upload exercises

exercises/exerciseB/numerical_integration.py

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+"""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()