solving single nonlinear equation

Question

Dominique on 29 Apr 2013

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https://www.mathworks.com/matlabcentral/answers/73952-solving-single-nonlinear-equation

Hey all

I have a mathematical problem solving nonlinear equation: (d / d(delta(d))) omega = 0 (derivation to delta(d))

with omega(delta(d)) = sum(Di-Dj)² --> min(delta(d)) with i and j the 3 different colorchannels (RGB)

So we have 3 different calibrationcurves of the form c+(b/(d-a)) that give D (solution) for the 3 RGB channels (input = d = optical density and a,b,c = fitting constants)

If i now take a pixel with known d and I want to solve this to a minimum for the 3 channels, how do I do that best? (So i get the best fitted Dx for all 3 curves).

I have sorted this already out using lsqnonlin function, but this takes 1.5 hour for a 550 x 550 matrix of pixels. Any suggestions to simplify the maths of the problem or using another function to speed up the proces?

if true
  for i=1:(film_size(1,1))
      for j=1:film_size(1,2)
          d0 = [input(i,j,1) input(i,j,2) input(i,j,3)];
          Drgb=@(d) [(cR+(bR/(d(1)-aR));(cG+(bG/(d(2)-aG));(cB+(bB/(d(3)-aB))];
          f=@(d) [1 0 -1; 0 -1 1; -1 1 0]*Drgb(d);
          options = optimset('Display','off');
          lowerbounds=[d0(1)-500 d0(2)-500 d0(3)-1000];
          upperbounds=[d0(1)+500 d0(2)+500 d0(3)+1000];
          [d,resnorm] = lsqnonlin(f,d0,lowerbounds,upperbounds,options);
      output(i,j) = d;  //d with values for the 3 colorchannels
      end
  end
end