Why do I get a size mismatch error when trying to fit a surface using an external function?

Hello MathWorks community!

I'm using the Curve Fitting Toolbox to fit a surface using an external function. My function does a series of operations including things like FFTs, so defining an explicit fitting equation is non-trivial.

I've successfuly used an external function like this to fit a curve (x v. y), but I am struggling to make it work when applied to a surface (x&y v. z). Specifically, I get the following error in fittype:

Custom equations must produce an output vector, matrix, or array that is the same size and shape as the input data. This custom equation fails to meet that requirement:

I've double-checked the size of my output matrix and it matches the dimensions of x and y. I've also played around with transpose to see if something easy could make it work. To make things simpler, I then tried replacing my external function with one that doesn't have a lot of calculation steps or operations:

function z = TestFit(x, y, n2)

% a meaningless function to test fittype

l_x = length(x); l_y = length(y); 
z = zeros(l_x, l_y);

for i = 1:l_x
    for j = 1:l_y
        
        z(i, j) = 2.*x(i) + 3.*y(j).*n2
        
    end
    
end

I get the same error when I use this function instead, even though the dimensions of z match the dimensions of x & y. Furthermore, I noticed that if I remove the loop, the function will work with Curve Fitting Toolbox app and calls of fittype.

I'd prefer to keep loops within my original function, as I'm not sure I can make it work without them. Does anyone have any insight into how to make that work? Any help would be greatly appreciated!

Answer 1

[Walter Roberson]

Data is passed in in scattered form, not in grid form. Your function needs to return something the same size as x not length(x) by length(y)

[Clayton Casper]

I did not run into any more size mismatch errors once I followed your advice. Now my fitting will not converge, but that is a problem separate from this, I think. Thank you for your help!

Answer 2

[Torsten]

So you say

function z = TestFit(x, y, n2)
  z = 2*x+3*y*n2;
end

works, but

function z = TestFit(x, y, n2)
  % a meaningless function to test fittype
  l_x = length(x); l_y = length(y); 
  z = zeros(l_x, l_y);
  for i = 1:l_x
    for j = 1:l_y    
        z(i, j) = 2.*x(i) + 3.*y(j).*n2      
    end  
  end
end

doesn't ?

I think you will have to use

l_x1 = size(x,1); l_x2 = size(x,2); 
z = zeros(l_x1,l_x2);
for i = 1:l_x1
  for j = 1:l_x2    
    z(i,j) = 2*x(i,j) + 3*y(i,j)*n2     
  end  
end