Added Leaky ReLU Activation Function (#8962)

* Added Leaky ReLU activation function

* Added Leaky ReLU activation function

* Added Leaky ReLU activation function

* Formatting and spelling fixes done

DIRECTORY.md

@@ -62,7 +62,7 @@
 ## Boolean Algebra
   * [And Gate](boolean_algebra/and_gate.py)
   * [Nand Gate](boolean_algebra/nand_gate.py)
-  * [Norgate](boolean_algebra/norgate.py)
+  * [Nor Gate](boolean_algebra/nor_gate.py)
   * [Not Gate](boolean_algebra/not_gate.py)
   * [Or Gate](boolean_algebra/or_gate.py)
   * [Quine Mc Cluskey](boolean_algebra/quine_mc_cluskey.py)

neural_network/activation_functions/leaky_rectified_linear_unit.py

@@ -0,0 +1,39 @@
+"""
+Leaky Rectified Linear Unit (Leaky ReLU)
+
+Use Case: Leaky ReLU addresses the problem of the vanishing gradient.
+For more detailed information, you can refer to the following link:
+https://en.wikipedia.org/wiki/Rectifier_(neural_networks)#Leaky_ReLU
+"""
+
+import numpy as np
+
+
+def leaky_rectified_linear_unit(vector: np.ndarray, alpha: float) -> np.ndarray:
+    """
+        Implements the LeakyReLU activation function.
+
+        Parameters:
+            vector (np.ndarray): The input array for LeakyReLU activation.
+            alpha (float): The slope for negative values.
+
+        Returns:
+            np.ndarray: The input array after applying the LeakyReLU activation.
+
+        Formula: f(x) = x if x > 0 else f(x) = alpha * x
+
+    Examples:
+    >>> leaky_rectified_linear_unit(vector=np.array([2.3,0.6,-2,-3.8]), alpha=0.3)
+    array([ 2.3 ,  0.6 , -0.6 , -1.14])
+
+    >>> leaky_rectified_linear_unit(np.array([-9.2, -0.3, 0.45, -4.56]), alpha=0.067)
+    array([-0.6164 , -0.0201 ,  0.45   , -0.30552])
+
+    """
+    return np.where(vector > 0, vector, alpha * vector)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()