?? nnd12cg.m
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function nnd12cg(cmd,arg1)
%NND12CG Conjugate gradient backpropagation demonstration.
%
% This demonstration requires the Neural Network Toolbox.
% First Version, 8-31-95.
%==================================================================
% CONSTANTS
me = 'nnd12cg';
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
cont_axis = H(3); % error contour axis
cont_ptr = H(4); % pointer to error contour handles
radios = H(5:7); % radio buttons
option_ptr = H(8); % index of active radio
path_ptr = H(9); % 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','Conjugate Gradient Backprop','','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')
% RADIO BUTTONS
option = 1;
radio1 = uicontrol(...
'units','points',...
'position',[20 335 130 20],...
'style','radio',...
'string','W1(1,1), W2(1,1)',...
'back',nnltgray,...
'callback',[me '(''radio'',1)'],...
'value',1);
radio2 = uicontrol(...
'units','points',...
'position',[155 335 115 20],...
'style','radio',...
'string','W1(1,1), b1(1)',...
'back',nnltgray,...
'callback',[me '(''radio'',2)']);
radio3 = uicontrol(...
'units','points',...
'position',[270 335 105 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',[50 40 280 280],...
'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
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 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',...
'conjugate gradient',...
'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 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')
set(path,'erasemode','normal');
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
Lx = x;
Ly = y;
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
A1 = logsig(W1*P,b1);
A2 = logsig(W2*A1,b2);
E = T-A2;
fa=sumsqr(E);
D2 = feval('deltalog',A2,E);
D1 = feval('deltalog',A1,D2,W2);
[gW1,gb1] = feval('learnbp',P,D1,1);
[gW2,gb2] = feval('learnbp',A1,D2,1);
if (option == 1)
nrmo = gW1(1,1)^2 + gW2(1,1)^2;
elseif(option == 2)
nrmo = gW1(1,1)^2 + gb1(1)^2;
else
nrmo = gb1(1)^2 + gb1(2)^2;
end
% NORM OF GRADIENT
nrmrt=sqrt(nrmo);
% INITIALIZE DIRECTION
dW1old=gW1;db1old=gb1;dW2old=gW2;db2old=gb2;
dW1=gW1/nrmrt;db1=gb1/nrmrt;dW2=gW2/nrmrt;db2=gb2/nrmrt;
% ASSIGN PARAMETERS
tau=0.618;
tau1=1-tau;
scaletol=20;
delta=0.32;
delta1=.03;
tol=delta1/scaletol;
scale=2.0;
bmax=26;
n=2; %number of steps before reset
% MAIN LOOP
max_epoch = 15;
xx = [x zeros(1,max_epoch)];
yy = [y zeros(1,max_epoch)];
for i=2:(max_epoch+1)
% INITIALIZE A
a=0;
aold=0;
b=delta;
faold=fa;
% CALCULATE INITIAL SSE
W1t = W1; b1t = b1;
W2t = W2; b2t = b2;
if (option == 1)
newx = W1(1,1) + b*dW1(1,1); W1t(1,1) = newx;
newy = W2(1,1) + b*dW2(1,1); W2t(1,1) = newy;
elseif(option == 2)
newx = W1(1,1) + b*dW1(1,1); W1t(1,1) = newx;
newy = b1(1) + b*db1(1); b1t(1) = newy;
else
newx = b1(1) + b*db1(1); b1t(1) = newx;
newy = b1(2) + b*db1(2); b1t(2) = newy;
end
fb = sumsqr(T - logsig(W2t*logsig(W1t*P,b1t),b2t));
% FIND INITIAL INTERVAL WHERE SSE MINIMUM OCCURS
while (fa>fb)&(b<bmax)
aold=a;
faold=fa;
fa=fb;
a=b;
b=scale*b;
if (option == 1)
newx = W1(1,1) + b*dW1(1,1); W1t(1,1) = newx;
newy = W2(1,1) + b*dW2(1,1); W2t(1,1) = newy;
elseif(option == 2)
newx = W1(1,1) + b*dW1(1,1); W1t(1,1) = newx;
newy = b1(1) + b*db1(1); b1t(1) = newy;
else
newx = b1(1) + b*db1(1); b1t(1) = newx;
newy = b1(2) + b*db1(2); b1t(2) = newy;
end
fb = sumsqr(T - logsig(W2t*logsig(W1t*P,b1t),b2t));
end
a=aold;
fa=faold;
% SHOW INITIAL INTERVAL
if (option == 1)
newx = W1(1,1) + a*dW1(1,1);
newy = W2(1,1) + a*dW2(1,1);
elseif(option == 2)
newx = W1(1,1) + a*dW1(1,1);
newy = b1(1) + a*db1(1);
else
newx = b1(1) + a*db1(1);
newy = b1(2) + a*db1(2);
end
if (option == 1)
newx = W1(1,1) + b*dW1(1,1);
newy = W2(1,1) + b*dW2(1,1);
elseif(option == 2)
newx = W1(1,1) + b*dW1(1,1);
newy = b1(1) + b*db1(1);
else
newx = b1(1) + b*db1(1);
newy = b1(2) + b*db1(2);
end
% INITIALIZE C AND D
c=a+tau1*(b-a);
if (option == 1)
newx = W1(1,1) + c*dW1(1,1); W1t(1,1) = newx;
newy = W2(1,1) + c*dW2(1,1); W2t(1,1) = newy;
elseif(option == 2)
newx = W1(1,1) + c*dW1(1,1); W1t(1,1) = newx;
newy = b1(1) + c*db1(1); b1t(1) = newy;
else
newx = b1(1) + c*db1(1); b1t(1) = newx;
newy = b1(2) + c*db1(2); b1t(2) = newy;
end
fc = sumsqr(T - logsig(W2t*logsig(W1t*P,b1t),b2t));
d=b-tau1*(b-a);
if (option == 1)
newx = W1(1,1) + d*dW1(1,1); W1t(1,1) = newx;
newy = W2(1,1) + d*dW2(1,1); W2t(1,1) = newy;
elseif(option == 2)
newx = W1(1,1) + d*dW1(1,1); W1t(1,1) = newx;
newy = b1(1) + d*db1(1); b1t(1) = newy;
else
newx = b1(1) + d*db1(1); b1t(1) = newx;
newy = b1(2) + d*db1(2); b1t(2) = newy;
end
fd = sumsqr(T - logsig(W2t*logsig(W1t*P,b1t),b2t));
% MINIMIZE ALONG A LINE
k=0;
while (b-a)>tol
if ( (fc<fd)&(fb>=min([fa fc fd])) ) | fa<min([fb fc fd])
b=d; d=c; fb=fd;
c=a+tau1*(b-a);
fd=fc;
if (option == 1)
newx = W1(1,1) + c*dW1(1,1); W1t(1,1) = newx;
newy = W2(1,1) + c*dW2(1,1); W2t(1,1) = newy;
elseif(option == 2)
newx = W1(1,1) + c*dW1(1,1); W1t(1,1) = newx;
newy = b1(1) + c*db1(1); b1t(1) = newy;
else
newx = b1(1) + c*db1(1); b1t(1) = newx;
newy = b1(2) + c*db1(2); b1t(2) = newy;
end
fc = sumsqr(T - logsig(W2t*logsig(W1t*P,b1t),b2t));
else
a=c; c=d; fa=fc;
d=b-tau1*(b-a);
fc=fd;
if (option == 1)
newx = W1(1,1) + d*dW1(1,1); W1t(1,1) = newx;
newy = W2(1,1) + d*dW2(1,1); W2t(1,1) = newy;
elseif(option == 2)
newx = W1(1,1) + d*dW1(1,1); W1t(1,1) = newx;
newy = b1(1) + d*db1(1); b1t(1) = newy;
else
newx = b1(1) + d*db1(1); b1t(1) = newx;
newy = b1(2) + d*db1(2); b1t(2) = newy;
end
fd = sumsqr(T - logsig(W2t*logsig(W1t*P,b1t),b2t));
end
end
% UPDATE VARIABLES
if (option == 1)
newx = W1(1,1) + a*dW1(1,1); W1(1,1) = newx;
newy = W2(1,1) + a*dW2(1,1); W2(1,1) = newy;
elseif(option == 2)
newx = W1(1,1) + a*dW1(1,1); W1(1,1) = newx;
newy = b1(1) + a*db1(1); b1(1) = newy;
else
newx = b1(1) + a*db1(1); b1(1) = newx;
newy = b1(2) + a*db1(2); b1(2) = newy;
end
xx(i) = newx;
yy(i) = newy;
% CALCULATE GRADIENT
A1 = logsig(W1*P,b1);
A2 = logsig(W2*A1,b2);
E = T-A2;
D2 = feval('deltalog',A2,E);
D1 = feval('deltalog',A1,D2,W2);
[gW1,gb1] = feval('learnbp',P,D1,1);
[gW2,gb2] = feval('learnbp',A1,D2,1);
% NORM SQUARE OF GRADIENT
if (option == 1)
nrmn = gW1(1,1)^2 + gW2(1,1)^2;
elseif(option == 2)
nrmn = gW1(1,1)^2 + gb1(1)^2;
else
nrmn = gb1(1)^2 + gb1(2)^2;
end
% CALCULATE DIRECTION
if rem(i,n)==0
Z=0;
else
Z=nrmn/nrmo;
end
% CALCULATE NEW DIRECTIONS
dW1new = gW1 + dW1old*Z; db1new = gb1 + db1old*Z;
dW2new = gW2 + dW2old*Z; db2new = gb2 + db2old*Z;
% SAVE NEW DIRECTIONS
dW1old = dW1new; db1old = db1new;
dW2old = dW2new; db2old = db2new;
nrmo=nrmn;
%NORMALIZE DIRECTIONS
if (option == 1)
nrm = sqrt(dW1new(1,1)^2 + dW2new(1,1)^2);
elseif(option == 2)
nrm = sqrt(dW1new(1,1)^2 + db1new(1)^2);
else
nrm = sqrt(db1new(1)^2 + db1new(2)^2);
end
dW1=dW1new/nrm;db1=db1new/nrm;dW2=dW2new/nrm;db2=db2new/nrm;
end
% CONTOUR PLOT
path = [path; plot(xx,yy,'color',nnred); 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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