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Shamrock math derivatives functions#
This example shows how to use Shamrock math derivatives functions
10 from math import *
11
12 import matplotlib.pyplot as plt
13 import numpy as np
14
15 from shamrock.math import *
Compute the error associated to a derivative function
22 def err_plot(deriv_func, x, f, df, label):
23 h = np.logspace(-16, 0, 100)
24 err = []
25
26 for i in range(len(h)):
27 _err = deriv_func(x, h[i], f) - df(x)
28 err.append(fabs(_err))
29 plt.plot(h, err, "o", label=label)
30
31
32 def analysis(f, df, x0, label):
33 plt.figure()
34
35 # fmt: off
36 err_plot(deriv_func=derivative_upwind, x=x0, f=f, df=df, label="derivative_upwind")
37 err_plot(deriv_func=derivative_centered, x=x0, f=f, df=df, label="derivative_centered")
38 err_plot(deriv_func=derivative_3point_forward, x=x0, f=f, df=df, label="derivative_3point_forward")
39 err_plot(deriv_func=derivative_3point_backward, x=x0, f=f, df=df, label="derivative_3point_backward")
40 err_plot(deriv_func=derivative_5point_midpoint, x=x0, f=f, df=df, label="derivative_5point_midpoint")
41 # fmt: on
42
43 plt.xscale("log")
44 plt.yscale("log")
45
46 ymin, ymax = plt.gca().get_ylim()
47 plt.ylim(ymin, ymax)
48
49 for i in range(1, 4):
50 print(i, estim_deriv_step(i))
51 plt.vlines(estim_deriv_step(i), 1e-50, 1e50, color="grey", alpha=0.3)
52
53 plt.xlabel("h")
54 plt.ylabel("error")
55 plt.title(label)
56 plt.legend()
Exemple of analysis
63 def f1(x):
64 return exp(x)
65
66
67 def df1(x):
68 return exp(x)
69
70
71 analysis(f1, df1, 0, "exp(0)")
72 analysis(f1, df1, 100, "exp(100)")
73
74
75 def f2(x):
76 return sin(x**2)
77
78
79 def df2(x):
80 return cos(x**2) * 2 * x
81
82
83 analysis(f2, df2, 0, "sin(0)")
84 analysis(f2, df2, 100, "sin(100)")
85
86 plt.show()
1 1.4901161193847656e-08
2 6.055454452393344e-06
3 0.0001220703125
1 1.4901161193847656e-08
2 6.055454452393344e-06
3 0.0001220703125
1 1.4901161193847656e-08
2 6.055454452393344e-06
3 0.0001220703125
1 1.4901161193847656e-08
2 6.055454452393344e-06
3 0.0001220703125
Total running time of the script: (0 minutes 0.894 seconds)
Estimated memory usage: 63 MB