On 17 Oct 2014 02:38, "Benjamin Root" <ben.root@ou.edu> wrote:
That isn't what I meant. Higher order doesn't "necessarily" mean more
accurate. The results simply have different properties. The user needs to choose the differentiation order that they need. One interesting effect in data assimilation/modeling is that even-order differentiation can often have detrimental effects while higher odd order differentiation are better, but it is highly dependent upon the model. To be clear, we aren't talking about different degrees of differentiation, we're talking about different approximations to the first derivative. I just looked up the original pull request and it contains a pretty convincing graph in which the old code has large systematic errors and the new code doesn't: https://github.com/numpy/numpy/issues/3603 I think the claim is that the old code had approximation error that grows like O(1/n), and the new code has errors like O(1/n**2). (Don't ask me what n is though.)
This change in gradient broke a unit test in matplotlib (for a new feature, so it isn't *that* critical). We didn't notice it at first because we weren't testing numpy 1.9 at the time. I want the feature (I have need for it elsewhere), but I don't want the change in default behavior.
You say it's bad, the original poster says it's good, how are we poor maintainers to know what to do? :-) Can you say any more about why you you prefer so-called lower accuracy approximations here by default? -n