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

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kimy 2021-3-16

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评论： kimy 2021-3-17

hello guys,

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

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

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Matt J 2021-3-16

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编辑：Matt J 2021-3-16

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

kimy 2021-3-17

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

Mathieu NOE 2021-3-17

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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 2021-3-17

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I suspect na is n*a

kimy 2021-3-17

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

Matt J 2021-3-17

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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 2021-3-17

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

Mathieu NOE 2021-3-17

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在 MATLAB Online 中打开

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 2021-3-17

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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 2021-3-17

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

kimy 2021-3-17

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figure1.fig

I uploaded this figure to you. thanks

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Matt J 2021-3-17

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lsqnonlin would be worth a try.

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

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kimy 2021-3-17

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