ext
Behavior if x not in knot sequence (0 extrapolate, 1 return 0, 2 raise ValueError)
Applied to the current example, this translates into the following:
In [ 44 ]: ipo = spi.splrep(x, f(x), k= 1 )
In [ 45 ]: iy = spi.splev(x, ipo)
As Figure 9-11 shows, the interpolation already seems really good with linear splines (i.e.,
k=1):
In [ 46 ]: plt.plot(x, f(x), ‘b’, label=‘f(x)’)
plt.plot(x, iy, ‘r.’, label=‘interpolation’)
plt.legend(loc= 0 )
plt.grid(True)
plt.xlabel(‘x’)
plt.ylabel(‘f(x)’)
Figure 9-11. Example plot with linear interpolation
This can be confirmed numerically:
In [ 47 ]: np.allclose(f(x), iy)
Out[47]: True
Spline interpolation is often used in finance to generate estimates for dependent values of
independent data points not included in the original observations. To this end, let us pick a
much smaller interval and have a closer look at the interpolated values with the linear
splines:
In [ 48 ]: xd = np.linspace(1.0, 3.0, 50 )
iyd = spi.splev(xd, ipo)
Figure 9-12 reveals that the interpolation function indeed interpolates linearly between
two observation points. For certain applications this might not be precise enough. In
addition, it is evident that the function is not continuously differentiable at the original
data points — another drawback:
In [ 49 ]: plt.plot(xd, f(xd), ‘b’, label=‘f(x)’)
plt.plot(xd, iyd, ‘r.’, label=‘interpolation’)
plt.legend(loc= 0 )
plt.grid(True)
plt.xlabel(‘x’)
plt.ylabel(‘f(x)’)
