MATLAB: How to add tolerance for isequal

isequalMATLABstruct

Hi,
I am comparing two .mat files, both have very complicated struct type data but they should be almost identical. In this case, I don't found other method except for isequal can perform the comparsion. 
data = load('MMC4_cpu_HVDC.mat');
data_ref = load('MMC4_cpu_HVDC_ref.mat');
isequal(data,data_ref)
The code above produced ans = 0. I checked using visdiff, found that it is due to some very small difference in number.
visdiff('MMC4_cpu_HVDC.mat', 'MMC4_cpu_HVDC_ref.mat')
% 13.581349668075767
% ans =

%    13.5813

% 13.581349668075765
% ans =
%    13.5813
I would like to ask if it is possible to add a tolerance factor to isequal? or are there other ways to compare these two .mat files? Example data are attached. Many thanks.
Andy

Best Answer

If you had asked for tolerances for regular arrays this would've been reasonably straightforward. Something like this:
isapproximatelyequal = @(x1,x2,tol) all(abs(real(x1(:)-x2(:)))<tol) & all(abs(imag(x1(:)-x2(:)))<tol);
But for structs this is a too unspecified operation, in my opinion. What with a pair of structs where one has an additional field 'OK' that is just a simple flag. Are those structs similar enough if everything else i identical? Perhaps you can wrap the isapproximatelyequal above into a function that compares fields in your structs. Something like this:
function OK = isapproximatelyequal_structs(S1,S2,tol)
OK = 0;
fields2 = fieldnames(S2);
fields1 = fieldnames(S1);
toCheck = intersect(fields1,fields2); % for example
for iField = numel(toCheck):-1:1
  curr_field = toCheck(iField)';
  OK(iField) = isapproximatelyequal(S1.(curr_field{:}),S2.(curr_field{:}),tol);
end
if all(OK)
  OK = 1;
else
  OK = 0;
end
function OK = isapproximatelyequal(x1,x2,tol)
OK = 0;
try
  OK = all(abs(real(x1-x2))<tol) & all(abs(imag(x1-x2))<tol);
catch
  OK = 0;
end
This function will not work for structs with more complicated structure, for that you'll have to call the function recursively untill you reach fields that are arrays where isapproximatelyequal will work as you want. You should also have checks on array-sizes since the new implicit expansion might give false positives in isapproximatelyequal.
HTH
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