在 numpy 一维数组中查找拐点和固定点

Question

假设我有以下 numpy 数组：

import numpy as np
import matplotlib.pyplot as plt
x = np.array([11.53333333, 11.86666667, 11.1, 10.66666667, 11.2, 11.3,
              11.06666667, 12.06666667, 11.8, 13.03333333, 12.4,
              12.33333333, 12.53333333, 13.33333333, 12.43333333, 13., 13.2,
              13.76666667, 14.96666667, 19.16666667, 25.1, 32.,
              83.33333333, 103.76666667, 110.7, 118.63333333, 129.26666667,
              139.06666667, 150.3, 161.53333333, 171.16666667, 184.56666667,
              196.6, 210.26666667, 221.63333333, 231.3, 244.16666667,
              253.5, 254.66666667, 255., 255., 255., 255.,
              255., 255., 255., 255., 255., 255.,
              255., 255., 255., 255., 255., 255.,
              255., 255., 255., 255., 255.])

plt.plot(x)
plt.show()

这是绘制的输出：

如何轻松获得此图中的转折点？例如，第一个转折点在 x=20 处，另一个转折点在 x=37.

有没有可能把所有的转折点按降序排列，然后我就可以抓取最有特色的3个转折点？

更新： 我有兴趣获得 Inflection Points as well as the Stationary points。 numpy / scipy?

中有简单的解决方案吗

Answer 1

有很多可能的答案 -- 取决于您的实际需要。一种想法是通过采用移动平均线或样条曲线或其他方法来平滑数据，然后采用二阶导数并寻找何时改变符号。这会找到近似的 "inflection points" 或 "turning points"——从字面上看，它会在凹面发生变化时找到。

参见：

How to smooth a curve in the right way?
Derivative of an array in python?

Answer 2

我也在找这个答案。这是在 python:

中找到拐点的一种方法

How to find the inflection point in a noisy curve?

拐点为[x0,y0]

#!/usr/bin/env python2.7
# -*- coding: utf-8 -*-
import matplotlib.pyplot as plt
import numpy as np
from scipy.ndimage import gaussian_filter


def generate_fake_data():
    """Generate data that looks like an example given."""
    xs = np.arange(0, 25, 0.05)
    ys = - 20 * 1./(1 + np.exp(-(xs - 5.)/0.3))
    m = xs > 7.
    ys[m] = -20.*np.exp(-(xs - 7.)[m] / 5.)

    # add noise
    ys += np.random.normal(0, 0.2, xs.size)
    return xs, ys


def main():
    xs, ys = generate_fake_data()

    # smooth out noise
    smoothed = gaussian_filter(ys, 3.)

    # find the point where the signal goes above the background noise
    # level (assumed to be zero here).
    base = 0.
    std = (ys[xs < 3] - base).std()
    m = smoothed < (base - 3. * std)
    x0 = xs[m][0]
    y0 = ys[m][0]

    plt.plot(xs, ys, '.')
    plt.plot(xs, smoothed, '-')
    plt.plot(x0, y0, 'o')
    plt.show()


if __name__ == '__main__':
    main()

Example output of how to find inflection point in python

在 numpy 一维数组中查找拐点和固定点

Find Inflection and Stationary points in a numpy 1d-array

python

arrays

numpy