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127 lines
3.9 KiB
Python
127 lines
3.9 KiB
Python
"""
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Author : Syed Faizan ( 3rd Year IIIT Pune )
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Github : faizan2700
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Purpose : You have one function f(x) which takes float integer and returns
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float you have to integrate the function in limits a to b.
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The approximation proposed by Thomas Simpsons in 1743 is one way to calculate
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integration.
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( read article : https://cp-algorithms.com/num_methods/simpson-integration.html )
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simpson_integration() takes function,lower_limit=a,upper_limit=b,precision and
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returns the integration of function in given limit.
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"""
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# constants
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# the more the number of steps the more accurate
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N_STEPS = 1000
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def f(x: float) -> float:
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return x * x
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"""
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Summary of Simpson Approximation :
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By simpsons integration :
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1. integration of fxdx with limit a to b is =
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f(x0) + 4 * f(x1) + 2 * f(x2) + 4 * f(x3) + 2 * f(x4)..... + f(xn)
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where x0 = a
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xi = a + i * h
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xn = b
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"""
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def simpson_integration(function, a: float, b: float, precision: int = 4) -> float:
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"""
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Args:
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function : the function which's integration is desired
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a : the lower limit of integration
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b : upper limit of integraion
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precision : precision of the result,error required default is 4
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Returns:
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result : the value of the approximated integration of function in range a to b
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Raises:
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AssertionError: function is not callable
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AssertionError: a is not float or integer
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AssertionError: function should return float or integer
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AssertionError: b is not float or integer
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AssertionError: precision is not positive integer
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>>> simpson_integration(lambda x : x*x,1,2,3)
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2.333
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>>> simpson_integration(lambda x : x*x,'wrong_input',2,3)
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Traceback (most recent call last):
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...
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AssertionError: a should be float or integer your input : wrong_input
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>>> simpson_integration(lambda x : x*x,1,'wrong_input',3)
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Traceback (most recent call last):
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...
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AssertionError: b should be float or integer your input : wrong_input
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>>> simpson_integration(lambda x : x*x,1,2,'wrong_input')
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Traceback (most recent call last):
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...
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AssertionError: precision should be positive integer your input : wrong_input
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>>> simpson_integration('wrong_input',2,3,4)
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Traceback (most recent call last):
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...
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AssertionError: the function(object) passed should be callable your input : ...
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>>> simpson_integration(lambda x : x*x,3.45,3.2,1)
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-2.8
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>>> simpson_integration(lambda x : x*x,3.45,3.2,0)
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Traceback (most recent call last):
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...
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AssertionError: precision should be positive integer your input : 0
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>>> simpson_integration(lambda x : x*x,3.45,3.2,-1)
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Traceback (most recent call last):
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...
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AssertionError: precision should be positive integer your input : -1
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"""
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assert callable(
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function
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), f"the function(object) passed should be callable your input : {function}"
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assert isinstance(a, float) or isinstance(
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a, int
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), f"a should be float or integer your input : {a}"
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assert isinstance(function(a), float) or isinstance(function(a), int), (
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"the function should return integer or float return type of your function, "
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f"{type(a)}"
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)
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assert isinstance(b, float) or isinstance(
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b, int
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), f"b should be float or integer your input : {b}"
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assert (
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isinstance(precision, int) and precision > 0
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), f"precision should be positive integer your input : {precision}"
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# just applying the formula of simpson for approximate integraion written in
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# mentioned article in first comment of this file and above this function
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h = (b - a) / N_STEPS
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result = function(a) + function(b)
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for i in range(1, N_STEPS):
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a1 = a + h * i
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result += function(a1) * (4 if i % 2 else 2)
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result *= h / 3
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return round(result, precision)
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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