main

function main
%%
% This is example how to fit multi dimensional polynomial
%
% The example fits between CMYK to LAB
% It assume that LAB is a polynomial function of CMYK
% The polynomial is limited by the deg, which is max(sum(n1,n2,n3,n4))
% The polynomial is in the form:
%
%       Y=...
%       a(1) * (c^0) * (m^0) * (y^0) * (k^0) +...
%       a(2) * (c^1) * (m^0) * (y^0) * (k^0) +...
%       a(3) * (c^0) * (m^1) * (y^0) * (k^0) +...
%       a(4) * (c^0) * (m^0) * (y^1) * (k^0) +...
%       a(5) * (c^0) * (m^0) * (y^0) * (k^1) +...
%       ...
%
% The example is base on the mathematics in:
% http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html
%


%% starting
fclose all; close all; clear all;
clc; fprintf('starting\n'); pause(0.1);


%% defining
filename='cmykLab.csv';
deg=4;
warning off; %matrixIsCloseToSingular


%% loading
data=csvread(filename);
cmyk=data(:,1:4);
lab=data(:,5:7);


%% fiting
mat=vanMat4dim(cmyk,deg); %creatingTheVanMatrix
coe=((mat'*mat)\mat')*lab; %usingTheVanMatrixToFindCoe
fprintf('===============\n');
fprintf('size(coe)=[%d,%d]\n',size(coe,1),size(coe,2));
labFromFit=vanMat4dim(cmyk,deg)*coe; %usingTheCoeToFindLabFromCmyk


%% checkOneExample
fprintf('===============\n');
fprintf('cmyk=[%d,%d,%d,%d]\n',cmyk(1,1),cmyk(1,2),cmyk(1,3),cmyk(1,4));
fprintf('lab=[%.2f,%.2f,%.2f]\n',lab(1,1),lab(1,2),lab(1,3));
fprintf('labFromFit=[%.2f,%.2f,%.2f]\n',labFromFit(1,1),labFromFit(1,2),labFromFit(1,3));


%% checkMeanDifference
dE=sqrt(sum((lab-labFromFit).^2,2)); %errorInTheMultiDimensional
fprintf('===============\n');
fprintf('mean(dE)=%.3f\n',mean(dE));


%% ending
fclose all; fprintf('ending\n');