[SciPy-User] Monotonic Piecewise Cubic Hermite Interpolator (Matlab pchip() equivalent).

[Chris Michalski]

Recently, I had a need for a monotonic piece-wise cubic Hermite  
interpolator.   Matlab provides the function "pchip" (Piecewise Cubic  
Hermite Interpolator), but when I Googled I didn't find any Python  
equivalent.   I tried "interp1d()" from scipy.interpolate but this was  
a standard cubic spline using all of the data - not a piece-wise cubic  
spline.  This type of interpolator wasn't up to my needs because it  
tends to ring between points where there are sharp transitions because  
it isn't monotonic and it uses all of the data - which makes the  
interpolator "miss" sharp breaks in the data.

I had access to Matlab documentation, so I spent a some time tracing  
through the code to figure out how I might write a Python duplicate.   
This was an massive exercise in frustration and a potent reminder on  
why I love Python and use Matlab only under duress.  I find typical  
Matlab code is poorly documented (if at all) and that apparently  
includes the code included in their official releases.  I also find  
Matlab syntax “dated” and the code very difficult to “read”.

Wikipedia to the rescue:

http://en.wikipedia.org/wiki/Cubic_Hermite_spline
http://en.wikipedia.org/wiki/Monotone_cubic_interpolation

Not to be deterred, these two very well written Wikipedia entries  
explained in simple language how to compute the interpolant.  Hats off  
to whoever wrote these entries – they are excellent.  The result was a  
surprising small amount of code considering the Matlab code was  
approaching 10 pages of incomprehensible code. Again - strong evidence  
that things are just better in Python...

The resulting code:

along with a matplotlib plot showing the results:
As the plot shows, the "pchip" does preserve monotonicity compared to  
a "straight" piecewise cubic Hermite interpolation.  In addition, both  
of the piecewise interpolators result in less "ringing" away from  
transitions because they only consider the data points in the  
immediate vicinity of the desired output point.

Hope this is helpful in filling the void that several have asked about.
















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