Animating a dynamic random normal multivariate sampling with matplotlib example.

animation.py

import math
import numpy

from scipy.stats import chi2
from matplotlib import pyplot as plt
from matplotlib import animation
from matplotlib.patches import Ellipse


def cov_patch(centroid, cov, perc, alpha=0.5, color='b'):
    """Example from matplotlib mailing list :
    http://www.mail-archive.com/[email protected]/msg14153.html
    
    Combine with the computation of contours from :
    http://jtemplin.coe.uga.edu/files/multivariate/mv11icpsr/mv11icpsr_lecture04.pdf
    http://courses.education.illinois.edu/EdPsy584/lectures/MultivariateNormal-online.pdf
    """
    c = chi2.isf(1 - perc, 2)
    U, s, _ = numpy.linalg.svd(cov)

    width = 2.0 * math.sqrt(s[0] * c)
    height = 2.0 * math.sqrt(s[1] * c)
    orient = math.atan2(U[1][0], U[0][0]) * 180 / math.pi

    return Ellipse(xy=centroid, width=width, height=height, angle=orient, alpha=alpha, color=color, zorder=10)


N_ITER = 50
def scatter_animation():
    fig = plt.figure()
    ax = plt.subplot(111)

    # Create dummy data
    centroids = [numpy.zeros(2) + numpy.ones(2) * i for i in range(N_ITER)]
    covs = [numpy.eye(2) * 4] * N_ITER
    points_array = [numpy.random.multivariate_normal(centroids[i], covs[i], 100)
                    for i in range(N_ITER)]

    # Update plot limits based on the data
    x_min, y_min = numpy.min(numpy.min(points_array, axis=1), axis=0)
    x_max, y_max = numpy.max(numpy.max(points_array, axis=1), axis=0)
    ax.set_xlim(x_min, x_max)
    ax.set_ylim(y_min, y_max)

    # Initial scatter that will be modified
    points_scatter = ax.scatter(None, None, s=2, zorder=0)

    def animate(i):
        # Update scatter plot
        points_scatter.set_offsets(points_array[i])

        # Create new patches as they cannot be updated simply
        del ax.patches[:]
        ax.add_patch(cov_patch(centroids[i], covs[i], 0.8))

    anim = animation.FuncAnimation(fig, animate,
                                   frames=len(points_array),
                                   interval=100, # Time per frame in ms
                                   blit=False # Required with Mac OS X backend
                                   )
    anim.save("{prefix}.mp4".format(prefix="test"), dpi=90,
              extra_args=['-vcodec', 'libx264', '-pix_fmt', 'yuv420p'])

    # To show the final result in loop
    plt.show()

if __name__ == "__main__":
    scatter_animation()