#### Gaussian Error Linear Unit

p
```"""
This script demonstrates an implementation of the Gaussian Error Linear Unit function.
* https://en.wikipedia.org/wiki/Activation_function#Comparison_of_activation_functions

The function takes a vector of K real numbers as input and returns x * sigmoid(1.702*x).
Gaussian Error Linear Unit (GELU) is a high-performing neural network activation
function.

This script is inspired by a corresponding research paper.
* https://arxiv.org/abs/1606.08415
"""

import numpy as np

def sigmoid(vector: np.ndarray) -> np.ndarray:
"""
Mathematical function sigmoid takes a vector x of K real numbers as input and
returns 1/ (1 + e^-x).
https://en.wikipedia.org/wiki/Sigmoid_function

>>> sigmoid(np.array([-1.0, 1.0, 2.0]))
array([0.26894142, 0.73105858, 0.88079708])
"""
return 1 / (1 + np.exp(-vector))

def gaussian_error_linear_unit(vector: np.ndarray) -> np.ndarray:
"""
Implements the Gaussian Error Linear Unit (GELU) function

Parameters:
vector (np.ndarray): A  numpy array of shape (1, n) consisting of real values

Returns:
gelu_vec (np.ndarray): The input numpy array, after applying gelu

Examples:
>>> gaussian_error_linear_unit(np.array([-1.0, 1.0, 2.0]))
array([-0.15420423,  0.84579577,  1.93565862])

>>> gaussian_error_linear_unit(np.array([-3]))
array([-0.01807131])
"""
return vector * sigmoid(1.702 * vector)

if __name__ == "__main__":
import doctest

doctest.testmod()
```