diff --git a/digital_image_processing/morphological_operations/erosion_operation.py b/digital_image_processing/morphological_operations/erosion_operation.py
index c2cde2ea6990..c0e1ef847237 100644
--- a/digital_image_processing/morphological_operations/erosion_operation.py
+++ b/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]]))
diff --git a/digital_image_processing/rotation/rotation.py b/digital_image_processing/rotation/rotation.py
index 958d16fafb91..0f5e36ddd5be 100644
--- a/digital_image_processing/rotation/rotation.py
+++ b/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))
diff --git a/maths/average_median.py b/maths/average_median.py
index cd1ec1574893..f24e525736b3 100644
--- a/maths/average_median.py
+++ b/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 (
diff --git a/maths/euler_modified.py b/maths/euler_modified.py
index 14bddadf4c53..d02123e1e2fb 100644
--- a/maths/euler_modified.py
+++ b/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.
diff --git a/maths/gaussian_error_linear_unit.py b/maths/gaussian_error_linear_unit.py
index 7b5f875143b9..18384bb6c864 100644
--- a/maths/gaussian_error_linear_unit.py
+++ b/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
diff --git a/maths/jaccard_similarity.py b/maths/jaccard_similarity.py
index 32054414c0c2..6b6243458fa8 100644
--- a/maths/jaccard_similarity.py
+++ b/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__":
diff --git a/maths/newton_raphson.py b/maths/newton_raphson.py
index 2c9cd1de95b0..f6b227b5c9c1 100644
--- a/maths/newton_raphson.py
+++ b/maths/newton_raphson.py
@@ -1,16 +1,20 @@
"""
- 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
@@ -18,7 +22,14 @@ def calc_derivative(f, a, h=0.001):
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__":
diff --git a/maths/qr_decomposition.py b/maths/qr_decomposition.py
index a8414fbece87..670b49206aa7 100644
--- a/maths/qr_decomposition.py
+++ b/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
diff --git a/maths/sigmoid.py b/maths/sigmoid.py
index 147588e8871f..cb45bde2702c 100644
--- a/maths/sigmoid.py
+++ b/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
diff --git a/maths/tanh.py b/maths/tanh.py
index ddab3e1ab717..38a369d9118d 100644
--- a/maths/tanh.py
+++ b/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.