Mercurial > octave-nkf
view scripts/sparse/cgs.m @ 14237:11949c9795a0
Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Add clf() to all demos using plot features to get reproducibility.
Use 64 as input to all colormaps (jet (64)) to get reproducibility.
* bicubic.m, cell2mat.m, celldisp.m, cplxpair.m, interp1.m, interp2.m,
interpft.m, interpn.m, profile.m, profshow.m, convhull.m, delaunay.m,
griddata.m, inpolygon.m, voronoi.m, autumn.m, bone.m, contrast.m, cool.m,
copper.m, flag.m, gmap40.m, gray.m, hot.m, hsv.m, image.m, imshow.m, jet.m,
ocean.m, pink.m, prism.m, rainbow.m, spring.m, summer.m, white.m, winter.m,
condest.m, onenormest.m, axis.m, clabel.m, colorbar.m, comet.m, comet3.m,
compass.m, contour.m, contour3.m, contourf.m, cylinder.m, daspect.m,
ellipsoid.m, errorbar.m, ezcontour.m, ezcontourf.m, ezmesh.m, ezmeshc.m,
ezplot.m, ezplot3.m, ezpolar.m, ezsurf.m, ezsurfc.m, feather.m, fill.m,
fplot.m, grid.m, hold.m, isosurface.m, legend.m, loglog.m, loglogerr.m,
pareto.m, patch.m, pbaspect.m, pcolor.m, pie.m, pie3.m, plot3.m, plotmatrix.m,
plotyy.m, polar.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m, ribbon.m,
rose.m, scatter.m, scatter3.m, semilogx.m, semilogxerr.m, semilogy.m,
semilogyerr.m, shading.m, slice.m, sombrero.m, stairs.m, stem.m, stem3.m,
subplot.m, surf.m, surfc.m, surfl.m, surfnorm.m, text.m, title.m, trimesh.m,
triplot.m, trisurf.m, uigetdir.m, uigetfile.m, uimenu.m, uiputfile.m,
waitbar.m, xlim.m, ylim.m, zlim.m, mkpp.m, pchip.m, polyaffine.m, spline.m,
bicgstab.m, cgs.m, gplot.m, pcg.m, pcr.m, treeplot.m, strtok.m, demo.m,
example.m, rundemos.m, speed.m, test.m, calendar.m, datestr.m, datetick.m,
weekday.m: Revamp %!demos to use Octave coding conventions on spacing, etc.
author | Rik <octave@nomad.inbox5.com> |
---|---|
date | Fri, 20 Jan 2012 12:59:53 -0800 |
parents | 72c96de7a403 |
children | 3edba8b5f430 |
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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} =} cgs (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{M1}, @var{M2}, @var{x0}) ## @deftypefnx {Function File} {@var{x} =} cgs (@var{A}, @var{b}, @var{rtol}, @var{maxit}, @var{P}) ## @deftypefnx {Function File} {[@var{x}, @var{flag}, @var{relres}, @var{iter}, @var{resvec}] =} cgs (@var{A}, @var{b}, @dots{}) ## Solve @code{A x = b}, where @var{A} is a square matrix, using the ## Conjugate Gradients Squared 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{pcg, bicgstab, bicg, gmres} ## @end deftypefn function [x, flag, relres, iter, resvec] = cgs (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 (["cgs: 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 ("cgs: 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 ("cgs: 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 x = x0; res = b - Ax (x); norm_b = norm (b); ## Vector of the residual norms for each iteration. resvec = norm (res) / norm_b; ro = 0; ## Default behavior we don't reach tolerance tol within maxit iterations. flag = 1; for iter = 1:maxit z = precon (res); ## Cache. ro_old = ro; ro = res' * z; if (iter == 1) p = z; else beta = ro / ro_old; p = z + beta * p; endif ## Cache. q = Ax (p); alpha = ro / (p' * q); x = x + alpha * p; res = res - alpha * q; 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 < 1) if (flag == 0) printf ("cgs converged at iteration %i to a solution with relative residual %e\n", iter, relres); elseif (flag == 3) printf (["cgs stopped at iteration %i without converging to the desired tolerance %e\n", "because the method stagnated.\n", "The iterate returned (number %i) has relative residual %e\n"], iter, tol, iter, relres); else printf (["cgs stopped at iteration %i without converging to the desired tolerance %e\n", "because the maximum number of iterations was reached.\n", "The iterate returned (number %i) has relative residual %e\n"], iter, tol, iter, 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]; %! [a,b,c,d,e] = cgs (A,b) %!shared A, b, n, M %! %!test %! n = 100; %! A = spdiags ([-ones(n,1) 4*ones(n,1) -ones(n,1)], -1:1, n, n); %! b = sum (A, 2); %! tol = 1e-8; %! maxit = 1000; %! M = 4*eye (n); %! [x, flag, relres, iter, resvec] = cgs (A, b, tol, maxit, M); %! assert (x, ones (size (b)), 1e-7); %! %!test %! tol = 1e-8; %! maxit = 15; %! %! [x, flag, relres, iter, resvec] = cgs (@(x) A * x, b, tol, maxit, M); %! 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] = cgs (A, b, tol, [], diag (diag (A))); %! assert (x, ones (size (b)), 1e-7);