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# tfp.vi.dual_csiszar_function

Calculates the dual Csiszar-function in log-space.

A Csiszar-function is a member of,

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

The Csiszar-dual is defined as:

``````f^*(u) = u f(1 / u)
``````

where `f` is some other Csiszar-function.

For example, the dual of `kl_reverse` is `kl_forward`, i.e.,

``````f(u) = -log(u)
f^*(u) = u f(1 / u) = -u log(1 / u) = u log(u)
``````

The dual of the dual is the original function:

``````f^**(u) = {u f(1/u)}^*(u) = u (1/u) f(1/(1/u)) = f(u)
``````

`logu` `float`-like `Tensor` representing `log(u)` from above.
`csiszar_function` Python `callable` representing a Csiszar-function over log-domain.
`name` Python `str` name prefixed to Ops created by this function.

`dual_f_of_u` `float`-like `Tensor` of the result of calculating the dual of `f` at `u = exp(logu)`.

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