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The log1p-abs Csiszar-function in log-space.

A Csiszar-function is a member of,

F = { f:R_+ to R : f convex }.

The Log1p-Abs Csiszar-function is:

f(u) = u**(sign(u-1)) - 1

This function is so-named because it was invented from the following recipe. Choose a convex function g such that g(0)=0 and solve for f:

log(1 + f(u)) = g(log(u)).
f(u) = exp(g(log(u))) - 1

That is, the graph is identically g when y-axis is log1p-domain and x-axis is log-domain.


  • logu: float-like Tensor representing log(u) from above.
  • name: Python str name prefixed to Ops created by this function.


  • log1p_abs_of_u: float-like Tensor of the Csiszar-function evaluated at u = exp(logu).