import tensorflow as tf
from quant_analytics_flow.analytics import constants
[docs]def phi_smooth(x,y):
return (x + y + constants.DELTA + (x - y) ** 2 / constants.DELTA / 4.)/2.
[docs]def max_if(x,y):
return tf.where(tf.abs(x-y)>constants.BOUNDARY,tf.maximum(x,y),phi_smooth(x,y))
[docs]def hyperbolic(x):
""" Using the hyperbolic function
.. _target hyperbolic_function:
.. math::
f(x) = \\frac{1}{2} \\left(x + \sqrt{1 + x^2} \\right)
Args:
x (tensor(shape=(...))): M-dimensional tensor
Returns:
y (tensor(shape=(...))): Hyperbolic function
"""
return (x + tf.sqrt(1. + x*x))/2.
[docs]def soft_max_hypterbolic(x,eps=constants.EPSILON):
""" Using the :ref:`hyperbolic function <target hyperbolic_function>` to approximate :math:`\max(x,0)`
.. _target soft_max_hyperbolic:
.. math::
g_(x) = f(x/\\epsilon)\cdot \\epsilon
Args:
x (tensor(shape=(...))): M-dimensional tensor
eps (float64): scaling parameter
Returns:
y (tensor(shape=(...))): Hyperbolic function
"""
return hyperbolic(x/eps)*eps