fitting curve with constrained parameter estimation

[Hany Ferdinando]

Hi,

I have xdata-ydata pair and would like to estimate parameters of my own function to fit it to xdata-ydata pair. Using examples in https://www.inverseproblem.co.nz/OPTI/index.php/Probs/NLS as a guidance, I set up linear constraints to A and b, assigned value for upper and lower bounds. 

fun = @(x,t)((((x(1)*lognpdf(t,log(x(2)),x(3))+x(4)*lognpdf(t,log(x(5)),x(6))+x(7)*lognpdf(t,log(x(8)),x(9))+x(10)*lognpdf(t,log(x(11)),x(12))+x(13)*lognpdf(t,log(x(14)),x(15))))));

Opt = opti('fun', fun, 'data', xdata, ydata, 'ineq', A, B, 'bounds', lb, ub, 'x0', x0, 'solver', 'levmar');

It converged in about 1 s. Is there any way to speed up this computation? Did I use the correct method?

Thanks a lot

Best

Hany

[Jonathan Currie]

Hi,

For a 15 variable constrained NLS fitting problem, especially one calling statistical functions, 1s sounds pretty fast to me. However if you want to add the gradient to OPTI (rather than finite difference), it might help. Below is an example of how to do this using the symbolic toolbox:

% Core of lognpdf.m:

lognpdf = @(x,mu,sigma) exp(-0.5 * ((log(x) - mu)./sigma).^2) ./ (x .* sqrt(2*pi) .* sigma);

% Your objective

fun = @(x,t)((((x(1)*lognpdf(t,log(x(2)),x(3))+x(4)*lognpdf(t,log(x(5)),x(6))+x(7)*lognpdf(t,log(x(8)),x(9))+x(10)*lognpdf(t,log(x(11)),x(12))+x(13)*lognpdf(t,log(x(14)),x(15))))));

% Create symbolic version

x = sym('x',[15,1]);

t = sym('t');

fSym = fun(x,t)

% Calculate analytic gradient

gradSym = jacobian(fSym,x)

% And convert to anonymous function

gradVec = matlabFunction(gradSym, 'vars', {x,t})

% Reshape to matrix

grad = @(x,xdata) reshape(gradVec(x,xdata), length(xdata), length(x0));

% Solve it

opts = optiset('display','iter','solver','levmar');

Opt = opti('fun', fun, 'grad', grad, 'data', xdata, ydata, 'ineq', A, B, 'bounds', lb, ub, 'x0', x0, 'opts', opts)

[x,f,e,i] = solve(Opt)

% And plot solution

plot(Opt)

Jonathan

--
You received this message because you are subscribed to the Google Groups "OPTI Toolbox Forum" group.
To unsubscribe from this group and stop receiving emails from it, send an email to opti-toolbox-fo...@googlegroups.com.
To post to this group, send email to opti-tool...@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.