annotate scripts/sparse/gmres.m @ 14363:f3d52523cde1

Use Octave coding conventions in all m-file %!test blocks * wavread.m, acosd.m, acot.m, acotd.m, acoth.m, acsc.m, acscd.m, acsch.m, asec.m, asecd.m, asech.m, asind.m, atand.m, cosd.m, cot.m, cotd.m, coth.m, csc.m, cscd.m, csch.m, sec.m, secd.m, sech.m, sind.m, tand.m, accumarray.m, accumdim.m, bitcmp.m, bitget.m, bitset.m, blkdiag.m, cart2pol.m, cart2sph.m, celldisp.m, chop.m, circshift.m, colon.m, common_size.m, cplxpair.m, cumtrapz.m, curl.m, dblquad.m, deal.m, divergence.m, flipdim.m, fliplr.m, flipud.m, genvarname.m, gradient.m, idivide.m, int2str.m, interp1.m, interp1q.m, interp2.m, interp3.m, interpft.m, interpn.m, isa.m, isdir.m, isequal.m, isequalwithequalnans.m, issquare.m, logspace.m, nargchk.m, narginchk.m, nargoutchk.m, nextpow2.m, nthargout.m, num2str.m, pol2cart.m, polyarea.m, postpad.m, prepad.m, profile.m, profshow.m, quadgk.m, quadv.m, randi.m, rat.m, repmat.m, rot90.m, rotdim.m, shift.m, shiftdim.m, sph2cart.m, structfun.m, trapz.m, triplequad.m, convhull.m, dsearch.m, dsearchn.m, griddata3.m, griddatan.m, rectint.m, tsearchn.m, __makeinfo__.m, doc.m, get_first_help_sentence.m, help.m, type.m, unimplemented.m, which.m, imread.m, imwrite.m, dlmwrite.m, fileread.m, is_valid_file_id.m, strread.m, textread.m, textscan.m, commutation_matrix.m, cond.m, condest.m, cross.m, duplication_matrix.m, expm.m, housh.m, isdefinite.m, ishermitian.m, issymmetric.m, logm.m, normest.m, null.m, onenormest.m, orth.m, planerot.m, qzhess.m, rank.m, rref.m, trace.m, vech.m, ans.m, bincoeff.m, bug_report.m, bzip2.m, comma.m, compare_versions.m, computer.m, edit.m, fileparts.m, fullfile.m, getfield.m, gzip.m, info.m, inputname.m, isappdata.m, isdeployed.m, ismac.m, ispc.m, isunix.m, list_primes.m, ls.m, mexext.m, namelengthmax.m, news.m, orderfields.m, paren.m, recycle.m, rmappdata.m, semicolon.m, setappdata.m, setfield.m, substruct.m, symvar.m, ver.m, version.m, warning_ids.m, xor.m, fminbnd.m, fsolve.m, fzero.m, lsqnonneg.m, optimset.m, pqpnonneg.m, sqp.m, matlabroot.m, __gnuplot_drawnow__.m, __plt_get_axis_arg__.m, ancestor.m, cla.m, clf.m, close.m, colorbar.m, colstyle.m, comet3.m, contourc.m, figure.m, gca.m, gcbf.m, gcbo.m, gcf.m, ginput.m, graphics_toolkit.m, gtext.m, hggroup.m, hist.m, hold.m, isfigure.m, ishghandle.m, ishold.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m, line.m, loglog.m, loglogerr.m, meshgrid.m, ndgrid.m, newplot.m, orient.m, patch.m, plot3.m, plotyy.m, __print_parse_opts__.m, quiver3.m, refreshdata.m, ribbon.m, semilogx.m, semilogxerr.m, semilogy.m, stem.m, stem3.m, subplot.m, title.m, uigetfile.m, view.m, whitebg.m, compan.m, conv.m, deconv.m, mkpp.m, mpoles.m, pchip.m, poly.m, polyaffine.m, polyder.m, polyfit.m, polygcd.m, polyint.m, polyout.m, polyval.m, polyvalm.m, ppder.m, ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, intersect.m, ismember.m, powerset.m, setdiff.m, setxor.m, union.m, unique.m, autoreg_matrix.m, bartlett.m, blackman.m, detrend.m, fftconv.m, fftfilt.m, fftshift.m, freqz.m, hamming.m, hanning.m, ifftshift.m, sinc.m, sinetone.m, sinewave.m, unwrap.m, bicg.m, bicgstab.m, gmres.m, gplot.m, nonzeros.m, pcg.m, pcr.m, spaugment.m, spconvert.m, spdiags.m, speye.m, spfun.m, spones.m, sprand.m, sprandsym.m, spstats.m, spy.m, svds.m, treelayout.m, bessel.m, beta.m, betaln.m, factor.m, factorial.m, isprime.m, lcm.m, legendre.m, nchoosek.m, nthroot.m, perms.m, pow2.m, primes.m, reallog.m, realpow.m, realsqrt.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, rosser.m, vander.m, __finish__.m, center.m, cloglog.m, corr.m, cov.m, gls.m, histc.m, iqr.m, kendall.m, kurtosis.m, logit.m, mahalanobis.m, mean.m, meansq.m, median.m, mode.m, moment.m, ols.m, ppplot.m, prctile.m, probit.m, quantile.m, range.m, ranks.m, run_count.m, runlength.m, skewness.m, spearman.m, statistics.m, std.m, table.m, var.m, zscore.m, betacdf.m, betainv.m, betapdf.m, betarnd.m, binocdf.m, binoinv.m, binopdf.m, binornd.m, cauchy_cdf.m, cauchy_inv.m, cauchy_pdf.m, cauchy_rnd.m, chi2cdf.m, chi2inv.m, chi2pdf.m, chi2rnd.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, discrete_rnd.m, empirical_cdf.m, empirical_inv.m, empirical_pdf.m, empirical_rnd.m, expcdf.m, expinv.m, exppdf.m, exprnd.m, fcdf.m, finv.m, fpdf.m, frnd.m, gamcdf.m, gaminv.m, gampdf.m, gamrnd.m, geocdf.m, geoinv.m, geopdf.m, geornd.m, hygecdf.m, hygeinv.m, hygepdf.m, hygernd.m, kolmogorov_smirnov_cdf.m, laplace_cdf.m, laplace_inv.m, laplace_pdf.m, laplace_rnd.m, logistic_cdf.m, logistic_inv.m, logistic_pdf.m, logistic_rnd.m, logncdf.m, logninv.m, lognpdf.m, lognrnd.m, nbincdf.m, nbininv.m, nbinpdf.m, nbinrnd.m, normcdf.m, norminv.m, normpdf.m, normrnd.m, poisscdf.m, poissinv.m, poisspdf.m, poissrnd.m, stdnormal_cdf.m, stdnormal_inv.m, stdnormal_pdf.m, stdnormal_rnd.m, tcdf.m, tinv.m, tpdf.m, trnd.m, unidcdf.m, unidinv.m, unidpdf.m, unidrnd.m, unifcdf.m, unifinv.m, unifpdf.m, unifrnd.m, wblcdf.m, wblinv.m, wblpdf.m, wblrnd.m, kolmogorov_smirnov_test.m, kruskal_wallis_test.m, base2dec.m, bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m, findstr.m, hex2dec.m, index.m, isletter.m, mat2str.m, rindex.m, str2num.m, strcat.m, strjust.m, strmatch.m, strsplit.m, strtok.m, strtrim.m, strtrunc.m, substr.m, validatestring.m, demo.m, example.m, fail.m, speed.m, addtodate.m, asctime.m, clock.m, ctime.m, date.m, datenum.m, datetick.m, datevec.m, eomday.m, etime.m, is_leap_year.m, now.m: Use Octave coding conventions in all m-file %!test blocks
author Rik <octave@nomad.inbox5.com>
date Mon, 13 Feb 2012 07:29:44 -0800
parents 72c96de7a403
children b76f0740940e
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rev   line source
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1 ## Copyright (C) 2009-2012 Carlo de Falco
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by the
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7 ## Free Software Foundation; either version 3 of the License, or (at your
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8 ## option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but WITHOUT
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11 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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12 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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13 ## for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{x} =} gmres (@var{A}, @var{b}, @var{m}, @var{rtol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
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21 ## @deftypefnx {Function File} {@var{x} =} gmres (@var{A}, @var{b}, @var{m}, @var{rtol}, @var{maxit}, @var{P})
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22 ## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} gmres (@dots{})
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23 ## Solve @code{A x = b} using the Preconditioned GMRES iterative method
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24 ## with restart, a.k.a. PGMRES(m).
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25 ##
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26 ## @itemize @minus
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27 ## @item @var{rtol} is the relative tolerance,
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28 ## if not given or set to [] the default value 1e-6 is used.
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29 ##
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30 ## @item @var{maxit} is the maximum number of outer iterations,
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31 ## if not given or set to [] the default value
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32 ## @code{min (10, numel (b) / restart)} is used.
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33 ##
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34 ## @item @var{x0} is the initial guess,
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35 ## if not given or set to [] the default value @code{zeros(size (b))} is used.
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36 ##
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37 ## @item @var{m} is the restart parameter,
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38 ## if not given or set to [] the default value @code{numel (b)} is used.
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39 ## @end itemize
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40 ##
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41 ## Argument @var{A} can be passed as a matrix, function handle, or
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42 ## inline function @code{f} such that @code{f(x) = A*x}.
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43 ##
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44 ## The preconditioner @var{P} is given as @code{P = M1 * M2}.
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45 ## Both @var{M1} and @var{M2} can be passed as a matrix, function handle, or
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46 ## inline function @code{g} such that @code{g(x) = M1\x} or @code{g(x) = M2\x}.
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47 ##
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48 ## Besides the vector @var{x}, additional outputs are:
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49 ##
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50 ## @itemize @minus
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51 ## @item @var{flag} indicates the exit status:
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52 ## @table @asis
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53 ## @item 0 : iteration converged to within the specified tolerance
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54 ##
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55 ## @item 1 : maximum number of iterations exceeded
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56 ##
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57 ## @item 2 : unused, but skipped for compatibility
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58 ##
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59 ## @item 3 : algorithm reached stagnation
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60 ## @end table
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61 ##
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62 ## @item @var{relres} is the final value of the relative residual.
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63 ##
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64 ## @item @var{iter} is a vector containing the number of outer iterations and
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65 ## total iterations performed.
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66 ##
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67 ## @item @var{resvec} is a vector containing the relative residual at each
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68 ## iteration.
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69 ## @end itemize
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70 ##
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71 ## @seealso{bicg, bicgstab, cgs, pcg}
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72 ## @end deftypefn
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73
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74 function [x, flag, presn, it, resids] = gmres (A, b, restart, rtol, maxit, M1, M2, x0)
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75
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76 if (nargin < 2 || nargin > 8)
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77 print_usage ();
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78 endif
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79
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80 if (ischar (A))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
81 Ax = str2func (A);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
82 elseif (ismatrix (A))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
83 Ax = @(x) A*x;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
84 elseif (isa (A, "function_handle"))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
85 Ax = A;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
86 else
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
87 error ("gmres: A must be a function or matrix");
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
88 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
89
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
90 if (nargin < 3 || isempty (restart))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
91 restart = rows (b);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
92 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
93
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
94 if (nargin < 4 || isempty (rtol))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
95 rtol = 1e-6;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
96 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
97
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
98 if (nargin < 5 || isempty (maxit))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
99 maxit = min (rows (b)/restart, 10);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
100 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
101
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
102 if (nargin < 6 || isempty (M1))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
103 M1m1x = @(x) x;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
104 elseif (ischar (M1))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
105 M1m1x = str2func (M1);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
106 elseif (ismatrix (M1))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
107 M1m1x = @(x) M1 \ x;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
108 elseif (isa (M1, "function_handle"))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
109 M1m1x = M1;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
110 else
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
111 error ("gmres: preconditioner M1 must be a function or matrix");
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
112 endif
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
113
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
114 if (nargin < 7 || isempty (M2))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
115 M2m1x = @(x) x;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
116 elseif (ischar (M2))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
117 M2m1x = str2func (M2);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
118 elseif (ismatrix (M2))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
119 M2m1x = @(x) M2 \ x;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
120 elseif (isa (M2, "function_handle"))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
121 M2m1x = M2;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
122 else
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
123 error ("gmres: preconditioner M2 must be a function or matrix");
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
124 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
125
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
126 Pm1x = @(x) M2m1x (M1m1x (x));
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
127
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
128 if (nargin < 8 || isempty (x0))
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
129 x0 = zeros (size (b));
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
130 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
131
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
132 x_old = x0;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
133 x = x_old;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
134 prec_res = Pm1x (b - Ax (x_old));
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
135 presn = norm (prec_res, 2);
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
136
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
137 B = zeros (restart + 1, 1);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
138 V = zeros (rows (x), restart);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
139 H = zeros (restart + 1, restart);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
140
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
141 ## begin loop
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
142 iter = 1;
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
143 restart_it = restart + 1;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
144 resids = zeros (maxit, 1);
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
145 resids(1) = presn;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
146 prec_b_norm = norm (Pm1x (b), 2);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
147 flag = 1;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
148
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
149 while (iter <= maxit * restart && presn > rtol * prec_b_norm)
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
150
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
151 ## restart
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
152 if (restart_it > restart)
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
153 restart_it = 1;
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
154 x_old = x;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
155 prec_res = Pm1x (b - Ax (x_old));
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
156 presn = norm (prec_res, 2);
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
157 B(1) = presn;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
158 H(:) = 0;
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
159 V(:, 1) = prec_res / presn;
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
160 endif
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
161
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
162 ## basic iteration
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
163 tmp = Pm1x (Ax (V(:, restart_it)));
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
164 [V(:,restart_it+1), H(1:restart_it+1, restart_it)] = ...
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
165 mgorth (tmp, V(:,1:restart_it));
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
166
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
167 Y = (H(1:restart_it+1, 1:restart_it) \ B (1:restart_it+1));
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
168
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
169 little_res = B(1:restart_it+1) - ...
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
170 H(1:restart_it+1, 1:restart_it) * Y(1:restart_it);
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
171
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
172 presn = norm (little_res, 2);
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
173
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
174 x = x_old + V(:, 1:restart_it) * Y(1:restart_it);
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
175
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
176 resids(iter) = presn;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
177 if (norm (x - x_old, inf) <= eps)
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
178 flag = 3;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
179 break
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
180 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
181
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
182 restart_it++ ;
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
183 iter++;
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
184 endwhile
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
185
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
186 if (presn > rtol * prec_b_norm)
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
187 flag = 0;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
188 endif
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
189
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
190 resids = resids(1:iter-1);
13861
4d8317915db9 fix extra output parameters in gmres
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13175
diff changeset
191 it = [ceil(iter / restart), rem(iter, restart)];
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 12763
diff changeset
192
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
193 endfunction
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
194
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
195
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
196 %!shared A, b, dim
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
197 %! dim = 100;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
198 %!test
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
199 %! A = spdiags ([-ones(dim,1) 2*ones(dim,1) ones(dim,1)], [-1:1], dim, dim);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
200 %! b = ones (dim, 1);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
201 %! x = gmres (A, b, 10, 1e-10, dim, @(x) x ./ diag (A), [], b);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
202 %! assert (x, A\b, 1e-9*norm (x, Inf));
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
203 %!
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
204 %!test
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
205 %! x = gmres (A, b, dim, 1e-10, 1e4, @(x) diag (diag (A)) \ x, [], b);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
206 %! assert(x, A\b, 1e-7*norm (x, Inf));
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
207 %!
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
208 %!test
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
209 %! A = spdiags ([[1./(2:2:2*(dim-1)) 0]; 1./(1:2:2*dim-1); [0 1./(2:2:2*(dim-1))]]', -1:1, dim, dim);
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
210 %! A = A'*A;
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
211 %! b = rand (dim, 1);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
212 %! [x, resids] = gmres (@(x) A*x, b, dim, 1e-10, dim, @(x) x./diag (A), [], []);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
213 %! assert (x, A\b, 1e-9*norm (x, Inf));
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
214 %! x = gmres (@(x) A*x, b, dim, 1e-10, 1e6, @(x) diag (diag (A)) \ x, [], []);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
215 %! assert (x, A\b, 1e-9*norm (x, Inf));
12509
e742720c5e71 Add mgorth and gmres functions from Octave Forge
Carlo de Falco <kingcrimson@tiscali.it>
parents:
diff changeset
216 %!test
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
217 %! x = gmres (@(x) A*x, b, dim, 1e-10, 1e6, @(x) x./diag(A), [], []);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
218 %! assert (x, A\b, 1e-7*norm (x, Inf));
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
219