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view main/optim/inst/cg_min.m @ 9930:d30cfca46e8a octave-forge
optim: upgrade license to GPLv3+ and mention on DESCRIPTION the other package licenses
author | carandraug |
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date | Fri, 30 Mar 2012 15:14:48 +0000 |
parents | a5fa14594ca4 |
children | f82660cf7dee |
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## Copyright (C) 2002 Etienne Grossmann <etienne@isr.ist.utl.pt> ## Copyright (C) 2009 Levente Torok <TorokLev@gmail.com> ## ## This program 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. ## ## This program 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 ## this program; if not, see <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{x0},@var{v},@var{nev}]} cg_min ( @var{f},@var{df},@var{args},@var{ctl} ) ## NonLinear Conjugate Gradient method to minimize function @var{f}. ## ## @subheading Arguments ## @itemize @bullet ## @item @var{f} : string : Name of function. Return a real value ## @item @var{df} : string : Name of f's derivative. Returns a (R*C) x 1 vector ## @item @var{args}: cell : Arguments passed to f.@* ## @item @var{ctl} : 5-vec : (Optional) Control variables, described below ## @end itemize ## ## @subheading Returned values ## @itemize @bullet ## @item @var{x0} : matrix : Local minimum of f ## @item @var{v} : real : Value of f in x0 ## @item @var{nev} : 1 x 2 : Number of evaluations of f and of df ## @end itemize ## ## @subheading Control Variables ## @itemize @bullet ## @item @var{ctl}(1) : 1 or 2 : Select stopping criterion amongst : ## @item @var{ctl}(1)==0 : Default value ## @item @var{ctl}(1)==1 : Stopping criterion : Stop search when value doesn't ## improve, as tested by @math{ ctl(2) > Deltaf/max(|f(x)|,1) } ## where Deltaf is the decrease in f observed in the last iteration ## (each iteration consists R*C line searches). ## @item @var{ctl}(1)==2 : Stopping criterion : Stop search when updates are small, ## as tested by @math{ ctl(2) > max @{ dx(i)/max(|x(i)|,1) | i in 1..N @}} ## where dx is the change in the x that occured in the last iteration. ## @item @var{ctl}(2) : Threshold used in stopping tests. Default=10*eps ## @item @var{ctl}(2)==0 : Default value ## @item @var{ctl}(3) : Position of the minimized argument in args Default=1 ## @item @var{ctl}(3)==0 : Default value ## @item @var{ctl}(4) : Maximum number of function evaluations Default=inf ## @item @var{ctl}(4)==0 : Default value ## @item @var{ctl}(5) : Type of optimization: ## @item @var{ctl}(5)==1 : "Fletcher-Reves" method ## @item @var{ctl}(5)==2 : "Polak-Ribiere" (Default) ## @item @var{ctl}(5)==3 : "Hestenes-Stiefel" method ## @end itemize ## ## @var{ctl} may have length smaller than 4. Default values will be used if ctl is ## not passed or if nan values are given. ## @subheading Example: ## ## function r=df( l ) b=[1;0;-1]; r = -( 2*l@{1@} - 2*b + rand(size(l@{1@}))); endfunction @* ## function r=ff( l ) b=[1;0;-1]; r = (l@{1@}-b)' * (l@{1@}-b); endfunction @* ## ll = @{ [10; 2; 3] @}; @* ## ctl(5) = 3; @* ## [x0,v,nev]=cg_min( "ff", "df", ll, ctl ) @* ## ## Comment: In general, BFGS method seems to be better performin in many cases but requires more computation per iteration ## @seealso{ bfgsmin, http://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient } ## @end deftypefn function [x,v,nev] = cg_min (f, dfn, args, ctl) verbose = 0; crit = 1; # Default control variables tol = 10*eps; narg = 1; maxev = inf; method = 2; if nargin >= 4, # Read arguments if !isnan (ctl(1)) && ctl(1) ~= 0, crit = ctl(1); end if length (ctl)>=2 && !isnan (ctl(2)) && ctl(2) ~= 0, tol = ctl(2); end if length (ctl)>=3 && !isnan (ctl(3)) && ctl(3) ~= 0, narg = ctl(3); end if length (ctl)>=4 && !isnan (ctl(4)) && ctl(4) ~= 0, maxev = ctl(4); end if length (ctl)>=5 && !isnan (ctl(5)) && ctl(5) ~= 0, method= ctl(5); end end if iscell (args), # List of arguments x = args{narg}; else # Single argument x = args; args = {args}; end if narg > length (args), # Check error ("cg_min : narg==%i, length (args)==%i\n", narg, length (args)); end [R, C] = size(x); N = R*C; x = reshape (x,N,1) ; nev = [0, 0]; v = feval (f, args); nev(1)++; dxn = lxn = dxn_1 = -feval( dfn, args ); nev(2)++; done = 0; ## TEMP ## tb = ts = zeros (1,100); # Control params for line search ctlb = [10*sqrt(eps), narg, maxev]; if crit == 2, ctlb(1) = tol; end x0 = x; v0 = v; nline = 0; while nev(1) <= maxev , ## xprev = x ; ctlb(3) = maxev - nev(1); # Update # of evals ## wiki alg 4. [alpha, vnew, nev0] = brent_line_min (f, dxn, args, ctlb); nev += nev0; ## wiki alg 5. x = x + alpha * dxn; if nline >= N, if crit == 1, done = tol > (v0 - vnew) / max (1, abs (v0)); else done = tol > norm ((x-x0)(:)); end nline = 1; x0 = x; v0 = vnew; else nline++; end if done || nev(1) >= maxev, return end if vnew > v + eps , printf("cg_min: step increased cost function\n"); keyboard end # if abs(1-(x-xprev)'*dxn/norm(dxn)/norm(x-xprev))>1000*eps, # printf("cg_min: step is not in the right direction\n"); # keyboard # end # update x at the narg'th position of args cellarray args{narg} = reshape (x, R, C); v = feval (f, args); nev(1)++; if verbose, printf("cg_min : nev=%4i, v=%8.3g\n",nev(1),v) ; end ## wiki alg 1: dxn = -feval (dfn, args); nev(2)++; # wiki alg 2: switch method case 1 # Fletcher-Reenves method nu = dxn' * dxn; de = dxn_1' * dxn_1; case 2 # Polak-Ribiere method nu = (dxn-dxn_1)' * dxn; de = dxn_1' * dxn_1; case 3 # Hestenes-Stiefel method nu = (dxn-dxn_1)' * dxn; de = (dxn-dxn_1)' * lxn; otherwise error("No method like this"); endswitch if nu == 0, return endif if de == 0, error("Numerical instability!"); endif beta = nu / de; beta = max( 0, beta ); ## wiki alg 3. update dxn, lxn, point dxn_1 = dxn; dxn = lxn = dxn_1 + beta*lxn ; end if verbose, printf ("cg_min: Too many evaluatiosn!\n"); end endfunction %!demo %! P = 15; # Number of parameters %! R = 20; # Number of observations (must have R >= P) %! %! obsmat = randn (R, P); %! truep = randn (P, 1); %! xinit = randn (P, 1); %! obses = obsmat * truep; %! %! msq = @(x) mean (x (!isnan(x)).^2); %! ff = @(x) msq (obses - obsmat * x{1}) + 1; %! dff = @(x) 2 / rows (obses) * obsmat.' * (-obses + obsmat * x{1}); %! %! tic; %! [xlev,vlev,nlev] = cg_min (ff, dff, xinit) ; %! toc; %! %! printf (" Costs : init=%8.3g, final=%8.3g, best=%8.3g\n", ... %! ff ({xinit}), vlev, ff ({truep})); %! %! if (max (abs (xlev-truep)) > 100*sqrt (eps)) %! printf ("Error is too big : %8.3g\n", max (abs (xlev-truep))); %! else %! printf ("All tests ok\n"); %! endif %!demo %! N = 1 + floor (30 * rand ()); %! truemin = randn (N, 1); %! offset = 100 * randn (); %! metric = randn (2 * N, N); %! metric = metric.' * metric; %! %! if (N > 1) %! [u,d,v] = svd (metric); %! d = (0.1+[0:(1/(N-1)):1]).^2; %! metric = u * diag (d) * u.'; %! endif %! %! testfunc = @(x) sum((x{1}-truemin)'*metric*(x{1}-truemin)) + offset; %! dtestf = @(x) metric' * 2*(x{1}-truemin); %! %! xinit = 10 * randn (N, 1); %! %! [x, v, niter] = cg_min (testfunc, dtestf, xinit); %! %! if (any (abs (x-truemin) > 100 * sqrt(eps))) %! printf ("NOT OK 1\n"); %! else %! printf ("OK 1\n"); %! endif %! %! if (v-offset > 1e-8) %! printf ("NOT OK 2\n"); %! else %! printf ("OK 2\n"); %! endif %! %! printf ("nev=%d N=%d errx=%8.3g errv=%8.3g\n",... %! niter (1), N, max (abs (x-truemin)), v-offset); %!demo %! P = 2; # Number of parameters %! R = 3; # Number of observations %! %! obsmat = randn (R, P); %! truep = randn (P, 1); %! xinit = randn (P, 1); %! %! obses = obsmat * truep; %! %! msq = @(x) mean (x (!isnan(x)).^2); %! ff = @(xx) msq (xx{3} - xx{2} * xx{1}) + 1; %! dff = @(xx) 2 / rows(xx{3}) * xx{2}.' * (-xx{3} + xx{2}*xx{1}); %! %! tic; %! x = {xinit, obsmat, obses}; %! [xlev, vlev, nlev] = cg_min (ff, dff, x); %! toc; %! %! xinit_ = {xinit, obsmat, obses}; %! xtrue_ = {truep, obsmat, obses}; %! printf (" Costs : init=%8.3g, final=%8.3g, best=%8.3g\n", ... %! ff (xinit_), vlev, ff (xtrue_)); %! %! if (max (abs(xlev-truep)) > 100*sqrt (eps)) %! printf ("Error is too big : %8.3g\n", max (abs (xlev-truep))); %! else %! printf ("All tests ok\n"); %! endif