[SciPy-Dev] Differentiate function

[josef.pktd at gmail.com]

On Fri, Nov 11, 2016 at 6:57 PM, Scott Sievert <sievert.scott at gmail.com>
wrote:

> 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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>
To throw one more in here

local polynomial regression (local kernel or windows) would be another way.
AFAIR, it would be similar to Savitsky-Golay for non-equal spaced grid.
IIRC, the slope coefficient of the local linear regression is the
derivative of the smooth function and has relatively good edge behavior
because of the local linear structure.
I think higher order derivatives would follow from the coefficients of
higher order polynomial regression.

That would be the kernel regression analog of smoothing splines version.

Josef
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