# Import of packages: import matplotlib.pyplot as plt import numpy as np # Functions calculating alternative numerical derivatives: def fun_f(x): f = x**3 + 1 return f # Generating x and y: x_start = 0 x_stop = 1 dx = 0.1 N = int((x_stop - x_start)/dx + 1) # Number of samples x_array = np.linspace(x_start, x_stop, N) # Not included if y is an existing data series: y_array = fun_f(x_array) # Preallocation of arrays: # np.nan (not-a-number) makes plotting code simpler. dy_dx_backward_array = np.zeros(N) + np.nan # Calculation of the derivative in a for loop: for k in range(1, N): dy_dx_backward_array[k] = (y_array[k] - y_array[k-1])/dx # Continuous dy_dx for comparison with backward dy_dx: dy_dx_cont_array = 3*x_array**2 x_cont_start = 0 x_cont_stop = 1 dx_cont = 0.001 N_cont = int((x_stop - x_start)/dx_cont + 1) x_cont_array = np.linspace(x_start, x_stop, N_cont) y_cont_array = x_cont_array**3 + 1 dy_dx_cont_array = 3*x_cont_array**2 # Plotting: plt.close('all') # Closes all figures before plotting plt.figure(num=1, figsize=(24/2.54, 18/2.54)) # Inch plt.subplot(2, 1, 1) plt.plot(x_array, y_array, 'or', label='y') plt.plot(x_cont_array, y_cont_array, 'b-',label='y_cont') plt.legend() plt.grid(which='both', color='grey') plt.subplot(2, 1, 2) plt.plot(x_array, dy_dx_backward_array, 'or', label='dy_dx_backward') plt.plot(x_cont_array, dy_dx_cont_array, 'b-', label='dy_dx_cont') plt.legend() plt.grid(which='both', color='grey') plt.xlabel('x') # plt.savefig('num_diff_backward.pdf') # pdf plt.show()