Trying to understand scipy and numpy interpolation

Question

If I have some measured data whose function I don't know (let's say it's either not important, or computationally difficult), such as

x2 = [0, 1, 10, 25, 30]
y2 = [5, 12, 50, 73, 23]

and I use numpy.interp to find the intermediate values, it gives me a linear interpolant between the points and I get a straight line:

xinterp = np.arange(31)
yinterp1 = np.interp(xinterp, x2, y2)
plt.scatter(xinterp, yinterp1)
plt.plot(x2, y2, color = 'red', marker = '.')

The example from the scipy.interpolate docs gives

x = np.linspace(0, 10, num=11, endpoint=True)
y = np.cos(-x**2/9.0)
f = interp1d(x, y)
f2 = interp1d(x, y, kind='cubic')
xnew = np.linspace(0, 10, num=41, endpoint=True)
plt.plot(x, y, 'o', xnew, f(xnew), '-', xnew, f2(xnew), '--')
plt.legend(['data', 'linear', 'cubic'], loc='best')
plt.show()

with different kinds of interpolation for a smoother curve. But what if I want the points in a smooth curve, rather than just the curve? Is there a function in NumPy or SciPy that can give the discrete points along the smoothed curve?

Solution

You can generate the function points and reassign them to a variable similarly to when you generated them and plotted them:

y_lin = f(xnew)
y_cub = f2(xnew)

interp1d returns you a function that you can then use to generate the data which in turns can be reassigned to other variables and used any way you want. Both outputs plotted together:

plt.plot(x, y, 'o', xnew, f(xnew), xnew, y_lin, '-', xnew, f2(xnew), xnew, y_cub, '--')
plt.legend(['data', 'linear' ,'reassigned linear', 'cubic', 'reassigned cubic'], loc='best')
plt.show()