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September 3, 2017 06:32
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Calculation of Pi Using the Monte Carlo Method
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| "n次元球の体積を用いたモンテカルロ法による$\\pi$の計算" | |
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| "execution_count": 36, | |
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| "source": [ | |
| "import numpy as np\n", | |
| "import math" | |
| ] | |
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| "def calc_pi(dim, N):\n", | |
| " \"\"\" \n", | |
| " モンテカルロ法によるpiの計算\n", | |
| " dim : 次元数\n", | |
| " N : シミュレーション回数\n", | |
| " \"\"\"\n", | |
| " cnt = 0 # n次元球に含まれた回数\n", | |
| " for i in range(N):\n", | |
| " r = np.sqrt(sum([np.random.rand()**2 for j in range(dim)]))\n", | |
| " if r <= 1:\n", | |
| " cnt += 1\n", | |
| " return (math.gamma(dim/2 + 1) * 2**dim * (cnt/N)) ** (2/dim)" | |
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| " n: pi\n", | |
| " 2: 3.1409000000000002\n", | |
| " 3: 3.1414798328376796\n", | |
| " 4: 3.1413364752511876\n", | |
| " 5: 3.138091181495231\n", | |
| " 6: 3.1412505533837036\n", | |
| " 7: 3.134955270430082\n", | |
| " 8: 3.141221866515699\n", | |
| " 9: 3.1557226840558945\n", | |
| "10: 3.1594762405237438\n", | |
| "11: 3.178616355914686\n", | |
| "12: 3.1487253337751135\n", | |
| "13: 3.147298729896722\n", | |
| "14: 2.791857664186204\n", | |
| "15: 1.9255313462211525\n", | |
| "16: 1.817653756143045\n", | |
| "17: 0.0\n", | |
| "18: 0.0\n", | |
| "19: 0.0\n", | |
| "20: 0.0\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "print(\" n: pi\")\n", | |
| "for i in range(2, 21):\n", | |
| " print(\"{:2d}: {}\".format(i, np.mean([calc_pi(i, 100000) for j in range(10)])))" | |
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