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Sigmoid Function

Implement the sigmoid (logistic) function that maps any real number to the range $(0, 1)$ .

$\sigma(z) = \frac{1}{1 + e^{-z}}$

Given a list of values, apply the sigmoid function to each and return the results.

To avoid overflow for large negative values, use the identity: for $z < 0$ , compute $\sigma(z) = \frac{e^z}{1 + e^z}$ .

Round each result to 4 decimal places.

Input:

z = [0, 2, -2]

Output:

[0.5, 0.8808, 0.1192]

Reasoning:

For each value $z$ in the input list, apply the sigmoid function: if $z \geq 0$ , compute $\sigma(z) = \frac{1}{1 + e^{-z}}$ , otherwise compute $\sigma(z) = \frac{e^z}{1 + e^z}$ to avoid overflow.
Calculate the sigmoid for each input value:
- For $z = 0$ , $\sigma(0) = \frac{1}{1 + e^{0}} = \frac{1}{1 + 1} = 0.5$
- For $z = 2$ , $\sigma(2) = \frac{1}{1 + e^{-2}} \approx 0.8808$
- For $z = -2$ , $\sigma(-2) = \frac{e^{-2}}{1 + e^{-2}} \approx 0.1192$
Round each result to 4 decimal places.
The final output is $[0.5, 0.8808, 0.1192]$

Editor

Python 3.13.1

0/0

Run code to see test results.

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