parameters: (logu, alpha=1., self_normalized=False, name=None)
docstring: The Amari-alpha Csiszar-function in log-space.
  
    A Csiszar-function is a member of,
  
    ```none
    F = { f:R_+ to R : f convex }.
    ```
  
    When `self_normalized = True`, the Amari-alpha Csiszar-function is:
  
    ```none
    f(u) = { -log(u) + (u - 1),     alpha = 0
           { u log(u) - (u - 1),    alpha = 1
           { [(u**alpha - 1) - alpha (u - 1)] / (alpha (alpha - 1)),    otherwise
    ```
  
    When `self_normalized = False` the `(u - 1)` terms are omitted.
  
    Warning: when `alpha != 0` and/or `self_normalized = True` this function makes
    non-log-space calculations and may therefore be numerically unstable for
    `|logu| >> 0`.
  
    For more information, see:
      A. Cichocki and S. Amari. "Families of Alpha-Beta-and GammaDivergences:
      Flexible and Robust Measures of Similarities." Entropy, vol. 12, no. 6, pp.
      1532-1568, 2010.
  
    Args:
      logu: Floating-type `Tensor` representing `log(u)` from above.
      alpha: Floating-type Python scalar. (See Mathematical Details for meaning.)
      self_normalized: Python `bool` indicating whether `f'(u=1)=0`. When
        `f'(u=1)=0` the implied Csiszar f-Divergence remains non-negative even
        when `p, q` are unnormalized measures.
      name: Python `str` name prefixed to Ops created by this function.
  
    Returns:
      amari_alpha_of_u: Floating-type `Tensor` of the Csiszar-function evaluated
        at `u = exp(logu)`.
  
    Raises:
      TypeError: if `alpha` is `None` or a `Tensor`.
      TypeError: if `self_normalized` is `None` or a `Tensor`.
docstring_summary: The Amari-alpha Csiszar-function in log-space.
docstring_tokens: The Amari - alpha Csiszar - function in log - space .
function: def amari_alpha(logu, alpha=1., self_normalized=False, name=None):
    """The Amari-alpha Csiszar-function in log-space.
  
    A Csiszar-function is a member of,
  
    ```none
    F = { f:R_+ to R : f convex }.
    ```
  
    When `self_normalized = True`, the Amari-alpha Csiszar-function is:
  
    ```none
    f(u) = { -log(u) + (u - 1),     alpha = 0
           { u log(u) - (u - 1),    alpha = 1
           { [(u**alpha - 1) - alpha (u - 1)] / (alpha (alpha - 1)),    otherwise
    ```
  
    When `self_normalized = False` the `(u - 1)` terms are omitted.
  
    Warning: when `alpha != 0` and/or `self_normalized = True` this function makes
    non-log-space calculations and may therefore be numerically unstable for
    `|logu| >> 0`.
  
    For more information, see:
      A. Cichocki and S. Amari. "Families of Alpha-Beta-and GammaDivergences:
      Flexible and Robust Measures of Similarities." Entropy, vol. 12, no. 6, pp.
      1532-1568, 2010.
  
    Args:
      logu: Floating-type `Tensor` representing `log(u)` from above.
      alpha: Floating-type Python scalar. (See Mathematical Details for meaning.)
      self_normalized: Python `bool` indicating whether `f'(u=1)=0`. When
        `f'(u=1)=0` the implied Csiszar f-Divergence remains non-negative even
        when `p, q` are unnormalized measures.
      name: Python `str` name prefixed to Ops created by this function.
  
    Returns:
      amari_alpha_of_u: Floating-type `Tensor` of the Csiszar-function evaluated
        at `u = exp(logu)`.
  
    Raises:
      TypeError: if `alpha` is `None` or a `Tensor`.
      TypeError: if `self_normalized` is `None` or a `Tensor`.
    """
    with ops.name_scope(name, "amari_alpha", [logu]):
      if alpha is None or contrib_framework.is_tensor(alpha):
        raise TypeError("`alpha` cannot be `None` or `Tensor` type.")
      if self_normalized is None or contrib_framework.is_tensor(self_normalized):
        raise TypeError("`self_normalized` cannot be `None` or `Tensor` type.")
  
      logu = ops.convert_to_tensor(logu, name="logu")
  
      if alpha == 0.:
        f = -logu
      elif alpha == 1.:
        f = math_ops.exp(logu) * logu
      else:
        f = math_ops.expm1(alpha * logu) / (alpha * (alpha - 1.))
  
      if not self_normalized:
        return f
  
      if alpha == 0.:
        return f + math_ops.expm1(logu)
      elif alpha == 1.:
        return f - math_ops.expm1(logu)
      else:
        return f - math_ops.expm1(logu) / (alpha - 1.)
function_tokens: def amari_alpha ( logu , alpha = 1. , self_normalized = False , name = None ) : with ops . name_scope ( name , "amari_alpha" , [ logu ] ) : if alpha is None or contrib_framework . is_tensor ( alpha ) : raise TypeError ( "`alpha` cannot be `None` or `Tensor` type." ) if self_normalized is None or contrib_framework . is_tensor ( self_normalized ) : raise TypeError ( "`self_normalized` cannot be `None` or `Tensor` type." ) logu = ops . convert_to_tensor ( logu , name = "logu" ) if alpha == 0. : f = - logu elif alpha == 1. : f = math_ops . exp ( logu ) * logu else : f = math_ops . expm1 ( alpha * logu ) / ( alpha * ( alpha - 1. ) ) if not self_normalized : return f if alpha == 0. : return f + math_ops . expm1 ( logu ) elif alpha == 1. : return f - math_ops . expm1 ( logu ) else : return f - math_ops . expm1 ( logu ) / ( alpha - 1. )