Obtaining a equation in two variables (x and y) from a set of data points

I have a Matrix. The colums represent the X values and the rows represent the Y values and the matrix element Z represents the value at (X,Y). So, in my case, X runs from 1 to 250 and Y runs from 1 to 3500. I would like to fit an equation (I suspect that the data is going to be of high order *say 50) so maybe spline?) such that Z=f(X,Y) where Z is the matrix element

Example :

Say I choose X=10 and Y=2300 in the matrix. The matrix will have a particular value Z (say 30000) at (10,2300). Now I want to fit a equation for Z as a function of X and Y. What do I do?

Answer 1

[Bjorn Gustavsson]

What you should do depends on your objective. If you very explicitly want a function you could use spap2 (and perhaps some of its siblings). It is a least-square-fitting spline function with 2-D capabilities.

If you can do all of the function evaluations at once you might be better off with interp2 (your data seems to be on a plaid grid), or griddata, scatteredInterp, triscatteredinterp functions (the latter might give you approximately your required function output), Otherwise there is always the gridfit function on the file exchange.

HTH

[Akaash Dragon]

Sorry for the late reply. I was reading a bit about splines before trying spap2. However, spap2 only works for 1D data right? I mean given x, i get only y. Am I wrong? Can I specify x an y to get z ?

[Bjorn Gustavsson]

No you can use it on multidimensional independent variables too, see the help and documentation. I have used it for scalar data on a 2-D grid, but it seems possible to use it on scattered data too - though I don't remember using it for that. It can be a bit fiddly to get it to work the first time, but that's nothing to hold you back.

HTH

[Akaash Dragon]

knotsx = augknt(linspace(x_r(1), x_r(end), 2000), 4);

knotsy = augknt(linspace(y_r(1), y_r(end), 200), 4);

bsp2 = spap2({knotsx,knotsy},[4 4], {x_r,y_r},f);

Running bsp2 in the command lin gives

>>bsp2

form: 'B-'

knots: {[1×2006 double] [1×206 double]}

coefs: [1×2002×202 double]

number: [2002 202]

order: [4 4]

dim: 1

I used the following commands and I was able to plot the fit of the data. However, I want the functional form (like f(x,y)), so what do I do? The reason I want the functional form is because I want to get the root mean square error between the actual data and the fit to the actual data. By doing this, I only get datas for 2002 x 202 datas in the structure bsp2. But in reality there are 3500 x 250 points. (The reason I used 2000 x 200 is because I don't want to overfit).

[Bjorn Gustavsson]

It was a "reasonably long time ago" I used fitting splines, but I remember that you could generate a function-call for evaluation of the spline at arbitrary points. After some snoping aroung I managed to find: fnval for you. If you check the help for that function you should be able to get to a function-call. Perhaps something like this:

knotsx = augknt(linspace(x_r(1), x_r(end), 2000), 4);
knotsy = augknt(linspace(y_r(1), y_r(end), 200), 4);
bsp2 =  spap2({knotsx,knotsy},[4 4], {x_r,y_r},f);
[X,Y] = meshgrid(x_roi,y_roi); % Yeah, yeah...
your_fun = @(x,y) fnval(bsp2,{x(:),y(:)});
Z = Y;
Z(:) = your_fun(X,Y);

Completely untested (TM)

HTH

[Akaash Dragon]

f2=csapi({x_r,y_r},f);
fnval(f2,[3;100])

These commands work.

Note that f2 structure looks like this:

form: 'pp'

breaks: {[1×3500 double] [1×250 double]}

coefs: [1×13996×996 double]

pieces: [3499 249]

order: [4 4]

dim: 1

However it doesn't work well if I use spap2. Using your code gives me something like this

Error using repmat
Requested 609000000x6 (27.2GB) array exceeds maximum array size preference. Creation of arrays greater than this
limit may take a long time and cause MATLAB to become unresponsive. See array size limit or preference panel for
more information.

Error in spval>spval1 (line 104)
   tx =reshape(t(repmat(2-k:k-1,d*lx,1)+repmat(dindex,1,2*(k-1))),d*lx,2*(k-1));

Error in spval (line 43)
         spval1(spmak(t{i},reshape(v,prod(sizev(1:m)),sizev(m+1))), ...

Error in fnval (line 95)
v = reshape(feval(ff,f,varargin{:}),[sizeval,sizex]);

Error in flats>@(x,y)fnval(bsp2,{x(:),y(:)})

Error in flats (line 17)
Z(:) = your_fun(X,Y);

This is the error I get.

Spap2 seems to be better than csapi and hence would prefer if you could help me use fnval with spap2. Thanks in advance!

[Akaash Dragon]

fnval(bsp2,[3;100])

This command works! Thank you very much!