使用值函数迭代的宏观经济模型的Matlab工具包.zip

function [xmin, ... % minimum search point of last iteration fmin, ... % function value of xmin counteval, ... % number of function evaluations done stopflag, ... % stop criterion reached out, ... % struct with various histories and solutions bestever ... % struct containing overall best solution (for convenience) ] = cmaes( ... fitfun, ... % name of objective/fitness function xstart, ... % objective variables initial point, determines N insigma, ... % initial coordinate wise standard deviation(s) inopts, ... % options struct, see defopts below varargin ... % arguments passed to objective function ) % Version for VFI Toolkit, lightly edited from: % cmaes.m, Version 3.61.beta, last change: April, 2012 % CMAES implements an Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) for nonlinear function minimization. For % introductory comments and copyright (GPL) see end of file (type 'type cmaes'). cmaes_vfitoolkit.m runs with MATLAB (Windows, Linux). % % OPTS = CMAES returns default options. % OPTS = CMAES('defaults') returns default options quietly. % OPTS = CMAES('displayoptions') displays options. % OPTS = CMAES('defaults', OPTS) supplements options OPTS with default % options. % % XMIN = CMAES(FUN, X0, SIGMA[, OPTS]) locates an approximate minimum % XMIN of function FUN starting from column vector X0 with the initial % coordinate wise search standard deviation SIGMA. % % Input arguments: % % FUN is a string function name like 'frosen'. FUN takes as argument % a column vector of size of X0 and returns a scalar. An easy way to % implement a hard non-linear constraint is to return NaN. Then, % this function evaluation is not counted and a newly sampled % point is tried immediately. % % X0 is a column vector, or a matrix, or a string. If X0 is a matrix, % mean(X0, 2) is taken as initial point. If X0 is a string like % '2*rand(10,1)-1', the string is evaluated first. % % SIGMA is a scalar, or a column vector of size(X0,1), or a string % that can be evaluated into one of these. SIGMA determines the % initial coordinate wise standard deviations for the search. % Setting SIGMA one third of the initial search region is % appropriate, e.g., the initial point in [0, 6]^10 and SIGMA=2 % means cmaes('myfun', 3*rand(10,1), 2). If SIGMA is missing and % size(X0,2) > 1, SIGMA is set to sqrt(var(X0')'). That is, X0 is % used as a sample for estimating initial mean and variance of the % search distribution. % % OPTS (an optional argument) is a struct holding additional input % options. Valid field names and a short documentation can be % discovered by looking at the default options (type 'cmaes' % without arguments, see above). Empty or missing fields in OPTS % invoke the default value, i.e. OPTS needs not to have all valid % field names. Capitalization does not matter and unambiguous % abbreviations can be used for the field names. If a string is % given where a numerical value is needed, the string is evaluated % by eval, where 'N' expands to the problem dimension % (==size(X0,1)) and 'popsize' to the population size. % % [XMIN, FMIN, COUNTEVAL, STOPFLAG, OUT, BESTEVER] = ... % CMAES(FITFUN, X0, SIGMA) % returns the best (minimal) point XMIN (found in the last generation); function value FMIN of XMIN; the number of needed % function evaluations COUNTEVAL; a STOPFLAG value as cell array, where possible entries are 'fitness', 'tolx', 'tolupx', 'tolfun', % 'maxfunevals', 'maxiter', 'stoptoresume', 'manual', 'warnconditioncov', 'warnnoeffectcoord', 'warnnoeffectaxis', % 'warnequalfunvals', 'warnequalfunvalhist', 'bug' (use e.g. any(strcmp(STOPFLAG, 'tolx')) or findstr(strcat(STOPFLAG, % 'tolx')) for further processing); a record struct OUT with some more output, where the struct SOLUTIONS.BESTEVER contains the overall % best evaluated point X with function value F evaluated at evaluation count EVALS. The last output argument BESTEVER equals % OUT.SOLUTIONS.BESTEVER. Moreover a history of solutions and parameters is written to files according to the Log-options. % % A regular manual stop can be achieved via the file signals.par. The program is terminated if the first two non-white sequences in any % line of this file are 'stop' and the value of the LogFilenamePrefix option (by default 'outcmaes'). Also a run can be skipped. % Given, for example, 'skip outcmaes run 2', skips the second run if option Restarts is at least 2, and another run will be started. % % To run the code completely silently set Disp, Save, and Log options to 0. With OPTS.LogModulo > 0 (1 by default) the most important % data are written to ASCII files permitting to investigate the results (e.g. plot with function plotcmaesdat) even while CMAES is % still running (which can be quite useful on expensive objective functions). When OPTS.SaveVariables==1 (default) everything is saved % in file OPTS.SaveFilename (default 'variablescmaes.mat') allowing to resume the search afterwards by using the resume option. % % To find the best ever evaluated point load the variables typing "es=load('variablescmaes')" and investigate the variable es.out.solutions.bestever. % % In case of a noisy objective function (uncertainties) set OPTS.Noise.on = 1. This option interferes presumably with some % termination criteria, because the step-size sigma will presumably not converge to zero anymore. If CMAES was provided with a % fifth argument (P1 in the below example, which is passed to the objective function FUN), this argument is multiplied with the % factor given in option Noise.alphaevals, each time the detected noise exceeds a threshold. This argument can be used within % FUN, for example, as averaging number to reduce the noise level. % % OPTS.DiagonalOnly > 1 defines the number of initial iterations, where the covariance matrix remains diagonal and the algorithm has % internally linear time complexity. OPTS.DiagonalOnly = 1 means keeping the covariance matrix always diagonal and this setting % also exhibits linear space complexity. This can be particularly useful for dimension > 100. The default is OPTS.DiagonalOnly = 0. % % OPTS.CMA.active = 1 turns on "active CMA" with a negative update of the covariance matrix and checks for positive definiteness. % OPTS.CMA.active = 2 does not check for pos. def. and is numerically faster. Active CMA usually speeds up the adaptation and might % become a default in near future. % % The primary strategy parameter to play with is OPTS.PopSize, which can be increased from its default value. Increasing the population % size (by default linked to increasing parent number OPTS.ParentNumber) improves global search properties in exchange to speed. Speed % decreases, as a rule, at most linearely with increasing population size. It is advisable to begin with the default small population % size. The options Restarts and IncPopSize can be used for an automated multistart where the population size is increased by the % factor IncPopSize (two by default) before each restart. X0 (given as string) is reevaluated for each restart. Stopping options % StopFunEvals, StopIter, MaxFunEvals, and Fitness terminate the program, all others including MaxIter invoke another restart, where % the iteration counter is reset to zero. % % Examples: % % XMIN = cmaes('myfun', 5*ones(10,1), 1.5); % % starts the search at 10D-point 5 and initially searches mainly % between 5-3 and 5+3 (+- two standard deviations), but this is not % a strict bound. 'myfun' is a name of a function that returns a % scalar from a 10D column vector. % % opts.LBounds = 0; opts.UBounds = 10; % opts.Restarts = 3; % doubles the popsize for each restart %