{"id":46037,"date":"2023-06-16T05:23:02","date_gmt":"2023-04-14T16:04:22","guid":{"rendered":"https:\/\/www.silicloud.com\/zh\/blog\/46037-2\/"},"modified":"2024-04-30T09:06:42","modified_gmt":"2024-04-30T01:06:42","slug":"46037-2","status":"publish","type":"post","link":"https:\/\/www.silicloud.com\/zh\/blog\/46037-2\/","title":{"rendered":""},"content":{"rendered":"

\u3053\u306e\u8a18\u4e8b\u306fNTT\u30b3\u30e0\u30a6\u30a7\u30a2 Advent Calendar 2022 24\u65e5\u76ee\u306e\u8a18\u4e8b\u3067\u3059\u3002<\/p>\n

NTT\u30b3\u30e0\u30a6\u30a7\u30a2\u306e\u53e4\u897f\u3067\u3059\u3002
\nJupyter\u4e0a\u30672\u6b21\u5143\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u306e\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u3092\u52d5\u304b\u3057\u3066\u307f\u307e\u3059\u3002\u307e\u305f\u3001\u307b\u3093\u306e\u5c11\u3057\u3060\u3051\u7269\u7406\u7684\u8003\u5bdf\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n

\u304d\u3063\u304b\u3051<\/p>\n

\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u3068\u306f\uff1f<\/p>\n

\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u3068\u306f\uff1f<\/p>\n

2\u6b21\u5143\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/p>\n

\u53c2\u8003\u6587\u732e<\/p>\n

\u304d\u3063\u304b\u3051<\/h3>\n

\u30aa\u30e9\u30a4\u30ea\u30fc\u30fb\u30b8\u30e3\u30d1\u30f3\u306e\u5b9f\u8df5 \u6642\u7cfb\u5217\u89e3\u6790\u3068\u3044\u3046\u672c\u306b\u3001\u7269\u7406\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306e\u4f8b\u3068\u3057\u3066\u30012\u6b21\u5143\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u304c\u8f09\u3063\u3066\u3044\u307e\u3059\u3002Python\u306e\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u304c\u8f09\u3063\u3066\u3044\u308b\u306e\u3067\u3059\u304c\u3001\u305d\u306e\u307e\u307e\u52d5\u304b\u3059\u3068\u521d\u671f\u72b6\u614b\u3068\u7d42\u72b6\u614b\u306e\u753b\u50cf\u306e\u307f\u3057\u304b\u8868\u793a\u3055\u308c\u306a\u3044\u305f\u3081\u3001\u3069\u3046\u305b\u306a\u3089\u9014\u4e2d\u306e\u72b6\u614b\u3092\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u3068\u3057\u3066\u8868\u793a\u3055\u305b\u305f\u3044\u3001\u3068\u601d\u3063\u305f\u3053\u3068\u304c\u304d\u3063\u304b\u3051\u3067\u3059\u3002
\n\u3053\u306e\u672c\u306e\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u306fGitHub\u4e0a\u306b\u516c\u958b\u3055\u308c\u3066\u304a\u308a1\u3001\u30b3\u30fc\u30c9\u306e\u4e00\u90e8\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u8a31\u53ef\u306f\u4e0d\u8981\u3068\u306e\u8a18\u8f09\u3082\u3042\u308b\u306e\u3067\u3001\u3053\u3061\u3089\u306e\u30b3\u30fc\u30c9\u3092\u3082\u3068\u306b\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u90e8\u5206\u306e\u8ffd\u52a0\u3092\u884c\u3044\u307e\u3059\u3002\u307e\u305f\u3001\u8003\u5bdf\u306e\u305f\u3081\u306b\u30c8\u30ec\u30fc\u30b9\u30d7\u30ed\u30c3\u30c8\u7b49\u306e\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u3057\u307e\u3059\u30022\u3002<\/p>\n

\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u3068\u306f\uff1f3<\/h3>\n

\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u3068\u306f\u3001\u30df\u30af\u30ed\u306a\u78c1\u77f3\u306e\u96c6\u5408\u4f53\u306e\u7269\u7406\u30e2\u30c7\u30eb\u3067\u3059\u3002
\n\u30df\u30af\u30ed\u306a\u78c1\u77f3\u306f\u305d\u308c\u305e\u308cN\u6975\u3068S\u6975\u3092\u3082\u3061\u307e\u3059\u3002\u305d\u308c\u305e\u308c\u306e\u30df\u30af\u30ed\u306e\u78c1\u77f3\u306f\u3001\u96a3\u3042\u3063\u305f\u78c1\u77f3\u304c\u540c\u3058\u5411\u304d\u3092\u5411\u304d\u305f\u304c\u308b\u6027\u8cea\u3092\u3082\u3063\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u3042\u308b\u78c1\u77f3\u306e\u524d\u5f8c\u5de6\u53f3\u306e\u78c1\u77f3\u304c\u5168\u3066\u4e0a\u5411\u304d\u306a\u3089\u3001\u305d\u306e\u78c1\u77f3\u3082\u4e0a\u5411\u304d\u3092\u5411\u304d\u305f\u304c\u308a\u307e\u3059\u3002\u3053\u306e\u6027\u8cea\u3060\u3051\u3060\u3068\u3001\u3084\u304c\u3066\u3059\u3079\u3066\u306e\u78c1\u77f3\u304c\u540c\u3058\u5411\u304d\u3092\u5411\u304d\u307e\u3059\u304c\u3001\u78c1\u77f3\u306e\u5411\u304d\u306b\u306f\u6e29\u5ea6\u306b\u5bfe\u3059\u308b\u4f9d\u5b58\u6027\u3092\u3082\u3063\u3066\u304a\u308a\u3001\u78c1\u77f3\u306e\u6e29\u5ea6\u304c\u9ad8\u304f\u306a\u308c\u3070\u306a\u308b\u307b\u3069\u96a3\u306e\u78c1\u77f3\u306e\u5411\u304d\u306b\u95a2\u308f\u3089\u305a\u3001\u30e9\u30f3\u30c0\u30e0\u306b\u53cd\u8ee2\u3057\u3084\u3059\u3044\u6027\u8cea\u3001\u3064\u307e\u308a\u5411\u304d\u304c\u30d0\u30e9\u30d0\u30e9\u306b\u306a\u308b\u6027\u8cea\u3092\u3082\u3063\u3066\u307e\u3059\u3002\u9006\u306b\u3001\u6e29\u5ea6\u304c\u4f4e\u3051\u308c\u3070\u4f4e\u3044\u307b\u3069\u53cd\u8ee2\u3057\u3065\u3089\u304f\u306a\u308a\u540c\u3058\u5411\u304d\u3092\u5411\u3044\u305f\u307e\u307e\u306b\u306a\u308a\u307e\u3059\u3002
\n\u521d\u671f\u72b6\u614b\u306f\u3001\u305d\u308c\u305e\u308c\u306e\u30df\u30af\u30ed\u306e\u78c1\u77f3\u304c\u4e0a\u5411\u304d\u3001\u4e0b\u5411\u304d\u30e9\u30f3\u30c0\u30e0\u306a\u65b9\u5411\u3092\u5411\u3044\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n

\"ising_image.png\"<\/div>\n

N\u6975\u304c\u4e0a\u3092\u5411\u3044\u3066\u3044\u308b\u3068\u304d\u3092 $s_i=+1$ \u306e\u72b6\u614b\u3001N\u6975\u304c\u4e0b\u3092\u5411\u3044\u3066\u3044\u308b(\u3064\u307e\u308aS\u5c40\u304c\u4e0a\u3092\u5411\u3044\u3066\u3044\u308b)\u6642\u306e\u72b6\u614b\u3092$s_i=-1$\u3068\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u78c1\u77f3\u306e\u5411\u304d\u304c\u63c3\u3044\u3084\u3059\u304f\u306a\u308b\u6982\u5ff5\u3092\u3001\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5927\u5c0f\u3067\u3042\u3089\u308f\u3059\u3068\u3001\u5404\u78c1\u77f3\u306e\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u30a8\u30cd\u30eb\u30ae\u30fc$E(s)$\u306f\u3001<\/p>\n

E(s) = - \\sum_{<i,j>} s_i s_j\r\n<\/code><\/pre>\n
\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001$<i,j>$\u306f\u3001\u96a3\u63a5\u3059\u308b\u7d44\u3068\u3044\u3046\u610f\u5473\u3067\u3059\u3002
\n1\u500b\u306e\u78c1\u77f3\u306e\u524d\u5f8c\u5de6\u53f34\u3064\u306e\u78c1\u77f3\u3068\u306e\u95a2\u4fc2\u3092\u8003\u3048\u308b\u306e\u3067\u3001\u4eca\u898b\u3066\u3044\u308b\u78c1\u77f3\u306e\u524d\u5f8c\u5de6\u53f34\u3064\u3068\u3082\u305d\u306e\u78c1\u77f3\u3068\u540c\u3058\u5411\u304d\u3092\u5411\u3044\u3066\u3044\u308b\u3068\u3001$E(s)=-4$\u30012\u3064\u3060\u3051\u9006\u3092\u5411\u3044\u3066\u3044\u308b\u3068$E(s)=0$\u30014\u3064\u3068\u3082\u9006\u3092\u5411\u3044\u3066\u3044\u308b\u5834\u5408\u306f$E(s)=+4$\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u77ac\u9593\u306e\u78c1\u77f3\u3067\u306f\u3001$E(s)= -4, -2, 0, +2, +4$\u306e\u3044\u305a\u308c\u304b\u306e\u5024\u3092\u6301\u3061\u307e\u3059\u3002
\n\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u3001\u5c0f\u3055\u3044\u5024\u307b\u3069\u5b89\u5b9a\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u8868\u3059\u306e\u3067\u3001\u5411\u304d\u304c\u63c3\u3063\u3066\u3044\u308b\u307b\u3046\u304c\u30a8\u30cd\u30eb\u30ae\u30fc\u7684\u306b\u5b89\u5b9a\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n
\u307e\u305f\u3001\u78c1\u77f3\u306e\u53cd\u8ee2\u3057\u3084\u3059\u3055\u3092\u3042\u3089\u308f\u3059\u78ba\u7387\u306f\u3001\u65e2\u77e5\u306e\u7269\u7406\u6cd5\u5247\u306b\u5f93\u3046\u3068\u30574\u3001\u6e29\u5ea6(\u7d76\u5bfe\u6e29\u5ea6)$T$\u3068\u3059\u308b\u3068\u3001\u6b21\u306e\u78ba\u7387\u30e2\u30c7\u30eb\u3067\u3042\u3089\u308f\u305b\u307e\u3059\u3002<\/p>\n
P(s) = \\frac{e^{-E(s)\/T}}{Z}\r\n<\/code><\/pre>\n
\u3053\u3053\u3067\u3001$Z$\u306f\u898f\u683c\u5316\u5b9a\u65705\u3067\u3001\u78c1\u77f3\u306e\u6570\u304c$N$\u500b\u306e\u5834\u5408<\/p>\n
Z = \\sum_{s=1}^N e^{-E(s)\/T}\r\n<\/code><\/pre>\n
\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u53cd\u8ee2\u306e\u3057\u3084\u3059\u3055\u304c\u6e29\u5ea6\u306b\u4f9d\u5b58\u3059\u308b\u3053\u3068\u3082\u3042\u3089\u308f\u305b\u3066\u3044\u307e\u3059\u3002<\/p>\n
\u3053\u3053\u3067\u3001\u3053\u306e\u78ba\u7387\u5206\u5e03\u3092\u8a08\u7b97\u3057\u3088\u3046\u3068\u3059\u308b\u3068\u3001\u898f\u683c\u5316\u5b9a\u6570 $Z$\u3092\u8a08\u7b97\u3057\u306a\u3044\u3068\u3044\u3051\u307e\u305b\u3093\u304c\u3001$N$\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u3001\u72b6\u614b\u548c\u306e\u8a08\u7b97\uff08\u4e00\u822c\u7684\u306b\u306f\u7a4d\u5206\u8a08\u7b97\uff09\u304c\u56f0\u96e3\u306b\u306a\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u30596\u3002\u3053\u308c\u3092\u6570\u5024\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306b\u3088\u308a\u8fd1\u4f3c\u7684\u306b\u6c42\u3081\u3088\u3046\u3068\u3059\u308b\u306e\u304c\u3001\u4eca\u56de\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u3082\u5229\u7528\u3059\u308b\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5(MCMC)\u3067\u3059\u3002<\/p>\n
\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5(MCMC)\u3068\u306f\uff1f7<\/h3>\n
\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u3068\u306f\u3001\u4e71\u6570\u3092\u7528\u3044\u305f\u6570\u5024\u8a08\u7b97\u624b\u6cd5\u306e\u7dcf\u79f0\u3067\u3059\u3002\u5b9f\u969b\u306b\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u3067\u6570\u5024\u8a08\u7b97\u3059\u308b\u5834\u5408\u306f\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u304c\u751f\u6210\u3059\u308b\u7591\u4f3c\u4e71\u6570\u3092\u7528\u3044\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3068\u306f\u306a\u3093\u3067\u3057\u3087\u3046\u304b\uff1f
\n\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3068\u306f\u3001\u6642\u70b9\u306b\u5f93\u3063\u3066\u8108\u3005\u3068\u5909\u5316\u3057\u3066\u3044\u304f\u78ba\u7387\u5909\u6570\u304c\u3042\u308b\u3068\u304d\u30011\u6642\u70b9\u524d\u306e\u5024\u3060\u3051\u3067\u6b21\u306e\u78ba\u7387\u5909\u6570\u304c\u304d\u307e\u308b\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001<\/p>\n
x_0 \\to x_1 \\to x_2 \\to \\dots \\to x_{n-1} \\to x_n\r\n<\/code><\/pre>\n
\u306e\u3068\u304d\u306e\u72b6\u614b\u9077\u79fb\u78ba\u7387$P$\u304c\u3001<\/p>\n
P(x_n | x_{n-1},x_{n-2}, \\dots , x_1) = P(x_n|x_{n-1})\r\n<\/code><\/pre>\n
\u3068\u306a\u308b\u3053\u3068\u3067\u3059\u3002\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5(MCMC)\u306f\u3001\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3067\u3067\u304d\u308b\u78ba\u7387\u5909\u6570\u3092\u5229\u7528\u3057\u3066\u7591\u4f3c\u4e71\u6570\u3092\u751f\u6210\u3059\u308b\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u306e\u3053\u3068\u3067\u3059\u3002\u3067\u306f\u3001\u5358\u7d14\u306a\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u3067\u306f\u306a\u304f\u3001MCMC\u3092\u5229\u7528\u3059\u308b\u5fc5\u8981\u6027\u306f\u3069\u3046\u3057\u3066\u3067\u3057\u3087\u3046\uff1f<\/p>\n
\u4e00\u822c\u306b\u3001\u591a\u5909\u91cf(\u9ad8\u6b21\u5143)\u306e\u5206\u5e03\u3067\u306e\u8a08\u7b97\u3067\u5358\u7d14\u306a\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u3067\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306f\u3001\u307b\u3068\u3093\u3069\u306e\u70b9\u3067\u5bfe\u8c61\u3068\u306a\u308b\u5206\u5e03\u95a2\u6570(\u88ab\u7a4d\u5206\u95a2\u6570)\u306e\u8a08\u7b97\u306b\u5bc4\u4e0e\u305b\u305a\u3001\u751f\u6210\u3057\u305f\u7591\u4f3c\u4e71\u6570\u306e\u307b\u3068\u3093\u3069\u304c\u7121\u99c4\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u3068\u3044\u3046\u554f\u984c\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u6b21\u5143\u304c\u9ad8\u304f\u306a\u308b\u3068\u3001\u89e3\u6790\u7684\u306a(\u771f\u306e\u610f\u5473\u306e)\u89e3\u3068\u3001\u6570\u5024\u8a08\u7b97\u3067\u306e\u8fd1\u4f3c\u89e3\u306b\u5927\u304d\u306a\u305a\u308c\u304c\u751f\u3058\u308b\u3053\u3068\u3082\u308f\u304b\u3063\u3066\u3044\u307e\u30598\u3002\u4eca\u56de\u306e\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u306e\u4f8b\u3067\u306f\u3001\u78c1\u77f3\u306e\u6570 $N$ \u304c\u3042\u307e\u308a\u306b\u5927\u304d\u304f\u306a\u308b\u3068\u5229\u7528\u3067\u304d\u306a\u3044\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002
\n\u5358\u7d14\u306a\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u304c\u4f7f\u3048\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u3068\u3057\u3066\u3001MCMC\u306e\u5834\u5408\u306f\u306a\u305c\u3046\u307e\u304f\u3044\u304f\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n
MCMC\u3067\u306f\u3001\u6642\u9593\u304c\u7d4c\u3064\u306b\u3064\u308c\u3066\u3001\u78ba\u7387\u5206\u5e03\u304c\u306a\u3093\u3089\u304b\u306e\u5909\u5316\u3057\u306a\u3044\u72b6\u614b\u306b\u53ce\u675f\u3059\u308b\u6027\u8cea\u3092\u3082\u3063\u3066\u304a\u308a(\u3064\u307e\u308a\u3001\u6642\u9593\u3092\u591a\u5c11\u524d\u5f8c\u3057\u3066\u3082\u78ba\u7387\u5206\u5e03\u304c\u5909\u5316\u3057\u306a\u3044\u72b6\u614b)\u3001\u3053\u308c\u3092\u5b9a\u5e38\u5206\u5e03\u3068\u547c\u3073\u307e\u30599\u3002\u5b9a\u5e38\u5206\u5e03\u3067\u306f\u3001\u8a08\u7b97\u306e\u5bfe\u8c61\u3068\u306a\u308b\u5206\u5e03\u95a2\u6570\u306b\u5bfe\u3059\u308b\u5bc4\u4e0e\u5ea6\u304c\u9ad8\u3044\u3068\u3053\u308d\u3067\u91cd\u70b9\u7684\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u304c\u884c\u308f\u308c\u308b\u305f\u3081\u3001\u591a\u5909\u91cf(\u9ad8\u6b21\u5143)\u306b\u306a\u3063\u3066\u3082\u4e0a\u624b\u304f\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002(\u8a00\u8449\u3067\u8aac\u660e\u3057\u3066\u3082\u308f\u304b\u308a\u3065\u3089\u3044\u306e\u3067\u3001\u3053\u306e\u5f8c\u306e\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u306e\u4e0b\u306b\u3042\u308b\u5b9a\u5e38\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002)<\/p>\n
\u3061\u306a\u307f\u306b\u3001\u5c11\u3057\u8131\u7dda\u3057\u307e\u3059\u304c\u3001MCMC\u306e\u6d3b\u7528\u306e\u5834\u3068\u3044\u3046\u3068\u3001\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u306e\u3088\u3046\u306a\u7269\u7406\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u4ee5\u5916\u306b\u3082\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u306e\u4e16\u754c\u3067\u4f7f\u308f\u308c\u308b\u3053\u3068\u304c\u591a\u304f\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u30d9\u30a4\u30ba\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u3067\u306f\u3001\u3042\u308b\u89b3\u6e2c\u30c7\u30fc\u30bf\u304b\u3089\u7d71\u8a08\u30e2\u30c7\u30eb\u306e\u4eee\u8aac\u3092\u7acb\u3066\u3066\u3001\u4e8b\u5f8c\u5206\u5e03\u306e\u8a08\u7b97\u3092\u884c\u3044\u307e\u3059\u304c\u3001\u4e8b\u5f8c\u5206\u5e03\u306b\u5f93\u3046\u7591\u4f3c\u4e71\u6570\u306e\u751f\u6210\u306b\u3001MCMC\u3092\u5229\u7528\u3057\u307e\u305910\u3002<\/p>\n
2\u6b21\u5143\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/h3>\n
\u4ee5\u4e0b\u306b\u30012\u6b21\u5143\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u306e\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u3092\u793a\u3057\u307e\u3059\u3002\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u306e\u8a2d\u5b9a\u3068MCMC\u306e\u8a08\u7b97\u306e\u95a2\u6570\u90e8\u5206\u306f\u3001\u30aa\u30ea\u30b8\u30ca\u30eb\u30bd\u30fc\u30b9\u306b\u6e96\u62e0\u3057\u3066\u3044\u307e\u3059\u3002
\n\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u5316\u3092\u3059\u308b\u305f\u3081\u306b\u3001matplotlib\u306eArtistAnimation\u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002ArtistAnimation\u3067\u306f\u3001\u3042\u3089\u304b\u3058\u3081\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u5316\u3059\u308b\u753b\u50cf\u3092\u8907\u6570\u679a\u7528\u610f\u3057\u3001\u30ea\u30b9\u30c8\u306b\u5165\u308c\u3066\u304a\u304d\u307e\u3059\u3002\u4eca\u56de\u306f\u3001\u5404\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u30b9\u30c6\u30c3\u30d7\u6bce\u306b\u51fa\u529b\u3055\u308c\u308b\u72b6\u614b\u56f3\u3092\u914d\u5217ims\u306b\u683c\u7d0d\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n
## Original source https:\/\/github.com\/PracticalTimeSeriesAnalysis\/BookRepo\/blob\/master\/Ch04\/Ising.ipynb\r\n## Modified for Animation by T.Konishi \r\n<\/span>import<\/span> numpy<\/span> as<\/span> np<\/span>\r\nimport<\/span> pandas<\/span> as<\/span> pd<\/span>\r\nimport<\/span> matplotlib.pyplot<\/span> as<\/span> plt<\/span>\r\nfrom<\/span> matplotlib<\/span> import<\/span> animation<\/span>,<\/span> rc<\/span>\r\nfrom<\/span> IPython.display<\/span> import<\/span> HTML<\/span>\r\n\r\n### \u8a2d\u5b9a\r\n<\/span>N<\/span>           =<\/span> 16<\/span>   # \u6a2a\u306e\u500b\u6570\r\n<\/span>M<\/span>           =<\/span> 16<\/span>   # \u7e26\u306e\u500b\u6570\r\n<\/span>T<\/span>           =<\/span> 1.0<\/span> # \u6e29\u5ea6 (\u4f4e\u6e29)\r\n#T            = 10.0  # \u6e29\u5ea6 (\u9ad8\u6e29)\r\n<\/span>n_steps<\/span> =<\/span> 1500<\/span>     # \u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u30b9\u30c6\u30c3\u30d7\u6570\r\n<\/span>energy<\/span> =<\/span> 0.0<\/span>      #\u30a8\u30cd\u30eb\u30ae\u30fc\u5024\u521d\u671f\u5316\r\n<\/span>energy_n_steps<\/span> =<\/span> [<\/span>energy<\/span>]<\/span> #\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u30b9\u30c6\u30c3\u30d7\u6bce\u306b\u9078\u629e\u3055\u308c\u305f\u30bb\u30eb\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u5dee\r\n<\/span>\r\nplt<\/span>.<\/span>style<\/span>.<\/span>use<\/span>(<\/span>\"<\/span>default<\/span>\"<\/span>)<\/span> # \u63cf\u753b\u30b9\u30bf\u30a4\u30eb\u3092\u30c7\u30d5\u30a9\u30eb\u30c8\u306b\u8a2d\u5b9a\r\n<\/span>np<\/span>.<\/span>random<\/span>.<\/span>seed<\/span>(<\/span>111<\/span>)<\/span>  # \u4e71\u6570\u306e\u7a2e\u3092\u8a2d\u5b9a\r\n<\/span>\r\n# \u7cfb\u306e\u521d\u671f\u5316\r\n<\/span>def<\/span> initRandState<\/span>(<\/span>N<\/span>,<\/span> M<\/span>):<\/span>\r\n    block<\/span> =<\/span> np<\/span>.<\/span>random<\/span>.<\/span>choice<\/span>([<\/span>-<\/span>1<\/span>,<\/span> 1<\/span>],<\/span> size<\/span> =<\/span> (<\/span>N<\/span>,<\/span> M<\/span>))<\/span>\r\n    return<\/span> block<\/span>\r\n\r\n# \u30a8\u30cd\u30eb\u30ae\u30fc\u5dee\u306e\u8a08\u7b97\r\n<\/span>def<\/span> energyForCenterState<\/span>(<\/span>state<\/span>,<\/span> i<\/span>,<\/span> j<\/span>,<\/span> n<\/span>,<\/span> m<\/span>):<\/span>\r\n    centerS<\/span> =<\/span> state<\/span>[<\/span>i<\/span>,<\/span> j<\/span>]<\/span>\r\n    neighbors<\/span> =<\/span> [((<\/span>i<\/span> +<\/span> 1<\/span>)<\/span> %<\/span> n<\/span>,<\/span> j<\/span>),<\/span> ((<\/span>i<\/span> -<\/span> 1<\/span>)<\/span> %<\/span> n<\/span>,<\/span> j<\/span>),<\/span>\r\n                 (<\/span>i<\/span>,<\/span> (<\/span>j<\/span> +<\/span> 1<\/span>)<\/span> %<\/span> m<\/span>),<\/span> (<\/span>i<\/span>,<\/span> (<\/span>j<\/span> -<\/span> 1<\/span>)<\/span> %<\/span> m<\/span>)]<\/span>\r\n    ## \u5468\u671f\u7684\u306a\u5883\u754c\u6761\u4ef6\u306e\u305f\u3081\u306b %n \u3068\u3057\u3066\u3044\u308b\u3002\r\n<\/span>\r\n    interactionE<\/span> =<\/span> [<\/span>state<\/span>[<\/span>x<\/span>,<\/span> y<\/span>]<\/span> *<\/span> centerS<\/span> for <\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span> in<\/span> neighbors<\/span>]<\/span>\r\n    return<\/span> np<\/span>.<\/span>sum<\/span>(<\/span>interactionE<\/span>)<\/span>\r\n\r\ndef<\/span> magnetizationForState<\/span>(<\/span>state<\/span>):<\/span>\r\n    return<\/span> np<\/span>.<\/span>sum<\/span>(<\/span>state<\/span>)<\/span>\r\n\r\n# MCMC\u306e\u8a08\u7b97\r\n<\/span>def<\/span> mcmcAdjust<\/span>(<\/span>state<\/span>):<\/span>\r\n    n<\/span> =<\/span> state<\/span>.<\/span>shape<\/span>[<\/span>0<\/span>]<\/span>\r\n    m<\/span> =<\/span> state<\/span>.<\/span>shape<\/span>[<\/span>1<\/span>]<\/span>\r\n    x<\/span>,<\/span> y<\/span> =<\/span> np<\/span>.<\/span>random<\/span>.<\/span>randint<\/span>(<\/span>0<\/span>,<\/span> n<\/span>),<\/span> np<\/span>.<\/span>random<\/span>.<\/span>randint<\/span>(<\/span>0<\/span>,<\/span> m<\/span>)<\/span>\r\n    centerS<\/span> =<\/span> state<\/span>[<\/span>x<\/span>,<\/span> y<\/span>]<\/span>\r\n    energy<\/span> =<\/span> energyForCenterState<\/span>(<\/span>state<\/span>,<\/span> x<\/span>,<\/span> y<\/span>,<\/span> n<\/span>,<\/span> m<\/span>)<\/span>\r\n    if<\/span> energy<\/span> <<\/span> 0<\/span>:<\/span>\r\n        centerS<\/span> *=<\/span> -<\/span>1<\/span>\r\n    elif<\/span> np<\/span>.<\/span>random<\/span>.<\/span>random<\/span>()<\/span> <<\/span> np<\/span>.<\/span>exp<\/span>(<\/span>-<\/span>energy<\/span> \/<\/span> T<\/span>):<\/span>\r\n        centerS<\/span> *=<\/span> -<\/span>1<\/span>\r\n    state<\/span>[<\/span>x<\/span>,<\/span> y<\/span>]<\/span> =<\/span> centerS<\/span>\r\n    return<\/span> state<\/span>,<\/span> energy<\/span>\r\n\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>5<\/span>,<\/span>5<\/span>))<\/span> # \u56f3\u306e\u30b5\u30a4\u30ba\r\n<\/span>ims<\/span>=<\/span>[]<\/span>\r\nstate<\/span> =<\/span> initRandState<\/span>(<\/span>N<\/span>,<\/span> M<\/span>)<\/span>\r\nmagnet_hist<\/span> =<\/span> []<\/span>\r\n    \r\nfor<\/span> i<\/span> in<\/span> range<\/span>(<\/span>n_steps<\/span>):<\/span>\r\n    state<\/span>,<\/span> energy<\/span> =<\/span> mcmcAdjust<\/span>(<\/span>state<\/span>)<\/span>\r\n    energy_n_steps<\/span>.<\/span>append<\/span>(<\/span>energy<\/span>)<\/span> \r\n    magnet_hist<\/span>.<\/span>append<\/span>(<\/span>magnetizationForState<\/span>(<\/span>state<\/span>))<\/span>\r\n    im<\/span> =<\/span> plt<\/span>.<\/span>imshow<\/span>(<\/span>state<\/span>,<\/span> animated<\/span>=<\/span>True<\/span>)<\/span>\r\n    ims<\/span>.<\/span>append<\/span>([<\/span>im<\/span>])<\/span>\r\n\r\n# \u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\r\n<\/span>anim<\/span> =<\/span> animation<\/span>.<\/span>ArtistAnimation<\/span>(<\/span>fig<\/span>,<\/span> ims<\/span>,<\/span> interval<\/span>=<\/span>10<\/span>)<\/span>\r\nrc<\/span>(<\/span>'<\/span>animation<\/span>'<\/span>,<\/span> html<\/span>=<\/span>'<\/span>jshtml<\/span>'<\/span>)<\/span>\r\nplt<\/span>.<\/span>close<\/span>()<\/span>\r\nanim<\/span>\r\n\r\n#\u52d5\u753bgif\u30d5\u30a1\u30a4\u30eb\u306e\u4fdd\u5b58\r\n<\/span>anim<\/span>.<\/span>save<\/span>(<\/span>\"<\/span>ising_temp_low.gif<\/span>\"<\/span>)<\/span>\r\n#anim.save(\"ising_temp_high.gif\")\r\n<\/span>\r\nplt<\/span>.<\/span>style<\/span>.<\/span>use<\/span>(<\/span>\"<\/span>ggplot<\/span>\"<\/span>)<\/span> #\u30b0\u30e9\u30d5\u63cf\u753b\u7528\u306b\u30b9\u30bf\u30a4\u30eb\u5909\u66f4\r\n<\/span>\r\ndf<\/span> =<\/span> pd<\/span>.<\/span>DataFrame<\/span>(<\/span>energy_n_steps<\/span>)<\/span>\r\n\r\n# \u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u30b9\u30c6\u30c3\u30d7\u6bce\u306b\u7b97\u51fa\u3059\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u5024\u306e\u30c8\u30ec\u30fc\u30b9\u30d7\u30ed\u30c3\u30c8\r\n<\/span>plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>[<\/span>5<\/span>,<\/span> 3<\/span>])<\/span>\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>df<\/span>[<\/span>0<\/span>])<\/span>\r\nplt<\/span>.<\/span>xlabel<\/span>(<\/span>\"<\/span>n_steps<\/span>\"<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylabel<\/span>(<\/span>\"<\/span>energy<\/span>\"<\/span>)<\/span>\r\nplt<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\nplt<\/span>.<\/span>savefig<\/span>(<\/span>\"<\/span>.\/energy_trace_plot_low.png<\/span>\"<\/span>)<\/span>\r\nplt<\/span>.<\/span>show<\/span>()<\/span>\r\n\r\n# \u7b97\u51fa\u3055\u308c\u305f\u30a8\u30cd\u30eb\u30ae\u30fc\u5024\u306e\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\r\n<\/span>plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>[<\/span>5<\/span>,<\/span> 3<\/span>])<\/span>\r\nplt<\/span>.<\/span>hist<\/span>(<\/span>df<\/span>[<\/span>0<\/span>],<\/span> align<\/span>=<\/span>'<\/span>mid<\/span>'<\/span>,<\/span> density<\/span> =<\/span> False<\/span>,<\/span> bins<\/span> =<\/span> 5<\/span>,<\/span> range<\/span> =<\/span> (<\/span>-<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> rwidth<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>xlabel<\/span>(<\/span>\"<\/span>energy<\/span>\"<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylabel<\/span>(<\/span>\"<\/span>count<\/span>\"<\/span>)<\/span>\r\nplt<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\nplt<\/span>.<\/span>savefig<\/span>(<\/span>\"<\/span>.\/energy_histgram_low.png<\/span>\"<\/span>)<\/span>\r\nplt<\/span>.<\/span>show<\/span>()<\/span>\r\n\r\n<\/code><\/pre>\n
\"artistanimation_init.png\"<\/div>\n
MCMC\u306e\u8a08\u7b97\u90e8\u5206\u304c\u30df\u30bd\u3067\u3059\u300211<\/p>\n
    \n
  • \n
      \u5404\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u30b9\u30c6\u30c3\u30d7\u6bce\u306b\u30011\u3064\u306e\u30bb\u30eb(\u30df\u30af\u30ed\u306a\u78c1\u77f3\u3092\u3053\u3053\u3067\u306f\u30bb\u30eb\u3068\u547c\u3076\u3053\u3068\u306b\u3057\u307e\u3059\u3002)\u3092\u9078\u3073\u3001\u305d\u306e\u5411\u304d\u3092\u53cd\u8ee2\u3055\u305b\u308b\u3002<\/ul>\n<\/li>\n<\/ul>\n
       <\/p>\n
        \n
      • \n
          \u53cd\u8ee2\u3057\u305f\u7d50\u679c\u3001\u5909\u5316\u3057\u305f\u30a8\u30cd\u30eb\u30ae\u30fc\u5dee\u3092\u8a08\u7b97\u3059\u308b\u3002<\/ul>\n<\/li>\n<\/ul>\n
          \u30a8\u30cd\u30eb\u30ae\u30fc\u5dee\u304c0\u3088\u308a\u5c0f\u3055\u3044\u5834\u5408\u3001\u5e38\u306b\u512a\u5148\u3055\u308c\u308b\u4f4e\u3044\u30a8\u30cd\u30eb\u30ae\u30fc\u72b6\u614b\u306b\u3078\u306e\u9077\u79fb\u3092\u610f\u5473\u3059\u308b\u305f\u3081\u3001\u53cd\u8ee2\u3092\u53d7\u3051\u5165\u308c\u3066\u6b21\u306b\u9032\u3080\u3002
          \n\u30a8\u30cd\u30eb\u30ae\u30fc\u5dee\u304c0\u4ee5\u4e0a\u3067\u3042\u308c\u3070\u3001$0 \uff5e 1$\u306e\u4e00\u69d8\u4e71\u6570\u3092\u751f\u6210\u305712\u3001$ e^{E \/ T}$ ($E$\u306f\u30a8\u30cd\u30eb\u30ae\u30fc\u5dee) \u3068\u6bd4\u8f03\u3057\u3066\u751f\u6210\u3057\u305f\u4e71\u6570\u304c\u5c0f\u3055\u3051\u308c\u3070\u3001\u53cd\u8ee2\u3092\u53d7\u3051\u5165\u308c\u3066\u6b21\u306b\u9032\u3080\u3002<\/p>\n
          \u4e0a\u8a18\u624b\u9806\u3092\u72b6\u614b\u304c\u53ce\u675f\u3059\u308b\u307e\u3067\u7e70\u308a\u8fd4\u3059\u3002<\/p>\n
          \u6e29\u5ea6\u304c\u4f4e\u3044\u6642$(T=1.0)$\u3068\u3001\u6e29\u5ea6\u304c\u9ad8\u3044\u6642$(T=10)$\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u7d50\u679c\u306e\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002
          \n\u6e29\u5ea6\u304c\u4f4e\u3044\u3068\u304d\u306f\u3001\u6642\u9593\u304c\u9032\u3080\u306b\u3064\u308c\u3066\u78c1\u77f3\u306e\u5411\u304d\u304c\u63c3\u3063\u3066\u5cf6\u72b6\u306e\u584a\u304c\u3067\u304d\u307e\u3059\u304c\u3001\u6e29\u5ea6\u304c\u9ad8\u3044\u3068\u304d\u306f\u3001\u30d0\u30e9\u30d0\u30e9\u306e\u307e\u307e\u3067\u3059\u3002\u307e\u305f\u3001\u6e29\u5ea6\u304c\u4f4e\u3044\u6642\u3001\u9ad8\u3044\u6642\u306b\u8a08\u7b97\u3055\u308c\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u5dee\u306e\u63a8\u79fb\u3092\u793a\u3059\u30c8\u30ec\u30fc\u30b9\u30d7\u30ed\u30c3\u30c8\u3068\u3001\u30d2\u30b9\u30c8\u30b0\u30e9\u30e013\u3092\u3042\u308f\u305b\u3066\u8f09\u305b\u3066\u304a\u304d\u307e\u3059\u3002\u6e29\u5ea6\u304c\u4f4e\u3044\u6642\u306f\u3001\u5404\u30bb\u30eb\u3092\u53cd\u8ee2\u3055\u305b\u305f\u969b\u306b\u30a8\u30cd\u30eb\u30ae\u30fc\u5dee\u304c\u5927\u304d\u304f\u306a\u308a\u304c\u3061\u3067\u3001\u304b\u3064\u53cd\u8ee2\u3055\u305b\u308b\u78ba\u7387\u3082\u4f4e\u304f\u306a\u308b\u305f\u3081\u3001\u30bb\u30eb\u306e\u5411\u304d\u306f\u305d\u308d\u3046\u65b9\u5411\u3068\u306a\u308a\u3001\u72b6\u614b\u304c\u53ce\u675f\u3057\u307e\u3059\u3002\u30c8\u30ec\u30fc\u30b9\u30d7\u30ed\u30c3\u30c8\u3092\u307f\u3066\u3082\u3001\u6642\u9593\u306b\u5bc4\u3089\u306a\u3044\u5b9a\u5e38\u5206\u5e03\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u6e29\u5ea6\u304c\u9ad8\u3044\u6642\u306f\u3001\u9006\u306b\u30a8\u30cd\u30eb\u30ae\u30fc\u5dee\u304c$0$\u4ed8\u8fd1\u3092\u4e2d\u5fc3\u306b\u5747\u7b49\u306b\u306a\u308a\u3001\u5b9a\u5e38\u5206\u5e03\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n
          \"energy_histgram_high.png\"<\/div>\n
          \u6e29\u5ea6\u304c\u4f4e\u3044\u3068\u304d\u306f\u30bb\u30eb\u306e\u5411\u304d\u304c\u63c3\u304a\u3046\u3068\u3059\u308b\u306e\u306b\u5bfe\u3057\u3001\u6e29\u5ea6\u304c\u9ad8\u3044\u6642\u306f\u30bb\u30eb\u306e\u5411\u304d\u304c\u30d0\u30e9\u30d0\u30e9\u306e\u307e\u307e\u306b\u306a\u308a\u307e\u3059\u304c\u3001\u305d\u308c\u3067\u306f\u3001\u305d\u306e\u5883\u754c\u3068\u306a\u308b\u6e29\u5ea6\u306f\u3069\u3053\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u304b\uff1f
          \n\u5b9f\u306f\u3001\u4eca\u56de\u306e\u3088\u3046\u306a\u6b63\u65b9\u683c\u5b50\u578b\u306e2\u6b21\u5143\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u3067\u306f\u3001$T=$2.27\u4ed8\u8fd1\u306e\u3068\u3053\u308d\u304c\u305d\u306e\u5883\u754c\u306b\u306a\u308b\u3053\u3068\u304c\u5206\u304b\u3063\u3066\u3044\u307e\u3059(\u3068\u3001\u3053\u308c\u306a\u3089\u308f\u304b\u308b\u6a5f\u68b0\u5b66\u7fd2\u5165\u9580\u306b\u66f8\u3044\u3066\u3042\u308b\u306e\u306714\u3001\u305d\u306e\u53d7\u3051\u58f2\u308a\u3067\u3059)\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u3042\u308b\u6e29\u5ea6\u3067\u72b6\u614b\u304c\u5909\u5316\u3059\u308b\u3053\u3068\u3092\u7269\u7406\u306e\u4e16\u754c\u3067\u306f\u76f8\u8ee2\u79fb\u3068\u8a00\u3044\u307e\u3059\u3002\u4eca\u56de\u306f\u3001\u7c21\u6613\u306a\u30e2\u30c7\u30eb\u3068\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306b\u3088\u308a\u30012\u6b21\u5143\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u306e\u76f8\u8ee2\u79fb\u306b\u3064\u3044\u3066\u69d8\u5b50\u3092\u898b\u3066\u307f\u307e\u3057\u305f\u3002<\/p>\n
          \u53c2\u8003\u6587\u732e<\/h3>\n
          \u5b9f\u8df5 \u6642\u7cfb\u5217\u89e3\u6790 \u7d71\u8a08\u3068\u6a5f\u68b0\u5b66\u7fd2\u306b\u3088\u308b\u4e88\u6e2c(Aileen Nielsen \u8457\u3001\u5c71\u5d0e \u90a6\u5b50\u3001\u5c71\u5d0e \u5eb7\u5b8f \u8a33\u3001\u30aa\u30e9\u30a4\u30ea\u30fc\u30fb\u30b8\u30e3\u30d1\u30f3) ISBN: 978-4-87311-960-1<\/p>\n
          \u30bf\u30a4\u30c8\u30eb\u306e\u3068\u304a\u308a\u3001\u6642\u7cfb\u5217\u89e3\u6790\u306e\u672c\u3067\u3059\u3002R\u3068Python\u306e\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u304c\u8c4a\u5bcc\u3067\u3059\u3002\u4eca\u56de\u306f\u3001\u3053\u306e\u672c\u306e\u5185\u5bb9\u3068\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u3092\u304d\u3063\u304b\u3051\u306b\u8a18\u4e8b\u3092\u66f8\u304d\u307e\u3057\u305f\u304c\u3001\u3053\u306e\u672c\u81ea\u4f53\u3067\u306f\u3001\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u3082MCMC\u30922\uff5e3\u30da\u30fc\u30b8\u306b\u89e6\u308c\u3089\u308c\u3066\u3044\u308b\u306e\u307f\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u6642\u7cfb\u5217\u89e3\u6790\u306e\u6982\u89b3\u3001\u524d\u51e6\u7406\u3001\u7d71\u8a08\u30e2\u30c7\u30eb\u3001\u9069\u7528\u4e8b\u4f8b\u7b49\u3092\u77e5\u308b\u305f\u3081\u306b\u306f\u826f\u3044\u672c\u3060\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n
          \u30bc\u30ed\u304b\u3089\u3067\u304d\u308bMCMC\u3000\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u306e\u5b9f\u8df5\u7684\u5165\u9580 (\u82b1\u7530\u653f\u7bc4\uff0f\u677e\u6d66\u58ee\u30fb\u8457) ISBN: 978-4-06-520174-9<\/p>\n
          MCMC\u306b\u3064\u3044\u3066\u306f\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u306e\u672c\u306b\u30e2\u30c7\u30ea\u30f3\u30b0\u624b\u6cd5\u3068\u3057\u3066\u7d39\u4ecb\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u591a\u3044\u306e\u3067\u3059\u304c\u3001\u3053\u306e\u672c\u306f\u9006\u3067\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u306e\u8aac\u660e\u304b\u3089\u306f\u3058\u307e\u3063\u3066\u4e00\u518a\u4e38\u3054\u3068MCMC\u306b\u95a2\u3057\u3066\u8a18\u8ff0\u3055\u308c\u3066\u3044\u3066\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u3084\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u7b49\u306e\u7269\u7406\u5b66\u3078\u306e\u5fdc\u7528\u306f\u305d\u306e\u9069\u7528\u4f8b\u3068\u3057\u3066\u51fa\u3066\u304d\u307e\u3059\u3002\u3053\u306e\u672c\u306b\u8f09\u3063\u3066\u3044\u308b\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u306fC\u304a\u3088\u3073C++\u3067\u4e00\u898b\u3068\u3063\u3064\u304d\u306b\u304f\u3044\u306e\u3067\u3059\u304c\u3001\u8aac\u660e\u304c\u4e01\u5be7\u306a\u306e\u3068\u3001\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u304c\u63b2\u8f09\u3055\u308c\u3066\u3044\u308bGithub\u4e0a\u306b\u306fC\u3001C++\u306e\u30b3\u30fc\u30c9\u306b\u52a0\u3048\u3066Python\u3067\u306e\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u3082\u63b2\u8f09\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n
          \u3053\u308c\u306a\u3089\u308f\u304b\u308b\u6a5f\u68b0\u5b66\u7fd2\u5165\u9580 (\u5bcc\u8c37\u662d\u592b\u30fb\u8457) ISBN: 978-4-06-522549-3<\/p>\n
          \u8457\u8005\u304c\u7269\u7406\u5b66\u304c\u5c02\u9580\u306a\u306e\u3067\u3001\u7269\u7406\u5b66\u5bc4\u308a\u306e\u6a5f\u68b0\u5b66\u7fd2\u5165\u9580\u3067\u3059\u3002\u4e00\u7ae0\u307e\u308b\u3054\u3068\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u306b\u5272\u304b\u308c\u3066\u304a\u308a\u3001\u8a18\u8ff0\u3082\u8a73\u3057\u3044\u3067\u3059\u3002\u305f\u3060\u3001\u30bf\u30a4\u30c8\u30eb\u306e\u300c\u3053\u308c\u306a\u3089\u308f\u304b\u308b\u300d\u306f\u591a\u5c11\u7591\u554f\u304c\u3042\u308a\u3001\u6a5f\u68b0\u5b66\u7fd2\u3068\u7269\u7406\u5b66\u306b\u95a2\u3057\u3066\u5168\u304f\u77e5\u898b\u304c\u306a\u3044\u3068\u8aad\u307f\u9032\u3081\u308b\u306e\u306f\u96e3\u3057\u3044\u3068\u601d\u3044\u307e\u3059\u3002\u9006\u306b\u77e5\u3063\u3066\u3044\u308b\u3068\u300c\u304f\u3059\u3063\u300d\u3068\u3059\u308b\u3068\u3053\u308d\u304c\u591a\u3005\u3042\u308a\u307e\u3059\u3002<\/p>\n
          \u3053\u308c\u4ee5\u5916\u306b\u3082\u3001\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u3067\u3042\u308c\u3070\u7d71\u8a08\u529b\u5b66\u306e\u6559\u79d1\u66f8\u3001MCMC\u3067\u3042\u308c\u3070\u6a5f\u68b0\u5b66\u7fd2\u3084\u30d9\u30a4\u30ba\u7d71\u8a08\u306e\u6559\u79d1\u66f8\u7b49\u826f\u3044\u5c02\u9580\u66f8\u304c\u591a\u304f\u3042\u308a\u307e\u3059\u3002\u7d71\u8a08\u529b\u5b66\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u3068\u3082\u306b\u6570\u5f0f\u304c\u591a\u7528\u3055\u308c\u3069\u3046\u3057\u3066\u3082\u5fcc\u907f\u3057\u3066\u3057\u307e\u3046\u3068\u3053\u308d\u304c\u3042\u308a\u307e\u3059\u304c15\u3001\u7406\u89e3\u304c\u3067\u304d\u308b\u3068\u6df1\u6df5\u306a\u4e16\u754c\u304c\u5e83\u304c\u3063\u3066\u3044\u307e\u3059\u3002\u307e\u305f\u3001\u6700\u8fd1\u306f\u753b\u50cf\u51e6\u7406\u7b49\u306b\u7d71\u8a08\u529b\u5b66\u7684\u306a\u624b\u6cd5\u304c\u4f7f\u308f\u308c\u308b\u7b49\u3001\u60c5\u5831\u3068\u7269\u7406\u306e\u4e21\u65b9\u306e\u5883\u754c\u9818\u57df\u306e\u3088\u3046\u306a\u5206\u91ce\u3082\u3042\u308a\u307e\u305916\u3002\u5c11\u3057\u3067\u3082\u8208\u5473\u304c\u3042\u308b\u3068\u3053\u308d\u304b\u3089\u3001\u66f8\u5e97\u3067\u8aad\u3081\u305d\u3046\u306a\u672c\u3092\u624b\u306b\u53d6\u3063\u3066\u4e00\u6b69\u9032\u3081\u3066\u3044\u305f\u3060\u3051\u305f\u3089\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n
          \n
          \u203b \u6587\u4e2d\u306b\u8a18\u8f09\u3055\u308c\u3066\u3044\u308b\u4f1a\u793e\u540d\u3001\u5546\u54c1\u540d\u3001\u88fd\u54c1\u540d\u306f\u5404\u793e\u306e\u5546\u6a19\u307e\u305f\u306f\u767b\u9332\u5546\u6a19\u3067\u3059\u3002<\/p>\n
          https:\/\/github.com\/PracticalTimeSeriesAnalysis\/BookRepo\/blob\/master\/Ch04\/Ising.ipynb \u21a9<\/p>\n
          \u30aa\u30ea\u30b8\u30ca\u30eb\u306e\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u3068\u306f\u3001\u4e00\u90e8\u8a18\u4e8b\u306e\u5185\u5bb9\u306b\u5408\u308f\u305b\u3066\u5909\u6570\u540d\u3092\u5909\u3048\u3066\u3044\u307e\u3059\u3002 \u21a9<\/p>\n
          \u53b3\u5bc6\u306a\u8aac\u660e\u306f\u79c1\u306e\u624b\u306b\u4f59\u308b\u306e\u3067\u3001\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3056\u3063\u304f\u308a\u3068\u3057\u305f\u8aac\u660e\u3057\u304b\u3057\u307e\u305b\u3093\u3002\u4e00\u822c\u5411\u3051\u306e\u5e73\u6613\u306a\u89e3\u8aac\u3068\u3057\u3066\u306f\u3001\u3053\u3061\u3089\u306eenakai00\u3055\u3093\u306e\u30d6\u30ed\u30b0\u8a18\u4e8b\u304c\u5206\u304b\u308a\u3084\u3059\u304f\u3066\u3088\u3044\u3068\u601d\u3044\u307e\u3059\u3002\u306a\u304a\u3001\u672c\u8a18\u4e8b\u306b\u3064\u3044\u3066\u660e\u3089\u304b\u306a\u9593\u9055\u3044\u3092\u898b\u3064\u3051\u305f\u6642\u306f\u3001\u3054\u6307\u6458\u304f\u3060\u3055\u3044\u3002 \u21a9<\/p>\n
          \u7269\u7406\u5b66(\u7d71\u8a08\u529b\u5b66)\u3067\u3044\u3046\u30dc\u30eb\u30c4\u30de\u30f3\u5206\u5e03\u3067\u3059\u3002 \u21a9<\/p>\n
          \u7d71\u8a08\u529b\u5b66\u306e\u4e16\u754c\u3067\u306f\u5206\u914d\u95a2\u6570\u3068\u547c\u3070\u308c\u307e\u3059\u3002 \u21a9<\/p>\n
          \u3046\u305d\u304a\u3063\u3057\u3083\u3044\u3002\u3053\u306e\u8a18\u4e8b\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u4f8b$(N=16 \\times 16)$\u3050\u3089\u3044\u3060\u3063\u305f\u3089\u3059\u3050\u306b\u8a08\u7b97\u3067\u304d\u308b\u3060\u308d\u3001\u3068\u3064\u3063\u3053\u307e\u306a\u3044\u3067\u304f\u3060\u3055\u3044\u3002\u4e00\u822c\u8ad6\u3092\u8a00\u3063\u3066\u3044\u307e\u3059\u3002 \u21a9<\/p>\n
          Markov chain Monte Carlo\u3001\u7565\u3057\u3066MCMC\u3067\u3059\u3002 \u21a9<\/p>\n
          \u6b21\u5143\u306e\u546a\u3044\u3068\u547c\u3070\u308c\u3066\u3044\u307e\u3059\u3002 \u21a9<\/p>\n
          MCMC\u3067\u5b9a\u5e38\u5206\u5e03\u3092\u4f5c\u308b\u624b\u6cd5\u306b\u306f\u3001\u30e1\u30c8\u30ed\u30dd\u30ea\u30b9\u6cd5\u3001\u30ae\u30d7\u30b9\u30fb\u30b5\u30f3\u30d7\u30e9\u30fc(\u71b1\u6d74\u6cd5)\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u7b49\u3001\u3044\u304f\u3064\u304b\u3042\u308a\u307e\u3059\u3002 \u21a9<\/p>\n
          \u79c1\u81ea\u8eab\u3001\u73fe\u5728\u306fAI\u3084\u30c7\u30fc\u30bf\u30b5\u30a4\u30a8\u30f3\u30b9\u95a2\u9023\u306e\u4ed5\u4e8b\u3092\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u5b9f\u306f\u307e\u3060\u76f4\u63a5MCMC\u304c\u5fc5\u8981\u306b\u306a\u308b\u4ed5\u4e8b\u306b\u51fa\u4f1a\u3063\u305f\u3053\u3068\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u3069\u3053\u306b\u3042\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u3061\u306a\u307f\u306b\u3001\u30d9\u30a4\u30ba\u7684\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u81ea\u4f53\u306b\u306f\u3061\u3087\u3063\u3068\u4ed5\u4e8b\u3067\u51fa\u4f1a\u3044\u307e\u3057\u305f\u3002 \u21a9<\/p>\n
          \u3053\u308c\u304c\u30e1\u30c8\u30ed\u30dd\u30ea\u30b9\u6cd5\u3067\u3059\u3002 \u21a9<\/p>\n
          \u5143\u3068\u306a\u3063\u305f\u30bd\u30fc\u30b9\u30d5\u30a1\u30a4\u30eb\u3067\u30010\u4ee5\u4e0a1\u672a\u6e80\u306e\u4e00\u69d8\u4e71\u6570\u306e\u751f\u6210\u306bnumpy.random.random\u304c\u4f7f\u3063\u3066\u3042\u3063\u3066\u6700\u521d\u898b\u305f\u3068\u304d\u306b\u300cnp.random.random\u3063\u3066\u306a\u306b\uff1fnp.random.rand\u3058\u3083\u306a\u3044\u306e\uff1f\u300d\u3068\u601d\u3063\u3066numpy.random.rand\u306e\u30de\u30cb\u30e5\u30a2\u30eb\u30da\u30fc\u30b8\u3092\u307f\u308b\u3068\u3001This is a convenience function for users porting code from Matlab, and wraps random_sample.\u3068\u66f8\u3044\u3066\u3042\u3063\u3066random.random\u306frandom.random_sample\u306e\u30a8\u30a4\u30ea\u30a2\u30b9\u306a\u306e\u3067\u3001\u7d50\u5c40\u306frandom.rand\u306frando.random_sample\u3092\u30e9\u30c3\u30d7\u3057\u3066\u3044\u308b\u3068\u8a8d\u8b58\u3057\u307e\u3057\u305f\u3002random_sample\u306e\u30de\u30cb\u30e5\u30a2\u30eb\u30da\u30fc\u30b8\u306b\u306f\u3001random.Generator.random which should be used for new code.\u3068\u3044\u3063\u305f\u3053\u3068\u3082\u66f8\u3044\u3066\u3042\u308a\u307e\u3059\u304c\u3001\u4eca\u56de\u306f\u5143\u30bd\u30fc\u30b9\u306e\u307e\u307erandom.random\u3092\u4f7f\u3063\u3066\u3044\u307e\u3059\u3002 \u21a9<\/p>\n
          \u3053\u306e\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u6700\u521d\u6b63\u898f\u5316(\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u30b9\u30c6\u30c3\u30d7\u6570\u3067\u5272\u3063\u3066\u78ba\u7387\u5bc6\u5ea6\u306e\u30b0\u30e9\u30d5\u306b\u3059\u308b)\u3057\u3088\u3046\u3068\u3057\u3066\u3001plt.hist\u306edensity\u30aa\u30d7\u30b7\u30e7\u30f3\u3092True\u306b\u3057\u3066\u307f\u305f\u306e\u3067\u3059\u304c\u3001\u306a\u305c\u304b\u5168\u4f53\u306e\u548c\u304c1.0\u306b\u306a\u3089\u305a\u898b\u305f\u76ee\u306b\u3082\u304a\u304b\u3057\u306a\u5024\u306e\u30b0\u30e9\u30d5\u306b\u306a\u308b\u306e\u3067\u4eca\u56de\u306e\u63b2\u8f09\u3067\u306f\u4e00\u65e6\u3042\u304d\u3089\u3081\u307e\u3057\u305f\u3002\u5f8c\u3067\u3001matplotlib.pyplot.hist\u306e\u30de\u30cb\u30e5\u30a2\u30eb\u30da\u30fc\u30b8\u306edensity\u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u3068\u3053\u308d\u306b\u300cIf True, draw and return a probability density: each bin will display the bin’s raw count divided by the total number of counts and the bin width (density = counts \/ (sum(counts) * np.diff(bins))),\u300d\u3068\u66f8\u3044\u3066\u3042\u308b\u306e\u306b\u6c17\u304c\u3064\u304d\u3001\u5272\u308b\u6570\u304c\u5404bin\u306e\u30ab\u30a6\u30f3\u30c8\u6570$\\times$bin\u5e45(\u4eca\u56de\u306e\u5834\u5408\u3001bin\u5e45\u304c2\u306a\u306e\u3067\u3001\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u30b9\u30c6\u30c3\u30d7\u65701500$\\times$2=3000)\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u3068\u7406\u89e3\u3057\u307e\u3057\u305f\u3002\u7bc4\u56f2\u3068bin\u6570\u306e\u8abf\u6574\u3092\u3059\u308c\u3070\u3044\u3051\u305d\u3046\u306a\u6c17\u304c\u3057\u307e\u3059\u3002 \u21a9<\/p>\n
          \u6b63\u78ba\u306b\u306f\u9006\u6e29\u5ea6($=1\/T$)\u304c0.440$\\dots$\u3068\u66f8\u3044\u3066\u3042\u308b\u306e\u3067\u3059\u304c\u3001\u3053\u306e\u8a18\u4e8b\u306e\u672c\u6587\u3067\u306f\u9006\u6e29\u5ea6\u3092\u3044\u3046\u8a00\u8449\u3092\u4f7f\u3063\u3066\u3044\u306a\u3044\u306e\u3067\u9006\u6570\u3092\u53d6\u3063\u3066\u3044\u307e\u3059\u3002 \u21a9<\/p>\n
          \u79c1\u81ea\u8eab\u3001\u6570\u5f0f\u304c\u3044\u3063\u3071\u3044\u3042\u308b\u3068\u8aad\u3081\u307e\u305b\u3093\u3002\u82e6\u624b\u610f\u8b58\u3092\u514b\u670d\u3059\u308b\u3060\u3051\u306e\u597d\u5947\u5fc3\u3068\u60c5\u71b1\u304c\u3044\u308a\u307e\u3059\u3002 \u21a9<\/p>\n
          \u30d9\u30a4\u30ba\u7d71\u8a08\u306e\u6709\u540d\u306a\u672c\u306b\u30d9\u30a4\u30ba\u7d71\u8a08\u306e\u7406\u8ad6\u3068\u65b9\u6cd5 (\u6e21\u8fba\u6f84\u592b\u8457\u3001\u30b3\u30ed\u30ca\u793e)\u3068\u3044\u3046\u672c\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u66f8\u5e97\u3067\u6700\u521d\u624b\u306b\u53d6\u3063\u305f\u3068\u304d3\u30da\u30fc\u30b8\u76ee\u306b\u300c\u9006\u6e29\u5ea6\u300d\u30014\u30da\u30fc\u30b8\u76ee\u306b\u300c\u5206\u914d\u95a2\u6570\u300d\u3068\u3044\u3046\u8a00\u8449\u304c\u51fa\u3066\u304d\u3066\u3001\u300c\u7d71\u8a08\u529b\u5b66\u77e5\u3089\u306a\u3044\u3068\u3053\u306e\u672c\u8aad\u3081\u306a\u3044\u3058\u3083\u3093(\u307e\u3060\u307e\u3060\u8aad\u3081\u306a\u3044\u306a)\u300d\u3068\u601d\u3063\u3066\u305d\u3063\u3068\u5143\u306e\u66f8\u68da\u306b\u623b\u3057\u307e\u3057\u305f\u3002 \u21a9<\/p>\n<\/section>\n","protected":false},"excerpt":{"rendered":"
          \u3053\u306e\u8a18\u4e8b\u306fNTT\u30b3\u30e0\u30a6\u30a7\u30a2 Advent Calendar 2022 24\u65e5\u76ee\u306e\u8a18\u4e8b\u3067\u3059\u3002 NTT\u30b3\u30e0\u30a6\u30a7\u30a2\u306e […]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-46037","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"\n- Blog - Silicon Cloud<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.silicloud.com\/zh\/blog\/46037-2\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:description\" content=\"\u3053\u306e\u8a18\u4e8b\u306fNTT\u30b3\u30e0\u30a6\u30a7\u30a2 Advent Calendar 2022 24\u65e5\u76ee\u306e\u8a18\u4e8b\u3067\u3059\u3002 NTT\u30b3\u30e0\u30a6\u30a7\u30a2\u306e […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.silicloud.com\/zh\/blog\/46037-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Blog - 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