2024-heraklion-parallel-python/exercises/exerciseB/numerical_integration.py
2024-08-29 18:23:32 +03:00

39 lines
962 B
Python

"""Exercise 2b: multiprocessing
"""
def integrate(f, a, b, n):
"Perform numerical integration of f in range [a, b], with n steps"
s = []
for i in range(n):
dx = (b - a) / n
x = a + (i + 0.5) * dx
y = f(x)
s = s + [y * dx]
return sum(s)
def f(x):
"A polynomial that we'll integrate"
return x ** 4 - 3 * x
def F(x):
"The analatic integral of f. (F' = f)"
return 1 / 5 * x ** 5 - 3 / 2 * x ** 2
def compute_error(n):
"Calculate the difference between the numerical and analytical integration results"
a = -1.0
b = +2.0
F_analytical = F(b) - F(a)
F_numerical = integrate(f, a, b, n)
return abs((F_numerical - F_analytical) / F_analytical)
def main():
ns = [10_000, 25_000, 50_000, 75_000]
errors = ... # TODO: write a for loop, serial map, and parallel map here
for n, e in zip(ns, errors):
print(f'{n} {e:.8%}')
if __name__ == '__main__':
main()