In [2]:
%matplotlib inline
import matplotlib.pyplot as plt
import matplotlib.cm as cmaps
import numpy as np
In [3]:
a = np.linspace(0,1,100)

Subtractive inhibition¶

$O = E - k$

In [6]:
f,ax = plt.subplots()
print (plt.get_cmap().name)

plt.register_cmap(name='viridis', cmap=cmaps.viridis)
plt.set_cmap(cmaps.viridis)

plt.set_cmap("gray")
print (plt.get_cmap().name)
ax.plot(a, a)
ax.plot(a, a - 0.2, '--', label="$O = E - 0.2$")
ax.plot(a, a - 0.4, '--', label="$O = E - 0.4$")
ax.plot(a, a - 0.6, '--', label="$O = E - 0.6$")
ax.plot(a, a - 0.8, '--', label="$O = E - 0.8$")
ax.set_xlabel("E")
ax.set_ylabel("O")
ax.set_ylim(ymin=0)
ax.set_xlim(xmin=0)
ax.set_title("Subtractive Inhibition")
ax.legend()
f.show()

viridis
gray

/usr/local/lib/python2.7/dist-packages/matplotlib/figure.py:402: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
  "matplotlib is currently using a non-GUI backend, "

Divisive inhibition¶

$O = E - k \times E$

In [7]:
f,ax = plt.subplots()
ax.plot(a, a)
ax.plot(a, a*0.8, '--', label="$O = E - E \\times 0.2$")
ax.plot(a, a*0.6, '--', label="$O = E - E \\times 0.4$")
ax.plot(a, a*0.4, '--', label="$O = E - E \\times 0.6$")
ax.plot(a, a*0.2, '--', label="$O = E - E \\times 0.8$")
ax.set_xlabel("E")
ax.set_ylabel("O")
ax.legend()
ax.set_title("Divisive Inhibition")
f.show()

Divisive normalization¶

$O = E - \frac{E}{E+(l/k)}*E$

In [8]:
f,ax = plt.subplots()
ax.plot(a, a)
#ax.plot(a, 0.8*a/(a+0.2), '--')
ax.plot(a, 0.4*a/(0.8*a+0.4), '--', label="$O = E - \\frac{0.8.E}{0.8.E+0.4}*E$")
ax.plot(a, 0.6*a/(0.8*a+0.6), '--', label="$O = E - \\frac{0.8.E}{0.8.E+0.6}*E$")
ax.plot(a, 0.4*a/(0.2*a+0.4), '--', label="$O = E - \\frac{0.2.E}{0.2.E+0.4}*E$")
ax.plot(a, 0.6*a/(0.2*a+0.6), '--', label="$O = E - \\frac{0.2.E}{0.2.E+0.6}*E$")
ax.set_xlabel("E")
ax.set_ylabel("O")
ax.legend()
ax.set_title("Divisive Normalization")
f.show()
In [8]:
f,ax = plt.subplots()
ax.plot(a, a)
#ax.plot(a, 0.8*a/(a+0.2), '--')
ax.plot(a, 0.4*a/(0.8*a+0.4), '--', label="$O = E - \\frac{0.8.E}{0.8.E+0.4}*E$")
ax.plot(a, 0.6*a/(0.8*a+0.6), '--', label="$O = E - \\frac{0.8.E}{0.8.E+0.6}*E$")
ax.plot(a, 0.4*a/(0.2*a+0.4), '--', label="$O = E - \\frac{0.2.E}{0.2.E+0.4}*E$")
ax.plot(a, 0.6*a/(0.2*a+0.6), '--', label="$O = E - \\frac{0.2.E}{0.2.E+0.6}*E$")
ax.set_xlabel("E")
ax.set_ylabel("O")
ax.legend()
ax.set_title("Divisive Normalization")
f.show()