Standard Deviations

This example is similar to the Matplotlib example Plot a confidence ellipse of a two-dimensional dataset. Ellipsoids represent boundaries for one, two and three standard deviations.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
import s3dlib.surface as s3d

#.. Confidence Ellipsoids

# 1. Define data to examine .........................................

N = 500
np.random.seed(0)

def get_correlated_dataset(n, dependency, mu, scale):
    latent = np.random.randn(n, 3)
    dependent = latent.dot(dependency)
    scaled = dependent * scale       
    scaled_with_offset = scaled + mu
    # return x y z of the new, correlated dataset
    return scaled_with_offset[:, 0], scaled_with_offset[:, 1], scaled_with_offset[:, 2]

corr = np.array([ [0.85, 0.35, 0.4], [0.15, -0.65, 0.6], [0.3, 0.7, 1.0] ])
mu = 1,2,3
sigma = .8,.5 , .7
x,y,z = get_correlated_dataset(N, corr, mu, sigma)
data = np.transpose([ x,y,z ])

# 2. Setup and map surfaces .........................................

confEllipsoid_1 = s3d.SphericalSurface(3, color='b', linewidth=0.05  )
confEllipsoid_1.map_geom_from_svd(data)
disArr = confEllipsoid_1.svd_dict['disarr']
trans = confEllipsoid_1.svd_dict['trans']
confEllipsoid_1.shade().set_facecolor([0,0,0,0])
confEllipsoid_2 = s3d.SphericalSurface(3, color='g', linewidth=0.05  )
trans2 = [trans[0], 2*trans[1], trans[2] ]
confEllipsoid_2.transform(*trans2)
confEllipsoid_2.shade().set_facecolor([0,0,0,0])
confEllipsoid_3 = s3d.SphericalSurface(3, color='r', linewidth=0.05  )
trans3 = [trans[0], 3*trans[1], trans[2] ]
confEllipsoid_3.transform(*trans3)
confEllipsoid_3.shade().set_facecolor([0,0,0,0])

colors_a = []
for val in disArr :
    color = [0,0,.5]
    if val>1. : color = [0.0,0.4,0.0]
    if val>2. : color = [0.6,0.0,0.0]
    if val>3. : color = [0.0,0.0,0.0]
    colors_a.append(color)

# 3. Construct figures, add surfaces, and plot .......................

fig = plt.figure(figsize=plt.figaspect(1))
ax = plt.axes(projection='3d', aspect='equal')
ax.set_title('N: '+str(N), fontsize='small')
ax.set(xlim=(-2,4), ylim=(-1,5), zlim=(0,6) )
s3d.setupAxis(ax, length=2, width=1, negaxis=False )
ax.set_xticks( [i for i in range(-2,5)])
ax.set_yticks( [i for i in range(-1,6)])
ax.set_zticks( [i for i in range( 0,7)])

ax.scatter(x,y,z, c=colors_a, marker='.', s=10)
ax.add_collection(confEllipsoid_1)
ax.add_collection(confEllipsoid_2)
ax.add_collection(confEllipsoid_3)

fig.tight_layout()
plt.show()