how to represents a function at three variables from data collected on the field?

hi, i need to create and represent function of the shape t=f(x,y,z) from the arrays t,x,y,z.create a program which has input t,x,y,z and output the representation of that function

[John BG]

look for hgtransform

Answer 1

[John D'Errico]

Congratulations! You are the 1 millionth person to ask this same question. Only kidding. It just seems like a million.

Your problem is one of empirical modeling, i.e., to find a function that represents some relationship purely from measured data. In multiple dimensions where you cannot easily visualize the surface, this is often quite difficult.

A simple solution is a tool like my polyfitn, as found on the file exchange. However, as easy as they are to fit, polynomial models have many serious problems.

Alternatives are tools like radial basis functions, spline models of many forms, neural nets, etc.

In the end, it will depend on which tools you have available, upon your skills in modeling, and most importantly, what you will do with that model when it is achieved.

[John BG]

this is not an answer, just a comment

Answer 2

[Greg Heath]

If the function is not too weird, the regression neural network FITNET should fill the bill.

Assuming x,y,z and t are rows of length N:

 input   = [ x; y; z ]; 
 target  = t ;
 [ I N ] = size(input)  % I = 3
 [ O N ] = size(target) % O = 1

See the documentation example

 help fitnet
 doc fitnet

Additional help can be obtained from some of my tutorials. Search both NEWSGROUP and ANSWERS using

                    NEWSGROUP   ANSWERS
tutorial fitnet        28        17
tutorial fitnet greg   27        16

Hope this helps.

Thank you for formally accepting my answer

Greg