maths.weddles_rule

Functions

apply_weights(→ list[float])	Apply Weddle's rule weights to the values in the table.
compute_solution(→ float)	Compute the final solution using the weighted values and table.
compute_table(→ tuple[numpy.ndarray, float])	Compute the table of function values based on the limits and accuracy.
get_inputs(→ tuple[str, float, float])	Get user input for the function, lower limit, and upper limit.
safe_function_eval(→ collections.abc.Callable)	Safely evaluates the function by substituting x value using sympy.

Module Contents

maths.weddles_rule.apply_weights(table: list[float]) → list[float]

Apply Weddle’s rule weights to the values in the table.

Args:

table (List[float]): A list of computed function values.

Returns:

List[float]: A list of weighted values.

Example:

>>> apply_weights([0.0, 0.866, 1.0, 0.866, 0.0, -0.866, -1.0])
[4.33, 1.0, 5.196, 0.0, -4.33]

maths.weddles_rule.compute_solution(add: list[float], table: list[float], step_size: float) → float

Compute the final solution using the weighted values and table.

Args:

add (List[float]): A list of weighted values from apply_weights. table (List[float]): A list of function values. step_size (float): The step size calculated from the limits and accuracy.

Returns:

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)
0.7853975

maths.weddles_rule.compute_table(func: collections.abc.Callable, lower_limit: float, upper_limit: float, acc: int) → tuple[numpy.ndarray, float]

Compute the table of function values based on the limits and accuracy.

Args:

func (Callable): The mathematical function as a callable. lower_limit (float): The lower limit of the integral. upper_limit (float): The upper limit of the integral. acc (int): The number of subdivisions for accuracy.

Returns:

Tuple[np.ndarray, float]: A tuple containing the table of values and the step size (h).

Example:

>>> 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)

maths.weddles_rule.get_inputs() → tuple[str, float, float]

Get user input for the function, lower limit, and upper limit.

Returns:

Tuple[str, float, float]: 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
>>> inputs = ['1/(1+x**2)', 1.0, -1.0]
>>> with patch('builtins.input', side_effect=inputs):
...     get_inputs()
('1/(1+x**2)', 1.0, -1.0)

maths.weddles_rule.safe_function_eval(func_str: str) → collections.abc.Callable

Safely evaluates the function by substituting x value using sympy.

Args:

func_str (str): Function expression as a string.

Returns:

Callable: A callable lambda function for numerical evaluation.

Examples:

>>> f = safe_function_eval('x**2')
>>> f(3)
9
>>> f = safe_function_eval('x + x**2')
>>> f(2)
6