In [2]:

    

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


    

In [3]:

    

from astroML.plotting import setup_text_plots
setup_text_plots(fontsize=8, usetex=True)


    

In [4]:

    

np.random.seed(42)
r = 0.9


    

In [5]:

    

sigma1 = 0.25
sigma2 = 0.08
rotation = np.pi / 6
s = np.sin(rotation)
c = np.cos(rotation)

X = np.random.normal(0, [sigma1, sigma2], size=(100, 2)).T
R = np.array([[c, -s],
              [s, c]])
X = np.dot(R, X)


    

In [6]:

    

fig = plt.figure(figsize=(5, 5), facecolor='w')
ax = plt.axes((0, 0, 1, 1), xticks=[], yticks=[], frameon=False)


    

In [7]:

    

ax.annotate(r'$x$', (-r, 0), (r, 0),
            ha='center', va='center',
            arrowprops=dict(arrowstyle='<->', color='k', lw=1))
ax.annotate(r'$y$', (0, -r), (0, r),
            ha='center', va='center',
            arrowprops=dict(arrowstyle='<->', color='k', lw=1))


    

    
Out[7]:





<matplotlib.text.Annotation at 0x11a49c390>

In [8]:

    

ax.annotate(r'$x^\prime$', (-r * c, -r * s), (r * c, r * s),
            ha='center', va='center',
            arrowprops=dict(color='k', arrowstyle='<->', lw=1))
ax.annotate(r'$y^\prime$', (r * s, -r * c), (-r * s, r * c),
            ha='center', va='center',
            arrowprops=dict(color='k', arrowstyle='<->', lw=1))


    

    
Out[8]:





<matplotlib.text.Annotation at 0x11a49cf50>

In [9]:

    

ax.scatter(X[0], X[1], s=25, lw=0, c='k', zorder=2)


    

    
Out[9]:





<matplotlib.collections.PathCollection at 0x11a49c1d0>

In [10]:

    

vnorm = np.array([s, -c])
for v in (X.T):
    d = np.dot(v, vnorm)
    v1 = v - d * vnorm
    ax.plot([v[0], v1[0]], [v[1], v1[1]], '-k')


    

In [11]:

    

for sigma in (1, 2, 3):
    ax.add_patch(Ellipse((0, 0), 2 * sigma * sigma1, 2 * sigma * sigma2,
                         rotation * 180. / np.pi,
                         ec='k', fc='gray', alpha=0.2, zorder=1))


    

In [12]:

    

%matplotlib inline


    

In [13]:

    

ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)

plt.show()


    

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