Customize isequal behavior for handle objects?

Is it possible to customize the isequal function for own classes, i.e. to define when two handle-class objects are considered as equal by content? I would like to explain my question in more detail below:

Please consider the following simple data class

classdef Data < handle
    properties 
        value
    end
    
    methods
        function self = Data(value)
            self.value = value;
        end
    end
end

Following MathWorks --- Equality of Handle Objects one can check if two objects of the Data class point to the same reference using the == operator. In contrast, one can test if two objects are equal by content using the Matlab built-in isequal function.

This works fine. However, I now would like to override the isequal behaviour for my class. For example, I would like to define that two Data objects are equal by content if the values of their property value are equal within an absolute tolerance of 1e-8. How could I achieve that?

Note:

Im aware of the possibility of overriding the eq-method of the Data class:

classdef Data < handle
    properties 
        value
    end
    
    methods
        function self = Data(value)
            self.value = value;
        end
    
        function is_eq = eq(self, other)
            if not(strcmp(class(self), class(other)))
                is_eq = false;
                return
            end
            
            is_eq = abs(self.value - other.value) < 1e-8;
        end
    end
end

Therewith I can test the equality of two objects by content using the == operator. However, from my point of view this is problematic because: i) It is inconsistent with the initial/previous behavior because the == operator no longer compares two objects by reference but by content instead. And, ii) in addition, I lose the possiblity to check if two objects have the same reference.

Answer 1

[Steven Lord]

If you want to overload what isequal means for your object, overload isequal.

isequal and eq are somewhat related, but they are independent functions.

[Thomas Kiefer]

I wasn't aware about the fact isequal could be overload for own classes. Thank you very much!

Answer 2

[Thomas Kiefer]

One more subsequent question: When overriding isequal in a custom class, i.e. in the Data class, how could one access the previous definition of isequal (as if I would not have overriden the method)? Because isequal is not a member method of the base class handle.

I.e., what I would like to do in my custom isequal method is to make some quick checks on the objects by which I can verfiy that the objects are different and only if these checks are passed use the full isequal-test. Like that:

classdef Data < handle
    properties 
        value
    end    

    methods
        function self = Data(value)
            self.value = value;
        end    

        function is_eq = isequal(self, other)
            %% Make some user specific tests
            %% Which help to quickly decide if self and 
            %  other are unequal
            %...
            %...
            
            %% If all criteria above are fulfilled use the
            %% Matlab default isequal... like isequal@superclass(self, other)
            is_equal = isequal(self, other);
        end
    end

end

[Walter Roberson]

builtin('isequal', self, other)

[Thomas Kiefer]

Great! That solves my problem. Thank you very much!