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integral_calculator.py
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integral_calculator.py
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from math import sin, pi, exp
function = sin # (0, pi) 2
function1 = lambda x: x / (x ** 4 + 16) ** 0.5 # (0, 3**0.5) ~0,.35
function2 = lambda x: exp(1 / x) / x ** 2 # (1, 2) e - e ** 0.5
function3 = lambda x: exp(-x ** 2)
def rectangle_method(lower_bound:float, upper_bound:float,
interval_count: int, function):
if interval_count == 0:
return
if lower_bound > upper_bound:
lower_bound, upper_bound = upper_bound, lower_bound
result = 0
step = (upper_bound - lower_bound) / interval_count
while lower_bound < upper_bound:
result += function(lower_bound) * step
lower_bound += step
return result
def trapezium_method(lower_bound:float, upper_bound:float,
interval_count:int, function):
if interval_count == 0:
return
if lower_bound > upper_bound:
lower_bound, upper_bound = upper_bound, lower_bound
result = 0
step = (upper_bound - lower_bound) / interval_count
while lower_bound < upper_bound:
result += (function(lower_bound) + function(lower_bound + step))\
/ 2 * step
lower_bound += step
return result
def simpson_method(lower_bound:float, upper_bound:float,
interval_count:int, function):
if interval_count == 0:
return
if lower_bound > upper_bound:
lower_bound, upper_bound = upper_bound, lower_bound
result = 0
step = (upper_bound - lower_bound) / interval_count
while lower_bound < upper_bound:
result += step / 3 * (
function(lower_bound) +
4 * function(lower_bound + step) +
function(lower_bound + 2 * step)
)
lower_bound += 2 * step
return result
def floating_quad(lower_bound:float, upper_bound:float,
interval_count:int, function, precision:float=0.01):
if interval_count == 0:
return
if lower_bound >= upper_bound:
lower_bound, upper_bound = upper_bound, lower_bound
result = 0
step = (upper_bound - lower_bound) / interval_count
while lower_bound < upper_bound:
inner_step = step
delta = abs(function(lower_bound + inner_step) - function(lower_bound))
while delta > precision:
inner_step = delta / interval_count
delta = function(lower_bound + inner_step) - function(lower_bound)
inner_upper = lower_bound + step
while lower_bound < lower_bound + inner_step:
result += function(lower_bound) * inner_step
lower_bound += inner_step
return result
if __name__ == "__main__":
rm = rectangle_method(0, pi, 10000, function)
tm = trapezium_method(0, pi, 10000, function)
sm = simpson_method(0, pi, 10000, function)
#fm = floating_quad(0, pi, 10000, function, precision=1e-3)
print(f"Rectangle method: {rm}, delta: {abs(2 - rm)}")
print(f"Trapezium method: {tm}, delta: {abs(2 - tm)}")
print(f"Simpson method: {sm}, delta: {abs(2 - sm)}")
print()
#print(f"Floating quad: {fm}, delta: {abs(2 - fm)}")
rm = rectangle_method(0, 3 ** 0.5, 10000, function1)
tm = trapezium_method(0, 3 ** 0.5, 10000, function1)
sm = simpson_method(0, 3 ** 0.5, 10000, function1)
print(f"Rectangle method: {rm}, delta: {abs(0.35 - rm)}")
print(f"Trapezium method: {tm}, delta: {abs(0.35 - tm)}")
print(f"Simpson method: {sm}, delta: {abs(0.35 - sm)}")
print()
rm = rectangle_method(1, 2, 10000, function2)
tm = trapezium_method(1, 2, 10000, function2)
sm = simpson_method(1, 2, 10000, function2)
print(f"Rectangle method: {rm}, delta: {abs((exp(1) - exp(0.5)) - rm)}")
print(f"Trapezium method: {tm}, delta: {abs((exp(1) - exp(0.5)) - tm)}")
print(f"Simpson method: {sm}, delta: {abs((exp(1) - exp(0.5)) - sm)}")
print()
rm = rectangle_method(0, 2, 10000, function3)
tm = trapezium_method(0, 2, 10000, function3)
sm = simpson_method(0, 2, 10000, function3)
print(f"Rectangle method: {rm}")
print(f"Trapezium method: {tm}")
print(f"Simpson method: {sm}")
print()