yellowfin.py 文件源码

def get_cubic_root(self):
    # We have the equation x^2 D^2 + (1-x)^4 * C / h_min^2
    # where x = sqrt(mu).
    # We substitute x, which is sqrt(mu), with x = y + 1.
    # It gives y^3 + py = q
    # where p = (D^2 h_min^2)/(2*C) and q = -p.
    # We use the Vieta's substution to compute the root.
    # There is only one real solution y (which is in [0, 1] ).
    # http://mathworld.wolfram.com/VietasSubstitution.html
    # assert_array = \
    #   [tf.Assert(tf.logical_not(tf.is_nan(self._dist_to_opt_avg) ), [self._dist_to_opt_avg,]), 
    #   tf.Assert(tf.logical_not(tf.is_nan(self._h_min) ), [self._h_min,]), 
    #   tf.Assert(tf.logical_not(tf.is_nan(self._grad_var) ), [self._grad_var,]),
    #   tf.Assert(tf.logical_not(tf.is_inf(self._dist_to_opt_avg) ), [self._dist_to_opt_avg,]), 
    #   tf.Assert(tf.logical_not(tf.is_inf(self._h_min) ), [self._h_min,]), 
    #   tf.Assert(tf.logical_not(tf.is_inf(self._grad_var) ), [self._grad_var,])]
    # with tf.control_dependencies(assert_array):
    # EPS in the numerator to prevent momentum being exactly one in case of 0 gradient
    p = (self._dist_to_opt_avg + EPS)**2 * (self._h_min + EPS)**2 / 2 / (self._grad_var + EPS)
    w3 = (-tf.sqrt(p**2 + 4.0 / 27.0 * p**3) - p) / 2.0
    w = tf.sign(w3) * tf.pow(tf.abs(w3), 1.0/3.0)
    y = w - p / 3.0 / (w + EPS)
    x = y + 1
    return x