test_findiff.py

import numpy as np
from findiff import FinDiff
import matplotlib.pyplot as plt
import findiff
print(findiff.__version__)

def f(x):
    return x * np.exp(-x**2)

def df_dx(x):
    return np.exp(-x**2) - 2*x**2*np.exp(-x**2)

def df_dx_2(x):
    return 2*np.exp(-x**2)*x*(-3 + 2*x**2)

x_fine = np.linspace(0, 10, 200)
f_fine = f(x_fine)

# plt.plot(x_fine, f_fine)
# plt.xlabel("x")
# plt.ylabel("f")
# plt.show(block=False)

x1 = np.linspace(0, 10, 20)
x2 = np.linspace(0, 10, 100)
f1 = f(x1)
f2 = f(x2)

# fig = plt.figure(figsize=(16,4))
# ax1 = fig.add_subplot(121)
# ax2 = fig.add_subplot(122)

# ax1.plot(x_fine, f_fine)
# ax2.plot(x_fine, f_fine)
# ax1.plot(x1, f1, 'o')
# ax2.plot(x2, f2, 'o')
# plt.show(block=False)

dx1 = x1[1] - x1[0]
dx2 = x2[1] - x2[0]

d_dx1 = FinDiff(0, dx1, acc=2)
d_dx2 = FinDiff(0, dx2)

df_dx1 = d_dx1(f1)
df_dx2 = d_dx2(f2)
df_dx_exact = df_dx(x_fine)
df_dx2_exact = df_dx_2(x_fine)

# fig = plt.figure(figsize=(16,4))
# ax1 = fig.add_subplot(121)
# ax2 = fig.add_subplot(122)

# ax1.plot(x_fine, df_dx_exact)
# ax2.plot(x_fine, df_dx_exact)
# ax1.plot(x1, df_dx1, 'o')
# ax2.plot(x2, df_dx2, 'o')
# plt.show(block=False)

x_nu = np.r_[np.linspace(0, 0.5, 3, endpoint=False), np.linspace(0.5, 1.2, 7, endpoint=False),
             np.linspace(1.2, 1.9, 2, endpoint=False), np.linspace(1.9, 2.9, 5, endpoint=False),
             np.linspace(2.9, 10, 3)]
f_nu = f(x_nu)
# plt.figure()
# plt.plot(x_fine, f_fine)
# plt.plot(x_nu, f_nu, 'o')
# plt.show(block=False)

d_dx = FinDiff(0, 10**10, 1, coords=[x_nu], acc=2)
df_dx_nu = d_dx(f_nu)

# plt.figure()
# plt.plot(x_fine, df_dx_exact)
# plt.plot(x_nu, df_dx_nu, 'o')
# plt.show(block=False)

d_dx2 = FinDiff(0, 10**10, 2, coords=[x_nu], acc=2)
df_dx2_nu = d_dx2(f_nu)

# plt.figure()
# plt.plot(x_fine, df_dx2_exact)
# plt.plot(x_nu, df_dx2_nu, 'o')
# plt.show(block=True)

fig = plt.figure(figsize=(10,4))
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122)
ax1.plot(x_fine, df_dx_exact)
ax1.plot(x_nu, df_dx_nu, 'o')
ax2.plot(x_fine, df_dx2_exact)
ax2.plot(x_nu, df_dx2_nu, 'o')
plt.show()