RFC: Return n-th derivative of a Taylor1 as a Taylor1

[PerezHz]

Current implementation returns the derivative of a Taylor1 as a Taylor1, but higher-order derivatives of a Taylor1 are returned as single values. This PR is intended to instead return higher-order derivatives of a Taylor1 polynomial as a Taylor1 polynomial. In order to do this, this PR adds a new method to derivative(n::Int, a::Taylor1) and renames the existing method for the value of the n-th derivative of a Taylor1 polynomial as derivativeval (name suggestions are more than welcome 😛!). This was done in order to get the whole n-th derivative polynomial when it's needed, but the existing method for the value of the n-th derivative is faster when only the numerical value is needed, so it was kept for performance reasons.

[coveralls]

Changes Unknown when pulling ef69c86 on PerezHz:jp/derivative into ** on JuliaDiff:master**.

[lbenet]

I like the idea of adding such method.

Currently, we have derivative(a) which returns the Taylor1 series of the derivative, and derivative(n, a) which returns the value of the n-th derivative of the polynomial (evaluated at zero). What about adding derivative(a, n) with the behavior you propose? The advantage is that such a change would break any current code.

Any opinion on this @dpsanders?

[dpsanders]

I think having derivative(a, n) be different from derivative(n, a) is confusing, but I don't really have a better suggestion.

[lbenet]

Or use keyword variables like derivative(a, ord=n) to return what is proposed here...

[PerezHz]

Just updated derivative with the latest agreed convention: derivative(n,a) returns just the value of the n-th derivative evaluated at the original point of expansion; derivative(a,n) returns the whole n-th derivative polynomial

[coveralls]

Changes Unknown when pulling 021d0c3 on PerezHz:jp/derivative into ** on JuliaDiff:master**.

[coveralls]

Changes Unknown when pulling be9e6a4 on PerezHz:jp/derivative into ** on JuliaDiff:master**.

[lbenet]

I am in favor of merging this.

Yet, aside from the sole comment on this PR, there are two other points to note: First, since #136 is merged you have to rebase to current master. Second, there seems to be a problem with (at least) one test in travis; see this; I suggest to correct the failing test (Julia v0.7-dev only), and wait to see if there are other issues with travis.

Any commets @dpsanders?

[coveralls]

Coverage decreased (-0.04%) to 95.937% when pulling 02af848 on PerezHz:jp/derivative into 8a8d3fb on JuliaDiff:master.

[lbenet]

Thanks a lot!

I'll wait to the green lights of travis before merging.

Maybe also @dpsanders has other comments.

[PerezHz]

First, since #136 is merged you have to rebase to current master.

Thanks; done! 😄

Second, there seems to be a problem with (at least) one test in travis; see this; I suggest to correct the failing test (Julia v0.7-dev only), and wait to see if there are other issues with travis.

I just corrected this (at least locally; let's see if travis agrees), and also added some tests for the new derivative! function and jacobian for mixtures as well to keep coverage up!

[PerezHz]

Thank you for all your comments and suggestions!

[coveralls]

Coverage decreased (-0.04%) to 95.937% when pulling 06d731f on PerezHz:jp/derivative into 8a8d3fb on JuliaDiff:master.

[coveralls]

Coverage increased (+0.2%) to 96.163% when pulling 1d2e6e0 on PerezHz:jp/derivative into 8a8d3fb on JuliaDiff:master.

[coveralls]

Coverage increased (+0.2%) to 96.163% when pulling 1d2e6e0 on PerezHz:jp/derivative into 8a8d3fb on JuliaDiff:master.

[lbenet]

Thanks a lot! I'm merging this!