Matlab - Fit a Curve with Constrained Parameters -

for (x,y) dataset, let have curve given expression in a, b,c... etc, such f='a*exp(b*x)+c', fitted cfit=fit(x,y,f).

suppose have set of constraint such b>0, c+b>a/2. how should use fit command in case?.

for constraints numeric values, such b > 0, can use 'lower' , 'upper' bounds arguments specify those. more complex relationships, c+b>a/2, you'll have take approach james suggests, setting function output high value flintmax generate large error. example, let's define function this:

function y = my_fcn(a, b, c, x)   if (c+b > a/2)     y = a.*exp(b.*x)+c;   else     y = flintmax().*ones(size(x));   end end 

i can create set of noisy test data follows:

a = 4; b = 2; c = 1; x = (0:0.01:2).'; y = my_fcn(a, b, c, x) + 40.*(rand(size(x))-0.5); 

and fit curve (note have use anonymous function, since function handle won't work reason):

params = fit(x, y, @(a, b, c, x) my_fcn(a, b, c, x), ...              'startpoint', [1 1 1], ...  % starting guesses [a b c]              'lower', [-inf 0 -inf]);    % set bound 'b'  params =        general model:      params(x) = my_fcn(a,b,c,x)      coefficients (with 95% confidence bounds):        =       4.297  (2.985, 5.609)        b =       1.958  (1.802, 2.113)        c =      0.1908  (-4.061, 4.442) 

note fitted values close original values, don't match due noise. can visualize fit so:

plot(x, y); hold on; plot(x, my_fcn(params.a, params.b, params.c, x), 'r');