📄 nnd12m.m
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function nnd12m(cmd,arg1)
%NND12M Marquardt backpropagation demonstration.
%
% This demonstration requires the Neural Network Toolbox.
% First Version, 8-31-95.
%==================================================================
% CONSTANTS
me = 'nnd12m';
max_t = 0.5;
w_max = 10;
p_max = 2;
circle_size = 6;
% FLAGS
change_func = 0;
% DEFAULTS
if nargin == 0, cmd = ''; else cmd = lower(cmd); end
% FIND WINDOW IF IT EXISTS
fig = nnfgflag(me);
if length(get(fig,'children')) == 0, fig = 0; end
% GET WINDOW DATA IF IT EXISTS
if fig
H = get(fig,'userdata');
fig_axis = H(1); % window axis
desc_text = H(2); % handle to first line of text sequence
mu_bar = H(3); % mu slider bar
mu_text = H(4); % mu text
nu_bar = H(5); % nu slider bar
nu_text = H(6); % nu text
cont_axis = H(7); % error contour axis
cont_ptr = H(8); % pointer to error contour handles
radios = H(9:11); % radio buttons
option_ptr = H(12); % index of active radio
path_ptr = H(13); % pointer to training path handles
end
%==================================================================
% Activate the window.
%
% ME() or ME('')
%==================================================================
if strcmp(cmd,'')
if fig
figure(fig)
set(fig,'visible','on')
else
feval(me,'init')
end
%==================================================================
% Close the window.
%
% ME() or ME('')
%==================================================================
elseif strcmp(cmd,'close') & (fig)
delete(fig)
%==================================================================
% Initialize the window.
%
% ME('init')
%==================================================================
elseif strcmp(cmd,'init') & (~fig)
% CHECK FOR NNT
if ~nntexist(me), return, end
% CONSTANTS
W1 = [10; 10];
b1 = [-5;5];
W2 = [1 1];
b2 = [-1];
P = -2:0.1:2;
T = logsig(W2*logsig(W1*P,b1),b2);
% NEW DEMO FIGURE
fig = nndemof2(me,'DESIGN','Marquardt Backpropagation','','Chapter 12');
set(fig, ...
'windowbuttondownfcn',nncallbk(me,'down'), ...
'BackingStore','off',...
'nextplot','add');
H = get(fig,'userdata');
fig_axis = H(1);
desc_text = H(2);
% ICON
nndicon(12,458,363,'shadow')
% MU SLIDER BAR
mu = 0.01;
x = 20;
y = 60;
text(x,y,'Initial MU:',...
'color',nndkblue,...
'fontw','bold',...
'fontsize',12,...
'horizontalalignment','left')
mu_text = text(x+160,y,num2str(mu),...
'color',nndkblue,...
'fontw','bold',...
'fontsize',12,...
'horizontalalignment','right');
text(x,y-38,'0.01',...
'color',nndkblue,...
'fontw','bold',...
'fontsize',12,...
'horizontalalignment','left')
text(x+160,y-38,'0.10',...
'color',nndkblue,...
'fontw','bold',...
'fontsize',12,...
'horizontalalignment','right');
mu_bar = uicontrol(...
'units','points',...
'position',[x y-25 160 16],...
'style','slider',...
'backg',nnltgray,...
'callback',[me '(''mu'')'],...
'min',0.01,...
'max',0.10,...
'value',mu);
% NU SLIDER BAR
nu = 5;
x = 200;
y = 60;
text(x,y,'Constant NU:',...
'color',nndkblue,...
'fontw','bold',...
'fontsize',12,...
'horizontalalignment','left')
nu_text = text(x+160,y,num2str(nu),...
'color',nndkblue,...
'fontw','bold',...
'fontsize',12,...
'horizontalalignment','right');
text(x,y-38,'1.0',...
'color',nndkblue,...
'fontw','bold',...
'fontsize',12,...
'horizontalalignment','left')
text(x+160,y-38,'10.0',...
'color',nndkblue,...
'fontw','bold',...
'fontsize',12,...
'horizontalalignment','right');
nu_bar = uicontrol(...
'units','points',...
'position',[x y-25 160 16],...
'style','slider',...
'backg',nnltgray,...
'callback',[me '(''nu'')'],...
'min',1,...
'max',10,...
'value',nu);
% RADIO BUTTONS
option = 1;
radio1 = uicontrol(...
'units','points',...
'position',[20 80 130 20],...
'style','radio',...
'string','W1(1,1), W2(1,1)',...
'back',nnltgray,...
'callback',[me '(''radio'',1)'],...
'value',1);
radio2 = uicontrol(...
'units','points',...
'position',[155 80 115 20],...
'style','radio',...
'string','W1(1,1), b1(1)',...
'back',nnltgray,...
'callback',[me '(''radio'',2)']);
radio3 = uicontrol(...
'units','points',...
'position',[270 80 105 20],...
'style','radio',...
'string','b1(1), b1(2)',...
'back',nnltgray,...
'callback',[me '(''radio'',3)']);
% ERROR SURFACE
load nndbp1
cont_axis = nnsfo('a2','',v1,v2,'');
set(cont_axis, ...
'units','points',...
'position',[90 140 200 200],...
'color',nnltyell,...
'xlim',range1,...
'ylim',range2,...
'colororder',[0 0 0])
[dummy,cont_h] = contour(x2,y2,E2,levels);
set(cont_h,'erasemode','none');
plot3(range1([1 2 2 1 1]),range2([1 1 2 2 1]),1000*ones(1,5),...
'color',nndkblue);
cont_h2 = plot(optx,opty,'+','color',nnred);
cont_h = [cont_h; cont_h2];
view(2)
% BUTTONS
uicontrol(...
'units','points',...
'position',[400 110 60 20],...
'string','Contents',...
'callback','nndtoc')
uicontrol(...
'units','points',...
'position',[400 75 60 20],...
'string','Close',...
'callback',[me '(''close'')'])
% DATA POINTERS
dummy = 0;
cont_ptr = uicontrol('visible','off','userdata',cont_h);
option_ptr = uicontrol('visible','off','userdata',option);
path_ptr = uicontrol('visible','off','userdata',[]);
% SAVE WINDOW DATA AND LOCK
H = [fig_axis desc_text mu_bar mu_text nu_bar nu_text cont_axis cont_ptr ...
radio1 radio2 radio3 option_ptr path_ptr];
set(fig,'userdata',H,'nextplot','new')
% INSTRUCTION TEXT
feval(me,'instr');
% LOCK WINDOW
set(fig,'nextplot','new','color',nnltgray);
nnchkfs;
%==================================================================
% Display the instructions.
%
% ME('instr')
%==================================================================
elseif strcmp(cmd,'instr') & (fig)
nnsettxt(desc_text,...
'Use the radio buttons',...
'to select the network',...
'parameters to train',...
'with backpropagation.',...
'',...
'The corresponding',...
'contour plot is',...
'shown to the left.',...
'',...
'Click in the contour',...
'graph to start the',...
'Marquardt backprop',...
'learning algorithm.')
%==================================================================
% Respond to radio buttons.
%
% ME('radio',i)
%==================================================================
elseif strcmp(cmd,'radio') & (fig) & (nargin == 2)
% GET DATA
option = get(option_ptr,'userdata');
% ALTER TRAINABLE PARAMETERS
if (arg1 ~= option)
% HIGHLIGHT NEW RADIO BUTTON
set(radios(option),'value',0)
set(radios(arg1),'value',1)
option = arg1;
% CLEAR AXES
delete(get(cont_axis,'children'))
% CONSTANTS
W1 = [10; 10];
b1 = [-5;5];
W2 = [1 1];
b2 = [-1];
P = -2:0.1:2;
T = logsig(W2*logsig(W1*P,b1),b2);
% ERROR SURFACE & VARIABLE NAMES
if option == 1
load nndbp1
elseif option == 2
load nndbp2
else
load nndbp3
end
set(fig,'nextplot','add')
axes(cont_axis)
set(get(cont_axis,'xlabel'),'string',v1)
set(get(cont_axis,'ylabel'),'string',v2)
set(cont_axis,'xlim',range1,'ylim',range2)
[dummy,cont_h] = contour(x2,y2,E2,levels);
set(cont_h,'erasemode','none');
plot3(range1([1 2 2 1 1]),range2([1 1 2 2 1]),1000*ones(1,5),...
'color',nndkblue);
cont_h2 = plot(optx,opty,'+','color',nnred);
cont_h = [cont_h; cont_h2];
view(2)
% STORE DATA
set(cont_ptr,'userdata',cont_h);
set(path_ptr,'userdata',[]);
set(option_ptr,'userdata',option);
end
%==================================================================
% Respond to mu slider.
%
% ME('mu')
%==================================================================
elseif strcmp(cmd,'mu')
mu = get(mu_bar,'value');
set(mu_text,'string',sprintf('%4.2f',round(mu*100)*0.01))
%==================================================================
% Respond to nu slider.
%
% ME('nu')
%==================================================================
elseif strcmp(cmd,'nu')
nu = get(nu_bar,'value');
set(nu_text,'string',sprintf('%4.1f',round(nu*10)*0.1))
%==================================================================
% Respond to mouse down.
%
% ME('down')
%==================================================================
elseif strcmp(cmd,'down') & (fig) & (nargin == 1)
pt = get(cont_axis,'currentpoint');
x = pt(1);
y = pt(3);
xlim = get(cont_axis,'xlim');
ylim = get(cont_axis,'ylim');
if (x > xlim(1) & x < xlim(2) & y > ylim(1) & y < ylim(2))
% GET DATA
option = get(option_ptr,'userdata');
path = get(path_ptr,'userdata');
cont_h = get(cont_ptr,'userdata');
% REMOVE PREVIOUS PATH
set(fig,'nextplot','add')
delete(path);
% INITIAL VALUES
W1 = [10; 10];
b1 = [-5;5];
W2 = [1 1];
b2 = [-1];
P = -2:0.1:2;
T = logsig(W2*logsig(W1*P,b1),b2);
% PLOT START POINT
dkblue = nndkblue;
red = nnred;
axes(cont_axis);
path = [...
plot(x,y,'o','color',dkblue,'markersize',8,'erasemode','none');
plot(x,y,'o','color',[1 1 1],'markersize',10,'erasemode','none');
plot(x,y,'o','color',dkblue,'markersize',12,'erasemode','none')];
drawnow
% PLOT PATH
set(fig,'pointer','watch')
% INITIALIZE TRAINING
if option == 1
W1(1,1) = x;
W2(1,1) = y;
elseif option == 2
W1(1,1) = x;
b1(1) = y;
else
b1(1) = x;
b1(2) = y;
end
mu_initial = get(mu_bar,'value');
v = get(nu_bar,'value');
A1 = logsig(W1*P,b1);
A2 = logsig(W2*A1,b2);
E1 = T-A2;
f1 = sumsqr(E1);
% DEFINE SIZES
[R,Q] = size(P);
[S2,Q] = size(T);
S1 = 2;
RS = S1*R; RS1 = RS+1; RSS = RS + S1; RSS1 = RSS + 1;
RSS2 = RSS + S1*S2; RSS3 = RSS2 + 1; RSS4 = RSS2 + S2;
% ASSIGN PARAMETERS
disp_freq = 1;
max_epoch = 11;
err_goal = 0.00000000001;
maxmu=1e10;
mingrad=.00002;
mu=mu_initial;
ii=eye(2);
meu=zeros(max_epoch,1);
mer=meu;grad=meu;
xx = [x zeros(1,max_epoch)];
yy = [y zeros(1,max_epoch)];
% MAIN LOOP
for k=2:(max_epoch+1)
% INITIALIZE A
mu=mu/v;
mer(k)=f1;
meu(k)=mu;
tst=1;
% FIND JACOBIAN
A1 = kron(A1,ones(1,S2));
D2 = nnmdlog(A2);
D1 = nnmdlog(A1,D2,W2);
jac1 = nnlmarq(kron(P,ones(1,S2)),D1);
jac2 = nnlmarq(A1,D2);
jac=[jac1,D1',jac2,D2'];
% PULL OUT APPROPRIATE TERMS
if (option == 1)
jac = [jac(:,1) jac(:,5)];
elseif(option == 2)
jac = [jac(:,1) jac(:,3)];
else
jac = [jac(:,3) jac(:,4)];
end
% CHECK THE MAGNITUDE OF THE GRADIENT
E1=E1(:);
je=jac'*E1;
grad(k)=norm(je);
if grad(k)<mingrad,
mer=mer(1:k);
meu=meu(1:k);
grad=grad(1:k);
disp('Gradient too small.')
fprintf('Magnitude of gradient = %g.\n',grad(k));
fprintf('Minimum gradient magnitude = %g.\n',mingrad);
break
end
% INNER LOOP, INCREASE mu UNTIL THE ERRORS ARE REDUCED
jj=jac'*jac;
while tst>0,
dw=-(jj+ii*mu)\je;
W1n=W1;b1n=b1;W2n=W2;b2n=b2;
% UPDATE VARIABLES
if (option == 1)
newx = W1(1,1) + dw(1); W1n(1,1) = newx;
newy = W2(1,1) + dw(2); W2n(1,1) = newy;
elseif(option == 2)
newx = W1(1,1) + dw(1); W1n(1,1) = newx;
newy = b1(1) + dw(2); b1n(1) = newy;
else
newx = b1(1) + dw(1); b1n(1) = newx;
newy = b1(2) + dw(2); b1n(2) = newy;
end
A1 = logsig(W1n*P,b1n);
A2 = logsig(W2n*A1,b2n);
E2 = T-A2;
f2=sumsqr(E2);
if f2>=f1,
mu=mu*v;
% TEST FOR MAXIMUM mu
if (mu > maxmu),
mer=mer(1:k);
meu=[meu(1:k);mu];
grad=grad(1:k);
disp('Maximum mu exceeded.')
fprintf('mu = %g.\n',mu);
fprintf('Maximum allowable mu = %g.\n',maxmu);
break;
end
else
tst=0;
end
end
% TEST IF THE ERROR REACHES THE ERROR GOAL
if f2<=err_goal,
f1=f2;
W1=W1n;b1=b1n;W2=W2n;b2=b2n;
mer=[mer(1:k);f2];
meu=[meu(1:k);mu];
grad=grad(1:k);
disp('Error goal reached.')
break;
end
if(mu>maxmu),
disp('Maximum mu exceeded.')
fprintf('mu = %g.\n',mu);
fprintf('Maximum allowable mu = %g.\n',maxmu);
break;
end
W1=W1n;b1=b1n;W2=W2n;b2=b2n;E1=E2;f1=f2;
% DISPLAY PROGRESS
if rem(k,disp_freq) == 0
xx(k) = newx;
yy(k) = newy;
end
end
% CONTOUR PLOT
ind = find(xx == 0);
if length(ind)
ind = ind(1);
xx = xx(1:(ind-1));
yy = yy(1:(ind-1));
end
path = [path; plot(xx,yy,'color',nnred,'linewidth',1)];
path = [path; plot(xx,yy,'o','color',nnred,'markersize',6)];
set(fig,'nextplot','new')
% SAVE DATA
set(path_ptr,'userdata',path);
set(fig,'pointer','arrow')
end
end
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