fitting function of two variables

hi could any one help me on this problem: i have a vector x with some values and vector y with some values too,y isn't function of x and i need to fit them in a function f(x,y)how can i do this in matlab??

[Yoav Livneh]

Can you clarify? Are you trying to find the relation between x and y (y=f(x)) or are both x and y inputs into f which an output z (z=f(x,y))?

[SAM alimostafa]

i mean that i need z=f(x,y)

Answer 1

[Ivan van der Kroon]

If you have a predevined function, f(x,y) with unknown coefficients, you can find those with the optimalization toolbox.

If you're just wondering how to do it for multiple vectors, I always concatenate them. If your arrays are constraints (so known values) remember that the vector to be optimized are the coefficients of your function.

Sorry, lot of if's, but your question is not really clear to me.

Good luck, Ivan

[SAM alimostafa]

i mean that i need to apply least square method to fit a function of two variables x and y

Answer 2

[Yoav Livneh]

You can use fminsearch to optimize your coefficients, but you still need to know the basic form of the function. Write a function (in my example it's called "my_fun") that for every pair of (x,y) values compares (subtracts) f(x,y) to the data you want to fit it to. It's inputs are the coefficients you want to optimize. Then write:

coeffs_init = [1 1 1] % Initial guess of coefficients. Can be any size, depending on number of coefficients.

Results = fminsearch(@(t)my_fun(t,x,y,Comp_Data),coeffs_init);

I hope I made myself clear. If not I'll try and rephrase. You can also type in the command line "doc fminsearch" to see examples.

[SAM alimostafa]

thank you

[Arun Jose]

z=f(x,y) is my function.but i know data points (x ,y) and corresponding z values only. I know that z is of the form z=a*g(x,y)+b*h(x,y) i want find a,b in a least squre sense. Can i use 'lsqcurvefit' function?? If i can't what can i use??

[Alan Weiss]

This example might help. It has z = f(x), but just take [x,y] as your x and you'll be fine.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 3

[Image Analyst]

I use polyfitn http://www.mathworks.com/matlabcentral/fileexchange/34765-polyfitn to fit a 2D vignetted background image to a quadratic. See attached demo below in blue.

Or you can try this : http://www.mathworks.com/matlabcentral/fileexchange/13719-2d-weighted-polynomial-fitting-and-evaluation