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Author: Soham-KT

maths/weddles_rule.py

@@ -1,12 +1,14 @@
-from math import *
+import numpy as np
+from sympy import lambdify, symbols, sympify
 
 
 def get_inputs():
     """
     Get user input for the function, lower limit, and upper limit.
 
     Returns:
-        tuple: A tuple containing the function as a string, the lower limit (a), and the upper limit (b) as floats.
+        tuple: A tuple containing the function as a string, the lower limit (a),
+               and the upper limit (b) as floats.
 
     Example:
         >>> from unittest.mock import patch
@@ -21,6 +23,24 @@ def get_inputs():
     return func, a, b
 
 
+def safe_function_eval(func_str):
+    """
+    Safely evaluates the function by substituting x value using sympy.
+
+    Args:
+        func_str (str): Function expression as a string.
+
+    Returns:
+        float: The evaluated function result.
+    """
+    x = symbols('x')
+    func_expr = sympify(func_str)
+
+    # Convert the function to a callable lambda function
+    lambda_func = lambdify(x, func_expr, modules=["numpy"])
+    return lambda_func
+
+
 def compute_table(func, a, b, acc):
     """
     Compute the table of function values based on the limits and accuracy.
@@ -35,14 +55,19 @@ def compute_table(func, a, b, acc):
         tuple: A tuple containing the table of values and the step size (h).
 
     Example:
-        >>> compute_table('1/(1+x**2)', 1, -1, 1)
-        ([0.5, 0.4235294117647058, 0.36, 0.3076923076923077, 0.26470588235294124, 0.22929936305732482, 0.2], -0.3333333333333333)
+        >>> compute_table(
+        ...     safe_function_eval('1/(1+x**2)'), 1, -1, 1
+        ... )
+        (array([0.5       , 0.69230769, 0.9       , 1.        , 0.9       ,
+               0.69230769, 0.5       ]), -0.3333333333333333)
     """
-    h = (b - a) / (acc * 6)
-    table = [0 for _ in range(acc * 6 + 1)]
-    for j in range(acc * 6 + 1):
-        x = a + j / (acc * 6)
-        table[j] = eval(func)
+    # Weddle's rule requires number of intervals as a multiple of 6 for accuracy
+    n_points = acc * 6 + 1
+    h = (b - a) / (n_points - 1)
+    x_vals = np.linspace(a, b, n_points)
+
+    # Evaluate function values at all points
+    table = func(x_vals)
     return table, h
 
 
@@ -86,25 +111,25 @@ def compute_solution(add, table, h):
         float: The final computed integral solution.
 
     Example:
-        >>> compute_solution([4.33, 6.0, 0.0, -4.33], [0.0, 0.866, 1.0, 0.866, 0.0, -0.866, -1.0], 0.5235983333333333)
+        >>> compute_solution([4.33, 6.0, 0.0, -4.33], [0.0, 0.866, 1.0, 0.866, 0.0,
+        ... -0.866, -1.0], 0.5235983333333333)
         0.7853975
     """
     return 0.3 * h * (sum(add) + table[0] + table[-1])
 
 
 if __name__ == "__main__":
     from doctest import testmod
-
     testmod()
-
+    
     func, a, b = get_inputs()
     acc = 1
     solution = None
 
-    while acc <= 100000:
+    while acc <= 100_000:
         table, h = compute_table(func, a, b, acc)
         add = apply_weights(table)
         solution = compute_solution(add, table, h)
         acc *= 10
 
-    print(f"Solution: {solution}")
+    print(f'Solution: {solution}')