Jump to content

File:Gauss Newton illustration.png

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (1,532 × 1,236 pixels, file size: 53 KB, MIME type: image/png)

Description Illustration of Gauss-Newton applied to a curve-fitting problem with noisy data. What is plotted is the best fit curve versus the data with the fitting parameters obtained via Gauss-Newton.
Date (UTC)
Source self-made with Matlab
Author Oleg Alexandrov

Source code

function [X, Y] = main()
   
   f=inline('beta1*x/(beta2+x)', 'beta1', 'beta2', 'x');
   f1=inline('x/(beta2+x)', 'beta1', 'beta2', 'x');
   f2=inline('-beta1*x/(beta2+x)^2', 'beta1', 'beta2', 'x');

   X = [0.038 	0.194 	    0.425 	0.626 	1.253 	2.500 	3.740];
   Y = [0.05    0.127       0.094    0.2122    0.2729    0.2665    0.3317];

   beta10 = 0.9; beta20 = 0.2;

   m = length(X);
   R = zeros(m, 1);
   J = zeros(m, 2);

   v = [beta10, beta20]';
   
   for k=0:10 % iterate
      
      for i=1:length(X)
	 R(i)    = Y(i) - f (beta10, beta20, X(i));
	 J(i, 1) =       -f1(beta10, beta20, X(i));
	 J(i, 2) =       -f2(beta10, beta20, X(i));
      end

      disp(sprintf('%d %0.9g %0.9g %0.9g', k, v(1), v(2), norm(R)));

      v = v - (J'*J)\(J'*R);

      
      beta10 = v(1);
      beta20 = v(2);

   end
   
   % KSmrq's colors
   red=[0.867 0.06 0.14];
   blue = [0, 129, 205]/256;
   green = [0, 200,  70]/256;
   black = [0, 0, 0];
   white = 0.99*[1, 1, 1];
   gray = 0.8*white;

   fs = 30;
   lw = 7;

   figure(1); clf; hold on;
   set(gca, 'fontsize', fs);

   Hx=xlabel('[S]')
   set(gca, 'linewidth', lw/2);

   Hy=ylabel('reaction rate');

   
   hold on; %axis equal;
   
   h=0.1;
   xs = 0; xl = max(X)+0.2;
   Xe = xs:h:xl;
   Ye = 0*Xe;
   for i=1:length(Xe)
      Ye(i) = f(beta10, beta20, Xe(i));
   end
   plot(Xe, Ye, 'color', blue, 'linewidth', lw);

   for i=1:length(X)
      plot(X(i), Y(i), 'color', red, 'marker', 'd', 'linewidth', lw);
   end



   axis([0 4 0 0.35]);
   set(gca, 'XTick', [0 1 2 3 4]);
   set(gca, 'YTick', [0 0.05 0.1 0.15 0.2 0.25 0.3 0.35]);

   saveas(gcf, 'Gauss_Newton_illustration.eps', 'psc2'); % save as eps
   return
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}.


It is recommended to name the SVG file “Gauss Newton illustration.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

20 April 2008

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current21:36, 20 April 2008Thumbnail for version as of 21:36, 20 April 20081,532 × 1,236 (53 KB)Oleg Alexandrov{{Information |Description=Illustration of en:Gauss-Newton algorithm |Source=self-made with Matlab |Date=~~~~~ |Author= Oleg Alexandrov |Permission= see below |other_versions= }} ==Source code== <source lang="matlab"> funct

The following 2 pages use this file:

Global file usage

The following other wikis use this file: