Polynomial Curve Fitting

pcf.m

inputSamp = (0:0.1:1)';
result = sin(2*pi*inputSamp);
gsNoise = randn(11,1)*0.1;
observation = result + gsNoise;
x=(0:0.01:1)';
y=sin(2*pi*x);
%{
figure;
plot(inputSamp, observation, '*', x, y, '--r.');
set(gca, 'XLim', [-0.2 1.2]);
set(gca, 'YLim', [-1.5 1.5]);
%}

%Y = w0+w1*x+w2*(x^2)+.....
theta = zeros(4,1);
theta = CalcParameter(inputSamp,observation, theta);
predVal = CalValue(x, theta);
figure;
plot(inputSamp, observation, '*', x, y, '--r.', x, predVal, '--g.');
set(gca, 'XLim', [-0.2 1.2]);
set(gca, 'YLim', [-1.5 1.5]);

CalcParameter.m

function theta = CalcParameter(inputSamp,observation, theta)
MaxIteration = 8000;
alpha = 1;
m = length(theta);
n = length(inputSamp);
data = ones(m, n);
data(1,:)=ones(1, n);
for i = 2:m
    data(i,:) = data(i-1,:).*inputSamp';
end

for i = 1:MaxIteration
    predVal = data'*theta;
    error = predVal - observation;
    grad = data*error;
    theta = theta  - alpha*grad/n;
    er = mean(abs(error));
    fprintf('Iter %d: error : %f\n', i, er);
end

end

CalValue.m

function predVal = CalValue(x, theta)
m = length(theta);
n = length(x);
data = ones(n, m);
for i = 2:m
    data(:,i) = data(:,i-1).*x;
end
predVal = data*theta;
end