View source on GitHub |
Computes Lambert W of z
element-wise.
tfp.substrates.jax.math.lambertw(
z, name=None
)
The Lambert W function is the inverse of z = u * exp(u)
, i. e., it is the
function that satisfies u = W(z) * exp(W(z))
. The solution cannot be
expressed as a composition of elementary functions and is thus part of the
special functions in mathematics. See
https://en.wikipedia.org/wiki/Lambert_W_function
In general it is a complex-valued function with multiple branches. The k=0
branch is known as the principal branch of the Lambert W function and is
implemented here. See also scipy.special.lambertw
.
This code returns only the real part of the image of the Lambert W function.
References
Corless, R.M., Gonnet, G.H., Hare, D.E.G. et al. On the LambertW function. Adv Comput Math 5, 329-359 (1996) doi:10.1007/BF02124750
Args | |
---|---|
z
|
A Tensor with type float32 or float64 .
|
name
|
A name for the operation (optional). |
Returns | |
---|---|
lambertw
|
The Lambert W function evaluated at z . A Tensor with same shape
and same dtype as z .
|