1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
|
from __future__ import print_function
import numpy as np
def cshift(arr, offset):
return np.roll(arr, offset)
def deriv(x, y):
if len(x.shape) != 1 or x.shape[0] != y.shape[0]:
raise TypeError("deriv: x and y must be 1D numpy arrays of the same length")
x0 = cshift(x, 1)
x2 = cshift(x, -1)
x01 = x0 - x
x02 = x0 - x2
x12 = x - x2
d = cshift(y, 1) * (x12 / (x01 * x02)) + \
y * (1.0/x12 - 1.0/x01) - \
cshift(y, -1) * (x01 / (x02 * x12))
d[0] = y[0] * (x01[1]+x02[1])/(x01[1]*x02[1]) - \
y[1] * x02[1]/(x01[1]*x12[1]) + \
y[2] * x01[1]/(x02[1]*x12[1])
d[-1] = -y[-3] * x12[-2]/(x01[-2]*x02[-2]) + \
y[-2] * x02[-2]/(x01[-2]*x12[-2]) - \
y[-1] * (x02[-2]+x12[-2]) / (x02[-2]*x12[-2])
return d
if __name__ == "__main__":
x = np.linspace(0.0, 10.0, 1001, dtype=np.float64)
y = np.sin(x)
dy = deriv(x, y)
print("max diff {}".format(np.max(np.abs(dy - np.cos(x)))))
|
