tfp.math.round_exponential_bump_function

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Function supported on [-1, 1], smooth on the real line, with a round top.

tfp.math.round_exponential_bump_function(
    x, name=None
)

Define

f(x) := exp(-1 / (1 - x**2)) * exp(1), for x in (-1, 1)
f(x) := 0, for |x| >= 1.

One can show that f(x)...

• is C^\infty on the real line.
• is supported on [-1, 1].
• is equal to 1 at x = 0.
• is strictly increasing on (-1, 0).
• is strictly decreasing on (0, 1).
• has gradient = 0 at 0.

See Bump Function