Mercurial > octave-nkf
view scripts/sparse/bicgstab.m @ 14868:5d3a684236b0
maint: Use Octave coding conventions for cuddling parentheses in scripts directory
* lin2mu.m, loadaudio.m, wavread.m, accumarray.m, bicubic.m, celldisp.m,
colon.m, cplxpair.m, dblquad.m, divergence.m, genvarname.m, gradient.m,
int2str.m, interp1.m, interp1q.m, interp2.m, interpn.m, loadobj.m, nthargout.m,
__isequal__.m, __splinen__.m, quadgk.m, quadl.m, quadv.m, rat.m, rot90.m,
rotdim.m, saveobj.m, subsindex.m, triplequad.m, delaunay3.m, griddata.m,
inpolygon.m, tsearchn.m, voronoi.m, get_first_help_sentence.m, which.m,
gray2ind.m, pink.m, dlmwrite.m, strread.m, textread.m, textscan.m, housh.m,
ishermitian.m, issymmetric.m, krylov.m, logm.m, null.m, rref.m,
compare_versions.m, copyfile.m, dump_prefs.m, edit.m, fileparts.m,
getappdata.m, isappdata.m, movefile.m, orderfields.m, parseparams.m,
__xzip__.m, rmappdata.m, setappdata.m, swapbytes.m, unpack.m, ver.m, fminbnd.m,
fminunc.m, fsolve.m, glpk.m, lsqnonneg.m, qp.m, sqp.m, configure_make.m,
copy_files.m, describe.m, get_description.m, get_forge_pkg.m, install.m,
installed_packages.m, is_architecture_dependent.m, load_package_dirs.m,
print_package_description.m, rebuild.m, repackage.m, save_order.m, shell.m,
allchild.m, ancestor.m, area.m, axes.m, axis.m, clabel.m, close.m, colorbar.m,
comet.m, comet3.m, contour.m, cylinder.m, ezmesh.m, ezsurf.m, findobj.m,
fplot.m, hist.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m,
mesh.m, meshz.m, pareto.m, pcolor.m, peaks.m, plot3.m, plotmatrix.m, plotyy.m,
polar.m, print.m, __add_datasource__.m, __add_default_menu__.m,
__axes_limits__.m, __bar__.m, __clabel__.m, __contour__.m, __errcomm__.m,
__errplot__.m, __ezplot__.m, __file_filter__.m, __fltk_print__.m,
__ghostscript__.m, __gnuplot_print__.m, __go_draw_axes__.m,
__go_draw_figure__.m, __interp_cube__.m, __marching_cube__.m, __patch__.m,
__pie__.m, __plt__.m, __print_parse_opts__.m, __quiver__.m, __scatter__.m,
__stem__.m, __tight_eps_bbox__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m,
__uiputfile_fltk__.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m,
ribbon.m, scatter.m, semilogy.m, shading.m, slice.m, subplot.m, surface.m,
surfl.m, surfnorm.m, text.m, uigetfile.m, uiputfile.m, whitebg.m, deconv.m,
mkpp.m, pchip.m, polyaffine.m, polyder.m, polygcd.m, polyout.m, polyval.m,
ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, splinefit.m,
addpref.m, getpref.m, setpref.m, ismember.m, setxor.m, arch_fit.m, arch_rnd.m,
arch_test.m, autoreg_matrix.m, diffpara.m, fftconv.m, filter2.m, hanning.m,
hurst.m, periodogram.m, triangle_sw.m, sinc.m, spectral_xdf.m, spencer.m,
stft.m, synthesis.m, unwrap.m, yulewalker.m, bicgstab.m, gmres.m, pcg.m, pcr.m,
__sprand_impl__.m, speye.m, spfun.m, sprandn.m, spstats.m, svds.m,
treelayout.m, treeplot.m, bessel.m, factor.m, legendre.m, perms.m, primes.m,
magic.m, toeplitz.m, corr.m, cov.m, mean.m, median.m, mode.m, qqplot.m,
quantile.m, ranks.m, zscore.m, logistic_regression_likelihood.m,
bartlett_test.m, chisquare_test_homogeneity.m, chisquare_test_independence.m,
kolmogorov_smirnov_test.m, run_test.m, u_test.m, wilcoxon_test.m, z_test.m,
z_test_2.m, bin2dec.m, dec2base.m, mat2str.m, strcat.m, strchr.m, strjust.m,
strtok.m, substr.m, untabify.m, assert.m, demo.m, example.m, fail.m, speed.m,
test.m, now.m: Use Octave coding conventions for cuddling parentheses in
scripts directory.
author | Rik <octave@nomad.inbox5.com> |
---|---|
date | Tue, 17 Jul 2012 07:08:39 -0700 |
parents | 72b8b39e12be |
children | 12005245b645 |
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## Copyright (C) 2008-2012 Radek Salac ## Copyright (C) 2012 Carlo de Falco ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{x} =} bicgstab (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0}) ## @deftypefnx {Function File} {@var{x} =} bicgstab (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{P}) ## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} bicgstab (@var{A}, @var{b}, @dots{}) ## Solve @code{A x = b} using the stabilizied Bi-conjugate gradient iterative ## method. ## ## @itemize @minus ## @item @var{rtol} is the relative tolerance, if not given or set to ## [] the default value 1e-6 is used. ## ## @item @var{maxit} the maximum number of outer iterations, if not ## given or set to [] the default value @code{min (20, numel (b))} is ## used. ## ## @item @var{x0} the initial guess, if not given or set to [] the ## default value @code{zeros (size (b))} is used. ## @end itemize ## ## @var{A} can be passed as a matrix or as a function handle or ## inline function @code{f} such that @code{f(x) = A*x}. ## ## The preconditioner @var{P} is given as @code{P = M1 * M2}. ## Both @var{M1} and @var{M2} can be passed as a matrix or as a function ## handle or inline function @code{g} such that @code{g(x) = M1 \ x} or ## @code{g(x) = M2 \ x}. ## ## If called with more than one output parameter ## ## @itemize @minus ## @item @var{flag} indicates the exit status: ## ## @itemize @minus ## @item 0: iteration converged to the within the chosen tolerance ## ## @item 1: the maximum number of iterations was reached before convergence ## ## @item 3: the algorithm reached stagnation ## @end itemize ## (the value 2 is unused but skipped for compatibility). ## ## @item @var{relres} is the final value of the relative residual. ## ## @item @var{iter} is the number of iterations performed. ## ## @item @var{resvec} is a vector containing the relative residual at each iteration. ## @end itemize ## ## @seealso{bicg, cgs, gmres, pcg} ## ## @end deftypefn function [x, flag, relres, iter, resvec] = bicgstab (A, b, tol, maxit, M1, M2, x0) if (nargin >= 2 && nargin <= 7 && isvector (full (b))) if (ischar (A)) A = str2func (A); elseif (ismatrix (A)) Ax = @(x) A * x; elseif (isa (A, "function_handle")) Ax = @(x) feval (A, x); else error (["bicgstab: first argument is expected " ... "to be a function or a square matrix"]); endif if (nargin < 3 || isempty (tol)) tol = 1e-6; endif if (nargin < 4 || isempty (maxit)) maxit = min (rows (b), 20); endif if (nargin < 5 || isempty (M1)) M1m1x = @(x) x; elseif (ischar (M1)) M1m1x = str2func (M1); elseif (ismatrix (M1)) M1m1x = @(x) M1 \ x; elseif (isa (M1, "function_handle")) M1m1x = @(x) feval (M1, x); else error (["bicgstab: preconditioner is " ... "expected to be a function or matrix"]); endif if (nargin < 6 || isempty (M2)) M2m1x = @(x) x; elseif (ischar (M2)) M2m1x = str2func (M2); elseif (ismatrix (M2)) M2m1x = @(x) M2 \ x; elseif (isa (M2, "function_handle")) M2m1x = @(x) feval (M2, x); else error (["bicgstab: preconditioner is "... "expected to be a function or matrix"]); endif precon = @(x) M2m1x (M1m1x (x)); if (nargin < 7 || isempty (x0)) x0 = zeros (size (b)); endif ## specifies initial estimate x0 if (nargin < 7) x = zeros (rows (b), 1); else x = x0; endif norm_b = norm (b); res = b - Ax (x); rr = res; ## Vector of the residual norms for each iteration. resvec = norm (res) / norm_b; ## Default behaviour we don't reach tolerance tol within maxit iterations. flag = 1; for iter = 1:maxit rho_1 = res' * rr; if (iter == 1) p = res; else beta = (rho_1 / rho_2) * (alpha / omega); p = res + beta * (p - omega * v); endif phat = precon (p); v = Ax (phat); alpha = rho_1 / (rr' * v); s = res - alpha * v; shat = precon (s); t = Ax (shat); omega = (t' * s) / (t' * t); x = x + alpha * phat + omega * shat; res = s - omega * t; rho_2 = rho_1; relres = norm (res) / norm_b; resvec = [resvec; relres]; if (relres <= tol) ## We reach tolerance tol within maxit iterations. flag = 0; break; elseif (resvec(end) == resvec(end - 1)) ## The method stagnates. flag = 3; break; endif endfor if (nargout < 2) if (flag == 0) printf ("bicgstab converged at iteration %i ", iter); printf ("to a solution with relative residual %e\n", relres); elseif (flag == 3) printf ("bicgstab stopped at iteration %i ", iter); printf ("without converging to the desired tolerance %e\n", tol); printf ("because the method stagnated.\n"); printf ("The iterate returned (number %i) ", iter); printf ("has relative residual %e\n", relres); else printf ("bicgstab stopped at iteration %i ", iter); printf ("without converging to the desired toleranc %e\n", tol); printf ("because the maximum number of iterations was reached.\n"); printf ("The iterate returned (number %i) ", iter); printf ("has relative residual %e\n", relres); endif endif else print_usage (); endif endfunction %!demo %! % Solve system of A*x=b %! A = [5 -1 3;-1 2 -2;3 -2 3]; %! b = [7;-1;4]; %! [x, flag, relres, iter, resvec] = bicgstab (A, b) %!shared A, b, n, M1, M2 %! %!test %! n = 100; %! A = spdiags ([-2*ones(n,1) 4*ones(n,1) -ones(n,1)], -1:1, n, n); %! b = sum (A, 2); %! tol = 1e-8; %! maxit = 15; %! M1 = spdiags ([ones(n,1)/(-2) ones(n,1)],-1:0, n, n); %! M2 = spdiags ([4*ones(n,1) -ones(n,1)], 0:1, n, n); %! [x, flag, relres, iter, resvec] = bicgstab (A, b, tol, maxit, M1, M2); %! assert (x, ones (size (b)), 1e-7); %! %!test %!function y = afun (x, a) %! y = a * x; %!endfunction %! %! tol = 1e-8; %! maxit = 15; %! %! [x, flag, relres, iter, resvec] = bicgstab (@(x) afun (x, A), b, %! tol, maxit, M1, M2); %! assert (x, ones (size (b)), 1e-7); %!test %! n = 100; %! tol = 1e-8; %! a = sprand (n, n, .1); %! A = a'*a + 100 * eye (n); %! b = sum (A, 2); %! [x, flag, relres, iter, resvec] = bicgstab (A, b, tol, [], diag (diag (A))); %! assert (x, ones (size (b)), 1e-7);