How to write one universal function to evaluate many equations?

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Simon 2023-7-2

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编辑： Simon 2023-7-4

I am working on verifying whether if equations are valid over a large data set. The challenge is that the number of equations to be verified is huge even though they are simple arithmetic equations and identities. In order to avoid writing a different function for each equation, I try to represent an equation as a 'model' and write only one universal function to eval each model. Here is a toy example to explain what I intend to do. My questions are 1.) whether if my approach is generally in right direction 2.) is there any way to avoid eval( ) in function foo( )? Thanks for your insights!

x = 7;
y = 3;
modelA = [x, y; "+", "-"];
foo(modelA)
ans = 4
z = -21;
modelB = [x, y, z; "-", "*", "=="];
foo(modelB)
ans = logical
   1
function out = foo(model)
data = string(model(1,:));
operators = model(2,:);
a = strcat(operators, data);
out = eval(strcat(a{:}));
end

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Stephen23 2023-7-2

编辑：Stephen23 2023-7-2

"I could certainly write function for each accounting equation; as a matter of fact, I have done a couple of that. Then I found this task is too tedious."

I don‘t see that it makes any difference: if you can define those string arrays then you can just as easily define some anonymous functions e.g. using STR2FUNC.

"Othere disadvantages include 1.) function naming and tracking would be out of control"

The approach you show in your question also requires lots of individually-named functions. You could easily avoid that with a cell array of anonymous functions or function handles. Or just one function with suitable SWITCH or other logical operations to perform the calculations. Or some suitable nesting of local functions, called based on some logical criteria.

"2.) accounting equations and their purposes are hidden inside functions, which I feel uncomfortable about."

Those are benefits: Mfile functions allow you to neatly and efficiently encapsulate some functionality and provide a documented interface, as well as limitless help, comments, etc. Calling functions is also very efficient. Your string arrays provide none of those benefits.

Simon 2023-7-2

编辑：Simon 2023-7-2

@John D'Errico Thanks for the feedback. 'NEVER TEST FOR EXACT EQUALITY BETWEEN FLOATING POINT NUMBERS.'

I am aware of that potential pitfall. Fortunately, only integer variables will be check for exact equality. The double-valued ratios will just be output of the universalFunction(data, equation script).

'I'd suggest you start rethinking what you need to do, and find a better way than using eval anyway. Eval is slow as hell. It will surely cause you problems down the line too.'

I totally agree. I have read @Stephen23's tutorial post for Matlab beginner. It has in-depth discussion about eval( ). I have indeed been thinking really hard about this problem. I could have taken a more conventional approach, writing many functions. But trying a very different way to tackle this problem is very seductive :-)

'For example, you might decide to reduce this to a set of generic expresssions. Now, write one function for each of those generic classes. Pass in your variables, get a result.'

Good advice. think I can divide them into two types: logical equality comparison and numeric calculation.

'In the case where a ratio is involved, then you will probably need to apply a tolerance on the result.'

Good advice.

Paul 2023-7-2

在 MATLAB Online 中打开

Comments can be stored using either the cell array or struct, if a cell array or struct with named fields happen to be the way to go.

C{1,1} = @(x,y,z) x - y == z;
C{1,2} = "this is the foo function";
C
C = 1×2 cell array
    {@(x,y,z)x-y==z}    {["this is the foo function"]}
% or
S.foo.eqn = @(x,y,z) x - y == z;
S.foo.comment = "this is the foo function";
S.foo
ans = struct with fields:
        eqn: @(x,y,z)x-y==z
    comment: "this is the foo function"

Simon 2023-7-4

编辑：Simon 2023-7-4

@Paul I tried out your idea (structure of function handels). It works pretty well. Thanks!!

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