-
Notifications
You must be signed in to change notification settings - Fork 28
/
parabolic.py
57 lines (39 loc) · 1.61 KB
/
parabolic.py
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
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
# -*- coding: utf-8 -*-
from __future__ import division
import numpy as np
def parabolic(f, x):
"""Quadratic interpolation for estimating the true position of an
inter-sample maximum when nearby samples are known.
f is a vector and x is an index for that vector.
Returns (vx, vy), the coordinates of the vertex of a parabola that goes
through point x and its two neighbors.
Example:
Defining a vector f with a local maximum at index 3 (= 6), find local
maximum if points 2, 3, and 4 actually defined a parabola.
In [3]: f = [2, 3, 1, 6, 4, 2, 3, 1]
In [4]: parabolic(f, argmax(f))
Out[4]: (3.2142857142857144, 6.1607142857142856)
"""
xv = 1/2. * (f[x-1] - f[x+1]) / (f[x-1] - 2 * f[x] + f[x+1]) + x
yv = f[x] - 1/4. * (f[x-1] - f[x+1]) * (xv - x)
return (xv, yv)
def parabolic_polyfit(f, x, n):
"""Use the built-in polyfit() function to find the peak of a parabola
f is a vector and x is an index for that vector.
n is the number of samples of the curve used to fit the parabola.
"""
a, b, c = np.polyfit(arange(x-n//2, x+n//2+1), f[x-n//2:x+n//2+1], 2)
xv = -0.5 * b/a
yv = a * xv**2 + b * xv + c
return (xv, yv)
if __name__=="__main__":
from numpy import argmax
import matplotlib.pyplot as plt
y = [2, 1, 4, 8, 11, 10, 7, 3, 1, 1]
xm, ym = argmax(y), y[argmax(y)]
xp, yp = parabolic(y, argmax(y))
plot = plt.plot(y)
plt.hold(True)
plt.plot(xm, ym, 'o', color='silver')
plt.plot(xp, yp, 'o', color='blue')
plt.title('silver = max, blue = estimated max')