www.pudn.com > starter.zip > autoHess.m, change:2011-01-04,size:901b


function [f,g,H] = autoHess(x,useComplex,funObj,varargin) % Numerically compute Hessian of objective function from gradient values  p = length(x);  if useComplex % Use Complex Differentials     mu = 1e-150;      diff = zeros(p);     for j = 1:p         e_j = zeros(p,1);         e_j(j) = 1;         [f(j) diff(:,j)] = funObj(x + mu*i*e_j,varargin{:});     end     f = mean(real(f));     g = mean(real(diff),2);     H = imag(diff)/mu; else % Use finite differencing     mu = 2*sqrt(1e-12)*(1+norm(x))/norm(p);          [f,g] = funObj(x,varargin{:});     diff = zeros(p);     for j = 1:p         e_j = zeros(p,1);         e_j(j) = 1;         [f diff(:,j)] = funObj(x + mu*e_j,varargin{:});     end     H = (diff-repmat(g,[1 p]))/mu; end  % Make sure H is symmetric H = (H+H')/2;  if 0 % DEBUG CODE     [fReal gReal HReal] = funObj(x,varargin{:});     [fReal f]     [gReal g]     [HReal H]     pause; end