Add Soboleva Modified Hyberbolic Tangent function (#10043)

* Add Sobovela Modified Hyberbolic Tangent function

* fix: typo

* Update and rename sobovela_modified_hyperbolic_tangent.py to soboleva_modified_hyperbolic_tangent.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* fix: typo

* Apply suggestions from code review

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

Author: 3 people

neural_network/activation_functions/soboleva_modified_hyperbolic_tangent.py

@@ -0,0 +1,49 @@
+"""
+This script implements the Soboleva Modified Hyperbolic Tangent function.
+
+The function applies the Soboleva Modified Hyperbolic Tangent function
+to each element of the vector.
+
+More details about the activation function can be found on:
+https://en.wikipedia.org/wiki/Soboleva_modified_hyperbolic_tangent
+"""
+
+
+import numpy as np
+
+
+def soboleva_modified_hyperbolic_tangent(
+    vector: np.ndarray, a_value: float, b_value: float, c_value: float, d_value: float
+) -> np.ndarray:
+    """
+    Implements the Soboleva Modified Hyperbolic Tangent function
+
+    Parameters:
+        vector (ndarray): A vector that consists of numeric values
+        a_value (float): parameter a of the equation
+        b_value (float): parameter b of the equation
+        c_value (float): parameter c of the equation
+        d_value (float): parameter d of the equation
+
+    Returns:
+        vector (ndarray): Input array after applying SMHT function
+
+    >>> vector = np.array([5.4, -2.4, 6.3, -5.23, 3.27, 0.56])
+    >>> soboleva_modified_hyperbolic_tangent(vector, 0.2, 0.4, 0.6, 0.8)
+    array([ 0.11075085, -0.28236685,  0.07861169, -0.1180085 ,  0.22999056,
+            0.1566043 ])
+    """
+
+    # Separate the numerator and denominator for simplicity
+    # Calculate the numerator and denominator element-wise
+    numerator = np.exp(a_value * vector) - np.exp(-b_value * vector)
+    denominator = np.exp(c_value * vector) + np.exp(-d_value * vector)
+
+    # Calculate and return the final result element-wise
+    return numerator / denominator
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()