[SciPy-User] Fitting Polynomial With Shape Restrictions

[josef.pktd at gmail.com]

On Sun, May 7, 2017 at 2:45 PM, Jared Vacanti <jaredvacanti at gmail.com>
wrote:

> I am trying to fit a polynomial to observational data with shape
> restrictions - in this particular case monotonicity (decreasing) of the
> function and an always positive second derivative.
>
> Some of the interpolation classes have a mathematical "built-in"
> restriction - like scipy.interpolate.Rbf's thin-plate roughness penalty
> imposes some restrictions, but it's not explicit or adjustable.
>
> What are my options for imposing boundary conditions or shape restrictions
> on the spline?
>
> I have sample data here:
>
> import pandas as pd
> df = pd.read_csv("https://bpaste.net/raw/3e20878b5237")
>
> or available independently at https://bpaste.net/raw/3e20878b5237
>
> I have tried using a interior point convex optimization solver, but the
> results seem to be numerically finicky. Are there other alternatives?
>

As far as I know, pchip is the only one with monotonicity constraints
https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.pchip_interpolate.html

Josef



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