Fix minor typing errors in maths/ (TheAlgorithms#8959)

* updating DIRECTORY.md

* types(maths): Fix pylance issues in maths

* reset(vsc): Reset settings changes

* Update maths/jaccard_similarity.py

Co-authored-by: Tianyi Zheng <[email protected]>

* revert(erosion_operation): Revert erosion_operation

* test(jaccard_similarity): Add doctest to test alternative_union

* types(newton_raphson): Add typehints to func bodies

---------

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <[email protected]>

Author: 3 people

digital_image_processing/morphological_operations/erosion_operation.py

@@ -21,6 +21,7 @@ def rgb2gray(rgb: np.array) -> np.array:
 def gray2binary(gray: np.array) -> np.array:
     """
     Return binary image from gray image
+
     >>> gray2binary(np.array([[127, 255, 0]]))
     array([[False,  True, False]])
     >>> gray2binary(np.array([[0]]))

digital_image_processing/rotation/rotation.py

@@ -10,12 +10,12 @@ def get_rotation(
 ) -> np.ndarray:
     """
     Get image rotation
-    :param img: np.array
+    :param img: np.ndarray
     :param pt1: 3x2 list
     :param pt2: 3x2 list
     :param rows: columns image shape
     :param cols: rows image shape
-    :return: np.array
+    :return: np.ndarray
     """
     matrix = cv2.getAffineTransform(pt1, pt2)
     return cv2.warpAffine(img, matrix, (rows, cols))

maths/average_median.py

@@ -19,7 +19,9 @@ def median(nums: list) -> int | float:
     Returns:
         Median.
     """
-    sorted_list = sorted(nums)
+    # The sorted function returns list[SupportsRichComparisonT@sorted]
+    # which does not support `+`
+    sorted_list: list[int] = sorted(nums)
     length = len(sorted_list)
     mid_index = length >> 1
     return (

maths/euler_modified.py

@@ -5,7 +5,7 @@
 
 def euler_modified(
     ode_func: Callable, y0: float, x0: float, step_size: float, x_end: float
-) -> np.array:
+) -> np.ndarray:
     """
     Calculate solution at each step to an ODE using Euler's Modified Method
     The Euler Method is straightforward to implement, but can't give accurate solutions.

maths/gaussian_error_linear_unit.py

@@ -13,7 +13,7 @@
 import numpy as np
 
 
-def sigmoid(vector: np.array) -> np.array:
+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).
@@ -25,7 +25,7 @@ def sigmoid(vector: np.array) -> np.array:
     return 1 / (1 + np.exp(-vector))
 
 
-def gaussian_error_linear_unit(vector: np.array) -> np.array:
+def gaussian_error_linear_unit(vector: np.ndarray) -> np.ndarray:
     """
     Implements the Gaussian Error Linear Unit (GELU) function
 

maths/jaccard_similarity.py

@@ -14,7 +14,11 @@
 """
 
 
-def jaccard_similarity(set_a, set_b, alternative_union=False):
+def jaccard_similarity(
+    set_a: set[str] | list[str] | tuple[str],
+    set_b: set[str] | list[str] | tuple[str],
+    alternative_union=False,
+):
     """
     Finds the jaccard similarity between two sets.
     Essentially, its intersection over union.
@@ -37,41 +41,52 @@ def jaccard_similarity(set_a, set_b, alternative_union=False):
     >>> set_b = {'c', 'd', 'e', 'f', 'h', 'i'}
     >>> jaccard_similarity(set_a, set_b)
     0.375
-
     >>> jaccard_similarity(set_a, set_a)
     1.0
-
     >>> jaccard_similarity(set_a, set_a, True)
     0.5
-
     >>> set_a = ['a', 'b', 'c', 'd', 'e']
     >>> set_b = ('c', 'd', 'e', 'f', 'h', 'i')
     >>> jaccard_similarity(set_a, set_b)
     0.375
+    >>> set_a = ('c', 'd', 'e', 'f', 'h', 'i')
+    >>> set_b = ['a', 'b', 'c', 'd', 'e']
+    >>> jaccard_similarity(set_a, set_b)
+    0.375
+    >>> set_a = ('c', 'd', 'e', 'f', 'h', 'i')
+    >>> set_b = ['a', 'b', 'c', 'd']
+    >>> jaccard_similarity(set_a, set_b, True)
+    0.2
+    >>> set_a = {'a', 'b'}
+    >>> set_b = ['c', 'd']
+    >>> jaccard_similarity(set_a, set_b)
+    Traceback (most recent call last):
+        ...
+    ValueError: Set a and b must either both be sets or be either a list or a tuple.
     """
 
     if isinstance(set_a, set) and isinstance(set_b, set):
-        intersection = len(set_a.intersection(set_b))
+        intersection_length = len(set_a.intersection(set_b))
 
         if alternative_union:
-            union = len(set_a) + len(set_b)
+            union_length = len(set_a) + len(set_b)
         else:
-            union = len(set_a.union(set_b))
+            union_length = len(set_a.union(set_b))
 
-        return intersection / union
+        return intersection_length / union_length
 
-    if isinstance(set_a, (list, tuple)) and isinstance(set_b, (list, tuple)):
+    elif isinstance(set_a, (list, tuple)) and isinstance(set_b, (list, tuple)):
         intersection = [element for element in set_a if element in set_b]
 
         if alternative_union:
-            union = len(set_a) + len(set_b)
-            return len(intersection) / union
+            return len(intersection) / (len(set_a) + len(set_b))
         else:
-            union = set_a + [element for element in set_b if element not in set_a]
+            # Cast set_a to list because tuples cannot be mutated
+            union = list(set_a) + [element for element in set_b if element not in set_a]
             return len(intersection) / len(union)
-
-        return len(intersection) / len(union)
-    return None
+    raise ValueError(
+        "Set a and b must either both be sets or be either a list or a tuple."
+    )
 
 
 if __name__ == "__main__":

maths/newton_raphson.py

@@ -1,24 +1,35 @@
 """
-    Author: P Shreyas Shetty
-    Implementation of Newton-Raphson method for solving equations of kind
-    f(x) = 0. It is an iterative method where solution is found by the expression
-        x[n+1] = x[n] + f(x[n])/f'(x[n])
-    If no solution exists, then either the solution will not be found when iteration
-    limit is reached or the gradient f'(x[n]) approaches zero. In both cases, exception
-    is raised. If iteration limit is reached, try increasing maxiter.
-    """
+Author: P Shreyas Shetty
+Implementation of Newton-Raphson method for solving equations of kind
+f(x) = 0. It is an iterative method where solution is found by the expression
+    x[n+1] = x[n] + f(x[n])/f'(x[n])
+If no solution exists, then either the solution will not be found when iteration
+limit is reached or the gradient f'(x[n]) approaches zero. In both cases, exception
+is raised. If iteration limit is reached, try increasing maxiter.
+"""
+
 import math as m
+from collections.abc import Callable
+
+DerivativeFunc = Callable[[float], float]
 
 
-def calc_derivative(f, a, h=0.001):
+def calc_derivative(f: DerivativeFunc, a: float, h: float = 0.001) -> float:
     """
     Calculates derivative at point a for function f using finite difference
     method
     """
     return (f(a + h) - f(a - h)) / (2 * h)
 
 
-def newton_raphson(f, x0=0, maxiter=100, step=0.0001, maxerror=1e-6, logsteps=False):
+def newton_raphson(
+    f: DerivativeFunc,
+    x0: float = 0,
+    maxiter: int = 100,
+    step: float = 0.0001,
+    maxerror: float = 1e-6,
+    logsteps: bool = False,
+) -> tuple[float, float, list[float]]:
     a = x0  # set the initial guess
     steps = [a]
     error = abs(f(a))
@@ -36,7 +47,7 @@ def newton_raphson(f, x0=0, maxiter=100, step=0.0001, maxerror=1e-6, logsteps=Fa
     if logsteps:
         # If logstep is true, then log intermediate steps
         return a, error, steps
-    return a, error
+    return a, error, []
 
 
 if __name__ == "__main__":

maths/qr_decomposition.py

@@ -1,7 +1,7 @@
 import numpy as np
 
 
-def qr_householder(a):
+def qr_householder(a: np.ndarray):
     """Return a QR-decomposition of the matrix A using Householder reflection.
 
     The QR-decomposition decomposes the matrix A of shape (m, n) into an

maths/sigmoid.py

@@ -11,7 +11,7 @@
 import numpy as np
 
 
-def sigmoid(vector: np.array) -> np.array:
+def sigmoid(vector: np.ndarray) -> np.ndarray:
     """
     Implements the sigmoid function
 

maths/tanh.py

@@ -12,12 +12,12 @@
 import numpy as np
 
 
-def tangent_hyperbolic(vector: np.array) -> np.array:
+def tangent_hyperbolic(vector: np.ndarray) -> np.ndarray:
     """
         Implements the tanh function
 
         Parameters:
-            vector: np.array
+            vector: np.ndarray
 
         Returns:
             tanh (np.array): The input numpy array after applying tanh.