%% construct a network
net.nIn=2; %the input layer has 1 ANN
net.nHidden=20; %the hidden layer has 10 ANN
net.nOut=1; %the output layer has 1 ANN
w=2*(rand(net.nHidden,net.nIn)-1/2); %the weight coefficient of the hidden layer.
b=2*(rand(net.nHidden,1)-1/2); %the threshold
net.w1=[w,b]; %the weight coefficient and the threshold are linked up.
W=2*(rand(net.nOut,net.nHidden)-1/2); %the weight coefficient of the output layer.
B=2*(rand(net.nOut,1)-1/2); %the threshold
net.w2=[W,B]; %the weight coefficient and the threshold are linked up.
%% set the parameters
mc=0.00005; %set the momentum term
eta=0.0001; %set the learning rate
maxiter=200000; %set the max iteration times
trainnum=121; %the amount of the training samples
testnum=441; %the amount of the testing samples
errRec=zeros(1,maxiter); %used to store the error vector
%% set the training samples and the testing samples
trainin=zeros(2,121); %used to store the input of the training samples
testin=zeros(2,441); %used to store the input of the testing samples
for i=1:121 %produce the input of the training samples
trainin(1,i)=2*ceil(i/11)-12;
trainin(2,i)=2*rem(i-1,11)-10;
end
sampin=[trainin;ones(1,trainnum)];
for i=1:441 %produce the input the testing samples
testin(1,i)=ceil(i/21)-11;
testin(2,i)=rem(i-1,21)-10;
end
trainout=ones(1,121); %used to store the output of the training samples
for i=-10:2:10 %produce the output of the training samples
for j=-10:2:10
trainout(1,61+5.5*i+0.5*j)=sin(i)/i*sin(j)/j;
end
end
for i=1:121 %produce the output by calculating the lim
if i>=56&i<=66
j=rem(i-1,11)*2-10;
trainout(1,i)=sin(j)/j;
end
if rem(i,11)==6
j=ceil(i/11)*2-12;
trainout(1,i)=sin(j)/j;
end
end
trainout(1,61)=1;
expectout=trainout;
testout=ones(1,441); %used to store the output of the testing samples
for i=1:441 %produce the output of the testing samples
testout(1,i)=sin(ceil(i/21)-11)/(ceil(i/21)-11)*sin(rem(i-1,21)-10)/(rem(i-1,21)-10);
end
for i=1:441 %calculate the lim
if i>=211&i<=231
j=rem(i-1,21)-10;
testout(1,i)=sin(j)/j;
end
if rem(i,21)==11
j=ceil(i/21)-11;
testout(1,i)=sin(j)/j;
end
end
testout(1,221)=1;
%% the training procedure
for i=1:maxiter;
hid_input=net.w1*sampin; %calculate the weighting sum of the hidden layer
hid_out=tansig(hid_input); %calculate the output of the hidden layer.
ou_input1=[hid_out;ones(1,trainnum)]; %the input of the output layer, and the input of the threshold is a constan 1.
ou_input2=net.w2*ou_input1; %calculate the weighting sum of the output layer.
out_out=2*tansig(ou_input2); %calculate the output of the output layer.
err=expectout-out_out; %calculate the error vector
sse=sumsqr(err); %calculate the square sum of the error.
errRec(i)=sse; %store the error
%% the back-propagation of error
DELTA=err.*dtansig(ou_input2,out_out/2); %the gradient of between the hidden layer and the output layer
delta=net.w2(:,1:end-1)'*DELTA.*dtansig(hid_input,hid_out);%the gradient of between the input layer and the hidden layer
dWEX=DELTA*ou_input1'; %the delta of the weight coefficient of the output layer
dwex=delta*sampin'; %the delta of the weight coefficient of the hidden layer
if i==1 %if it is the first time to revise the coefficient, we do not use the momentum term
net.w2=net.w2+eta*dWEX;
net.w1=net.w1+eta*dwex;
else %else we use the momentum term.
net.w2=net.w2+(1-mc)*eta*dWEX+mc*dWEXOld;
net.w1=net.w1+(1-mc)*eta*dwex+mc*dwexOld;
end
dWEXOld=dWEX; %record the delta of the last revision
dwexOld=dwex;
end
%% the testing procedure
realin=[testin;ones(1,testnum)]; %the input of the testing samples
realhid_input=net.w1*realin; %calculate the weighting sum of the hidden layer
realhid_out=tansig(realhid_input); %calculate the output of the hidden layer.
realou_input1=[realhid_out;ones(1,testnum)]; %the input of the output layer, and the input of the threshold is a constan 1.
realou_input2=net.w2*realou_input1; %calculate the weighting sum of the output layer.
realout_out=2*tansig(realou_input2); %calculate the output of the output layer.
realerr=testout-realout_out; %caiculate the error vector
realsse=sumsqr(realerr); %calculate the square sum of the error.
%% the display of the results
subplot(1,3,1);
plot(errRec); %plot the error
title('error curve');
xlabel('iteration times');
ylabel('training error');
x1=-10:10; %the curve of the standard function
x2=-10:10;
[X1,X2]=meshgrid(x1,x2);
yd=sin(X1)./X1.*sin(X2)./X2;
for i=1:21
for j=1:21
if j==11
yd(i,j)=sin(i-11)/(i-11);
end
if i==11
yd(i,j)=sin(j-11)/(j-11);
end
end
end
yd(11,11)=1;
subplot(1,3,2)
mesh(X1,X2,yd); %plot the standand function
title('sinx/x*siny/y curve');
xlabel('x');
ylabel('y');
zlabel('z');
hold on;
y1=-10:10; %the curve of the testing results
y2=-10:10;
[Y1,Y2]=meshgrid(y1,y2);
yf=zeros(21,21);
for i=1:21
for j=1:21
yf(i,j)=realout_out(1,21*(i-1)+j);
end
end
subplot(1,3,3);
mesh(Y1,Y2,yf); %plot the output of the testing procedure
xlabel('x');
ylabel('y');
zlabel('testing output')
title('testing curve');
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最新推荐文章于 2025-02-05 13:22:27 发布