Mercurial > hg > octave-nkf
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,
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vander.m, __finish__.m, center.m, cloglog.m, corr.m, cov.m, gls.m, histc.m,
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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> |
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date | Mon, 13 Feb 2012 07:29:44 -0800 |
parents | 11949c9795a0 |
children | 3edba8b5f430 |
rev | line source |
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1 ## Copyright (C) 2008-2012 Radek Salac |
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2 ## Copyright (C) 2012 Carlo de Falco |
8416 | 3 ## |
4 ## This file is part of Octave. | |
5 ## | |
6 ## Octave is free software; you can redistribute it and/or modify it | |
7 ## under the terms of the GNU General Public License as published by | |
8 ## the Free Software Foundation; either version 3 of the License, or (at | |
9 ## your option) any later version. | |
10 ## | |
11 ## Octave is distributed in the hope that it will be useful, but | |
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 ## General Public License for more details. | |
15 ## | |
16 ## You should have received a copy of the GNU General Public License | |
17 ## along with Octave; see the file COPYING. If not, see | |
18 ## <http://www.gnu.org/licenses/>. | |
19 | |
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}. |
8416 | 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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70 ## @end deftypefn | |
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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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"]); |
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86 endif |
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87 |
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88 if (nargin < 3 || isempty (tol)) |
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89 tol = 1e-6; |
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90 endif |
8416 | 91 |
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92 if (nargin < 4 || isempty (maxit)) |
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93 maxit = min (rows (b), 20); |
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94 endif |
8416 | 95 |
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96 if (nargin < 5 || isempty (M1)) |
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97 M1m1x = @(x) x; |
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98 elseif (ischar (M1)) |
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99 M1m1x = str2func (M1); |
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100 elseif (ismatrix (M1)) |
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101 M1m1x = @(x) M1 \ x; |
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102 elseif (isa (M1, "function_handle")) |
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103 M1m1x = @(x) feval (M1, x); |
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104 else |
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105 error (["bicgstab: preconditioner is " ... |
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106 "expected to be a function or matrix"]); |
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107 endif |
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108 |
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109 if (nargin < 6 || isempty (M2)) |
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110 M2m1x = @(x) x; |
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111 elseif (ischar (M2)) |
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112 M2m1x = str2func (M2); |
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113 elseif (ismatrix (M2)) |
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114 M2m1x = @(x) M2 \ x; |
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115 elseif (isa (M2, "function_handle")) |
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116 M2m1x = @(x) feval (M2, x); |
8416 | 117 else |
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118 error (["bicgstab: preconditioner is "... |
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119 "expected to be a function or matrix"]); |
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120 endif |
8416 | 121 |
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122 precon = @(x) M2m1x (M1m1x (x)); |
8416 | 123 |
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124 if (nargin < 7 || isempty (x0)) |
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125 x0 = zeros (size (b)); |
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126 endif |
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127 |
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128 ## specifies initial estimate x0 |
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129 if (nargin < 7) |
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130 x = zeros (rows (b), 1); |
8416 | 131 else |
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132 x = x0; |
8416 | 133 endif |
134 | |
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135 norm_b = norm (b); |
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136 |
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137 res = b - Ax (x); |
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138 rr = res; |
8416 | 139 |
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140 ## Vector of the residual norms for each iteration. |
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141 resvec = norm(res) / norm_b; |
8416 | 142 |
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143 ## Default behaviour we don't reach tolerance tol within maxit iterations. |
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144 flag = 1; |
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145 |
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146 for iter = 1:maxit |
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147 rho_1 = res' * rr; |
8416 | 148 |
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149 if (iter == 1) |
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150 p = res; |
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151 else |
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152 beta = (rho_1 / rho_2) * (alpha / omega); |
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153 p = res + beta * (p - omega * v); |
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154 endif |
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155 |
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156 phat = precon (p); |
8416 | 157 |
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158 v = Ax (phat); |
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159 alpha = rho_1 / (rr' * v); |
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160 s = res - alpha * v; |
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161 |
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162 shat = precon (s); |
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163 |
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164 t = Ax (shat); |
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165 omega = (t' * s) / (t' * t); |
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166 x = x + alpha * phat + omega * shat; |
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167 res = s - omega * t; |
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168 rho_2 = rho_1; |
8416 | 169 |
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170 relres = norm (res) / norm_b; |
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171 resvec = [resvec; relres]; |
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172 |
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173 if (relres <= tol) |
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174 ## We reach tolerance tol within maxit iterations. |
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175 flag = 0; |
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176 break; |
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177 elseif (resvec(end) == resvec(end - 1)) |
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178 ## The method stagnates. |
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179 flag = 3; |
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180 break; |
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181 endif |
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182 endfor |
8416 | 183 |
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184 if (nargout < 2) |
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185 if (flag == 0) |
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186 printf ("bicgstab converged at iteration %i ", iter); |
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187 printf ("to a solution with relative residual %e\n", relres); |
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188 elseif (flag == 3) |
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189 printf ("bicgstab stopped at iteration %i ", iter); |
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190 printf ("without converging to the desired tolerance %e\n", tol); |
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191 printf ("because the method stagnated.\n"); |
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192 printf ("The iterate returned (number %i) ", iter); |
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193 printf ("has relative residual %e\n", relres); |
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194 else |
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195 printf ("bicgstab stopped at iteration %i ", iter); |
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196 printf ("without converging to the desired toleranc %e\n", tol); |
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197 printf ("because the maximum number of iterations was reached.\n"); |
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198 printf ("The iterate returned (number %i) ", iter); |
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199 printf ("has relative residual %e\n", relres); |
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200 endif |
9278 | 201 endif |
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202 |
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203 else |
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204 print_usage (); |
9278 | 205 endif |
206 | |
8416 | 207 endfunction |
208 | |
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209 |
8416 | 210 %!demo |
211 %! % Solve system of A*x=b | |
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212 %! A = [5 -1 3;-1 2 -2;3 -2 3]; |
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213 %! b = [7;-1;4]; |
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214 %! [x, flag, relres, iter, resvec] = bicgstab (A, b) |
8416 | 215 |
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216 %!shared A, b, n, M1, M2 |
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217 %! |
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218 %!test |
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219 %! n = 100; |
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220 %! A = spdiags ([-2*ones(n,1) 4*ones(n,1) -ones(n,1)], -1:1, n, n); |
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221 %! b = sum (A, 2); |
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222 %! tol = 1e-8; |
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223 %! maxit = 15; |
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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 |