Hello,
I need to fit some data (y_data = f(x1_data,x2_data)) in a certain function. I used 'objfcn', but I have to apply some boundary conditions (i.e. the curve must intersect a certain point, the second derivative must be positive, etc.).
Does anybody know if there is a way to do it with Matlab? (Well, I could artificially add the desired points to my data, but I guess this is not cientifically correct?)
I also checked lsqcurvefit, but, if I understood it well, you can only specify the ranges of the coefficients, but not the data.
In the following you find the case I need to solve, just in case my question was not clear.
Thank you in advance!
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I would like to fit some data in the following equation:
y_data = f(x1_data, x2_data)
Where f(x1, x2) = e^((a*x2^3 + b*x2^2 + c*x2 + d )*(-1/x1)) – z
and a,b,c,d and z are the coefficients to be determined.
There are many constraints:
1) 0 =< x2 =< 1
2) 0 =< y =< 1
(My data ranges from x2 = [0.3, 0.95] and y = [0.02,0.95])
3) x2 = 0 –> f = 0
(This is way I added the coefficient z. It is a kind of correction, since e^0 = 1, and there is otherwise no way to make it 0).
4) x2 = 1 –> f = 1
5) x2 = 1 –> f' = 1
6) x2 = 0 –> f'' > 0
To accomplish constraints 3, 4 and 5 I resolved the equations, so that dependent coefficients are obtained:
z = -e^(-d/x1)
c = -x1/(1+e^(-d/x1)) – 3*a -2*b
I tried to solve it as follows:
objfcn = @(b,x1,x2) exp(-1./x1.*( b(1).*x2.^3 + b(2).*x2.^2 + (-x1./(1+exp(b(3).*(-1./(x1))))-3*b(1)-2*b(2)).*x2 + b(3))) - exp(b(3).*(-1./(x1)));[B,resnorm] = fminsearch(@(b) norm(y - objfcn(b,x1,x2)), [1;1;1]);However, I don't know how to implement 1, 2 and 6.
*Here my questions:
– Is it possible to introduce constraints 3,4 and 5 with a Matlab function, instead of solving equations?
– Do you know if it is possible to apply constraints 1,2 and 6?*
Thanks!!!
Best Answer