2.7.4.3. Smooth vs non-smooth

Draws a figure to explain smooth versus non smooth optimization.

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import numpy as np
import pylab as pl

x = np.linspace(-1.5, 1.5, 101)

# A smooth function
pl.figure(1, figsize=(3, 2.5))
pl.clf()

pl.plot(x, np.sqrt(.2 + x**2), linewidth=2)
pl.text(-1, 0, '$f$', size=20)

pl.ylim(ymin=-.2)
pl.axis('off')
pl.tight_layout()

# A non-smooth function
pl.figure(2, figsize=(3, 2.5))
pl.clf()
pl.plot(x, np.abs(x), linewidth=2)
pl.text(-1, 0, '$f$', size=20)

pl.ylim(ymin=-.2)
pl.axis('off')
pl.tight_layout()
pl.show()

Total running time of the script: ( 0 minutes 0.144 seconds)