def softmax(a, b, alpha=1, normalize=0):
"""The softmaximum of softmax(a,b) = log(e^a + a^b).
normalize should be zero if a or b could be negative and can be 1.0 (more accurate)
if a and b are strictly positive.
Also called \alpha-quasimax:
J. Cook. Basic properties of the soft maximum.
Working Paper Series 70, UT MD Anderson CancerCenter Department of Biostatistics,
2011. http://biostats.bepress.com/mdandersonbiostat/paper7
"""
return np.log(np.exp(a * alpha) + np.exp(b * alpha) - normalize) / alpha
def softmax_smooth(a, b, smooth=0):
"""The smoothed softmaximum of softmax(a,b) = log(e^a + a^b).
With smooth=0.0, is softmax; with smooth=1.0, averages a and b"""
t = smooth / 2.0
return np.log(np.exp((1 - t) * a + b * t) +
np.exp((1 - t) * b + t * a)) - np.log(1 + smooth)
def softmax(a, b, alpha=1, normalize=0):
"""The softmaximum of softmax(a,b) = log(e^a + a^b).
normalize should be zero if a or b could be negative and can be 1.0 (more accurate)
if a and b are strictly positive.
"""
return np.log(np.exp(a * alpha) + np.exp(b * alpha) - normalize) / alpha
