# How to write back propagation code without using neural network toolbox?

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Arushi Bagga on 7 Apr 2020
Answered: Miljan Jeremic on 27 Mar 2022
%%HI, I am trying to write a back proagation code without the help of neural network toolbox. please suggest how to go about it

Wei-An Yang on 8 Jun 2020
function EBPTA2
input=[];
target=[];
out=[];
s=[];
y=[];
x1=[];
x2=[];
x3=[];
x4=[];
for i=1:1:600
x1=rand;
x2=rand;
x3=rand;
x4=rand;
s=[x1,x2,x3,x4];
input=[input;s];
y=0.8*x1*x2*x3*x4+x1.^2+x2.^2+x3.^3+x4.^2+x1+x2*0.7-x2.^2*x3.^2+0.5*x1*x4.^2+x4*x2.^3+(-x1)*x2+(x1*x2*x3*x4).^3+(x1-x2+x3-x4)+(x1*x4)-(x2*x3)-2;
target=[target;y];
end
outnet=[];
% initialize the weight matrix
outputmatrix=zeros(35,1);
for i=1:1:35
for j=1:1:1
outputmatrix(i,j)=rand;
end
end
hiddenmatrix=zeros(4,35);
for i=1:1:4
for j=1:1:35
hiddenmatrix(i,j)=rand;
end
end
RMSE1=zeros(100,1);
RMSE2=zeros(100,1);
% Training
for epoch=1:1:100
t1=[];
t2=[];
for iter=1:1:400
% forward «e¶Ç³¡¤À
% training
hiddensigma=input(iter,:)*hiddenmatrix;
hiddennet=logsig(hiddensigma); %LOGSIG Logarithmic sigmoid transfer function.
outputsigma=hiddennet*outputmatrix;
outputnet=purelin(outputsigma);
% simalation ---> if you don't have enough data, this part can be ignored
if iter+400<=600 % take the first 400 as training samples, the remaining 200 as simulations
hsigma=input(iter+400,:)*hiddenmatrix;
hnet=logsig(hsigma);
osigma=hnet*outputmatrix;
onet=purelin(osigma);
mis=target(iter+400)-onet;
t2=[t2;mis.^2];
end
% backward part ­Ë¶Ç³¡¤À
% delta of outputmatrix ¿é¥X¼hªº delta
doutputnet=dpurelin(outputsigma);
deltaoutput=(target(iter)-outputnet)*doutputnet;
error=target(iter)-outputnet;
t1=[t1;error.^2];
% delta of hidden layer ÁôÂÃ¼hªº delta
tempdelta=deltaoutput*outputmatrix;
transfer=dlogsig(hiddensigma,logsig(hiddensigma));
deltahidden=[];
for i=1:1:35
deltahidden=[deltahidden;tempdelta(i)*transfer(i)];
end
% output layer weight update ¿é¥X¼hÅv­«§ó·s
newoutputmatrix=outputmatrix+0.025*(deltaoutput*hiddennet)';
outputmatrix=newoutputmatrix;
% hidden layer ÁôÂÃ¼hÅv­«§ó·s
newhiddenmatrix=hiddenmatrix;
for i=1:1:35
for j=1:1:4
newhiddenmatrix(j,i)=hiddenmatrix(j,i)+0.025*deltahidden(i)*input(iter,j);
end
end
hiddenmatrix=newhiddenmatrix;
end
RMSE1(epoch) = sqrt(sum(t1)/400);
RMSE2(epoch) = sqrt(sum(t2)/200);
fprintf('epoch %.0f: RMSE = %.3f\n',epoch, sqrt(sum(t1)/400));
end
% end of trainging
fprintf('\nTotal number of epochs: %g\n', epoch);
fprintf('Final RMSE: %g\n', RMSE1(epoch));
figure(1);
plot(1:epoch,RMSE1(1:epoch),1:epoch,RMSE2(1:epoch));
legend('Training','Simulation');
ylabel('RMSE');xlabel('Epoch');
Train_Correct=0;
for i=1:400
hiddensigma=input(i,:)*hiddenmatrix;
hiddennet=logsig(hiddensigma);
outputsigma=hiddennet*outputmatrix;
outputnet=purelin(outputsigma);
out=[out;outputnet];
if outputnet > target(i)-0.5 & outputnet <= target(i)+0.5
Train_Correct=Train_Correct+ 1;
end
end
Simu_Correct=0;
for i=401:length(input)
hiddensigma=input(i,:)*hiddenmatrix;
hiddennet=logsig(hiddensigma);
outputsigma=hiddennet*outputmatrix;
outputnet=purelin(outputsigma);
outnet=[outnet;outputnet];
if outputnet > target(i)-0.5 & outputnet <= target(i)+0.5
Simu_Correct=Simu_Correct+ 1;
end
end
figure(2);
plot(401:length(input),target(401:length(input)),401:length(input),outnet(1:200))
legend('Function','Simulation');
Train_Percent= (Train_Correct) / 400;
Simu_Percent= (Simu_Correct) / (length(input)-400);
Train_correct_percent=Train_Percent
Simu_correct_percent=Simu_Percent
figure(3)
[m,b,r]=postreg(out',target(1:400)');

Miljan Jeremic on 27 Mar 2022
function EBPTA2
input=[];
target=[];
out=[];
s=[];
y=[];
x1=[];
x2=[];
x3=[];
x4=[];
for i=1:1:600
x1=rand;
x2=rand;
x3=rand;
x4=rand;
s=[x1,x2,x3,x4];
input=[input;s];
y=0.8*x1*x2*x3*x4+x1.^2+x2.^2+x3.^3+x4.^2+x1+x2*0.7-x2.^2*x3.^2+0.5*x1*x4.^2+x4*x2.^3+(-x1)*x2+(x1*x2*x3*x4).^3+(x1-x2+x3-x4)+(x1*x4)-(x2*x3)-2;
target=[target;y];
end
outnet=[];
% initialize the weight matrix
outputmatrix=zeros(35,1);
for i=1:1:35
for j=1:1:1
outputmatrix(i,j)=rand;
end
end
hiddenmatrix=zeros(4,35);
for i=1:1:4
for j=1:1:35
hiddenmatrix(i,j)=rand;
end
end
RMSE1=zeros(100,1);
RMSE2=zeros(100,1);
% Training
for epoch=1:1:100
t1=[];
t2=[];
for iter=1:1:400
% forward «e¶Ç³¡¤À
% training
hiddensigma=input(iter,:)*hiddenmatrix;
hiddennet=logsig(hiddensigma); %LOGSIG Logarithmic sigmoid transfer function.
outputsigma=hiddennet*outputmatrix;
outputnet=purelin(outputsigma);
% simalation ---> if you don't have enough data, this part can be ignored
if iter+400<=600 % take the first 400 as training samples, the remaining 200 as simulations
hsigma=input(iter+400,:)*hiddenmatrix;
hnet=logsig(hsigma);
osigma=hnet*outputmatrix;
onet=purelin(osigma);
mis=target(iter+400)-onet;
t2=[t2;mis.^2];
end
% backward part ­Ë¶Ç³¡¤À
% delta of outputmatrix ¿é¥X¼hªº delta
doutputnet=dpurelin(outputsigma);
deltaoutput=(target(iter)-outputnet)*doutputnet;
error=target(iter)-outputnet;
t1=[t1;error.^2];
% delta of hidden layer ÁôÂÃ¼hªº delta
tempdelta=deltaoutput*outputmatrix;
transfer=dlogsig(hiddensigma,logsig(hiddensigma));
deltahidden=[];
for i=1:1:35
deltahidden=[deltahidden;tempdelta(i)*transfer(i)];
end
% output layer weight update ¿é¥X¼hÅv­«§ó·s
newoutputmatrix=outputmatrix+0.025*(deltaoutput*hiddennet)';
outputmatrix=newoutputmatrix;
% hidden layer ÁôÂÃ¼hÅv­«§ó·s
newhiddenmatrix=hiddenmatrix;
for i=1:1:35
for j=1:1:4
newhiddenmatrix(j,i)=hiddenmatrix(j,i)+0.025*deltahidden(i)*input(iter,j);
end
end
hiddenmatrix=newhiddenmatrix;
end
RMSE1(epoch) = sqrt(sum(t1)/400);
RMSE2(epoch) = sqrt(sum(t2)/200);
fprintf('epoch %.0f: RMSE = %.3f\n',epoch, sqrt(sum(t1)/400));
end
% end of trainging
fprintf('\nTotal number of epochs: %g\n', epoch);
fprintf('Final RMSE: %g\n', RMSE1(epoch));
figure(1);
plot(1:epoch,RMSE1(1:epoch),1:epoch,RMSE2(1:epoch));
legend('Training','Simulation');
ylabel('RMSE');xlabel('Epoch');
Train_Correct=0;
for i=1:400
hiddensigma=input(i,:)*hiddenmatrix;
hiddennet=logsig(hiddensigma);
outputsigma=hiddennet*outputmatrix;
outputnet=purelin(outputsigma);
out=[out;outputnet];
if outputnet > target(i)-0.5 & outputnet <= target(i)+0.5
Train_Correct=Train_Correct+ 1;
end
end
Simu_Correct=0;
for i=401:length(input)
hiddensigma=input(i,:)*hiddenmatrix;
hiddennet=logsig(hiddensigma);
outputsigma=hiddennet*outputmatrix;
outputnet=purelin(outputsigma);
outnet=[outnet;outputnet];
if outputnet > target(i)-0.5 & outputnet <= target(i)+0.5
Simu_Correct=Simu_Correct+ 1;
end
end
figure(2);
plot(401:length(input),target(401:length(input)),401:length(input),outnet(1:200))
legend('Function','Simulation');
Train_Percent= (Train_Correct) / 400;
Simu_Percent= (Simu_Correct) / (length(input)-400);
Train_correct_percent=Train_Percent
Simu_correct_percent=Simu_Percent
figure(3)
[m,b,r]=postreg(out',target(1:400)');