Determine differentiability of a x and y dataset

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Christian 2017-3-8

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编辑： Christian 2017-3-27

Hello everybody,

I have a dataset (x old, y old). Now I do some math on it and get a new dataset (x new, y new). To check whether my calculations are correct, the curve of the new datset must be differentiable.

Do you have any ideas, how I could do this "check"?

Thank you

Cheers

Christian

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Christian 2017-3-8

编辑：Christian 2017-3-8

As you can see, the critical spot of the new dataset looks sometimes like this:

And now I need to find out, if the new curve is smooth or looks like above. It would be perfect if the code would give me a result which looks something like this:

new_dataset_1 = false ("not differentiable")

new_dataset_2 = true ("differentiable")

new_dataset_3 = true

new_dataset_4 = false...

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回答（1 个）

Guillaume 2017-3-8

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The concept of diferrentiable does not mean much for a discretised function. By definition dy/dx always exists when you have a vector of x and y values, unless one of y or x is infinite or NaN.

So really the only thing you could test is

assert(all(isfinite(xnew)) & all(isfinite(ynew)))

Guillaume is right: For a discretized function, the term "differentiable" has no meaning. A line like x=[1,2,3], y=[1,2,100] might or might not represent a differentiable function, because even a smooth function can contain a huge derivative in one point. There is also no to "proove" if sin(1/x) is differentiable in x=0 if all you have is a finite number of its values.

All you can decide based on a set of data points is if the difference between neighboring points exceeds a certain limit or not. But this does not mean differentiablility.

Christian 2017-3-8