matplotlib example plot confidence ellipse (snippet)

Python matplotlib example 'plot confidence ellipse'

Functions in program:

• def confidence_ellipse(x, y, ax, n_std=3.0, facecolor='none', **kwargs):

Modules used in program:

• import matplotlib.transforms as transforms
• import matplotlib.pyplot as plt
• import numpy as np

python plot confidence ellipse

Python matplotlib example: plot confidence ellipse

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse
import matplotlib.transforms as transforms

def confidence_ellipse(x, y, ax, n_std=3.0, facecolor='none', **kwargs):
    """
    Create a plot of the covariance confidence ellipse of `x` and `y`

    See how and why this works: https://carstenschelp.github.io/2018/09/14/Plot_Confidence_Ellipse_001.html

    This function has made it into the matplotlib examples collection:
    https://matplotlib.org/devdocs/gallery/statistics/confidence_ellipse.html#sphx-glr-gallery-statistics-confidence-ellipse-py

    Or, once matplotlib 3.1 has been released:
    https://matplotlib.org/gallery/index.html#statistics

    I update this gist according to the version there, because thanks to the matplotlib community
    the code has improved quite a bit.

    Parameters
    ----------
    x, y : array_like, shape (n, )
        Input data.

    ax : matplotlib.axes.Axes
        The axes object to draw the ellipse into.

    n_std : float
        The number of standard deviations to determine the ellipse's radiuses.

    Returns
    -------
    matplotlib.patches.Ellipse

    Other parameters
    ----------------
    kwargs : `~matplotlib.patches.Patch` properties
    """
    if x.size != y.size:
        raise ValueError("x and y must be the same size")

    cov = np.cov(x, y)
    pearson = cov[0, 1]/np.sqrt(cov[0, 0] * cov[1, 1])
    # Using a special case to obtain the eigenvalues of this
    # two-dimensionl dataset.
    ell_radius_x = np.sqrt(1 + pearson)
    ell_radius_y = np.sqrt(1 - pearson)
    ellipse = Ellipse((0, 0),
        width=ell_radius_x * 2,
        height=ell_radius_y * 2,
        facecolor=facecolor,
        **kwargs)

    # Calculating the stdandard deviation of x from
    # the squareroot of the variance and multiplying
    # with the given number of standard deviations.
    scale_x = np.sqrt(cov[0, 0]) * n_std
    mean_x = np.mean(x)

    # calculating the stdandard deviation of y ...
    scale_y = np.sqrt(cov[1, 1]) * n_std
    mean_y = np.mean(y)

    transf = transforms.Affine2D() \
        .rotate_deg(45) \
        .scale(scale_x, scale_y) \
        .translate(mean_x, mean_y)

    ellipse.set_transform(transf + ax.transData)
    return ax.add_patch(ellipse)
    # render plot with "plt.show()".

Python links

• Learn Python: https://pythonbasics.org/
• Python Tutorial: https://pythonprogramminglanguage.com