Spline Interpolation

import os
import matplotlib.pyplot as plt
import numpy as np
from scipy import interpolate
os.chdir(r'D:\data\scripts\web1\ex26')
os.getcwd()
def runge(x):
    return 1/(1 + 25 * x**2)

x = np.linspace(-1, 1, 11)
y = runge(x)
f = interpolate.interp1d(x, y, kind=3)
xx = np.linspace(-1, 1, 100)
fig, ax = plt.subplots(figsize=(8, 4))
ax.plot(xx, runge(xx), 'k', lw=1, label="Runge's function")
ax.plot(x, y, 'ro', label='sample points')
ax.plot(xx, f(xx), 'r--', lw=2, label='spline order 3')
ax.legend()
ax.set_ylim(0, 1.1)
ax.set_xticks([-1, -0.5, 0, 0.5, 1])
ax.set_ylabel(r"$y$", fontsize=18)
ax.set_xlabel(r"$x$", fontsize=18)
fig.tight_layout()
ax.set_title("Spline Interpolation")
fig.tight_layout()
plt.savefig("example26.png", dpi=100)
plt.show()
plt.close()

<img class="  wp-image-131 aligncenter" src="https://gantovnik.com/bio-tips/wp-content/uploads/2019/01/example26.png" alt="example26" width="626" height="313" />

import os

import matplotlib.pyplot as plt

import numpy as np

from scipy import interpolate

os.chdir(r'D:\data\scripts\web1\ex26')

os.getcwd()

def runge(x):

return 1/(1 + 25 * x**2)

x = np.linspace(-1, 1, 11)

y = runge(x)

f = interpolate.interp1d(x, y, kind=3)

xx = np.linspace(-1, 1, 100)

fig, ax = plt.subplots(figsize=(8, 4))

ax.plot(xx, runge(xx), 'k', lw=1, label="Runge's function")

ax.plot(x, y, 'ro', label='sample points')

ax.plot(xx, f(xx), 'r--', lw=2, label='spline order 3')

ax.legend()

ax.set_ylim(0, 1.1)

ax.set_xticks([-1, -0.5, 0, 0.5, 1])

ax.set_ylabel(r"$y$", fontsize=18)

ax.set_xlabel(r"$x$", fontsize=18)

fig.tight_layout()

ax.set_title("Spline Interpolation")

fig.tight_layout()

plt.savefig("example26.png", dpi=100)

plt.show()

plt.close()

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