polyfitn_demo.zip_DEMO_polyfitn

% Author: John D'Errico % Release: 2.0 % Release date: 8/8/06 % What follows are example usages of polyfitn, polyvaln, poly2sympoly, polyn2sym %% Fit a 1-d model to cos(x). We only need the even order terms. x = -2:.1:2; y = cos(x); p = polyfitn(x,y,'constant x^2 x^4 x^6') if exist('sympoly') == 2 % Conversion to a sympoly. If nothing else, its a nice way to display the model. polyn2sympoly(p) end if exist('sym') == 2 % Conversion to a symbolic form. Its also nice. polyn2sym(p) end % Evaluate the regression model at some set of points polyvaln(p,[0 .5 1]) %% A surface model in 2-d, with all terms up to third order. % Use lots of data. n = 1000; x = rand(n,2); y = exp(sum(x,2)) + randn(n,1)/100; p = polyfitn(x,y,3) if exist('sympoly') == 2 polyn2sympoly(p) end if exist('sym') == 2 polyn2sym(p) end % Evaluate on a grid and plot: [xg,yg]=meshgrid(0:.05:1); zg = polyvaln(p,[xg(:),yg(:)]); surf(xg,yg,reshape(zg,size(xg))) hold on plot3(x(:,1),x(:,2),y,'o') hold off %% A linear model, but with no constant term, in 2-d uv = rand(100,2); w = sin(sum(uv,2)); p = polyfitn(uv,w,'u, v'); if exist('sympoly') == 2 polyn2sympoly(p) end if exist('sym') == 2 polyn2sym(p) end %% A model with various exponents, not all positive integers. % Note: with only 1 variable, x & y may be row or column vectors. x = 1:10; y = 3 + 2./x + sqrt(x) + randn(size(x))/100; p = polyfitn(x,y,'constant x^-1 x^0.5'); if exist('sympoly') == 2 polyn2sympoly(p) end if exist('sym') == 2 polyn2sym(p) end xi = 1:.1:10; yi = polyvaln(p,xi); plot(x,y,'ro',xi,yi,'b-')