how to use fitnlm with constraints

I have a custom equation and want to fit its coeffients.

coefficients are k

x is data

Equation is as follows:

modelfun = @(k,x) k(1).*x(:,1)+k(2).*log10(x(:,2) +k(3).*x(:,3)^2)

Kinit is vector of initial variables that I give

tbl contains my data x

I fit like this:

mdl = fitnlm(tbl,modelfun,Kinit);

I want to impose certain contraints on coefficients,

i.e.,

k(1) should be between 20 and 40

k(2) should be positive

k(3) should be negative.

How can I do that?

Thanks a lot for helping me out.

[Walter Roberson]

log10*x(:,2)

could you confirm that you assigned a value to log10 such that you can multiply it by an input? Or did you miss some () ?

[Haneya Qureshi]

@Walter Roberson sorry, i missed brackets..the function is definitely non-linear.

modelfun = @(k,x) k(1).*x(:,1)+k(2).*log10(x(:,2) +k(3).*x(:,3)^2)

Answer 1

[Walter Roberson]

No, fitnlm does not provide any way to put in constraitns.

You might consider lsqcurvefit from the Optimization Toolbox. Or you could consider using the Curve Fitting Toolbox; https://www.mathworks.com/help/curvefit/linear-and-nonlinear-regression.html

[Torsten]

The model function is linear in the parameters to be fitted. Thus using "lsqlin" should suffice.

[Walter Roberson]

hmmm... if log10 is a constant ???

[Torsten]

All models of the form

y = k(1)*f1(xdata)+k(2)*f2(xdata)+...+k(n)*fn(xdata)

are linear in the parameters independent of the functions f1,f2,...,fn (which can be nonlinear).

"lsqlin" can be used for all of these model functions.

[Walter Roberson]

However we can suspect that the actual function might possibly be

modelfun = @(k,x) k(1).*x(:,1)+k(2).*log10(x(:,2) +k(3).*x(:,3)^2)

which would not be linear in the parameters.

[Torsten]

I would have thought

modelfun = @(k,x) k(1)*x(:,1)+k(2)*log10(x(:,2)) +k(3)*x(:,3).^2

but I'm not sure.

[Haneya Qureshi]

@Torsten can't use lsqlin as function is non-linear. Sorry i missed brackets, have edited my question to make it correct.

[Haneya Qureshi]

@Walter Roberson i did try Curve Fitting Toolbox, but looks like it takes only 1 input, i.e., y=f(x). My equation is of form f(x1,x2,x3), it has 3 inputs.

[Walter Roberson]

Ah, yes. Curve Fitting Toolbox can support functions of two variables, creating a surface fit, but that is not enough for your purposes.

You could consider creating a residue function,

residue = @(k) sum((k(1) * x(:,1) + k(2) * log10(x(:,2)) + k(3)*x(:,3).^2) - Y).^2)

and minimizing that sum-of-squares using fmincon.

[Haneya Qureshi]

Got it, makes sense! Thanks so much!