Python interp1d vs. UnivariateSpline

Question

I'm trying to port some MatLab code over to Scipy, and I've tried two different functions from scipy.interpolate, interp1d and UnivariateSpline. The interp1d results match the interp1d MatLab function, but the UnivariateSpline numbers come out different - and in some cases very different.

f = interp1d(row1,row2,kind='cubic',bounds_error=False,fill_value=numpy.max(row2))
return  f(interp)

f = UnivariateSpline(row1,row2,k=3,s=0)
return f(interp)

Could anyone offer any insight? My x vals aren't equally spaced, although I'm not sure why that would matter.

Answer 1

I just ran into the same issue.

Short answer

Use InterpolatedUnivariateSpline instead:

f = InterpolatedUnivariateSpline(row1, row2)
return f(interp)

Long answer

UnivariateSpline is a 'one-dimensional smoothing spline fit to a given set of data points' whereas InterpolatedUnivariateSpline is a 'one-dimensional interpolating spline for a given set of data points'. The former smoothes the data whereas the latter is a more conventional interpolation method and reproduces the results expected from interp1d. The figure below illustrates the difference.

The code to reproduce the figure is shown below.

import scipy.interpolate as ip

#Define independent variable
sparse = linspace(0, 2 * pi, num = 20)
dense = linspace(0, 2 * pi, num = 200)

#Define function and calculate dependent variable
f = lambda x: sin(x) + 2
fsparse = f(sparse)
fdense = f(dense)

ax = subplot(2, 1, 1)

#Plot the sparse samples and the true function
plot(sparse, fsparse, label = 'Sparse samples', linestyle = 'None', marker = 'o')
plot(dense, fdense, label = 'True function')

#Plot the different interpolation results
interpolate = ip.InterpolatedUnivariateSpline(sparse, fsparse)
plot(dense, interpolate(dense), label = 'InterpolatedUnivariateSpline', linewidth = 2)

smoothing = ip.UnivariateSpline(sparse, fsparse)
plot(dense, smoothing(dense), label = 'UnivariateSpline', color = 'k', linewidth = 2)

ip1d = ip.interp1d(sparse, fsparse, kind = 'cubic')
plot(dense, ip1d(dense), label = 'interp1d')

ylim(.9, 3.3)

legend(loc = 'upper right', frameon = False)

ylabel('f(x)')

#Plot the fractional error
subplot(2, 1, 2, sharex = ax)

plot(dense, smoothing(dense) / fdense - 1, label = 'UnivariateSpline')
plot(dense, interpolate(dense) / fdense - 1, label = 'InterpolatedUnivariateSpline')
plot(dense, ip1d(dense) / fdense - 1, label = 'interp1d')

ylabel('Fractional error')
xlabel('x')
ylim(-.1,.15)

legend(loc = 'upper left', frameon = False)

tight_layout()