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R2096/basicML/linPend.m
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linPend.m
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%% load generated data
fileNameInput = 'pendulum.csv';
data = csvread(['../input/',fileNameInput]);
t = data(:,1);% time
q = data(:,2);% general coordinate
%% parameters
printGraph = 0;
pts_nb = length(t);%number of points
pts_train = floor(0.6*pts_nb);%number of points for the training set
pts_val = floor(0.4*pts_nb) + 1;%number of points for the validation set
pts_pre = pts_nb - (pts_train + pts_val);%number of points for the test set
seq_length = 5;%length of the sequence
alpha = 10^(-4);%learning rate for gradient descent
nb_iters = 1*10^5;%number of iterations
%% input and parameters inizialisation
X_all = ones(pts_nb - seq_length,seq_length);%preallocatin input
for ii=1:seq_length
X_all(:,ii) = q(ii:end - (seq_length+1) + ii);%input as "window" method
end
y_all = q(seq_length+1:end);
%split for training set
Xtrain = X_all(1:pts_train - seq_length,:);%train input
Xtrain = [ones(pts_train - seq_length,1),Xtrain];% add a column of ones for the bias
ytrain = q(seq_length + 1:pts_train);%data to compute the loss of the train set
%split for validation set
Xval = X_all(pts_train + 1:pts_train + pts_val - seq_length,:);%validation input
Xval = [ones(size(Xval,1),1),Xval];% add a column of ones for the bias
yval = q(pts_train + seq_length + 1:pts_train + pts_val);%data to compute the loss of the validation set
%split for predict set
ypre = q(pts_train + pts_val + 1:end);%data to compute the loss of the test set
%weights;
w = ones(seq_length+1,1);
w = 0.5.*w;
%% optimisation of theta and loss
[w, L_history] = gradientDescentLinear(Xtrain, ytrain, w, alpha, nb_iters);
Ltrain = computeCostLinear(Xtrain,ytrain,w);%Loss training set
Lval = computeCostLinear(Xval,yval,w);%Loss validation set
%% output
Otrain = ones(pts_train - seq_length,1);%preallocation output train
for j=1:(pts_train - seq_length)
tmp = 0;
for ii=1:seq_length + 1
if ii == 1
tmp = w(ii);%bias
else
tmp = tmp + w(ii)*Xtrain(j,ii);
end
end
Otrain(j) = tmp;
end
Oval = ones(pts_val - seq_length,1);%preallocation output validation
for j=1:(pts_val - seq_length)
tmp = 0;
for ii=1:seq_length + 1
if ii == 1
tmp = w(ii);%bias
else
tmp = tmp + w(ii)*Xval(j,ii);
end
end
Oval(j) = tmp;
end
%% prediction
predict = ones(pts_pre + seq_length,1);%preallocation prediction
for ii=1:seq_length%first seq_length points are from the validation set
predict(ii) = q(pts_train + pts_val - seq_length + ii);
end
for j=seq_length:(pts_pre + seq_length - 1)%predicting points 'in the future'
tmp = 0;
for ii=1:seq_length + 1
if ii == 1
tmp = w(ii);%bias
else
tmp = tmp + w(ii)*predict(j + (ii-1) - seq_length);
end
end
predict(j+1) = tmp;
end
predict = predict(seq_length + 1:end);%deleting the points of the validation set
Lpre= (1/(2*length(ypre)))*(predict - ypre)'*(predict - ypre);%Loss of the predict set
%% LMS estimator
% beta = (Xtrain'*Xtrain)^(-1)*(Xtrain'*ytrain);
%% Fig
figure(1)
set(gca,'FontSize',12)
% set(gcf,'units','normalized','outerposition',[0 0 1 1])
hold on
plot(t,q)
plot(t(1 + seq_length:pts_train),Otrain,'b')
plot(t(pts_train + seq_length + 1:pts_train + pts_val),Oval,'r')
plot(t(pts_train + pts_val + 1:end),predict,'o')
grid on
xlabel('time [s]')
ylabel('\theta [rad]')
% legend('a')
if printGraph == 1
figg = gcf;
figg.PaperUnits = 'centimeters';
figg.PaperPosition = [0 0 26 13];
print('linPend','-depsc');
end
hold off
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