# [SciPy-User] inverse function of a spline

Charles R Harris charlesr.harris@gmail....
Sat Oct 1 10:17:33 CDT 2011

```On Sat, Oct 1, 2011 at 8:52 AM, <josef.pktd@gmail.com> wrote:

>
>
> 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
>
>
IIRC, de Boor dealt with fitting distribution functions somewhere in his
book "A Practical Guide to Splines". I don't recall whether or not he
constrains things to positivity, but recalling one of the figures, I think
that he was fitting histograms, perhaps their area.

<snip>

Chuck
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