I'm using scipy.interpolate.UnivariateSpline to smoothly interpolate a large amount of data. Works great. I get an object which acts like a function.

Now I want to save the spline points for later and use them in Matlab (and also Python, but that's less urgent), without needing the original data. How can I do this?

In scipy I have no clue; UnivariateSpline does not seem to offer a constructor with the previously-computed knots and coefficients.

In MATLAB, I've tried the Matlab functions spline() and pchip(), and while both come close, they have errors near the endpoints that look kind of like Gibbs ears.

Here is a sample set of data that I have, in Matlab format: 

splinedata = struct('coeffs',[-0.0412739180955273 
-0.0236463479425733 0.42393753107602 -1.27274336116436

 0.255711720888164 1.93923263846732 

-2.30438927604816 1.02078680231079 0.997156858475075 

-2.35321792387215 0.667027554745454 0.777918416623834],...

 'knots',[0 0.125 0.1875 0.25 0.375 0.5 0.625 0.75 0.875 0.9999],...

 'y',[-0.0412739180955273 -0.191354308450615 -0.869601364377744

 -0.141538578624065 0.895258135865578 -1.04292294390242 

0.462652465278345 0.442550440125204 -1.03967756446455

 0.777918416623834])

The coefficients and knots are the result of calling get_coeffs() and get_knots() on the scipy UnivariateSpline. The 'y' values are the values of the UnivariateSpline at the  knots, or more precisely: 

y = f(f.get_knots())

where f is my UnivariateSpline.

How can I use this data to make a spline that matches the behavior of the UnivariateSpline, without having to use the Curve-Fitting Toolbox? I don't need to do any data fitting in Matlab, I just need to know how to construct a cubic spline from knots/coefficients/spline values. 

You can do it by using the functions _eval_args() and _from_tck() from the class UnivariateSpline. The first one gives returns the spline parameters, which you can store and later create a similar spline object using the the second one.

Here is an example: 

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import UnivariateSpline

x = np.linspace(-3, 3, 50)
y = np.exp(-x**2) + 0.1 * np.random.randn(50)

spl1 = UnivariateSpline(x, y, s=.5)

xi = np.linspace(-3, 3, 1000)

tck = spl1._eval_args

spl2 = UnivariateSpline._from_tck(tck)

plt.plot(x, y, 'ro', ms=5, label='data')
plt.plot(xi, spl1(xi), 'b', label='original spline')
plt.plot(xi, spl2(xi), 'y:', lw=4, label='recovered spline')

plt.legend()
plt.show()