min.m

利用matlab编制的利用单纯形处理工程问题的程序

        func_evals, how, fv(:,1),varargin{:});
    if stop  % Stop per user request.
        [x,fval,exitflag,output] = cleanUpInterrupt(xOutputfcn,optimValues);
        if  prnt > 0
            disp(output.message)
        end
        return;
    end
end
exitflag = 1;

% Main algorithm
% Iterate until the diameter of the simplex is less than tolx
%   AND the function values differ from the min by less than tolf,
%   or the max function evaluations are exceeded. (Cannot use OR instead of
%   AND.)
while func_evals < maxfun && itercount < maxiter
    if max(abs(fv(1)-fv(two2np1))) <= tolf && ...
            max(max(abs(v(:,two2np1)-v(:,onesn)))) <= tolx
        break
    end
    
    % Compute the reflection point
    
    % xbar = average of the n (NOT n+1) best points
    xbar = sum(v(:,one2n), 2)/n;
    xr = (1 + rho)*xbar - rho*v(:,end);
    x(:) = xr; fxr = funfcn(x,varargin{:});
    func_evals = func_evals+1;
    
    if fxr < fv(:,1)
        % Calculate the expansion point
        xe = (1 + rho*chi)*xbar - rho*chi*v(:,end);
        x(:) = xe; fxe = funfcn(x,varargin{:});
        func_evals = func_evals+1;
        if fxe < fxr
            v(:,end) = xe;
            fv(:,end) = fxe;
            how = 'expand';
        else
            v(:,end) = xr;
            fv(:,end) = fxr;
            how = 'reflect';
        end
    else % fv(:,1) <= fxr
        if fxr < fv(:,n)
            v(:,end) = xr;
            fv(:,end) = fxr;
            how = 'reflect';
        else % fxr >= fv(:,n)
            % Perform contraction
            if fxr < fv(:,end)
                % Perform an outside contraction
                xc = (1 + psi*rho)*xbar - psi*rho*v(:,end);
                x(:) = xc; fxc = funfcn(x,varargin{:});
                func_evals = func_evals+1;
                
                if fxc <= fxr
                    v(:,end) = xc;
                    fv(:,end) = fxc;
                    how = 'contract outside';
                else
                    % perform a shrink
                    how = 'shrink';
                end
            else
                % Perform an inside contraction
                xcc = (1-psi)*xbar + psi*v(:,end);
                x(:) = xcc; fxcc = funfcn(x,varargin{:});
                func_evals = func_evals+1;
                
                if fxcc < fv(:,end)
                    v(:,end) = xcc;
                    fv(:,end) = fxcc;
                    how = 'contract inside';
                else
                    % perform a shrink
                    how = 'shrink';
                end
            end
            if strcmp(how,'shrink')
                for j=two2np1
                    v(:,j)=v(:,1)+sigma*(v(:,j) - v(:,1));
                    x(:) = v(:,j); fv(:,j) = funfcn(x,varargin{:});
                end
                func_evals = func_evals + n;
            end
        end
    end
    [fv,j] = sort(fv);
    v = v(:,j);
    itercount = itercount + 1;
    if prnt == 3
        disp(sprintf(' %5.0f        %5.0f     %12.6g         %s', itercount, func_evals, fv(1), how))
    elseif prnt == 4
        disp(' ')
        disp(how)
        v
        fv
        func_evals
    end
    % OutputFcn call
    if haveoutputfcn
        [xOutputfcn, optimValues, stop] = callOutputFcn(outputfcn,x,xOutputfcn,'iter',itercount, ...
            func_evals, how, fv(:,1),varargin{:});
        if stop  % Stop per user request.
            [x,fval,exitflag,output] = cleanUpInterrupt(xOutputfcn,optimValues);
            if  prnt > 0
                disp(output.message)
            end
            return;
        end
    end
end   % while

x(:) = v(:,1);
if prnt == 4,
    % reset format
    set(0,{'format','formatspacing'},formatsave);
end
output.iterations = itercount;
output.funcCount = func_evals;
output.algorithm = 'Nelder-Mead simplex direct search';

fval = min(fv);

% OutputFcn call
if haveoutputfcn
    callOutputFcn(outputfcn,x,xOutputfcn,'done',itercount, func_evals, how, f, varargin{:});
end

if func_evals >= maxfun
    msg = sprintf(['Exiting: Maximum number of function evaluations has been exceeded\n' ...
                   '         - increase MaxFunEvals option.\n' ...
                   '         Current function value: %f \n'], fval);
    if prnt > 0
        disp(' ')
        disp(msg)
    end
    exitflag = 0;
elseif itercount >= maxiter
    msg = sprintf(['Exiting: Maximum number of iterations has been exceeded\n' ... 
                   '         - increase MaxIter option.\n' ...
                   '         Current function value: %f \n'], fval);
    if prnt > 0
        disp(' ')
        disp(msg)
    end
    exitflag = 0;
else
    msg = ...
      sprintf(['Optimization terminated:\n', ...
               ' the current x satisfies the termination criteria using OPTIONS.TolX of %e \n' ...
               ' and F(X) satisfies the convergence criteria using OPTIONS.TolFun of %e \n'], ...
               tolx, tolf);
    if prnt > 1
        disp(' ')
        disp(msg)
    end
    exitflag = 1;
end

output.message = msg;

%--------------------------------------------------------------------------
function [xOutputfcn, optimValues, stop] = callOutputFcn(outputfcn,x,xOutputfcn,state,iter,...
    numf,how,f,varargin)
% CALLOUTPUTFCN assigns values to the struct OptimValues and then calls the
% outputfcn.
%
% state - can have the values 'init','iter', or 'done'.
% We do not handle the case 'interrupt' because we do not want to update
% xOutputfcn or optimValues (since the values could be inconsistent) before calling
% the outputfcn; in that case the outputfcn is called directly rather than
% calling it inside callOutputFcn.

% For the 'done' state we do not check the value of 'stop' because the
% optimization is already done.
optimValues.iteration = iter;
optimValues.funccount = numf;
optimValues.fval = f;
optimValues.procedure = how;

xOutputfcn(:) = x;  % Set x to have user expected size
switch state
    case {'iter','init'}
        stop = outputfcn(xOutputfcn,optimValues,state,varargin{:});
    case 'done'
        stop = false;
        outputfcn(xOutputfcn,optimValues,state,varargin{:});
    otherwise
        error('MATLAB:min:InvalidState', ...
            'Unknown state in CALLOUTPUTFCN.')
end

%--------------------------------------------------------------------------
function [x,FVAL,EXITFLAG,OUTPUT] = cleanUpInterrupt(xOutputfcn,optimValues)
% CLEANUPINTERRUPT updates or sets all the output arguments of FMINBND when the optimization
% is interrupted.

x = xOutputfcn;
FVAL = optimValues.fval;
EXITFLAG = -1;
OUTPUT.iterations = optimValues.iteration;
OUTPUT.funcCount = optimValues.funccount;
OUTPUT.algorithm = 'golden section search, parabolic interpolation';
OUTPUT.message = 'Optimization terminated prematurely by user.';

%--------------------------------------------------------------------------
function f = checkfun(x,userfcn,varargin)
% CHECKFUN checks for complex or NaN results from userfcn.

f = userfcn(x,varargin{:});
% Note: we do not check for Inf as MIN handles it naturally.
if isnan(f)
    error('MATLAB:min:checkfun:NaNFval', ...
        'User function ''%s'' returned NaN when evaluated at %g;\n MIN cannot continue.', ...
        localChar(userfcn), x);  
elseif ~isreal(f)
    error('MATLAB:min:checkfun:ComplexFval', ...
        'User function ''%s'' returned a complex value when evaluated at %g;\n MIN cannot continue.', ...
        localChar(userfcn),x);  
end

%--------------------------------------------------------------------------
function strfcn = localChar(fcn)
% Convert the fcn to a string for printing

if ischar(fcn)
    strfcn = fcn;
elseif isa(fcn,'inline')
    strfcn = char(fcn);
elseif isa(fcn,'function_handle')
    strfcn = func2str(fcn);
else
    try
        strfcn = char(fcn);
    catch
        strfcn = '(name not printable)';
    end
end