[SciPy-Dev] Differentiate function

[Scott Sievert]

There’s also scipy.misc.derivative
<https://docs.scipy.org/doc/scipy/reference/generated/scipy.misc.derivative.html>
which
also finds the derivative of a function.

There’s not only the method of finite differences, but there’s also automatic
differentiation <https://en.wikipedia.org/wiki/Automatic_differentiation>
In this, you keep track of what operations are performed on the input, then
use the chain rule to find the derivative. Because it only keeps track of
the functions performed, this method support if-statments, while-loops and
recursion.

Here’s a package that implements this method with a thin wrapper around
NumPy: https://github.com/HIPS/autograd (though it looks like numdifftools
also support this)

Numerical Optimization 2nd edition by Stephen Wright also has more detail
on chapter 8 methods to compute derivatives (and chapter 9 is on derivative
free optimization!).

Scott

On November 11, 2016 at 5:04:12 PM, per.brodtkorb at ffi.no (
per.brodtkorb at ffi.no) wrote:

Maybe this addresses Robert's needs:

http://www.scholarpedia.org/article/Finite_difference_method#FD_formulas_in_higher-D

https://github.com/pbrod/numdifftools/blob/master/numdifftools/fornberg.py

Per A.

-----Original Message-----
From: SciPy-Dev [mailto:scipy-dev-bounces at scipy.org] On Behalf Of Jonathan
Stickel
Sent: 10. november 2016 18:32
To: scipy-dev at scipy.org
Subject: Re: [SciPy-Dev] Differentiate function

On 11/10/16 01:19 , Thomas Haslwanter wrote:
> The current discussion lacks a reference to the existing
> Savitzky-Golay filter
> https://scipy.github.io/devdocs/generated/scipy.signal.savgol_filter.h
> tml which - to my understanding - should solves most of Robert's
> problems.
>
> thomas
>


No, I don't think this addresses Robert's needs. That is simply a data
smoother (and arguably inferior to other data-smoothing methods).
Although it does have an option to provide a derivative, it presumes the
data are equally spaced.


> On Thu, Nov 10, 2016 at 8:10 AM, Ralf Gommers <ralf.gommers at gmail.com
> <mailto:ralf.gommers at gmail.com>> wrote:
>
>
>
> On Wed, Nov 9, 2016 at 8:01 AM, Pauli Virtanen <pav at iki.fi
> <mailto:pav at iki.fi>> wrote:
>
> Mon, 07 Nov 2016 19:52:09 +0300, Evgeni Burovski kirjoitti:
> > Note that `approx_derivative` implements several finite-difference
> > schemes,
>
> In addition, I'd remind of
>
> https://pypi.python.org/pypi/Numdifftools
> <https://pypi.python.org/pypi/Numdifftools>
>
>
> And
>
https://github.com/scipy/scipy/wiki/Proposal:-add-finite-difference-numerical-derivatives-as-scipy.diff
>
> <https://github.com/scipy/scipy/wiki/Proposal:-add-finite-difference-n
> umerical-derivatives-as-scipy.diff>
>
> Ralf


These are tools for finite-differences of a known function. Robert (and
I) are interested in finite-differences of y vs. x vectors, whether
obtained from experiment or as part of a higher-level numerical method.
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