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

Question

Lets assume I have the following numpy array:

import numpy as np
import matplotlib.pyplot as plt
x = np.array([11.53333333, 11.86666667, 11.1, 10.66666667, 1         


        

Answer 1

There are many possible answers -- depending what you actually want. One idea would be to smooth the data by taking moving averages or splines or something and then take the second derivative and look for when it changes sign. This would find approximate "inflection points" or "turning points" -- literally, it would find when the concavity changes.

See:

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

Answer 2

I was looking for this answer too. This is one way how to find inflection point in python:

How to find the inflection point in a noisy curve?

The inflection point is [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