Простейшая нейронная сеть для аппроксимации параболы

function targ_n_n_forum
% нейронная сеть с одним слоем
% двумя нейронами и единицей
% для аппроксимации параболы
% на выходе сети сумматор
b = 100; j = 0;
[x y w h i] = start2n;
while 1
  dE = dE_analytic(w, x, y);
  [w er] = naiskor_spusk(dE, w, x, y);
  if er < 0.005
    draw_h(w, x, h, i, er);
    break
  end
  i = i + 1;
  if mod(i, b) == 0
    h = draw_h(w, x, h, i, er);
  end
end
end
function [w er] = naiskor_spusk(dE, w, x, y)
a = 0.1; er1 = sumerr_n(x, y, w);
while 1
  w1 = w - a*dE;
  er = sumerr_n(x, y, w1);
  if er1 < er
    a = a/2;
  else
    w = w1; return
  end
end
end

function [x y w h i] = start2n
close all; clc; x = (0.1:0.05:0.9)';
y = (2*x - 1).^2 + 0.1; pot(x,y,'.');
axis([0 1 0 1])
set(gcf,'position',[1680 950 560 420])
[w er i h] = first_poisk_w(x, y);
end
function [w er i h] = first_poisk_w(x, y)
N = 100;
w = rand(6,1)-0.5; i = 0; m = 0.5;
y1 = ynet(x, w); h = plot(x,y1,'-w');
err = [];  pause(0.1);
er = sumerr_n(x, y, w); % return
while 1
  ww = w_plus_ww(w, m, N);
  [w er] = find_best(ww, x, y);
  i = i + 1; err  = [err; er];
  if er < 0.5
    h = draw_h(w, x, h, i, er);
    break
  end
end
end
function ww = w_plus_ww(w, m, N)
n = numel(w);
A = m*rand(n,N) - m/2;
ww = repmat(w, 1, N) + A;
ww = cat(2, w, ww);
end
function [w err] = find_best(ww, x, y)
[r c] = size(ww); er = zeros(c,1);
for i = 1:c
  w = ww(:,i);
  er(i) = sumerr_n(x, y, w);
end
[err ind] = min(er);
w = ww(:,ind);
end

function err = sumerr_n(x, y, w)
y1 = ynet(x, w);
d = y1 - y; err = sum(d.*d);
end
function y = ynet(x, w)
for i = 1:numel(x)
  y(i,1) = forward(x(i), w);
end
end
function f = forward(x, w)
% y = w5*f(xw1+w3)+w6*f(xw2+w4)
f1 = smd(x*w(1)+w(3));
f2 = smd(x*w(2)+w(4));
f = w(5)*f1 + w(6)*f2;
end
function dE = dE_analytic(w, x, y)
y1 = fnet(x, w); d = y1 - y;
for i = 1:numel(x)
  de1(i) = d(i)*x(i)*dsm(x(i)*w(1)+w(3));
  de2(i) = d(i)*x(i)*dsm(x(i)*w(2)+w(4));
  de3(i) = d(i)*dsm(x(i)*w(1)+w(3));
  de4(i) = d(i)*dsm(x(i)*w(2)+w(4));
  de5(i) = d(i)*smd(x(i)*w(1)+w(3));
  de6(i) = d(i)*smd(x(i)*w(2)+w(4));
end
dE1 = w(5)*sum(de1);
dE2 = w(6)*sum(de2);
dE3 = w(5)*sum(de3);
dE4 = w(6)*sum(de4);
dE5 = sum(de5);
dE6 = sum(de6);
dE = [dE1 dE2 dE3 dE4 dE5 dE6]';
end