annotate scripts/sparse/bicgstab.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 11949c9795a0
children 3edba8b5f430
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1 ## Copyright (C) 2008-2012 Radek Salac
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2 ## Copyright (C) 2012 Carlo de Falco
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ##
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22 ## @deftypefn {Function File} {@var{x} =} bicgstab (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0})
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23 ## @deftypefnx {Function File} {@var{x} =} bicgstab (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{P})
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24 ## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} bicgstab (@var{A}, @var{b}, @dots{})
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25 ## Solve @code{A x = b} using the stabilizied Bi-conjugate gradient iterative
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26 ## method.
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27 ##
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28 ## @itemize @minus
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29 ## @item @var{rtol} is the relative tolerance, if not given or set to
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30 ## [] the default value 1e-6 is used.
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31 ##
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32 ## @item @var{maxit} the maximum number of outer iterations, if not
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33 ## given or set to [] the default value @code{min (20, numel (b))} is
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34 ## used.
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35 ##
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36 ## @item @var{x0} the initial guess, if not given or set to [] the
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37 ## default value @code{zeros (size (b))} is used.
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38 ## @end itemize
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39 ##
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40 ## @var{A} can be passed as a matrix or as a function handle or
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41 ## inline function @code{f} such that @code{f(x) = A*x}.
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42 ##
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43 ## The preconditioner @var{P} is given as @code{P = M1 * M2}.
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44 ## Both @var{M1} and @var{M2} can be passed as a matrix or as a function
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45 ## handle or inline function @code{g} such that @code{g(x) = M1 \ x} or
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46 ## @code{g(x) = M2 \ x}.
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47 ##
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48 ## If called with more than one output parameter
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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 ## @itemize @minus
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53 ## @item 0: iteration converged to the within the chosen tolerance
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54 ##
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55 ## @item 1: the maximum number of iterations was reached before convergence
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56 ##
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57 ## @item 3: the algorithm reached stagnation
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58 ## @end itemize
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59 ## (the value 2 is unused but skipped for compatibility).
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60 ##
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61 ## @item @var{relres} is the final value of the relative residual.
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62 ##
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63 ## @item @var{iter} is the number of iterations performed.
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64 ##
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65 ## @item @var{resvec} is a vector containing the relative residual at each iteration.
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66 ## @end itemize
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67 ##
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68 ## @seealso{bicg, cgs, gmres, pcg}
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69 ##
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70 ## @end deftypefn
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71
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72 function [x, flag, relres, iter, resvec] = bicgstab (A, b, tol, maxit,
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73 M1, M2, x0)
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74
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75 if (nargin >= 2 && nargin <= 7 && isvector (full (b)))
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76
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77 if (ischar (A))
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78 A = str2func (A);
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79 elseif (ismatrix (A))
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80 Ax = @(x) A * x;
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81 elseif (isa (A, "function_handle"))
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82 Ax = @(x) feval (A, x);
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83 else
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84 error (["bicgstab: first argument is expected " ...
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85 "to be a function or a square matrix"]);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
86 endif
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
87
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13070
diff changeset
88 if (nargin < 3 || isempty (tol))
13061
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
89 tol = 1e-6;
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
90 endif
8416
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Radek Salac <salac.r@gmail.com>
parents:
diff changeset
91
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13070
diff changeset
92 if (nargin < 4 || isempty (maxit))
13061
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
93 maxit = min (rows (b), 20);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
94 endif
8416
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
95
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13070
diff changeset
96 if (nargin < 5 || isempty (M1))
13061
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Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
97 M1m1x = @(x) x;
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
98 elseif (ischar (M1))
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
99 M1m1x = str2func (M1);
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
100 elseif (ismatrix (M1))
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13070
diff changeset
101 M1m1x = @(x) M1 \ x;
13061
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parents: 11587
diff changeset
102 elseif (isa (M1, "function_handle"))
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13070
diff changeset
103 M1m1x = @(x) feval (M1, x);
13061
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
104 else
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
105 error (["bicgstab: preconditioner is " ...
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
106 "expected to be a function or matrix"]);
9279
1673a0dc019f fix & improve preconditioning strategy in cgs & bicgstab
Jaroslav Hajek <highegg@gmail.com>
parents: 9278
diff changeset
107 endif
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
108
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13070
diff changeset
109 if (nargin < 6 || isempty (M2))
13061
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Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
110 M2m1x = @(x) x;
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
111 elseif (ischar (M2))
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
112 M2m1x = str2func (M2);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
113 elseif (ismatrix (M2))
13091
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Carlo de Falco <kingcrimson@tiscali.it>
parents: 13070
diff changeset
114 M2m1x = @(x) M2 \ x;
13061
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Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
115 elseif (isa (M2, "function_handle"))
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13070
diff changeset
116 M2m1x = @(x) feval (M2, x);
8416
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Radek Salac <salac.r@gmail.com>
parents:
diff changeset
117 else
13061
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
118 error (["bicgstab: preconditioner is "...
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
119 "expected to be a function or matrix"]);
9279
1673a0dc019f fix & improve preconditioning strategy in cgs & bicgstab
Jaroslav Hajek <highegg@gmail.com>
parents: 9278
diff changeset
120 endif
8416
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
121
13091
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Carlo de Falco <kingcrimson@tiscali.it>
parents: 13070
diff changeset
122 precon = @(x) M2m1x (M1m1x (x));
8416
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
123
13091
e5aaba072d2b maint: style fixes in iterative linear solvers
Carlo de Falco <kingcrimson@tiscali.it>
parents: 13070
diff changeset
124 if (nargin < 7 || isempty (x0))
13061
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
125 x0 = zeros (size (b));
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parents: 11587
diff changeset
126 endif
13141
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John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
127
13061
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Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
128 ## specifies initial estimate x0
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
129 if (nargin < 7)
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
130 x = zeros (rows (b), 1);
8416
0a56e5c21c29 Add the bicgstab function
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parents:
diff changeset
131 else
13061
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
132 x = x0;
8416
0a56e5c21c29 Add the bicgstab function
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parents:
diff changeset
133 endif
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
134
13061
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
135 norm_b = norm (b);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
136
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
137 res = b - Ax (x);
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
138 rr = res;
8416
0a56e5c21c29 Add the bicgstab function
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parents:
diff changeset
139
13061
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
140 ## Vector of the residual norms for each iteration.
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
141 resvec = norm(res) / norm_b;
8416
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
142
13061
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
143 ## Default behaviour we don't reach tolerance tol within maxit iterations.
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parents: 11587
diff changeset
144 flag = 1;
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
145
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
146 for iter = 1:maxit
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
147 rho_1 = res' * rr;
8416
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
148
13061
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
149 if (iter == 1)
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
150 p = res;
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
151 else
addfc0ae69c0 Make bicgstab interface more compatible
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parents: 11587
diff changeset
152 beta = (rho_1 / rho_2) * (alpha / omega);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
153 p = res + beta * (p - omega * v);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
154 endif
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
155
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
156 phat = precon (p);
8416
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
157
13061
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
158 v = Ax (phat);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
159 alpha = rho_1 / (rr' * v);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
160 s = res - alpha * v;
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
161
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
162 shat = precon (s);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
163
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
164 t = Ax (shat);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
165 omega = (t' * s) / (t' * t);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
166 x = x + alpha * phat + omega * shat;
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
167 res = s - omega * t;
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
168 rho_2 = rho_1;
8416
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
169
13061
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
170 relres = norm (res) / norm_b;
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
171 resvec = [resvec; relres];
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
172
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
173 if (relres <= tol)
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
174 ## We reach tolerance tol within maxit iterations.
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
175 flag = 0;
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
176 break;
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
177 elseif (resvec(end) == resvec(end - 1))
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
178 ## The method stagnates.
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
179 flag = 3;
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
180 break;
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
181 endif
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
182 endfor
8416
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
183
13061
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
184 if (nargout < 2)
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
185 if (flag == 0)
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
186 printf ("bicgstab converged at iteration %i ", iter);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
187 printf ("to a solution with relative residual %e\n", relres);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
188 elseif (flag == 3)
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
189 printf ("bicgstab stopped at iteration %i ", iter);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
190 printf ("without converging to the desired tolerance %e\n", tol);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
191 printf ("because the method stagnated.\n");
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
192 printf ("The iterate returned (number %i) ", iter);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
193 printf ("has relative residual %e\n", relres);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
194 else
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
195 printf ("bicgstab stopped at iteration %i ", iter);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
196 printf ("without converging to the desired toleranc %e\n", tol);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
197 printf ("because the maximum number of iterations was reached.\n");
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
198 printf ("The iterate returned (number %i) ", iter);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
199 printf ("has relative residual %e\n", relres);
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
200 endif
9278
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
201 endif
13061
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
202
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
203 else
addfc0ae69c0 Make bicgstab interface more compatible
Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
204 print_usage ();
9278
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
205 endif
2b35cb600d50 improve bicgstab and cgs
Radek Salac <salac.r@gmail.com>
parents: 8920
diff changeset
206
8416
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
207 endfunction
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
208
14237
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
209
8416
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Radek Salac <salac.r@gmail.com>
parents:
diff changeset
210 %!demo
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
211 %! % Solve system of A*x=b
14237
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
212 %! A = [5 -1 3;-1 2 -2;3 -2 3];
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
213 %! b = [7;-1;4];
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
214 %! [x, flag, relres, iter, resvec] = bicgstab (A, b)
8416
0a56e5c21c29 Add the bicgstab function
Radek Salac <salac.r@gmail.com>
parents:
diff changeset
215
13061
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parents: 11587
diff changeset
216 %!shared A, b, n, M1, M2
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parents: 11587
diff changeset
217 %!
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Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
218 %!test
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
219 %! n = 100;
13061
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Carlo de Falco <kingcrimson@tiscali.it>
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diff changeset
220 %! A = spdiags ([-2*ones(n,1) 4*ones(n,1) -ones(n,1)], -1:1, n, n);
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
221 %! b = sum (A, 2);
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 13091
diff changeset
222 %! tol = 1e-8;
13061
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Carlo de Falco <kingcrimson@tiscali.it>
parents: 11587
diff changeset
223 %! maxit = 15;
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
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224 %! M1 = spdiags ([ones(n,1)/(-2) ones(n,1)],-1:0, n, n);
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225 %! M2 = spdiags ([4*ones(n,1) -ones(n,1)], 0:1, n, n);
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226 %! [x, flag, relres, iter, resvec] = bicgstab (A, b, tol, maxit, M1, M2);
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227 %! assert (x, ones (size (b)), 1e-7);
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228 %!
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229 %!test
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230 %!function y = afun (x, a)
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231 %! y = a * x;
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232 %!endfunction
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233 %!
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234 %! tol = 1e-8;
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235 %! maxit = 15;
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236 %!
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237 %! [x, flag, relres, iter, resvec] = bicgstab (@(x) afun (x, A), b,
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238 %! tol, maxit, M1, M2);
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239 %! assert (x, ones (size (b)), 1e-7);
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240
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241 %!test
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242 %! n = 100;
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243 %! tol = 1e-8;
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244 %! a = sprand (n, n, .1);
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245 %! A = a'*a + 100 * eye (n);
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246 %! b = sum (A, 2);
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247 %! [x, flag, relres, iter, resvec] = bicgstab (A, b, tol, [], diag (diag (A)));
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248 %! assert (x, ones (size (b)), 1e-7);
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249