%% Init.
clear all;
clf;
hold all;
%% Data Gen
for O=1:8
    N           =   O*10^3;
    B           =   gausswin(N);        %arbitrary data
    k           =   100*chebwin(N);     %arbitrary data
    x{O}        =   linspace(-1,1,N);   %arbitrary data

    %initialize
    I{O}           =   zeros(1,N);

    %sum the cosines
    tic
    for ai  = 1:N
        I{O}       =   I{O}    + B(ai)*cos(k(ai)*x{O});
    end
    plot(x{O},I{O});
end
save reddit x I;
%% Analysis.
clear all;
load reddit;
close all;
figure(1);hold all
In=1;
Out=2;
plot(x{Out},I{Out}./spline(x{In},I{In},x{Out}),x{Out},I{Out}./interp1(x{In},I{In},x{Out}));

In=1;
Out=3;
plot(x{Out},I{Out}./spline(x{In},I{In},x{Out}),x{Out},I{Out}./interp1(x{In},I{In},x{Out}));

In=2;
Out=3;
plot(x{Out},I{Out}./spline(x{In},I{In},x{Out}),x{Out},I{Out}./interp1(x{In},I{In},x{Out}));

%%
close all;
n=2;
for i=[1 3:8]
    figure(i);
    S=i./n; % Scaling factor.


    %         Resampling. Taking 'i' points and matching to 'n' points.
    Rs=spline(x{n},I{n}.*S,x{i}); % Resample  spline.
    Ri=interp1(x{n},I{n}.*S,x{i}); % Resample interp1
    subplot(2,1,1);
    plot(x{n},I{n}.*S,x{i},Rs,x{i},Ri,x{i},I{i}); hold all;
    legend(sprintf('Data %d scaled',n),sprintf('Data %d Spline Fit',n),sprintf('Data %d Interp1 Fit',n),sprintf('Data %d',i));

    Ares=abs(Rs-I{i}); % Absolute resample error spline
    Arei=abs(Ri-I{i}); % Absolute resample error interp1

    Prea=Ares./I{i}; % Percent ...
    Prei=Arei./I{i};

    SSEs=sqrt(sum(Ares.^2));
    SSEi=sqrt(sum(Arei.^2));

    subplot(2,1,2);
    plot(x{i},Ares,x{i},Arei);
    legend(sprintf('Spline SSE=%f',SSEs),sprintf('Interp1 SSE=%f',SSEi));
end