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# tfp.vi.log1p_abs

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)`.

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