Matlab - Error método Nelder-Mead

   
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Error método Nelder-Mead

Publicado por aL (5 intervenciones) el 25/11/2010 20:01:20
Hola.

Estoy intentando hacer un ejemplo del método de Nelder-Mead. Para ello, tengo el código de la función que os copio a continuación:

function [ x_opt, n_feval ] = nelder_mead ( x, function_handle, flag )
%
% Parameters:
%
% Input, real X(M+1,M), contains a list of distinct points that serve as
% initial guesses for the solution. If the dimension of the space is M,
% then the matrix must contain exactly M+1 points. For instance,
% for a 2D space, you supply 3 points. Each row of the matrix contains
% one point; for a 2D space, this means that X would be a
% 3x2 matrix.
%
% Input, handle FUNCTION_HANDLE, a quoted expression for the function,
% or the name of an M-file that defines the function, preceded by an
% "@" sign;
%
% Input, logical FLAG, an optional argument; if present, and set to 1,
% it will cause the program to display a graphical image of the contours
% and solution procedure. Note that this option only makes sense for
% problems in 2D, that is, with N=2.
%
% Output, real X_OPT, the optimal value of X found by the algorithm.
%
%
% Define algorithm constants
%
rho = 1; % rho > 0
xi = 2; % xi > max(rho, 1)
gam = 0.5; % 0 < gam < 1
sig = 0.5; % 0 < sig < 1

tolerance = 1e-6;
max_feval = 250;

% Initialization
[temp,n_dim] = size(x);

if (temp-n_dim ~= 1)
fprintf ( 1, '\n' );
fprintf ( 1, 'NELDER_MEAD - Fatal error!\n' );
error('number of points must be = number of design variables + 1\n');
end

if (nargin==2)
flag = 0;
end

if (flag)
xp = linspace(-5,5,101);
yp = xp;
for i=1:101
for j=1:101
fp(j,i) = feval(function_handle,[xp(i),yp(j)]);
end
end

figure(27)
hold on
contour(xp,yp,fp,linspace(0,200,25))

if (flag)
plot(x(1:2,1),x(1:2,2),'r')
plot(x(2:3,1),x(2:3,2),'r')
plot(x([1 3],1),x([1 3],2),'r')
pause
plot(x(1:2,1),x(1:2,2),'b')
plot(x(2:3,1),x(2:3,2),'b')
plot(x([1 3],1),x([1 3],2),'b')
end

end

index = 1:n_dim+1;

[f] = evaluate(x,function_handle);
n_feval = n_dim + 1;

[f,index] = sort ( f );
x = x(index,:);
%
% Begin the Nelder Mead iteration.
%
converged = 0;
diverged = 0;

while ( ~converged & ~diverged )
%
% Compute midpoint of simplex opposite worst point.
%
x_bar = sum(x(1:n_dim,:)) / n_dim;
%
% Compute reflection point.
%
x_r = (1+rho)*x_bar - rho*x(n_dim+1,:);
f_r = feval(function_handle,x_r); n_feval = n_feval+1;
%
% Accept the point:
%
if (f(1) <= f_r & f_r <= f(n_dim))

x(n_dim+1,:) = x_r;
f(n_dim+1 ) = f_r;

if (flag), title('reflection'), end
%
% Test for possible expansion.
%
elseif (f_r < f(1))

x_e = (1+rho*xi)*x_bar - rho*xi*x(n_dim+1,:);
f_e = feval(function_handle,x_e); n_feval = n_feval+1;

if (f_e<f_r) % accept the expanded point
x(n_dim+1,:) = x_e;
f(n_dim+1 ) = f_e;
if (flag), title('expansion'), end
else
x(n_dim+1,:) = x_r;
f(n_dim+1 ) = f_r;
if (flag), title('eventual reflection'), end
end

elseif (f(n_dim) <= f_r & f_r < f(n_dim+1)) % outside contraction
x_c = (1+rho*gam)*x_bar - rho*gam*x(n_dim+1,:);
f_c = feval(function_handle,x_c); n_feval = n_feval+1;

if (f_c <= f_r) % accept the contracted point
x(n_dim+1,:) = x_c;
f(n_dim+1 ) = f_c;
if (flag), title('outside contraction'), end
else
[x,f] = shrink(x,function_handle,sig); n_feval = n_feval+n_dim;
if (flag), title('shrink'), end
end

else % f_r must be >= f(n_dim+1), try an inside contraction
x_c = (1-gam)*x_bar + gam*x(n_dim+1,:);
f_c = feval(function_handle,x_c); n_feval = n_feval+1;

if (f_c < f(n_dim+1)) % accept the contracted point
x(n_dim+1,:) = x_c;
f(n_dim+1 ) = f_c;
if (flag), title('inside contraction'), end
else
[x,f] = shrink(x,function_handle,sig); n_feval = n_feval+n_dim;
if (flag), title('shrink'), end
end

end
%
% Resort the points. note that we are not implementing the usual
% Nelder-Mead tie-breaking rules (when f(1) = f(2) or f(n_dim) =
% f(n_dim+1)...
%
[ f, index ] = sort ( f );
x = x(index,:);
%
% test for convergence
%
converged = f(n_dim+1)-f(1) < tolerance;
%
% test for divergence
%
diverged = n_feval>max_feval;

if (flag)
plot(x(1:2,1),x(1:2,2),'r')
plot(x(2:3,1),x(2:3,2),'r')
plot(x([1 3],1),x([1 3],2),'r')
pause
plot(x(1:2,1),x(1:2,2),'b')
plot(x(2:3,1),x(2:3,2),'b')
plot(x([1 3],1),x([1 3],2),'b')

end
end

if ( 0 )
fprintf('The best point x^* was: %d %d\n',x(1,:));
fprintf('f(x^*) = %d\n',f(1));
end

x_opt = x(1,:);

if ( diverged )
fprintf ( 1, '\n' );
fprintf ( 1, 'NELDER_MEAD - Warning!\n' );
fprintf ( 1, ' The maximum number of function evaluations was exceeded\n')
fprintf ( 1, ' without convergence being achieved.\n' );
end

return
end
function f = evaluate(x,function_handle)

%*****************************************************************************80
%
%% EVALUATE handles the evaluation of the function at each point.
%
[temp,n_dim] = size(x);

f = zeros(1,n_dim+1);

for i=1:n_dim+1
f(i) = feval(function_handle,x(i,:));
end

return
end

function [ x, f ] = shrink(x,function_handle,sig)

%*****************************************************************************80
%
%% SHRINK ...
%
% In the worst case, we need to shrink the simplex along each edge towards
% the current "best" point. This is quite expensive, requiring n_dim new
% function evaluations.

[temp,n_dim] = size(x);

x1 = x(1,:);
f(1) = feval(function_handle,x1);

for i=2:n_dim+1
x(i,:) = sig*x(i,:) + (1-sig)*x(1,:);
f(i ) = feval(function_handle,x(i,:));
end

return
end


---------------------
Para probarlo, declaro:
>> syms x y z
>> function_handle=x^2+y^-3*z^2*x*y+5*sqrt(x*y)

function_handle =

x^2+1/y^2*z^2*x+5*(x*y)^(1/2)

y ahora llamo al método tal y como me indica la función:

>> [ x_opt, n_feval ] = nelder_mead ( x0, function_handle, 0)


Pero aquí me da un error al evaluar la función, porque me dice que la función FEVAL (usada en el código) debe recibir como argumento una cadena o function_handle.
¿Como puedo meterle la función como una funcion_handle????

Muchas gracias de antemano
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