which function should I use to get a relationship among x,y and extra parameter?

hello guys,

I wanna get the following relationship. Can I realize it in Matlab? thanks a lot.

(x)^(m+na)+(y)^(p+qa)=1

[Matt J]

What sre the unknowns? Are any of them constrained to be integers?

[kimy]

m,n,p,q are unknown. so my question is to get them according to above figure. thank you!

[Mathieu NOE]

why do we have 4 unknows ? seems to me m and na paly the same role , and idem for p and qa

so problem is to fit only two unknowns (m and p) to the data - would try with fminsearch

[Walter Roberson]

I suspect na is n*a

[kimy]

yes. (x)^(m+n*a)+(y)^(p+q*a)=1. Do you have any suggestion? thanks

[Matt J]

why do we have 4 unknows ? seems to me m and na paly the same role

I think the idea is to fit multiple curves (corresponding to different a) simultaneously. You could still try fminsearch, but its performance falls off rather quickly with increasing number of unknowns.

[kimy]

you are right. In fact, I assumed that relationship, could be also n*a, if m=0. Thanks. I will try.

[Mathieu NOE]

sticking to my idea of having only two parameters to fit , I generated some curves that are based on following equation :

y^b + x^a = 1;

the picture tells me that look pretty much like the OP data (or ?) so that's a model that should work

x = (0:0.01:1);
figure
hold on
for m = 1:5
    for n = 1:5
        a = 2+0.5*m;
        b = 1.5+0.8*n
        y = (1-x.^a).^(1/b);
        plot(x,y);
    end
end
hold off

[kimy]

I have 5 curves about x and y, with change of the value of a. So I need to get the relation among x,y and a. m,n,p,q are the expected fitted constants.

[Mathieu NOE]

well, If you would share your data, I could give it a try....

[kimy]

I uploaded this figure to you. thanks

Answer 1

[Matt J]

lsqnonlin would be worth a try.

https://www.mathworks.com/help/optim/ug/lsqnonlin.html

[kimy]

Thanks. yesterday, I had a look at this func but I did not find a solution so far. Do you have any other suggestion?