# [SciPy-User] inverse function of a spline

josef.pktd@gmai... josef.pktd@gmai...
Sat Oct 1 09:52:18 CDT 2011

```On Fri, Sep 30, 2011 at 12:37 PM, <josef.pktd@gmail.com> wrote:

> On Thu, Sep 29, 2011 at 12:37 PM, Jeff Brown <brownj@seattleu.edu> wrote:
> >  <josef.pktd <at> gmail.com> writes:
> >
> >>
> >> On Fri, May 7, 2010 at 4:37 PM, nicky van foreest <vanforeest <at>
> gmail.com>
> > wrote:
> >> > Hi Josef,
> >> >
> >> >> If I have a cubic spline, or any other smooth interpolator in scipy,
> >> >> is there a way to get the
> >> >> inverse function directly?
> >> >
> >> > How can you ensure that the cubic spline approx is non-decreasing? I
> >> > actually wonder whether using cubic splines is the best way to
> >> > approximate distribution functions.
> >>
> >> Now I know it's not, but I was designing the extension to the linear
> case
> >> on paper instead of in the interpreter, and got stuck on the wrong
> >> problem.
> >>
> >
> > There's an algorithm for making constrained-to-be-monotonic spline
> interpolants
> > (only in one dimension, though).  The reference is Dougherty et al 1989
> > Mathematics of Computation, vol 52 no 186 pp 471-494 (April 1989).  This
> is
> > available on-line at www.jstor.org.
>
> Thanks for the reference. Maybe Ann's interpolators in scipy that take
> derivatives could be used for this.
>

trying out how PiecewisePolynomial works, almost but not quite enough

Josef
spamming the world with messy examples

>
> Shape preserving splines or piecewise polynomials would make a nice
> addition to scipy, but I'm only a potential user.
>
> I have dropped this for the moment, after taking a detour with
> (global) orthonormal polynomial approximation, where I also haven't
> solved the integration and function inversion problem yet (nice pdf
> but only brute force cdf and ppf).
>
> Josef
>
> >
> > _______________________________________________
> > SciPy-User mailing list
> > SciPy-User@scipy.org
> > http://mail.scipy.org/mailman/listinfo/scipy-user
> >
>
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