How to use this for fractional derivatives at a point?

[shaunster0]

hi, i’d just like an example of how to use this to get fractional derivatives. I want to get fractional derivatives of a Gaussian. Seems like the RL function doesn’t return this (at least the numbers it returns do not seem to be the fractional derivative at a point, maybe they’re the integral of it or something)

So how would I do this?

[uniformlyMatt]

The RL function is for calculating the RL derivative at every point on a function's domain. You pass in an array of function values and get an array of fractional derivatives back.

The 'RLpoint' function is for calculating the RL derivative at a specific point. You can pass in the point as the 'domain_end' parameter.

Please let me know how this goes!

[shaunster0]

Matt, thanks for your reply!! it’d be good if there was a few clear examples of how to use it for some common functions ... the numbers that I got for fractional derivatives of a Gaussian weren’t right, I guess I’m using it the wrong way. Is the RL function reliable? So how would I use it to calculate the 0.5 order derivative of a Gaussian exp(-1/2 x^2) ? This gave me wrong answers- g = lambda x: np.exp(-x**2) g0p5 = df.RL(0.5, g) y = np.diff(g0p5)*100

…

Sent from my iPad

On 9 Jan 2020, at 5:27 am, Matt Adams ***@***.***> wrote: The RL function is for calculating the RL derivative at every point on a function's domain. You pass in an array of function values and get an array of fractional derivatives back. The 'RLpoint' function is for calculating the RL derivative at a specific point. You can pass in the point as the 'domain_end' parameter. Please let me know how this goes! — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub, or unsubscribe.

[uniformlyMatt]

It looks like you've found an oversight in the code. I'll have to revisit this after I review Diethelm et al, since it's been a long time since I wrote this.

[shaunster0]

thanks Matt! It’d be great if u could do this, I can see fractional derivatives becoming very important to some applications in physics and computer science (particularly for Gaussian type functions).

…

Sent from my iPhone

On 11 Jan 2020, at 8:03 am, Matt Adams ***@***.***> wrote:  It looks like you've found an oversight in the code. I'll have to revisit this after I review Diethelm et al, since it's been a long time since I wrote this. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub, or unsubscribe.

[cooperhatfield]

I've compared the result given by your code snippet with the expected result given by

Note, this is the theoretical result when the left endpoint is 0. For exponential functions, generally a left endpoint of negative infinity is used. But in any case, this is a comparison of the results:

In the case where the left endpoint decreases to -100, the result becomes

Which is likely closer to what you're expecting.

[shaunster0]

thanks Cooper!

[shaunster0]

it’d be good if a couple examples of this usage could be given on the project main page, this would be confusing to a new user … ie. setting the endpoint correctly on some common function

[cooperhatfield]

Hi shaunster0,
A github wiki page has been made for this repo here please let me know if that is helpful, or what you think could be improved!

And just a note WRT the wiki, the Caputo methods are only available on a fork currently, not on the main package.

[cooperhatfield]

Tomorrow I will update the readme with more examples though, you're right.

[shaunster0]

thanks, appreciate what ure doing here, this project needed a makeover … it was amazing to me that there was no good quality python library for fractional derivatives