VV) with Householder vectors
-# Q R = VV; Q may be obtained via routine krygetq; R is upper triangular
-#   if all rows of VV are nonzero; otherwise it's a permuted uppert
-#   triangular matrix with zero rows matching those of VV.
-# Inputs: 
-#   VV: matrix
-#   eps1: zero threshhold; default: 0.  Used to check if a column
-#     of reduced R is already upper triangular; entries with magnitude
-#     <= eps1 are considered to be 0.
-# Outputs:
-#   hv: matrix of householder reflection vectors as returned by housh
-#   alpha: vector of householder reflection values as returned by housh
-#   kb: computed rank of matrix
-# qrhouse is used in krylovb for block Arnoldi iteration
-#
-# Reference: Golub and Van Loan, MATRIX COMPUTATIONS, 2nd ed.
-
-# Written by A. S. Hodel, 1992
-
-if(nargin < 1 | nargin > 2)
-  usage("[hv,alph,kb] = qrhouse(VV{,eps1})");
-elseif(nargin == 1)     # default value for eps set to 0
-  eps1 = 0;
-endif
-
-
-# extract only those rows of VV that are nonzero
-if(is_vector(VV))	nzidx = find(abs(VV') > 0);
-else			nzidx = find(max(abs(VV')) > 0);    endif
-VVlen = rows(VV);	# remember original size
-
-if(is_vector(VV))	VV = VV(nzidx);
-else			VV = VV(nzidx,:);                   endif
-
-[Vr,Vc] = size(VV);	nits   = min(Vr,Vc);
-for ii = 1:nits;
-  # permute maximum row entry to (ii,ii) position
-  Vrowi = VV(ii,1:Vc);      # pivot maximum entry in this row to lead position
-  Vrm = max(abs(Vrowi));
-  Vmidx = min(find(abs(Vrowi) == Vrm));
-  if(Vmidx > eps1)
-    kb = ii;		# update computed rank
-    idx = kb-1;
-    if(Vmidx != ii)
-      [VV(:,kb),VV(:,Vmidx)] = swap(VV(:,kb),VV(:,Vmidx));
-    endif
-    hh = VV(:,ii);	# extract next column of VV; ignore items 1:(ii-1).
-    [hv(kb:Vr,kb),alph(kb),z] = housh(hh(kb:Vr),1,0);
-    if(kb>1)
-      hv(1:idx,kb) = 0;                 # zero top of hv for safety
-    endif
-    # project off of current Householder vector
-    VV = VV - alph(kb)*hv(:,kb)*(hv(:,kb)'*VV);
-  else
-    break;
-  endif
-endfor
-if(kb <=0)
-  hv = [];
-  alph = [];
-else
-  hvs = hv(:,1:kb);	# remove extraneous vectors, expand to original size
-  hv = zeros(VVlen,kb);
-  hv(nzidx,:) = hvs;
-  alph = alph(1:kb);
-end
-endfunction