Question

我计算2 * Volume sphere(dimension=4) / Volume cylinder(dimension=4)的{{1}}。我遇到的问题是解决问题的第一种方法。第二种方法给出了正确的答案。也就是说，当答案应该是1.17时，我得到1.14。这些程序有何不同？我无法发现差异。

import random

# FIRST WAY

print('elegant solution')

coordinates = [0] * 3
alpha = 0
delta = 0.1
deltas = [0] * 3
n_trials = 1000000
n_hits = 0

for a in range(6):
    for i in range(n_trials):
        # gets random deltas, and random alpha for 4th dimension
        deltas = [random.uniform(-delta, delta) for coordinate in deltas]
        alpha = random.uniform(-1.0, 1.0)

        # sum of the (n - 1) first components
        sum_components = sum((coordinates[j] + deltas[j])**2 for j in range(3))

        # if the sample is inside the cylinder
        if sum_components < 1.0:
            coordinates = [coordinates[j] + deltas[j] for j in range(3)]

        # if the sample is inside the sphere
        if sum_components + alpha**2 < 1.0:
            n_hits += 1

    print (2.0 * float(n_hits) / float(n_trials)) # 2V_sph(4) / V_cyl(4) where V_sph=hits Vcyl=trials
    coordinates = [0] * 3
    n_hits = 0

# SECOND WAY

print('typical solution')

x, y, z, alpha = 0.0, 0.0, 0.0, 0.0
delta = 0.1
n_trials = 1000000
n_hits = 0

for a in range (6):
    for i in range(n_trials):
        # gets random deltas, and random alpha for 4th dimension
        del_x, del_y, del_z, alpha = random.uniform(-delta, delta), random.uniform(-delta, delta), random.uniform(-delta, delta), random.uniform(-1, 1)

        # if the sample is inside the cylinder
        if (x + del_x)**2 + (y + del_y)**2 + (z + del_z)**2 < 1.0:
            x, y, z = x + del_x, y + del_y, z + del_z

        # if the sample is inside the sphere
        if x**2 + y**2 + z**2 + alpha**2 < 1.0:
            n_hits += 1

    print (2.0 * n_hits / float(n_trials)) # 2V_sph(4) / V_cyl(4) where V_sph=hits Vcyl=trials
    x, y, z = 0.0, 0.0, 0.0
    n_hits = 0

Answer 1

下一行：

if (sum_components + alpha**2) < 1.0:

不等于：

if (x**2 + y**2 + z**2 + alpha**2) < 1.0:

等于：

if ((x + del_x)**2 + (y + del_y)**2 + (z + del_z)**2 + alpha**2) < 1.0

你可以改变它：

if sum(c**2 for c in coordinates) + alpha**2 < 1.0

您的代码不是非常Pythonic。这是一些重构：

import random

delta = 0.1
n_trials = 1000000

for _ in range(6):
    coords = [0] * 3
    n_hits = 0

    for _ in range(n_trials):
        deltas = [random.uniform(-delta, delta) for _ in range(len(coords))]
        alpha = random.uniform(-1.0, 1.0)

        if sum((c + d)**2 for c, d in zip(coords, deltas)) < 1.0:
          coords = [c + d for c, d in zip(coords, deltas)]

        if sum(c**2 for c in coords) + alpha**2 < 1.0:
            n_hits += 1

    print(2.0 * n_hits / n_trials)

Python - 重构后的程序返回不同的结果

1 个答案: