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Hi.

I have a cell array with length 3 :

M_t={{[0,1],[0 0 2]},{[0,1.01],[0 0 2]},{[0,1],[0 .001 2]}};

I want to compare these 3 arrays with a specific tolerence. How can i do this?

I have tried intersect before.

Thanks.

Jan
on 20 Feb 2019

In the case

ismebertol([0,0,2],[0,0,2],1e-02)

the output has 3 elements, not "logical1 1". Is this a typo?

ismembertol uses a strange scaling: for the elements u of the array A and the elements v of the array B:

abs(u-v) <= tol*max(abs([A(:);B(:)]))

This means, that the tolerance is multiplied my the maximum absolute value of the arrays. I do not know a case, where this is really useful.

ismembertol([1, 900], [20, 1000], 1)

Is the result [true, true] expected?!

For all of my cases, ismembertol did not offer a useful method to apply the tolerence. What a pity.

By the way, you still did not mention, which kind of comparison you exactly want. "The absolute error" is not a unique definition. It can mean:

all(abs(a(:) - b(:)) < tol) % or <=

any(abs(a(:) - b(:)) < tol) % or <=

sum(abs(a(:) - b(:)) < tol) < numel(A) / 2

% or a method, which does not consider the order or the elements

You have mentioned ismembertol, which does not consider the order of elements. So it is not clear, if [1, 0] and [0, 1] should be considered as equal or not.

It is hard to find out, what you exactly want. I've spent some time to ask you specific question, but I do not get clear statements and in consequence I assume, that I cannot help you.

Rik
on 20 Feb 2019

The code below will iterate through the cell levels. The resulting output is only true if all dimensions are equal and all elements are within tolerance.

M_t={{[0,1],[0 0 2]},{[0,1.01],[0 0 2]},{[0,1],[0 .001 3]}};

clc

assert(ismembertol_nested(M_t(1),M_t(2),0.1),'test failed for equal arrays');

assert(~ismembertol_nested(M_t(1),M_t(3),0.1),'test failed for unequal arrays');

assert(~ismembertol_nested(M_t(1),M_t{2},0.1),'test failed for unequal inputs');

function tf=ismembertol_nested(A,B,tol)

%Un-nest cell arrays until ismembertol can be used on the inner arrays.

%This will return false instead of an error if the shapes are not equal on

%any level.

try

if isa(A,'cell')

tol_cell=num2cell(repmat(tol,size(A)));

tf=all(cellfun(@ismembertol_nested,A,B,tol_cell));

else

ia=ismembertol(A,B,tol);

ib=ismembertol(B,A,tol);

tf=all([ia,ib]);

end

catch

tf=false;

end

end

Rik
on 20 Feb 2019

That seems strange indeed. I think it would make much more sense if that scale factor would be 1 by default, not that max. So to get the behavior I expected you need to call this

ismembertol(A,B,'DataScale',1)

I can see what the usefullness is if you are using it to check for float rounding errors, but that is not what I suspect most people would be using it for. There doesn't seem to be an easy way to search the FEX for the use of a function, so I can't check that suspicion.

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