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curve_fitting.m
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curve_fitting.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Linear regression Matlab version 1.0
% created 08/29/2016 by Robert Herrera
% Problem 1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clc
clear all;
prompt = 'Please enter file path for curve_fit (problem 1): ';
user_input = input(prompt,'s');
if exist(user_input, 'file')
% ------------------------------------------------------------------------
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Read in file
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
fstring = fileread(user_input); % read the file as one string
fblocks = regexp(fstring,'[A-Za-z]','split'); % uses any single character as a separator
out = cell(size(fblocks));
for k = 1:numel(fblocks)
out{k} = textscan(fblocks{k},'%f %f','delimiter',' ','MultipleDelimsAsOne', 1);
out{k} = horzcat(out{k}{:});
end
a = out{1};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Assign values
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x = a(1:10,1); % read in x values from text file
t = a(1:10,2); % read in t values from text file
sep = 0.11; %0.11 -> 10 points , 0.01 -> 101 points
for M = 0:9
N = size(x);
phi_x = ones(N(1),M);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Load polynomial variations into phi(x)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i = 1:N(1)
for j = 0:M
phi_x(i,j+1) = x(i)^j;
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% - Find pseudo inverse of phi_x
% - Find parameter weights based on phi_x_inv * t
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
phi_x_t = pinv(phi_x);
w_user = phi_x_t * t;
disp(w_user)
w_user = fliplr(w_user');
x4 = x;
x_train_size = size(x4);
a = 0;
b = 1;
r = (b-a).*rand(1,10) + a;
x3 = 0:sep:1;%0:sep:1
x_size = size(x3);
x2 = linspace(0,1,100);%0:sep:1
x_test_size = size(x2);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% fit training data with parameterss
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
y4 = zeros(1,x_train_size(2));
for m = 0:M
y4 = y4 + w_user(m+1)*x4.^(M-m);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% fit training data with parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
y2 = zeros(1,x_test_size(2));
for m = 0:M
y2 = y2 + w_user(m+1)*x2.^(M-m);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Plot Data
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x_sin_point = 0:0.01:1;
y_sin = sin(2*pi*x_sin_point);
% Un comment for plots _________________
if M == 0 | M == 1 | M == 3 | M == 9
figure
plot(x_sin_point,y_sin,'g',x,t,'bo',x2,y2,'r')
xlim([-0.1 1.1])
ylim([-1.5 1.5])
str = ['M = ',num2str(M)];
xlabel('x')
ylabel('t')
text(0.8,1,str)
title('Polynomial Fitting')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% error mean square both train and test
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
e_train = 0.5*(y4 - t).^2; %training
noise_sig = sin(2*pi*x2) + (randn(size(x2))* sqrt(0.30));
e = 0.5*(y2 - noise_sig).^2; %testing
E_RMS(M+1) = sqrt((norm(e))/N(1));
E_RMS_Testing(M+1) = sqrt((norm(e_train'))/N(1));
end
m = 0:9;
figure
plot(m,E_RMS,'-ro',m,E_RMS_Testing,'-bo');
title('Polynomial Fitting :: Noisy Signal');
legend('testing','training')
xlabel('M')
ylabel('E_{RMS}')
xlim([0 9])
ylim([0 1])
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Fitted Noise corrupted sin signal with plots
for N = [15,100]
x_generated = linspace(0,1,N); %original size
size(x_generated);
t_generated = sin(2*pi*x_generated);
noise_signal = randn(size(x_generated)) * sqrt(0.30) + 0.0;
t_noise = t_generated + noise_signal;
for M = 9
n = size(x_generated);
phi_x = ones(n(2),M);
for i = 1:n(2)
for j = 0:M
phi_x(i,j+1) = x_generated(i)^j;
end
end
phi_x_t = pinv(phi_x);
w_user = phi_x_t * t_noise';
w_user = fliplr(w_user');
x4 = 0:0.01:1;
x_train_size = size(x4);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% fit training data with parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
y4 = zeros(1,x_train_size(2));
for m = 0:M
y4 = y4 + w_user(m+1)*x4.^(M-m);
end
figure;
plot(x_sin_point,y_sin,'g',x_generated,t_noise,'bo',x4,y4,'r');
input_string = ['N = ', num2str(n(2))];
xlabel('x')
ylabel('t')
title('Problem 1: Part d');
text(0.9,1.5,input_string)
end % end for M
end
% ------------------------------------------------------------------------
else
% File does not exist.
warningMessage = sprintf('Warning: file does not exist:\n%s', user_input);
uiwait(msgbox(warningMessage));
end