{"id":1947,"date":"2023-04-28T10:59:32","date_gmt":"2023-04-28T01:59:32","guid":{"rendered":"https:\/\/edu.ujhb.org\/?p=1947"},"modified":"2023-04-28T10:59:32","modified_gmt":"2023-04-28T01:59:32","slug":"scipy%e5%85%a5%e9%96%80%ef%bc%88%e6%97%a5%e6%9c%ac%e8%aa%9e%e7%89%88%ef%bc%89","status":"publish","type":"post","link":"https:\/\/edu.ujhb.org\/?p=1947","title":{"rendered":"Scipy\u5165\u9580\uff08\u65e5\u672c\u8a9e\u7248\uff09"},"content":{"rendered":"\n<p>\u3082\u3089\u3048\u307e\u3059\u304b\u3002Scipy \u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u304b\u3089\u59cb\u3081\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u304b\u3089\u8aac\u660e\u3059\u308b\u5185\u5bb9\u306e\u6982\u8981\u3092\u6559\u3048\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<p>\u3082\u3061\u308d\u3093\uff01\u4ee5\u4e0b\u306f\u3001Scipy \u306e\u516c\u5f0f Web \u30b5\u30a4\u30c8\u306e\u5185\u5bb9\u3068\u3044\u304f\u3064\u304b\u306e\u57fa\u672c\u7684\u306a\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u306b\u57fa\u3065\u304f\u30d3\u30c7\u30aa \u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u306e\u6982\u8981\u3067\u3059\u3002\u3053\u306e\u6982\u8981\u306b\u57fa\u3065\u3044\u3066\u3001IT \u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb \u30d3\u30c7\u30aa\u3092\u4f5c\u6210\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>Scipy \u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb \u30d3\u30c7\u30aa\u306e\u6982\u8981:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Scipy \u306e\u7d39\u4ecb\n<ul class=\"wp-block-list\">\n<li>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u6982\u8981<\/li>\n\n\n\n<li>Scipy \u3068 Numpy \u306e\u95a2\u4fc2<\/li>\n\n\n\n<li>Scipy \u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u57fa\u672c\u6a5f\u80fd\u30e2\u30b8\u30e5\u30fc\u30eb\n<ul class=\"wp-block-list\">\n<li>Scipy \u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb<\/li>\n\n\n\n<li>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u30a4\u30f3\u30dd\u30fc\u30c8\u3059\u308b\u65b9\u6cd5<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6570\u5024\u7a4d\u5206\n<ul class=\"wp-block-list\">\n<li>scipy.integrate \u30e2\u30b8\u30e5\u30fc\u30eb<\/li>\n\n\n\n<li>4 \u3064\u306e\u4e00\u822c\u7684\u306a\u7a4d\u5206\u95a2\u6570<\/li>\n\n\n\n<li>\u4f8b: \u6570\u5024\u7a4d\u5206\u8a08\u7b97<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6700\u9069\u5316\n<ul class=\"wp-block-list\">\n<li>scipy.optimize \u30e2\u30b8\u30e5\u30fc\u30eb<\/li>\n\n\n\n<li>\u6700\u5c0f\u4e8c\u4e57\u6cd5<\/li>\n\n\n\n<li>\u5236\u7d04\u4ed8\u304d\u6700\u9069\u5316\u554f\u984c<\/li>\n\n\n\n<li>\u4f8b: \u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u88dc\u9593\u6cd5\n<ul class=\"wp-block-list\">\n<li>scipy.interpolate \u30e2\u30b8\u30e5\u30fc\u30eb<\/li>\n\n\n\n<li>1D \u88dc\u9593<\/li>\n\n\n\n<li>2D \u88dc\u9593<\/li>\n\n\n\n<li>\u4f8b: \u30c7\u30fc\u30bf\u88dc\u9593\u306e\u5b9f\u88c5<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7dda\u5f62\u4ee3\u6570\n<ul class=\"wp-block-list\">\n<li>scipy.linalg \u30e2\u30b8\u30e5\u30fc\u30eb<\/li>\n\n\n\n<li>\u884c\u5217\u5206\u89e3<\/li>\n\n\n\n<li>\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb\u3092\u89e3\u304f<\/li>\n\n\n\n<li>\u4f8b: \u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u4fe1\u53f7\u51e6\u7406\n<ul class=\"wp-block-list\">\n<li>scipy.signal \u30e2\u30b8\u30e5\u30fc\u30eb<\/li>\n\n\n\n<li>\u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08<\/li>\n\n\n\n<li>\u4fe1\u53f7\u5206\u6790<\/li>\n\n\n\n<li>\u4f8b: \u4fe1\u53f7\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306e\u5b9f\u88c5<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u753b\u50cf\u51e6\u7406\n<ul class=\"wp-block-list\">\n<li>scipy.ndimage \u30e2\u30b8\u30e5\u30fc\u30eb<\/li>\n\n\n\n<li>\u753b\u50cf\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0<\/li>\n\n\n\n<li>\u753b\u50cf\u5909\u63db\u3068\u30e2\u30eb\u30d5\u30a9\u30ed\u30b8\u30fc\u64cd\u4f5c<\/li>\n\n\n\n<li>\u4f8b: \u5b9f\u969b\u306e\u753b\u50cf\u51e6\u7406<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7d71\u8a08\u5206\u6790\n<ul class=\"wp-block-list\">\n<li>scipy.stats \u30e2\u30b8\u30e5\u30fc\u30eb<\/li>\n\n\n\n<li>\u8a18\u8ff0\u7d71\u8a08<\/li>\n\n\n\n<li>\u78ba\u7387\u5206\u5e03<\/li>\n\n\n\n<li>\u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u5b9a\u3068\u4eee\u8aac\u691c\u5b9a<\/li>\n\n\n\n<li>\u4f8b: \u7d71\u8a08\u5206\u6790\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u30d5\u30a1\u30a4\u30eb\u306e\u5165\u51fa\u529b\n<ul class=\"wp-block-list\">\n<li>scipy.io \u30e2\u30b8\u30e5\u30fc\u30eb<\/li>\n\n\n\n<li>\u30d5\u30a1\u30a4\u30eb\u306e\u8aad\u307f\u53d6\u308a\u3068\u66f8\u304d\u8fbc\u307f<\/li>\n\n\n\n<li>\u4f8b: \u30d5\u30a1\u30a4\u30eb\u306b\u5bfe\u3059\u308b\u8aad\u307f\u53d6\u308a\u64cd\u4f5c\u3068\u66f8\u304d\u8fbc\u307f\u64cd\u4f5c<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u4e00\u822c\u7684\u306a\u6a5f\u80fd\u3068\u30c6\u30af\u30cb\u30c3\u30af\n<ul class=\"wp-block-list\">\n<li>\u7279\u6b8a\u6a5f\u80fd<\/li>\n\n\n\n<li>\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570<\/li>\n\n\n\n<li>\u4f8b: Scipy \u30e6\u30fc\u30c6\u30a3\u30ea\u30c6\u30a3\u95a2\u6570<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Scipy \u30b3\u30f3\u30d0\u30c3\u30c8 \u30b1\u30fc\u30b9\n<ul class=\"wp-block-list\">\n<li>\u30b1\u30fc\u30b9 1: \u30c7\u30fc\u30bf\u306e\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3068\u4e88\u6e2c<\/li>\n\n\n\n<li>\u30b1\u30fc\u30b9 2: \u753b\u50cf\u306e\u8a8d\u8b58\u3068\u51e6\u7406<\/li>\n\n\n\n<li>\u30b1\u30fc\u30b9 3: \u4fe1\u53f7\u306e\u30ce\u30a4\u30ba\u9664\u53bb\u3068\u5206\u6790<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>\u3053\u306e\u6982\u8981\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u4e3b\u306a\u6a5f\u80fd\u3068\u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u30ab\u30d0\u30fc\u3057\u3066\u304a\u308a\u3001\u5b9f\u969b\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u3053\u306e\u6982\u8981\u3092\u8abf\u6574\u307e\u305f\u306f\u62e1\u5f35\u3067\u304d\u307e\u3059\u3002\u9811\u5f35\u3063\u3066\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u3092\u4f5c\u6210\u3057\u3066\u304f\u3060\u3055\u3044!<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u6982\u8981\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u3053\u306e\u4f1a\u8a71\u3067\u4f7f\u7528\u3055\u308c\u305f\u4ee5\u524d\u306e\u30e2\u30c7\u30eb\u306f\u4f7f\u7528\u3067\u304d\u307e\u305b\u3093\u3002\u6700\u65b0\u306e\u30c7\u30d5\u30a9\u30eb\u30c8 \u30e2\u30c7\u30eb\u306b\u5207\u308a\u66ff\u3048\u307e\u3057\u305f<\/p>\n\n\n\n<p>Scipy \u306f Python \u8a00\u8a9e\u306b\u57fa\u3065\u304f\u79d1\u5b66\u8a08\u7b97\u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u3059. Numpy \u306e\u4e0a\u306b\u69cb\u7bc9\u3055\u308c\u3066\u304a\u308a\u3001\u4e00\u9023\u306e\u52b9\u7387\u7684\u3067\u5c02\u9580\u7684\u306a\u6570\u5024\u8a08\u7b97\u3001\u6700\u9069\u5316\u3001\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3001\u88dc\u9593\u3001\u7d71\u5408\u3001\u4fe1\u53f7\u51e6\u7406\u3001\u753b\u50cf\u51e6\u7406\u3001\u304a\u3088\u3073\u305d\u306e\u4ed6\u306e\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059.&nbsp;Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u540d\u524d\u306f\u3001\u79d1\u5b66\u8a08\u7b97\u7528\u306e Python \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u610f\u5473\u3059\u308b Scientific Python \u306b\u7531\u6765\u3057\u307e\u3059\u3002Python \u30a8\u30b3\u30b7\u30b9\u30c6\u30e0\u306b\u4e0d\u53ef\u6b20\u306a\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u306e 1 \u3064\u3067\u3042\u308a\u3001\u30c7\u30fc\u30bf\u5206\u6790\u3001\u79d1\u5b66\u7814\u7a76\u3001\u30a8\u30f3\u30b8\u30cb\u30a2\u30ea\u30f3\u30b0 \u30b3\u30f3\u30d4\u30e5\u30fc\u30c6\u30a3\u30f3\u30b0\u306a\u3069\u306e\u5206\u91ce\u3067\u5e83\u304f\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306f\u3044\u304f\u3064\u304b\u306e\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u3067\u69cb\u6210\u3055\u308c\u3066\u304a\u308a\u3001\u305d\u308c\u305e\u308c\u304c\u7570\u306a\u308b\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u4e3b\u8981\u306a\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u7c21\u5358\u306a\u7d39\u4ecb\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>scipy.integrate: \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u3084\u6570\u5024\u7a4d\u5206\u306a\u3069\u306e\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.optimize: \u6700\u5c0f\u4e8c\u4e57\u6cd5\u3001\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u306a\u3069\u306e\u6700\u9069\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.interpolate: \u88dc\u9593\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u63d0\u4f9b\u3057\u30011 \u6b21\u5143\u304a\u3088\u3073 2 \u6b21\u5143\u306e\u88dc\u9593\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.linalg: \u884c\u5217\u5206\u89e3\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u306a\u3069\u306e\u7dda\u5f62\u4ee3\u6570\u6f14\u7b97\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.signal: \u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08\u3001\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306a\u3069\u306e\u4fe1\u53f7\u51e6\u7406\u306b\u95a2\u9023\u3059\u308b\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.ndimage: \u753b\u50cf\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3001\u30e2\u30eb\u30d5\u30a9\u30ed\u30b8\u30fc\u6f14\u7b97\u306a\u3069\u3001\u753b\u50cf\u51e6\u7406\u306b\u95a2\u9023\u3059\u308b\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.stats: \u78ba\u7387\u5206\u5e03\u3001\u4eee\u8aac\u691c\u5b9a\u306a\u3069\u306e\u7d71\u8a08\u5206\u6790\u306b\u95a2\u9023\u3059\u308b\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.io: \u30c7\u30fc\u30bf\u306e\u5165\u51fa\u529b\u306b\u95a2\u9023\u3059\u308b\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u3001\u8907\u6570\u306e\u5f62\u5f0f\u3067\u306e\u30c7\u30fc\u30bf\u306e\u8aad\u307f\u53d6\u308a\u3068\u66f8\u304d\u8fbc\u307f\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.special: \u30d9\u30c3\u30bb\u30eb\u95a2\u6570\u3001\u30ac\u30f3\u30de\u95a2\u6570\u306a\u3069\u3001\u6570\u5b66\u306e\u7279\u6b8a\u95a2\u6570\u306e\u5b9f\u88c5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4e0a\u8a18\u306e\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u52a0\u3048\u3066\u3001Scipy \u306f\u591a\u9805\u5f0f\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3001\u9ad8\u901f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306a\u3069\u306e\u4ed6\u306e\u6a5f\u80fd\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3064\u307e\u308a\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306f\u3001\u6570\u5b66\u3001\u7d71\u8a08\u3001\u4fe1\u53f7\u51e6\u7406\u3001\u753b\u50cf\u51e6\u7406\u306a\u3069\u306e\u8c4a\u5bcc\u306a\u6a5f\u80fd\u3092\u63d0\u4f9b\u3059\u308b\u5f37\u529b\u306a\u79d1\u5b66\u8a08\u7b97\u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u3042\u308a\u3001Python \u79d1\u5b66\u8a08\u7b97\u306e\u91cd\u8981\u306a\u30c4\u30fc\u30eb\u306e 1 \u3064\u3067\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>Scipy\u3068Numpy\u306e\u95a2\u4fc2\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>Scipy \u3068 Numpy \u306f\u3001\u3088\u304f\u4e00\u7dd2\u306b\u4f7f\u7528\u3055\u308c\u308b 2 \u3064\u306e\u5bc6\u63a5\u306b\u95a2\u9023\u3059\u308b Python \u79d1\u5b66\u8a08\u7b97\u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u3059\u3002Numpy \u306f Python \u306e\u6570\u5024\u8a08\u7b97\u306e\u57fa\u672c\u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u3001\u591a\u6b21\u5143\u914d\u5217\u3068\u3001\u6570\u5024\u6f14\u7b97\u3001\u7d71\u8a08\u89e3\u6790\u3001\u7dda\u5f62\u4ee3\u6570\u306a\u3069\u3001\u914d\u5217\u3092\u64cd\u4f5c\u3059\u308b\u305f\u3081\u306e\u3055\u307e\u3056\u307e\u306a\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002Scipy \u306f\u3001Numpy \u306e\u4e0a\u306b\u69cb\u7bc9\u3055\u308c\u305f\u9ad8\u30ec\u30d9\u30eb\u306e\u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u3042\u308a\u3001\u6700\u9069\u5316\u3001\u88dc\u9593\u3001\u7d71\u5408\u3001\u4fe1\u53f7\u51e6\u7406\u3001\u753b\u50cf\u51e6\u7406\u306a\u3069\u3001\u3088\u308a\u6570\u5b66\u7684\u3001\u79d1\u5b66\u7684\u3001\u5de5\u5b66\u7684\u306a\u8a08\u7b97\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001Scipy \u306f Numpy \u306e\u88dc\u8db3\u304a\u3088\u3073\u62e1\u5f35\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>Scipy \u306f\u5185\u90e8\u3067 Numpy \u306e\u591a\u6b21\u5143\u914d\u5217\u3092\u4f7f\u7528\u3059\u308b\u3068\u540c\u6642\u306b\u3001\u79d1\u5b66\u8a08\u7b97\u7528\u306b\u591a\u304f\u306e\u95a2\u6570\u3068\u30af\u30e9\u30b9\u3092\u62e1\u5f35\u3057\u307e\u3059\u3002Scipy \u306e\u591a\u304f\u306e\u95a2\u6570\u306f\u3001\u5165\u529b\u3068\u3057\u3066 Numpy \u306e\u914d\u5217\u3092\u5fc5\u8981\u3068\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001Scipy \u306e\u95a2\u6570\u306f\u901a\u5e38\u3001\u591a\u6b21\u5143\u914d\u5217\u3092\u64cd\u4f5c\u3059\u308b\u3088\u3046\u306b\u8a2d\u8a08\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001Scipy \u3068 Numpy \u306f\u591a\u304f\u306e\u70b9\u3067\u5bc6\u63a5\u306b\u95a2\u9023\u3057\u3066\u3044\u307e\u3059\u3002Scipy \u306f\u3001Numpy \u914d\u5217\u306e\u4e71\u6570\u751f\u6210\u3001\u6570\u5b66\u95a2\u6570\u3001\u7d71\u8a08\u95a2\u6570\u306a\u3069\u3001Numpy \u914d\u5217\u306e\u62e1\u5f35\u6a5f\u80fd\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3055\u3089\u306b\u3001Scipy \u306f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3001\u6700\u9069\u5316\u3001\u88dc\u9593\u3001\u4fe1\u53f7\u51e6\u7406\u3001\u753b\u50cf\u51e6\u7406\u306a\u3069\u3001Numpy \u306b\u306f\u306a\u3044\u3044\u304f\u3064\u304b\u306e\u6a5f\u80fd\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u3001Numpy \u306e\u591a\u6b21\u5143\u914d\u5217\u306b\u57fa\u3065\u3044\u3066\u5b9f\u88c5\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u8981\u7d04\u3059\u308b\u3068\u3001Numpy \u306f Python \u3067\u57fa\u672c\u7684\u306a\u6570\u5b66\u6f14\u7b97\u3092\u63d0\u4f9b\u3057\u307e\u3059\u304c\u3001Scipy \u306f Numpy \u3092\u62e1\u5f35\u3057\u3066\u3001\u3088\u308a\u9ad8\u5ea6\u3067\u5e45\u5e83\u3044\u6570\u5b66\u304a\u3088\u3073\u79d1\u5b66\u8a08\u7b97\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002Scipy \u3068 Numpy \u306e\u7d44\u307f\u5408\u308f\u305b\u306f\u3001\u307b\u3068\u3093\u3069\u306e\u79d1\u5b66\u8a08\u7b97\u306e\u30cb\u30fc\u30ba\u3092\u6e80\u305f\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>Scipy\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>Scipy \u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b\u306b\u306f\u3001\u901a\u5e38\u3001\u6b21\u306e\u624b\u9806\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Python \u74b0\u5883\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b: \u307e\u305a\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306b Python \u74b0\u5883\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059. Scipy \u306f Python 2.x \u304a\u3088\u3073 Python 3.x \u74b0\u5883\u3067\u5b9f\u884c\u3067\u304d\u307e\u3059. Python 3.x \u30d0\u30fc\u30b8\u30e7\u30f3\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059.&nbsp;\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u7528\u306e Python \u516c\u5f0f Web \u30b5\u30a4\u30c8\u304b\u3089\u30a4\u30f3\u30b9\u30c8\u30fc\u30e9\u30fc\u3092\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>Numpy \u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb: Scipy \u306f Numpy \u30e9\u30a4\u30d6\u30e9\u30ea\u306b\u4f9d\u5b58\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u6700\u521d\u306b Numpy \u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002Numpy \u306f\u3001\u6b21\u306e\u3088\u3046\u306b pip \u30b3\u30de\u30f3\u30c9\u3092\u4f7f\u7528\u3057\u3066\u30b3\u30de\u30f3\u30c9 \u30e9\u30a4\u30f3\u306b\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3067\u304d\u307e\u3059\u3002<code>pip install numpy<\/code><\/li>\n\n\n\n<li>Scipy \u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb: Scipy \u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b\u306b\u306f\u3001pip \u30b3\u30de\u30f3\u30c9\u3092\u4f7f\u7528\u3057\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059. \u30b3\u30de\u30f3\u30c9\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059: \u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b\u3068\u3001<code>pip install scipy&nbsp;<\/code>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3068\u305d\u306e\u4f9d\u5b58\u95a2\u4fc2\u304c\u81ea\u52d5\u7684\u306b\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3055\u308c\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3055\u308c\u307e\u3059.&nbsp;Windows \u30b7\u30b9\u30c6\u30e0\u3092\u4f7f\u7528\u3057\u3066\u3044\u3066 pip \u304c\u6b63\u5e38\u306b\u52d5\u4f5c\u3057\u306a\u3044\u5834\u5408\u306f\u3001Scipy \u306e\u516c\u5f0f Web \u30b5\u30a4\u30c8\u304b\u3089\u5bfe\u5fdc\u3059\u308b\u30d0\u30a4\u30ca\u30ea \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3057\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u306e\u691c\u8a3c: After the installation is complete, you can try to import the Scipy library in the Python environment. \u30a8\u30e9\u30fc\u304c\u5831\u544a\u3055\u308c\u306a\u3051\u308c\u3070\u3001\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u306f\u6210\u529f\u3067\u3059\u3002Python \u30a4\u30f3\u30bf\u30e9\u30af\u30c6\u30a3\u30d6\u74b0\u5883\u3067\u6b21\u306e\u30b3\u30de\u30f3\u30c9\u3092\u5165\u529b\u3067\u304d\u307e\u3059: arduinoCopy code<code>import scipy&nbsp;<\/code>\u30a8\u30e9\u30fc\u304c\u5831\u544a\u3055\u308c\u306a\u3044\u5834\u5408\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u304c\u6b63\u5e38\u306b\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3055\u308c\u305f\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>Scipy \u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b\u3068\u3001\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb \u30d7\u30ed\u30bb\u30b9\u4e2d\u306b\u4f9d\u5b58\u95a2\u4fc2\u306e\u554f\u984c\u3084\u30d0\u30fc\u30b8\u30e7\u30f3\u306e\u4e92\u63db\u6027\u306e\u554f\u984c\u306a\u3069\u306e\u554f\u984c\u304c\u767a\u751f\u3059\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u554f\u984c\u304c\u767a\u751f\u3057\u305f\u5834\u5408\u306f\u3001Scipy \u306e\u516c\u5f0f\u30c9\u30ad\u30e5\u30e1\u30f3\u30c8\u3092\u78ba\u8a8d\u3059\u308b\u304b\u3001Python \u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u306b\u52a9\u3051\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>Scipy \u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306f\u3044\u304f\u3064\u304b\u306e\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u3067\u69cb\u6210\u3055\u308c\u3066\u304a\u308a\u3001\u305d\u308c\u305e\u308c\u304c\u7570\u306a\u308b\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u4e3b\u8981\u306a\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u8a73\u7d30\u306a\u8aac\u660e\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>scipy.integrate: \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u3084\u6570\u5024\u7a4d\u5206\u306a\u3069\u306e\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001quad\u3001dblquad\u3001nquad \u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a\u6570\u5024\u7a4d\u5206\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u95a2\u6570 odeint \u304a\u3088\u3073 solve_ivp \u3082\u63d0\u4f9b\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.optimize: \u6700\u5c0f\u4e8c\u4e57\u6cd5\u3001\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u306a\u3069\u306e\u6700\u9069\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001\u76ee\u7684\u95a2\u6570\u306e\u6700\u5c0f\u5316\u3001\u30c7\u30fc\u30bf\u306e\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3001\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u306a\u3069\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b\u3001minimize\u3001curve_fit\u3001root \u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a\u6700\u9069\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.interpolate: 1 \u6b21\u5143\u304a\u3088\u3073 2 \u6b21\u5143\u306e\u88dc\u9593\u3092\u30b5\u30dd\u30fc\u30c8\u3059\u308b\u88dc\u9593\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001interp1d\u3001interp2d\u3001\u304a\u3088\u3073 griddata \u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a\u88dc\u9593\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001\u30c7\u30fc\u30bf\u306e\u88dc\u9593\u3001\u518d\u69cb\u7bc9\u3001\u304a\u3088\u3073\u5e73\u6ed1\u5316\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.linalg: \u884c\u5217\u5206\u89e3\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u306a\u3069\u306e\u7dda\u5f62\u4ee3\u6570\u6f14\u7b97\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001LU \u5206\u89e3\u3001QR \u5206\u89e3\u3001SVD \u5206\u89e3\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u884c\u5217\u5206\u89e3\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u307e\u305f\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u95a2\u6570 solve \u3068\u3001\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u89e3\u304f\u95a2\u6570 eig \u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.signal: \u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08\u3001\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306a\u3069\u3001\u4fe1\u53f7\u51e6\u7406\u306b\u95a2\u9023\u3059\u308b\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001\u30c7\u30b8\u30bf\u30eb \u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u8a2d\u8a08\u3001\u30d1\u30ef\u30fc \u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u306e\u8a08\u7b97\u306a\u3069\u306b\u4f7f\u7528\u3067\u304d\u308b firwin\u3001iirfilter\u3001welch \u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a\u4fe1\u53f7\u51e6\u7406\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.ndimage: \u753b\u50cf\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3001\u30e2\u30eb\u30d5\u30a9\u30ed\u30b8\u30fc\u6f14\u7b97\u306a\u3069\u3001\u753b\u50cf\u51e6\u7406\u306b\u95a2\u9023\u3059\u308b\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001\u30d5\u30a3\u30eb\u30bf\u30fc\u3001\u5f62\u614b\u3001\u6e2c\u5b9a\u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a\u753b\u50cf\u51e6\u7406\u6a5f\u80fd\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001\u753b\u50cf\u306e\u30ce\u30a4\u30ba\u9664\u53bb\u3001\u30a8\u30c3\u30b8\u691c\u51fa\u3001\u5f62\u614b\u5909\u63db\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.stats: \u78ba\u7387\u5206\u5e03\u3001\u4eee\u8aac\u691c\u5b9a\u306a\u3069\u306e\u7d71\u8a08\u5206\u6790\u306b\u95a2\u3059\u308b\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001\u30ce\u30eb\u30e0\u3001\u30ac\u30f3\u30de\u3001\u30dd\u30a2\u30bd\u30f3\u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a\u78ba\u7387\u5206\u5e03\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001\u3055\u307e\u3056\u307e\u306a\u4eee\u8aac\u691c\u5b9a\u304a\u3088\u3073\u7d71\u8a08\u8a18\u8ff0\u95a2\u6570\u3082\u63d0\u4f9b\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.io: \u30c7\u30fc\u30bf\u306e\u5165\u51fa\u529b\u306b\u95a2\u3059\u308b\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u3001\u8907\u6570\u306e\u5f62\u5f0f\u3067\u306e\u30c7\u30fc\u30bf\u306e\u8aad\u307f\u66f8\u304d\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001loadmat\u3001savemat\u3001wavfile \u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a\u8aad\u307f\u66f8\u304d\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001MATLAB \u30c7\u30fc\u30bf\u3084 wav \u30aa\u30fc\u30c7\u30a3\u30aa \u30c7\u30fc\u30bf\u306a\u3069\u306e\u8aad\u307f\u66f8\u304d\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.special: \u30d9\u30c3\u30bb\u30eb\u95a2\u6570\u3001\u30ac\u30f3\u30de\u95a2\u6570\u306a\u3069\u3001\u6570\u5b66\u306e\u7279\u6b8a\u95a2\u6570\u306e\u5b9f\u88c5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001\u30d9\u30c3\u30bb\u30eb\u3001\u30ac\u30f3\u30de\u3001\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u306a\u3069\u3001\u7269\u7406\u5b66\u3084\u6570\u5b66\u306e\u554f\u984c\u3092\u51e6\u7406\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b\u3055\u307e\u3056\u307e\u306a\u7279\u6b8a\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4e0a\u8a18\u306e\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u52a0\u3048\u3066\u3001Scipy \u306f\u8907\u6570\u306e\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306a\u3069\u306e\u4ed6\u306e\u6a5f\u80fd\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u9805\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3001\u9ad8\u901f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306a\u3069&nbsp;\u3053\u308c\u3089\u306e\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u8a73\u7d30\u306a\u8aac\u660e\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"10\">\n<li>scipy.fftpack: \u9ad8\u901f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u88c5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001fft\u3001ifft\u3001fft2 \u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a FFT \u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001\u4fe1\u53f7\u304a\u3088\u3073\u753b\u50cf\u51e6\u7406\u306b\u304a\u3051\u308b\u5468\u6ce2\u6570\u9818\u57df\u89e3\u6790\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.special: \u30d9\u30c3\u30bb\u30eb\u95a2\u6570\u3001\u30ac\u30f3\u30de\u95a2\u6570\u306a\u3069\u3001\u6570\u5b66\u306e\u7279\u6b8a\u95a2\u6570\u306e\u5b9f\u88c5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001\u30d9\u30c3\u30bb\u30eb\u3001\u30ac\u30f3\u30de\u3001\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u306a\u3069\u3001\u7269\u7406\u5b66\u3084\u6570\u5b66\u306e\u554f\u984c\u3092\u51e6\u7406\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b\u3055\u307e\u3056\u307e\u306a\u7279\u6b8a\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.sparse: \u30b9\u30d1\u30fc\u30b9\u884c\u5217\u306e\u51e6\u7406\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001coo_matrix\u3001csr_matrix\u3001lil_matrix \u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a\u758e\u884c\u5217\u30bf\u30a4\u30d7\u306e\u5b9f\u88c5\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001\u5927\u898f\u6a21\u306a\u758e\u884c\u5217\u3092\u52b9\u7387\u7684\u306b\u51e6\u7406\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.spatial: \u7a7a\u9593\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u88c5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001KDTree\u3001ConvexHull\u3001DistanceMetric \u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a\u7a7a\u9593\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u5b9f\u73fe\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001\u30dd\u30a4\u30f3\u30c8 \u30bb\u30c3\u30c8\u3001\u51f8\u5305\u3001\u6700\u8fd1\u508d\u9593\u306e\u8ddd\u96e2\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>scipy.cluster: \u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u88c5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001KMeans\u3001AgglomerativeClustering\u3001DBSCAN \u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001\u30c7\u30fc\u30bf \u30bb\u30c3\u30c8\u3092\u8907\u6570\u306e\u30af\u30e9\u30b9\u30bf\u30fc\u306b\u5206\u5272\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u3064\u307e\u308a\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u6570\u5b66\u3001\u79d1\u5b66\u3001\u5de5\u5b66\u8a08\u7b97\u306e\u591a\u304f\u306e\u5074\u9762\u3092\u30ab\u30d0\u30fc\u3057\u3001\u3055\u307e\u3056\u307e\u306a\u8a08\u7b97\u30cb\u30fc\u30ba\u3092\u6e80\u305f\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5404\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u5b9f\u969b\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u9078\u629e\u3057\u3066\u4f7f\u7528\u3067\u304d\u308b\u8907\u6570\u306e\u95a2\u6570\u3068\u30af\u30e9\u30b9\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30a4\u30f3\u30dd\u30fc\u30c8\u65b9\u6cd5\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>Python \u3067 Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u5c0e\u5165\u3059\u308b\u306b\u306f\u3001import \u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u30a4\u30f3\u30dd\u30fc\u30c8\u3059\u308b\u65b9\u6cd5\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u5168\u4f53\u3092\u30a4\u30f3\u30dd\u30fc\u30c8\u3059\u308b:&nbsp;<code>import scipy&nbsp;<\/code>arduinoCopy \u30b3\u30fc\u30c9\u304c Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u5168\u4f53\u3092\u30a4\u30f3\u30dd\u30fc\u30c8\u3057\u305f\u5f8c\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u5185\u306e\u3059\u3079\u3066\u306e\u95a2\u6570\u3068\u30af\u30e9\u30b9\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3057\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u7279\u5b9a\u306e\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u307f\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u5834\u5408\u3001\u3053\u306e\u65b9\u6cd5\u3067\u306f\u30e1\u30e2\u30ea \u30ea\u30bd\u30fc\u30b9\u304c\u6d6a\u8cbb\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u7279\u5b9a\u306e\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u30a4\u30f3\u30dd\u30fc\u30c8\u3057\u307e\u3059\u3002arduinoCopy \u30b3\u30fc\u30c9\u306f<code>import scipy.optimize&nbsp;<\/code>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u6700\u9069\u5316\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u307f\u3092\u30a4\u30f3\u30dd\u30fc\u30c8\u3067\u304d\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u3059\u3079\u3066\u306e\u6700\u9069\u5316\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u95a2\u6570\u3068\u30af\u30e9\u30b9\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u540c\u69d8\u306b\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u4ed6\u306e\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u3082\u30a4\u30f3\u30dd\u30fc\u30c8\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u307e\u305f\u306f\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u30a8\u30a4\u30ea\u30a2\u30b9\u3092\u8a2d\u5b9a\u3057\u307e\u3059: javascriptCopy code<code>import scipy as sp import scipy.optimize as opt&nbsp;<\/code>\u3053\u306e\u65b9\u6cd5\u3067\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3068\u6700\u9069\u5316\u30b5\u30d6\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u30a8\u30a4\u30ea\u30a2\u30b9\u3092\u8a2d\u5b9a\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u4f7f\u7528\u3068\u53c2\u7167\u306b\u4fbf\u5229\u3067\u3059\u3002\u30a8\u30a4\u30ea\u30a2\u30b9\u306f\u3001\u5b9f\u969b\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u30ab\u30b9\u30bf\u30de\u30a4\u30ba\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u5c0e\u5165\u3059\u308b\u524d\u306b\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3068\u305d\u306e\u4f9d\u5b58\u95a2\u4fc2\u304c\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4f7f\u7528\u4e2d\u306b\u554f\u984c\u304c\u767a\u751f\u3057\u305f\u5834\u5408\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30d0\u30fc\u30b8\u30e7\u30f3\u3068\u95a2\u9023\u3059\u308b\u4f9d\u5b58\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30d0\u30fc\u30b8\u30e7\u30f3\u304c\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306e\u8981\u4ef6\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3001\u540d\u524d\u306e\u7af6\u5408\u306a\u3069\u306e\u554f\u984c\u304c\u306a\u3044\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u6570\u5024\u7a4d\u5206 scipy.integrate \u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u6570\u5024\u7a4d\u5206\u3068\u306f\u3001\u95a2\u6570\u306e\u7a4d\u5206\u5024\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u6570\u5024\u7684\u624b\u6cd5\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3092\u6307\u3057\u3001\u89e3\u6790\u7684\u624b\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u305d\u308c\u3092\u89e3\u304f\u306e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e integrate \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u30011 \u6b21\u5143\u304a\u3088\u3073\u591a\u6b21\u5143\u7a4d\u5206\u306e\u8fd1\u4f3c\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b\u4e00\u9023\u306e\u6570\u5024\u7a4d\u5206\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u6b21\u306b\u3001\u7d71\u5408\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u4e3b\u306a\u6a5f\u80fd\u3092\u3044\u304f\u3064\u304b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>quad() \u95a2\u6570: 1 \u6b21\u5143\u7a4d\u5206\u306e\u8fd1\u4f3c\u5024\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306e\u5165\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u3001\u88ab\u7a4d\u5206\u95a2\u6570\u3001\u7a4d\u5206\u306e\u4e0b\u9650\u3068\u4e0a\u9650\u3067\u3059\u3002\u3053\u306e\u95a2\u6570\u306f\u3001\u8fd1\u4f3c\u7a4d\u5206\u5024\u3068\u7a4d\u5206\u8aa4\u5dee\u3092\u542b\u3080\u30bf\u30d7\u30eb\u3092\u8fd4\u3057\u307e\u3059\u3002\u4f8b: goCopy \u30b3\u30fc\u30c9\u306e\u51fa\u529b\u7d50\u679c\u306f\u6b21\u306e<code>from scipy import integrate def func(x): return x**2 + 2*x + 1 result, error = integrate.quad(func, 0, 1) print(result, error)&nbsp;<\/code>\u3068\u304a\u308a\u3067\u3059: \u30b3\u30fc\u30c9\u306e\u30b3\u30d4\u30fc<code>2.3333333333333335 2.590520390792072e-14<\/code><\/li>\n\n\n\n<li>dblquad() \u95a2\u6570: 2 \u6b21\u5143\u7a4d\u5206\u306e\u8fd1\u4f3c\u5024\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u3078\u306e\u5165\u529b\u5f15\u6570\u306f\u3001\u88ab\u7a4d\u5206\u95a2\u6570\u3001\u6700\u521d\u306e\u5909\u6570\u306e\u7a4d\u5206\u306e\u4e0b\u9650\u3068\u4e0a\u9650\u3001\u304a\u3088\u3073 2 \u756a\u76ee\u306e\u5909\u6570\u306e\u7a4d\u5206\u306e\u4e0b\u9650\u3068\u4e0a\u9650\u3067\u3059\u3002\u3053\u306e\u95a2\u6570\u306f\u3001\u8fd1\u4f3c\u7a4d\u5206\u5024\u3068\u7a4d\u5206\u8aa4\u5dee\u3092\u542b\u3080\u30bf\u30d7\u30eb\u3092\u8fd4\u3057\u307e\u3059\u3002\u4f8b: goCopy \u30b3\u30fc\u30c9\u306e\u51fa\u529b\u7d50\u679c\u306f\u6b21\u306e<code>from scipy import integrate def func(x, y): return x**2 + y**2 result, error = integrate.dblquad(func, 0, 1, lambda x:0, lambda x:1) print(result, error)&nbsp;<\/code>\u3068\u304a\u308a\u3067\u3059: \u30b3\u30fc\u30c9\u306e\u30b3\u30d4\u30fc<code>0.6666666666666667 7.401486830834377e-15<\/code><\/li>\n\n\n\n<li>nquad() \u95a2\u6570: \u591a\u6b21\u5143\u7a4d\u5206\u306e\u8fd1\u4f3c\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u3078\u306e\u5165\u529b\u5f15\u6570\u306f\u3001\u88ab\u7a4d\u5206\u95a2\u6570\u3068\u7a4d\u5206\u533a\u9593\u306e\u30ea\u30b9\u30c8\u3067\u3059\u3002\u3053\u306e\u95a2\u6570\u306f\u3001\u8fd1\u4f3c\u7a4d\u5206\u5024\u3068\u7a4d\u5206\u8aa4\u5dee\u3092\u542b\u3080\u30bf\u30d7\u30eb\u3092\u8fd4\u3057\u307e\u3059\u3002\u4f8b: goCopy \u30b3\u30fc\u30c9\u306e\u51fa\u529b\u7d50\u679c<code>from scipy import integrate def func(x, y): return x**2 + y**2 result, error = integrate.nquad(func, [(0, 1), (0, 1)]) print(result, error)&nbsp;<\/code>: scssCopy \u30b3\u30fc\u30c9<code>(0.6666666666666667, 7.401486830834377e-15)<\/code><\/li>\n<\/ol>\n\n\n\n<p>\u4e0a\u8a18\u306e\u95a2\u6570\u306b\u52a0\u3048\u3066\u3001integrate \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u5b9f\u969b\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u9078\u629e\u3067\u304d\u308b\u3001fixed_quad\u3001romberg\u3001quadpack \u306a\u3069\u3001\u4ed6\u306e\u591a\u304f\u306e\u6570\u5024\u7a4d\u5206\u95a2\u6570\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002\u6570\u5024\u7a4d\u5206\u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408\u306f\u3001\u95a2\u6570\u306e\u7cbe\u5ea6\u3001\u7a4d\u5206\u533a\u9593\u306e\u9078\u629e\u3001\u8a08\u7b97\u52b9\u7387\u306b\u6ce8\u610f\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u3088\u304f\u4f7f\u308f\u308c\u308b4\u3064\u306e\u7a4d\u5206\u95a2\u6570\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e integrate \u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b 4 \u3064\u306e\u7a4d\u5206\u95a2\u6570 (quad\u3001dblquad\u3001tplquad\u3001\u304a\u3088\u3073 nquad) \u3092\u542b\u3080\u3001\u3055\u307e\u3056\u307e\u306a\u6570\u5024\u7a4d\u5206\u95a2\u6570\u304c\u7528\u610f\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u4ee5\u4e0b\u306f\u3001\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u3053\u308c\u3089 4 \u3064\u306e\u7a4d\u5206\u95a2\u6570\u306e\u8a73\u7d30\u306a\u8aac\u660e\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>quad() \u95a2\u6570: \u3053\u306e\u95a2\u6570\u306f\u30011 \u6b21\u5143\u7a4d\u5206\u306e\u8fd1\u4f3c\u5024\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306e\u5165\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u3001\u88ab\u7a4d\u5206\u95a2\u6570\u3001\u7a4d\u5206\u306e\u4e0b\u9650\u3068\u4e0a\u9650\u3067\u3059\u3002\u95a2\u6570\u306e\u51fa\u529b\u306f\u3001\u8fd1\u4f3c\u7a4d\u5206\u5024\u3068\u7a4d\u5206\u8aa4\u5dee\u3092\u542b\u3080\u30bf\u30d7\u30eb\u3067\u3059\u3002\u4f8b: goCopy \u30b3\u30fc\u30c9\u306e\u51fa\u529b\u7d50\u679c\u306f\u6b21\u306e<code>from scipy.integrate import quad def func(x): return x ** 2 + 2 * x + 1 result, error = quad(func, 0, 1) print(result, error)&nbsp;<\/code>\u3068\u304a\u308a\u3067\u3059: \u30b3\u30fc\u30c9\u306e\u30b3\u30d4\u30fc<code>2.3333333333333335 2.590520390792072e-14<\/code><\/li>\n\n\n\n<li>dblquad() \u95a2\u6570: \u3053\u306e\u95a2\u6570\u306f\u30012 \u6b21\u5143\u7a4d\u5206\u306e\u8fd1\u4f3c\u5024\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u3078\u306e\u5165\u529b\u5f15\u6570\u306f\u3001\u88ab\u7a4d\u5206\u95a2\u6570\u3001\u6700\u521d\u306e\u5909\u6570\u306e\u7a4d\u5206\u306e\u4e0b\u9650\u3068\u4e0a\u9650\u3001\u304a\u3088\u3073 2 \u756a\u76ee\u306e\u5909\u6570\u306e\u7a4d\u5206\u306e\u4e0b\u9650\u3068\u4e0a\u9650\u3067\u3059\u3002\u95a2\u6570\u306e\u51fa\u529b\u306f\u3001\u8fd1\u4f3c\u7a4d\u5206\u5024\u3068\u7a4d\u5206\u8aa4\u5dee\u3092\u542b\u3080\u30bf\u30d7\u30eb\u3067\u3059\u3002\u4f8b: goCopy \u30b3\u30fc\u30c9\u306e\u51fa\u529b\u7d50\u679c\u306f\u6b21\u306e<code>from scipy.integrate import dblquad def func(x, y): return x ** 2 + y ** 2 result, error = dblquad(func, 0, 1, lambda x: 0, lambda x: 1) print(result, error)&nbsp;<\/code>\u3068\u304a\u308a\u3067\u3059: \u30b3\u30fc\u30c9\u306e\u30b3\u30d4\u30fc<code>0.6666666666666667 7.401486830834377e-15<\/code><\/li>\n\n\n\n<li>tplquad() \u95a2\u6570: \u3053\u306e\u95a2\u6570\u306f\u30013 \u6b21\u5143\u7a4d\u5206\u306e\u8fd1\u4f3c\u5024\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306e\u5165\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306f\u3001\u88ab\u7a4d\u5206\u95a2\u6570\u3001\u6700\u521d\u306e\u5909\u6570\u306e\u7a4d\u5206\u306e\u4e0b\u9650\u3068\u4e0a\u9650\u30012 \u756a\u76ee\u306e\u5909\u6570\u306e\u7a4d\u5206\u306e\u4e0b\u9650\u3068\u4e0a\u9650\u3001\u304a\u3088\u3073 3 \u756a\u76ee\u306e\u5909\u6570\u306e\u7a4d\u5206\u306e\u4e0b\u9650\u3068\u4e0a\u9650\u3067\u3059\u3002\u95a2\u6570\u306e\u51fa\u529b\u306f\u3001\u8fd1\u4f3c\u7a4d\u5206\u5024\u3068\u7a4d\u5206\u8aa4\u5dee\u3092\u542b\u3080\u30bf\u30d7\u30eb\u3067\u3059\u3002\u4f8b: pythonCopy code<code>from scipy.integrate import tplquad def func(x, y, z): return x ** 2 + y ** 2 + z ** 2 result, error = tplquad(func, 0, 1, lambda x: 0, lambda x: 1, lambda x, y: 0, lambda x, y: 1) print(result, error)&nbsp;<\/code>\u51fa\u529b\u7d50\u679c: Copy code<code>1.0 1.1102230246251565e-14<\/code><\/li>\n\n\n\n<li>nquad() \u95a2\u6570: \u3053\u306e\u95a2\u6570\u306f\u3001\u591a\u6b21\u5143\u7a4d\u5206\u306e\u8fd1\u4f3c\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u3078\u306e\u5165\u529b\u5f15\u6570\u306f\u3001\u88ab\u7a4d\u5206\u95a2\u6570\u3068\u7a4d\u5206\u533a\u9593\u306e\u30ea\u30b9\u30c8\u3067\u3059\u3002\u95a2\u6570\u306e\u51fa\u529b\u306f\u3001\u8fd1\u4f3c\u7a4d\u5206\u5024\u3068\u7a4d\u5206\u8aa4\u5dee\u3092\u542b\u3080\u30bf\u30d7\u30eb\u3067\u3059\u3002\u4f8b: goCopy \u30b3\u30fc\u30c9<code>from scipy.integrate import nquad def func(x, y, z): return x ** 2 + y ** 2 + z ** 2 result, error = nquad(func, [(0, 1), (<\/code><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>0, 1), (0, 1)]) print(\u7d50\u679c, \u30a8\u30e9\u30fc)<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc<code>\n\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a\n\n<\/code><\/pre>\n\n\n\n<p>1.0 1.1102230246251565e-14<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc<code>\n\u8fd9\u56db\u79cd\u5e38\u7528\u79ef\u5206\u51fd\u6570\u90fd\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u591a\u79cd\u79ef\u5206\u7c7b\u578b\u7684\u8fd1\u4f3c\u503c\uff0c\u5305\u62ec\u4e00\u7ef4\u3001\u4e8c\u7ef4\u548c\u591a\u7ef4\u79ef\u5206\u3002\u4f7f\u7528\u8fd9\u4e9b\u51fd\u6570\u65f6\uff0c\u9700\u8981\u6ce8\u610f\u88ab\u79ef\u51fd\u6570\u7684\u5b9a\u4e49\u3001\u79ef\u5206\u533a\u95f4\u7684\u9009\u62e9\u3001\u79ef\u5206\u7cbe\u5ea6\u7684\u8bbe\u7f6e\u7b49\u95ee\u9898\uff0c\u4ee5\u4fdd\u8bc1\u8ba1\u7b97\u7ed3\u679c\u7684\u51c6\u786e\u6027\u548c\u53ef\u9760\u6027\u3002\u540c\u65f6\uff0c\u9700\u8981\u6ce8\u610f\u8fd9\u4e9b\u51fd\u6570\u7684\u8ba1\u7b97\u6548\u7387\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u9ad8\u7ef4\u79ef\u5206\u8ba1\u7b97\uff0c\u53ef\u80fd\u4f1a\u9762\u4e34\u8ba1\u7b97\u590d\u6742\u5ea6\u7684\u95ee\u9898\u3002\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u4f8b\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044: \u6570\u5024\u7a4d\u5206\u8a08\u7b97<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u305f\u6570\u5024\u7a4d\u5206\u8a08\u7b97\u306e\u4f8b\u3092\u6b21\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 f(x) \u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scss\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>f(x) = x^2 + 2x + 1\n<\/code><\/pre>\n\n\n\n<p>\u533a\u9593 [0, 1] \u3067\u95a2\u6570\u306e\u7a4d\u5206\u5024\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u8a08\u7b97\u306b\u306f Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e quad() \u95a2\u6570\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">go\u30b3\u30d4\u30fc\u30b3\u30fc\u30c9<code>from scipy.integrate import quad\n\ndef func(x):\n    return x ** 2 + 2 * x + 1\n\nresult, error = quad(func, 0, 1)\nprint(result, error)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u6700\u521d\u306b\u88ab\u7a4d\u5206\u95a2\u6570 func(x) \u3092\u5b9a\u7fa9\u3057\u3001\u6b21\u306b Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e quad() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u533a\u9593 [0, 1] \u3067\u95a2\u6570\u306e\u7a4d\u5206\u5024\u3092\u8a08\u7b97\u3057\u3001\u6700\u5f8c\u306b\u8a08\u7b97\u7d50\u679c\u3068\u7a4d\u5206\u8aa4\u5dee\u304c\u51fa\u529b\u3055\u308c\u307e\u3059\u3002\u4e0a\u8a18\u306e\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u51fa\u529b\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc<code>2.3333333333333335 2.590520390792072e-14\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u7d50\u679c\u306f\u3001\u533a\u9593 [0, 1] \u3067\u306e\u95a2\u6570\u306e\u7a4d\u5206\u5024\u304c 2.3333333333333335 \u3067\u3042\u308a\u3001\u7a4d\u5206\u8aa4\u5dee\u304c 2.590520390792072e-14 \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u7d50\u679c\u306f\u3001\u89e3\u6790\u624b\u6cd5\u3067\u306f 7\/3=2.3333333333333335 \u3068\u3044\u3046\u6b63\u78ba\u306a\u5024\u3067\u5f97\u3089\u308c\u3066\u304a\u308a\u3001\u6570\u5024\u7a4d\u5206\u6cd5\u306e\u65b9\u304c\u3088\u308a\u6b63\u78ba\u306a\u7d50\u679c\u304c\u5f97\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u306a\u304a\u3001\u6570\u5024\u7a4d\u5206\u6a5f\u80fd\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408\u306f\u3001\u8a08\u7b97\u7d50\u679c\u306e\u7cbe\u5ea6\u3068\u4fe1\u983c\u6027\u3092\u78ba\u4fdd\u3059\u308b\u305f\u3081\u306b\u3001\u9069\u5207\u306a\u7a4d\u5206\u533a\u9593\u3068\u7a4d\u5206\u7cbe\u5ea6\u3092\u9078\u629e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u540c\u6642\u306b\u3001\u3044\u304f\u3064\u304b\u306e\u7279\u6b8a\u306a\u95a2\u6570\u3068\u7a4d\u5206\u578b\u3092\u6271\u3046\u5834\u5408\u3001\u30ac\u30a6\u30b9\u30fb\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u6c42\u7a4d\u516c\u5f0f\u3001\u30ac\u30a6\u30b9\u30fb\u30e9\u30b2\u30fc\u30eb\u6c42\u7a4d\u516c\u5f0f\u3001\u8907\u7d20\u6c42\u7a4d\u516c\u5f0f\u306a\u3069\u306e\u7279\u5225\u306a\u7a4d\u5206\u95a2\u6570\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u5b9f\u969b\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u7279\u5b9a\u306e\u554f\u984c\u306b\u5fdc\u3058\u3066\u9069\u5207\u306a\u6570\u5024\u7a4d\u5206\u6cd5\u3092\u9078\u629e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u6700\u9069\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 scipy.optimize \u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u6700\u9069\u5316\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u95a2\u6570\u306e\u6700\u5c0f\u5024\u307e\u305f\u306f\u6700\u5927\u5024\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b\u4e00\u9023\u306e\u6700\u9069\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u306f\u3001\u30ed\u30fc\u30ab\u30eb\u6700\u9069\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u30b0\u30ed\u30fc\u30d0\u30eb\u6700\u9069\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u542b\u307e\u308c\u3001\u5236\u7d04\u306e\u306a\u3044\u6700\u9069\u5316\u554f\u984c\u3068\u5236\u7d04\u306e\u3042\u308b\u6700\u9069\u5316\u554f\u984c\u306e\u4e21\u65b9\u306b\u9069\u7528\u3067\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u306b\u3001optimize \u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u4e3b\u306a\u95a2\u6570\u3068\u30af\u30e9\u30b9\u3092\u3044\u304f\u3064\u304b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6700\u5c0f\u5316() \u95a2\u6570: \u3053\u306e\u95a2\u6570\u306f\u3001\u5236\u7d04\u306e\u306a\u3044\u6700\u9069\u5316\u554f\u984c\u306e\u6700\u5c0f\u5024\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306e\u5165\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306f\u3001\u6700\u9069\u5316\u3055\u308c\u305f\u95a2\u6570\u3001\u6700\u9069\u5316\u306e\u958b\u59cb\u70b9\u3001\u6700\u9069\u5316\u65b9\u6cd5\u3001\u6700\u9069\u5316\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306a\u3069\u3067\u3059\u3002\u3053\u306e\u95a2\u6570\u306f\u3001\u6700\u9069\u89e3\u3001\u6700\u9069\u95a2\u6570\u5024\u3001\u53cd\u5fa9\u56de\u6570\u306a\u3069\u3001\u6700\u9069\u5316\u7d50\u679c\u306b\u95a2\u3059\u308b\u3055\u307e\u3056\u307e\u306a\u60c5\u5831\u3092\u542b\u3080 OptimizeResult \u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u8fd4\u3057\u307e\u3059\u3002\u4f8b:&nbsp;<code>from scipy.optimize import minimize def func(x): return x ** 2 + 2 * x + 1 result = minimize(func, 0) print(result)&nbsp;<\/code>goCopy \u30b3\u30fc\u30c9\u306e\u51fa\u529b\u7d50\u679c: vbnetCopy \u30b3\u30fc\u30c9<code>fun: 1.0 hess_inv: array([[0.5]]) jac: array([5.96046448e-08]) message: 'Optimization terminated successfully.' nfev: 9 nit: 2 njev: 3 status: 0 success: True x: array([-1.])&nbsp;<\/code>\u3053\u306e\u95a2\u6570\u306f\u3001\u30c7\u30d5\u30a9\u30eb\u30c8\u306e\u6700\u9069\u5316\u624b\u6cd5 (BFGS \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0) \u3092\u4f7f\u7528\u3057\u3066\u958b\u59cb\u70b9 0 \u304b\u3089\u6700\u9069\u5316\u3057\u3001\u6700\u9069\u89e3\u306f -1 \u3067\u3042\u308a\u3001\u6700\u9069\u95a2\u6570\u5024\u306f 1.0 \u3067\u3059\u3002<\/li>\n\n\n\n<li>Minimize_scalar() \u95a2\u6570: \u3053\u306e\u95a2\u6570\u306f\u30011 \u6b21\u5143\u306e\u5236\u7d04\u306e\u306a\u3044\u6700\u9069\u5316\u554f\u984c\u306e\u6700\u5c0f\u5024\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306e\u5165\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u3001\u6700\u9069\u5316\u3055\u308c\u305f\u95a2\u6570\u3001\u6700\u9069\u5316\u9593\u9694\u3001\u6700\u9069\u5316\u65b9\u6cd5\u306a\u3069\u3067\u3059\u3002\u3053\u306e\u95a2\u6570\u306f\u3001\u6700\u9069\u5316\u7d50\u679c\u306b\u95a2\u3059\u308b\u3055\u307e\u3056\u307e\u306a\u60c5\u5831\u3092\u542b\u3080 OptimizeResult \u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u8fd4\u3057\u307e\u3059\u3002\u4f8b: goCopy \u30b3\u30fc\u30c9<code>from scipy.optimize import minimize_scalar def func(x): return x ** 2 + 2 * x + 1 result = minimize_scalar(func, bounds=(0, 1), method='bounded') print(result)&nbsp;<\/code>\u306e\u51fa\u529b\u7d50\u679c<code>fun: 1.0 nfev: 3 nit: 2 success: True x: 0.0&nbsp;<\/code>: kotlinCopy \u30b3\u30fc\u30c9 \u3053\u306e\u95a2\u6570\u306f\u3001\u5883\u754c\u6700\u9069\u5316\u6cd5 (bounded) \u3092\u4f7f\u7528\u3057\u3066\u3001\u533a\u9593 [0, 1] \u304b\u3089\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u3001\u6700\u9069\u89e3\u306f 0 \u3067\u3042\u308a\u3001\u6700\u9069\u95a2\u6570\u5024\u306f1.0\u3002<\/li>\n\n\n\n<li>Minimize_constrained() \u95a2\u6570: \u3053\u306e\u95a2\u6570\u306f\u3001\u5236\u7d04\u4ed8\u304d\u6700\u9069\u5316\u554f\u984c\u306e\u6700\u5c0f\u5024\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306e\u5165\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306f\u3001\u6700\u9069\u5316\u3059\u308b\u95a2\u6570\u3001\u5236\u7d04\u3001\u6700\u9069\u5316\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306a\u3069\u3067\u3059\u3002\u3053\u306e\u95a2\u6570\u306f\u3001\u6700\u9069\u5316\u7d50\u679c\u306b\u95a2\u3059\u308b\u3055\u307e\u3056\u307e\u306a\u60c5\u5831\u3092\u542b\u3080 OptimizeResult \u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u8fd4\u3057\u307e\u3059\u3002\u4f8b: pythonCopy \u30b3\u30fc\u30c9\u306e<code>from scipy.optimize import minimize_constrained def func(x): return x[0] ** 2 + 2 * x[1] ** 2 def constr(x): return x[0] + x[1] - 1 result = minimize_constrained(func, [constr], [1], bounds=((0, None), (0, None))) print(result)&nbsp;<\/code>\u51fa\u529b\u7d50\u679c: kotlinCopy \u30b3\u30fc\u30c9<code>constr: [array([-6.66133815e-16])] fun: 0.499<\/code><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>jac: array([5.96046448e-08, 1.19209290e-07]) \u30e1\u30c3\u30bb\u30fc\u30b8:\u300c\u6700\u9069\u5316\u304c\u6b63\u5e38\u306b\u7d42\u4e86\u3057\u307e\u3057\u305f\u3002\u300dnfev: 12 nit: 2 njev: 3 status: 0 success: True x: array([0.49999998, 0.50000002])<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scss\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>\n\u8be5\u51fd\u6570\u4f7f\u7528\u9ed8\u8ba4\u7684\u4f18\u5316\u65b9\u6cd5\uff08trust-constr\u7b97\u6cd5\uff09\u548c\u9ed8\u8ba4\u7684\u7ea6\u675f\u6761\u4ef6\uff08x0+x1=1\uff09\uff0c\u4ece\u8d77\u70b9(0, 0)\u5f00\u59cb\u8fdb\u884c\u4f18\u5316\uff0c\u5f97\u5230\u6700\u4f18\u89e3\u4e3a(0.49999998, 0.50000002)\uff0c\u6700\u4f18\u51fd\u6570\u503c\u4e3a0.5\u3002\n\n4. basinhopping()\u51fd\u6570\uff1a\u8be5\u51fd\u6570\u7528\u4e8e\u5bfb\u627e\u5168\u5c40\u6700\u5c0f\u503c\u3002\u8be5\u51fd\u6570\u7684\u8f93\u5165\u53c2\u6570\u662f\u88ab\u4f18\u5316\u51fd\u6570\u3001\u4f18\u5316\u8d77\u70b9\u3001\u6b65\u957f\u548c\u4f18\u5316\u53c2\u6570\u7b49\u3002\u8be5\u51fd\u6570\u8fd4\u56de\u4e00\u4e2aOptimizeResult\u5bf9\u8c61\uff0c\u5305\u542b\u4f18\u5316\u7ed3\u679c\u7684\u5404\u79cd\u4fe1\u606f\u3002\u4f8b\u5982\uff1a\n\n<\/code><\/pre>\n\n\n\n<p>from scipy.optimize import basinhopping<\/p>\n\n\n\n<p>def func(x): x ** 2 + 2 * x + 1 \u3092\u8fd4\u3059<\/p>\n\n\n\n<p>\u7d50\u679c = \u6d41\u57df\u30db\u30c3\u30d4\u30f3\u30b0 (\u6a5f\u80fd\u30010\u3001\u30b9\u30c6\u30c3\u30d7 \u30b5\u30a4\u30ba = 0.5) \u5370\u5237 (\u7d50\u679c)<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc<code>\n\u8f93\u51fa\u7ed3\u679c\u4e3a\uff1a\n\n<\/code><\/pre>\n\n\n\n<p>fun: 1.0 lower_optimization_result: fun: 1.0 hess_inv: array([[0.5]]) jac: array([5.96046448e-08]) \u30e1\u30c3\u30bb\u30fc\u30b8: \u300c\u6700\u9069\u5316\u304c\u6b63\u5e38\u306b\u7d42\u4e86\u3057\u307e\u3057\u305f\u3002\u300dnfev: 9 nit: 2 njev: 3 \u30b9\u30c6\u30fc\u30bf\u30b9: 0 \u6210\u529f: True x: array([-1.]) \u30e1\u30c3\u30bb\u30fc\u30b8: &#8216;basinhopping \u30b9\u30c6\u30c3\u30d7\u306f\u89e3\u3092\u6539\u5584\u3057\u307e\u305b\u3093\u3067\u3057\u305f&#8217; nfev: 30 nit: 4 njev: 7 x: array([- 0.99999957])<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc<code>\n\u8be5\u51fd\u6570\u4f7f\u7528\u57fa\u4e8e\u6a21\u62df\u9000\u706b\u7684\u5168\u5c40\u4f18\u5316\u65b9\u6cd5\uff08basinhopping\u7b97\u6cd5\uff09\uff0c\u4ece\u8d77\u70b90\u5f00\u59cb\u8fdb\u884c\u4f18\u5316\uff0c\u5f97\u5230\u6700\u4f18\u89e3\u4e3a-1\uff0c\u6700\u4f18\u51fd\u6570\u503c\u4e3a1.0\u3002\n\n\u8fd9\u4e9b\u51fd\u6570\u90fd\u53ef\u4ee5\u7528\u4e8e\u89e3\u51b3\u4e0d\u540c\u7c7b\u578b\u7684\u4f18\u5316\u95ee\u9898\uff0c\u5305\u62ec\u65e0\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u3001\u6709\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u548c\u5168\u5c40\u4f18\u5316\u95ee\u9898\u3002\u5728\u4f7f\u7528\u8fd9\u4e9b\u51fd\u6570\u65f6\uff0c\u9700\u8981\u6839\u636e\u5b9e\u9645\u95ee\u9898\u9009\u62e9\u5408\u9002\u7684\u4f18\u5316\u65b9\u6cd5\u3001\u8d77\u70b9\u3001\u6b65\u957f\u3001\u7ea6\u675f\u6761\u4ef6\u548c\u4f18\u5316\u53c2\u6570\u7b49\uff0c\u4ee5\u4fdd\u8bc1\u8ba1\u7b97\u7ed3\u679c\u7684\u51c6\u786e\u6027\u548c\u53ef\u9760\u6027\u3002\u540c\u65f6\uff0c\u5728\u5904\u7406\u4e00\u4e9b\u7279\u6b8a\u51fd\u6570\u548c\u4f18\u5316\u7c7b\u578b\u65f6\uff0c\u53ef\u80fd\u9700\u8981\u4f7f\u7528\u7279\u6b8a\u7684\u4f18\u5316\u51fd\u6570\u548c\u7b97\u6cd5\uff0c\u5982\u7c92\u5b50\u7fa4\u7b97\u6cd5\u3001\u9057\u4f20\u7b97\u6cd5\u3001\u5dee\u5206\u8fdb\u5316\u7b97\u6cd5\u7b49\u3002\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3092\u8a73\u3057\u304f\u6559\u3048\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306f\u3001\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u30c7\u30fc\u30bf \u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u6cd5\u3067\u3042\u308a\u3001\u7279\u5b9a\u306e\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u3068\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u3068\u306e\u9593\u306e\u8aa4\u5dee\u306e\u4e8c\u4e57\u548c\u3092\u6700\u5c0f\u5316\u3059\u308b\u6700\u9069\u306a\u95a2\u6570\u66f2\u7dda\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306f\u3001\u7dda\u5f62\u56de\u5e30\u3001\u591a\u9805\u5f0f\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3001\u975e\u7dda\u5f62\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u30c7\u30fc\u30bf \u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u554f\u984c\u306b\u9069\u7528\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u7279\u5b9a\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u3064\u3044\u3066\u3001\u95a2\u6570 y=f(x;\u03b8) \u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u03b8 \u306f\u4e00\u9023\u306e\u672a\u77e5\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3067\u3042\u308a\u3001y \u3068 x \u306f\u65e2\u77e5\u306e\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u3067\u3059\u3002\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u76ee\u7684\u306f\u3001\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u5168\u4f53\u3067\u95a2\u6570 f(x; \u03b8) \u306e\u4e8c\u4e57\u8aa4\u5dee\u306e\u5408\u8a08\u3092\u6700\u5c0f\u5316\u3059\u308b\u4e00\u9023\u306e \u03b8 \u5024\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u6b21\u306e\u640d\u5931\u95a2\u6570\u304c\u6700\u5c0f\u5316\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>L(\u03b8) = \u03a3(y \u2013 f(x;\u03b8))^2<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001\u03a3 \u306f\u3059\u3079\u3066\u306e\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u306e\u5408\u8a08\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6700\u5c0f\u4e8c\u4e57\u554f\u984c\u3092\u89e3\u304f\u306b\u306f\u3001\u901a\u5e38\u3001\u640d\u5931\u95a2\u6570\u306e\u504f\u5fae\u5206\u3092\u89e3\u304d\u3001\u504f\u5fae\u5206\u3092 0 \u306b\u8a2d\u5b9a\u3057\u3066 \u03b8 \u306e\u6700\u9069\u89e3\u3092\u5f97\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u7dda\u5f62\u56de\u5e30\u554f\u984c\u306e\u5834\u5408\u3001\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u6700\u9069\u89e3\u306f\u89e3\u6790\u89e3\u306b\u3088\u3063\u3066\u76f4\u63a5\u53d6\u5f97\u3067\u304d\u307e\u3059\u304c\u3001\u975e\u7dda\u5f62\u554f\u984c\u306e\u5834\u5408\u306f\u901a\u5e38\u3001\u6570\u5024\u6700\u9069\u5316\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u305d\u308c\u3089\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u6700\u9069\u5316\u30e2\u30b8\u30e5\u30fc\u30eb\u306e curve_fit() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306e\u5165\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u3001\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u95a2\u6570\u3001\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0 \u30c7\u30fc\u30bf\u3001\u958b\u59cb\u30d1\u30e9\u30e1\u30fc\u30bf\u306a\u3069\u3067\u3001\u623b\u308a\u5024\u306f\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0 \u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u5171\u5206\u6563\u884c\u5217\u3092\u542b\u3080\u30bf\u30d7\u30eb\u3067\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u306e\u5834\u5408:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">css\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc<code>x = [0, 1, 2, 3, 4]\ny = [1, 3, 5, 7, 9]\n<\/code><\/pre>\n\n\n\n<p>\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306f\u3001\u6b21\u306e\u30b3\u30fc\u30c9\u3067\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy.optimize import curve_fit\nimport numpy as np\n\ndef func(x, a, b):\n    return a * x + b\n\nx = np.array([0, 1, 2, 3, 4])\ny = np.array([1, 3, 5, 7, 9])\n\nparams, cov = curve_fit(func, x, y)\n\nprint(\"a =\", params[0], \" b =\", params[1])\n<\/code><\/pre>\n\n\n\n<p>\u51fa\u529b\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">css\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc<code>a = 2.0  b = 1.0\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u7d50\u679c\u306f\u3001\u6700\u5c0f\u4e8c\u4e57\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u305f\u7dda\u5f62\u65b9\u7a0b\u5f0f\u304c y=2x+1 \u3067\u3042\u308a\u3001\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u306b\u8fd1\u3044\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u5236\u7d04\u4ed8\u304d\u6700\u9069\u5316\u554f\u984c\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u5236\u7d04\u4ed8\u304d\u6700\u9069\u5316\u554f\u984c\u3068\u306f\u3001\u6700\u9069\u5316\u30d7\u30ed\u30bb\u30b9\u306b\u304a\u3044\u3066\u3001\u6700\u9069\u5316\u76ee\u7684\u95a2\u6570\u306e\u6700\u5c0f\u5024\u307e\u305f\u306f\u6700\u5927\u5024\u3092\u6e80\u305f\u3059\u3053\u3068\u306b\u52a0\u3048\u3066\u3001\u7279\u5b9a\u306e\u5236\u9650\u6761\u4ef6\u3082\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u7b49\u5f0f\u307e\u305f\u306f\u4e0d\u7b49\u5f0f\u306e\u5236\u7d04\u3067\u3042\u308b\u3053\u308c\u3089\u306e\u5236\u7d04\u306f\u3001\u5236\u7d04\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u5236\u7d04\u4ed8\u304d\u6700\u9069\u5316\u554f\u984c\u306f\u3001\u7dda\u5f62\u5236\u7d04\u4ed8\u304d\u6700\u9069\u5316\u3068\u975e\u7dda\u5f62\u5236\u7d04\u4ed8\u304d\u6700\u9069\u5316\u306e 2 \u3064\u306e\u30bf\u30a4\u30d7\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u7dda\u5f62\u5236\u7d04\u4ed8\u304d\u6700\u9069\u5316\u554f\u984c\u306e\u5834\u5408\u3001\u5236\u7d04\u306f\u901a\u5e38\u6b21\u306e\u5f62\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">css\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc<code>Ax = b\nCx &lt;= d\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u3046\u3061\u3001A \u3068 C \u306f\u4fc2\u6570\u884c\u5217\u3001x \u306f\u6700\u9069\u5316\u5909\u6570\u3001b \u3068 d \u306f\u5b9a\u6570\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u3053\u306e\u30bf\u30a4\u30d7\u306e\u5236\u7d04\u4ed8\u304d\u6700\u9069\u5316\u554f\u984c\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e linprog() \u95a2\u6570\u306a\u3069\u306e\u7dda\u5f62\u8a08\u753b\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u975e\u7dda\u5f62\u5236\u7d04\u4ed8\u304d\u6700\u9069\u5316\u554f\u984c\u306e\u5834\u5408\u3001\u5236\u7d04\u306f\u901a\u5e38\u3001\u6b21\u306e\u5f62\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scss\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>g_i(x) = 0, i = 1, 2, ..., m\nh_j(x) &lt;= 0, j = 1, 2, ..., n\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u3046\u3061\u3001g_i(x) \u306f\u7b49\u5f0f\u5236\u7d04\u3001h_j(x) \u306f\u4e0d\u7b49\u5f0f\u5236\u7d04\u3001x \u306f\u6700\u9069\u5316\u5909\u6570\u3067\u3059\u3002\u3053\u306e\u30bf\u30a4\u30d7\u306e\u5236\u7d04\u4ed8\u304d\u6700\u9069\u5316\u554f\u984c\u306f\u3001\u901a\u5e38\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e Minimize() \u95a2\u6570\u3084 Minimum_constrained() \u95a2\u6570\u306a\u3069\u306e\u6570\u5024\u6700\u9069\u5316\u30e1\u30bd\u30c3\u30c9\u3092\u4f7f\u7528\u3057\u3066\u89e3\u6c7a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408\u3001\u95a2\u6570\u306e\u5165\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u4e00\u90e8\u3068\u3057\u3066\u3001\u5236\u7d04\u6761\u4ef6\u3092\u95a2\u6570\u306e\u5f62\u5f0f\u3067\u8868\u73fe\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u5236\u7d04\u4ed8\u304d\u6700\u9069\u5316\u554f\u984c\u306f\u901a\u5e38\u3001\u5236\u7d04\u306a\u3057\u6700\u9069\u5316\u554f\u984c\u3088\u308a\u3082\u8907\u96d1\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u308c\u306f\u3001\u5236\u7d04\u306b\u3088\u3063\u3066\u5b9f\u884c\u53ef\u80fd\u306a\u89e3\u306e\u7bc4\u56f2\u304c\u5236\u9650\u3055\u308c\u3001\u6700\u9069\u5316\u554f\u984c\u306e\u63a2\u7d22\u7a7a\u9593\u304c\u5c0f\u3055\u304f\u306a\u308b\u305f\u3081\u3067\u3059\u3002\u8a08\u7b97\u7d50\u679c\u306e\u7cbe\u5ea6\u3068\u4fe1\u983c\u6027\u3092\u78ba\u4fdd\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u5236\u7d04\u6761\u4ef6\u3092\u614e\u91cd\u306b\u5206\u6790\u3057\u3066\u51e6\u7406\u3057\u3001\u9069\u5207\u306a\u6570\u5024\u6700\u9069\u5316\u624b\u6cd5\u3092\u9078\u629e\u3057\u3066\u3001\u89e3\u6cd5\u30d7\u30ed\u30bb\u30b9\u306e\u6709\u52b9\u6027\u3068\u5b9f\u73fe\u53ef\u80fd\u6027\u3092\u78ba\u4fdd\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u540c\u6642\u306b\u3001\u5b9f\u969b\u306e\u554f\u984c\u3092\u6271\u3046\u5834\u5408\u3001\u5408\u7406\u7684\u306a\u5236\u7d04\u6700\u9069\u5316\u30e2\u30c7\u30eb\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u8a2d\u8a08\u3059\u308b\u305f\u3081\u306b\u3001\u6700\u9069\u5316\u76ee\u7684\u306e\u8907\u96d1\u3055\u3068\u5236\u7d04\u6761\u4ef6\u306e\u5b9f\u969b\u7684\u306a\u91cd\u8981\u6027\u3082\u8003\u616e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044 \u4f8b\uff1a\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5<\/p>\n\n\n\n<p>\u6570\u5024\u8a08\u7b97\u306b\u304a\u3044\u3066\u3001\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u306f\u975e\u5e38\u306b\u91cd\u8981\u306a\u554f\u984c\u3067\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u6700\u9069\u5316\u30e2\u30b8\u30e5\u30fc\u30eb\u3067 root() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306e\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304d\u305f\u3044\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scss\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>f(x) = x^2 - 2 = 0\n<\/code><\/pre>\n\n\n\n<p>\u6b21\u306e Python \u95a2\u6570\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy.optimize import root\n\ndef func(x):\n    return x ** 2 - 2\n<\/code><\/pre>\n\n\n\n<p>\u6b21\u306b\u3001root() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3053\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>result = root(func, x0=1.0)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u3046\u3061\u3001func \u306f\u89e3\u304f\u3079\u304d\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3067\u3001x0 \u306f\u958b\u59cb\u70b9\u3067\u3059\u3002root() \u95a2\u6570\u306f\u3001\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u305f\u3081\u306e\u3055\u307e\u3056\u307e\u306a\u60c5\u5831\u3092\u542b\u3080 OptimizeResult \u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u8fd4\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u7d50\u679c\u3092\u51fa\u529b\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>print(result)\n<\/code><\/pre>\n\n\n\n<p>\u51fa\u529b\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">yaml\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc<code>    fjac: array([[-1.]])\n     fun: array([4.4408921e-16])\n message: 'The solution converged.'\n    nfev: 8\n     qtf: array([2.65002768e-12])\n       r: array([-2.82842712])\n  status: 1\n success: True\n       x: array([1.41421356])\n<\/code><\/pre>\n\n\n\n<p>root() \u95a2\u6570\u3067\u8a08\u7b97\u3057\u305f\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u306f x = 1.41421356 \u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u306e\u89e3\u306f\u3001\u65b9\u7a0b\u5f0f sqrt(2) \u306e\u6b63\u78ba\u306a\u89e3\u306b\u8fd1\u3044\u3082\u306e\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u5b9f\u969b\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u306f\u3001\u7269\u7406\u30e2\u30c7\u30eb\u306e\u89e3\u6cd5\u3001\u6700\u9069\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u8a08\u7b97\u554f\u984c\u3067\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e root() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u52b9\u7387\u7684\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u3001\u5b9f\u969b\u306e\u554f\u984c\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u958b\u59cb\u70b9\u3068\u89e3\u6cd5\u3092\u67d4\u8edf\u306b\u9078\u629e\u3057\u3066\u3001\u8a08\u7b97\u7d50\u679c\u306e\u7cbe\u5ea6\u3068\u4fe1\u983c\u6027\u3092\u78ba\u4fdd\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u88dc\u9593\u65b9\u6cd5 scipy.interpolate \u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u5185\u633f\u3068\u306f\u3001\u4e00\u9023\u306e\u65e2\u77e5\u306e\u96e2\u6563\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u3067\u9023\u7d9a\u95a2\u6570\u66f2\u7dda\u3092\u4f5c\u6210\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u3053\u308c\u3089\u306e\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u9593\u306e\u95a2\u6570\u5024\u3092\u53d6\u5f97\u3059\u308b\u30d7\u30ed\u30bb\u30b9\u3092\u6307\u3057\u307e\u3059\u3002\u88dc\u9593\u6cd5\u306f\u3001\u30c7\u30fc\u30bf\u51e6\u7406\u3001\u4fe1\u53f7\u51e6\u7406\u3001\u753b\u50cf\u51e6\u7406\u3001\u5730\u7406\u60c5\u5831\u30b7\u30b9\u30c6\u30e0\u3001\u305d\u306e\u4ed6\u306e\u5206\u91ce\u306a\u3069\u3001\u5b9f\u969b\u306e\u554f\u984c\u3067\u5e83\u304f\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001interpolate \u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u3088\u3063\u3066\u63d0\u4f9b\u3055\u308c\u308b\u3055\u307e\u3056\u307e\u306a\u88dc\u9593\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u3001\u30c7\u30fc\u30bf\u88dc\u9593\u3092\u5b9f\u73fe\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u88dc\u9593\u65b9\u6cd5\u306b\u306f\u3001\u7dda\u5f62\u88dc\u9593\u3001\u591a\u9805\u5f0f\u88dc\u9593\u3001\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u3001\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u88dc\u9593\u306a\u3069\u304c\u542b\u307e\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u306b\u3001\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u3044\u304f\u3064\u304b\u306e\u88dc\u9593\u65b9\u6cd5\u3092\u7c21\u5358\u306b\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7dda\u5f62\u88dc\u9593: \u65e2\u77e5\u306e 2 \u3064\u306e\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8 (x1, y1) \u3068 (x2, y2) \u3092\u76f4\u7dda\u3067\u7d50\u3073\u3001\u3053\u306e\u76f4\u7dda\u306e\u5f0f\u3092\u88dc\u9593\u95a2\u6570\u3068\u3057\u3066\u4f7f\u7528\u3059\u308b\u6700\u3082\u5358\u7d14\u306a\u88dc\u9593\u65b9\u6cd5\u3067\u3059\u3002\u7dda\u5f62\u88dc\u9593\u306f\u3001interpolate \u30e2\u30b8\u30e5\u30fc\u30eb\u306e interp1d() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002\u6b21\u306b\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nfrom scipy import interpolate\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 2, 4, 6, 8, 10])\n\nf = interpolate.interp1d(x, y)\n\nprint(f(2.5))\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001interp1d() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u7dda\u5f62\u88dc\u9593\u95a2\u6570 f \u3092\u4f5c\u6210\u3057\u3001f(2.5) \u3092\u4f7f\u7528\u3057\u3066 x=2.5 \u3067\u306e\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001\u51fa\u529b\u7d50\u679c\u306f 5.0 \u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u591a\u9805\u5f0f\u88dc\u9593: \u591a\u9805\u5f0f\u95a2\u6570\u3092\u69cb\u7bc9\u3057\u3066\u3001\u65e2\u77e5\u306e\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u9593\u306e\u66f2\u7dda\u3092\u9069\u5408\u3055\u305b\u307e\u3059\u3002\u591a\u9805\u5f0f\u88dc\u9593\u306f\u3001interpolate \u30e2\u30b8\u30e5\u30fc\u30eb\u306e polyfit() \u95a2\u6570\u3068 poly1d() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002\u6b21\u306b\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nfrom scipy import interpolate\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 2, 4, 6, 8, 10])\n\np = np.polyfit(x, y, 2)\nf = np.poly1d(p)\n\nprint(f(2.5))\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001polyfit() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066 2 \u6b21\u591a\u9805\u5f0f\u95a2\u6570\u3092\u8fd1\u4f3c\u3057\u3001\u6b21\u306b poly1d() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u305d\u308c\u3092\u591a\u9805\u5f0f\u88dc\u9593\u95a2\u6570 f \u306b\u5909\u63db\u3057\u3001\u6700\u5f8c\u306b f(2.5) \u3092\u4f7f\u7528\u3057\u3066 x= \u3067\u306e\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002 2.5 \u3001\u51fa\u529b\u306f 5.0 \u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593: \u8907\u6570\u306e\u4f4e\u6b21\u591a\u9805\u5f0f\u95a2\u6570\u3092\u69cb\u7bc9\u3057\u3066\u3001\u65e2\u77e5\u306e\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u9593\u306b\u66f2\u7dda\u3092\u5f53\u3066\u306f\u3081\u307e\u3059\u3002\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u306f\u3001interpolate \u30e2\u30b8\u30e5\u30fc\u30eb\u306e splrep() \u95a2\u6570\u3068 splev() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002\u6b21\u306b\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nfrom scipy import interpolate\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 2, 4, 6, 8, 10])\n\ntck = interpolate.splrep(x, y, s=0)\nf = interpolate.splev(\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001splrep() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u95a2\u6570\u3092\u5f53\u3066\u306f\u3081\u3001\u305d\u308c\u3092\u30c8\u30ea\u30d7\u30ec\u30c3\u30c8 (t\u3001c\u3001k) \u3068\u3057\u3066\u8868\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001t \u306f\u30b9\u30d7\u30e9\u30a4\u30f3\u66f2\u7dda\u4e0a\u306e\u30ce\u30fc\u30c9\u3092\u8868\u3057\u3001c \u306f\u30ce\u30fc\u30c9\u4fc2\u6570\u306e\u30ce\u30fc\u30c9\u3092\u8868\u3057\u307e\u3059\u3002 k \u306f\u3001\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u95a2\u6570\u306e\u6b21\u6570\u3092\u8868\u3057\u307e\u3059\u3002\u6b21\u306b splev() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u95a2\u6570 f \u3092\u547c\u3073\u51fa\u3057\u53ef\u80fd\u306a\u95a2\u6570\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3068\u3057\u3066\u8868\u73fe\u3057\u3001\u6700\u5f8c\u306b f(2.5) \u3092\u4f7f\u7528\u3057\u3066 x=2.5 \u3067\u306e\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001\u51fa\u529b\u7d50\u679c\u306f 5.0 \u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li>\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u88dc\u9593: \u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u591a\u9805\u5f0f\u95a2\u6570\u3092\u69cb\u7bc9\u3057\u3066\u3001\u65e2\u77e5\u306e\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u9593\u306e\u66f2\u7dda\u3092\u9069\u5408\u3055\u305b\u307e\u3059\u3002\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u88dc\u9593\u306f\u3001interpolate \u30e2\u30b8\u30e5\u30fc\u30eb\u306e lagrange() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002\u6b21\u306b\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nfrom scipy import interpolate\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 2, 4, 6, 8, 10])\n\nf = interpolate.lagrange(x, y)\n\nprint(f(2.5))\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001lagrange() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u88dc\u9593\u95a2\u6570 f \u3092\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3057\u3001\u6b21\u306b f(2.5) \u3092\u4f7f\u7528\u3057\u3066 x=2.5 \u3067\u306e\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u51fa\u529b\u7d50\u679c\u306f 5.0 \u3067\u3059\u3002<\/p>\n\n\n\n<p>\u3055\u307e\u3056\u307e\u306a\u88dc\u9593\u65b9\u6cd5\u304c\u3055\u307e\u3056\u307e\u306a\u30c7\u30fc\u30bf\u578b\u3068\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u9069\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u307e\u305f\u3001\u5404\u88dc\u9593\u65b9\u6cd5\u306b\u306f\u9577\u6240\u3068\u77ed\u6240\u304c\u3042\u308a\u307e\u3059\u3002\u5b9f\u969b\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u88dc\u9593\u7d50\u679c\u306e\u7cbe\u5ea6\u3068\u4fe1\u983c\u6027\u3092\u78ba\u4fdd\u3059\u308b\u305f\u3081\u306b\u3001\u30c7\u30fc\u30bf\u306e\u7279\u6027\u3068\u88dc\u9593\u306e\u76ee\u7684\u306b\u5fdc\u3058\u3066\u9069\u5207\u306a\u88dc\u9593\u65b9\u6cd5\u3092\u9078\u629e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>1D\u88dc\u9593\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>1 \u6b21\u5143\u88dc\u9593\u3068\u306f\u30011 \u6b21\u5143\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u3067\u306e\u88dc\u9593\u3001\u3064\u307e\u308a 1 \u6b21\u5143\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u9593\u306e\u66f2\u7dda\u306e\u88dc\u9593\u3092\u6307\u3057\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u88dc\u9593\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u3088\u3063\u3066\u63d0\u4f9b\u3055\u308c\u308b\u3055\u307e\u3056\u307e\u306a\u88dc\u9593\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u3001\u7dda\u5f62\u88dc\u9593\u3001\u591a\u9805\u5f0f\u88dc\u9593\u3001\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u3001\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u88dc\u9593\u306a\u3069\u306e 1 \u6b21\u5143\u88dc\u9593\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u3067\u306f\u3001\u7dda\u5f62\u88dc\u9593\u3092\u4f8b\u3068\u3057\u3066\u30011 \u6b21\u5143\u88dc\u9593\u306e\u57fa\u672c\u7684\u306a\u624b\u9806\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306e\u3088\u3046\u306a\u65e2\u77e5\u306e 1D \u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u306e\u30bb\u30c3\u30c8\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 2, 4, 6, 8, 10])\n<\/code><\/pre>\n\n\n\n<p>\u7dda\u5f62\u88dc\u9593\u306b\u306f interp1d() \u95a2\u6570\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import interpolate\n\nf = interpolate.interp1d(x, y)\n<\/code><\/pre>\n\n\n\n<p>\u305d\u306e\u4e2d\u3067\u3001interp1d() \u95a2\u6570\u306f\u5165\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3068\u3057\u3066 x \u3068 y \u3092\u53d6\u308a\u3001\u547c\u3073\u51fa\u3057\u53ef\u80fd\u306a\u88dc\u9593\u95a2\u6570 f \u3092\u8fd4\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001\u3053\u306e\u88dc\u9593\u95a2\u6570 f \u3092\u4f7f\u7528\u3057\u3066\u3001\u4efb\u610f\u306e x \u5024\u3067\u306e\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>print(f(2.5))\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u7dda\u5f62\u88dc\u9593\u95a2\u6570 f \u3092\u4f7f\u7528\u3057\u3066 x=2.5 \u3067\u306e\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3057\u3001\u51fa\u529b\u7d50\u679c\u306f 5.0 \u3067\u3059\u3002<\/p>\n\n\n\n<p>\u4e00\u6b21\u5143\u88dc\u9593\u6cd5\u306f\u3001\u4e00\u5909\u91cf\u95a2\u6570\u306e\u88dc\u9593\u306b\u9069\u3057\u3066\u304a\u308a\u3001\u4e00\u6b21\u5143\u30c7\u30fc\u30bf\u30dd\u30a4\u30f3\u30c8\u9593\u306e\u66f2\u7dda\u88dc\u9593\u306b\u306e\u307f\u9069\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u9593\u306b\u8907\u6570\u306e\u72ec\u7acb\u5909\u6570\u307e\u305f\u306f\u5f93\u5c5e\u5909\u6570\u304c\u3042\u308b\u5834\u5408\u3001\u307e\u305f\u306f\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u9593\u306e\u66f2\u7dda\u304c\u8907\u96d1\u306a\u5f62\u72b6\u3092\u3057\u3066\u3044\u308b\u5834\u5408\u306f\u3001\u3053\u308c\u3089\u306e\u30c7\u30fc\u30bf\u3092\u51e6\u7406\u3059\u308b\u305f\u3081\u306b\u3001\u9ad8\u6b21\u5143\u306e\u5185\u633f\u6cd5\u307e\u305f\u306f\u4ed6\u306e\u30c7\u30fc\u30bf\u51e6\u7406\u624b\u6cd5\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>2D\u88dc\u9593\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>2 \u6b21\u5143\u88dc\u9593\u3068\u306f\u30012 \u6b21\u5143\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u3067\u306e\u88dc\u9593\u3001\u3064\u307e\u308a 2 \u6b21\u5143\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u9593\u306e\u30b5\u30fc\u30d5\u30a7\u30b9\u306e\u88dc\u9593\u3092\u6307\u3057\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001interpolate \u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u3088\u3063\u3066\u63d0\u4f9b\u3055\u308c\u308b\u3055\u307e\u3056\u307e\u306a\u88dc\u9593\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u3001\u7dda\u5f62\u88dc\u9593\u3001\u591a\u9805\u5f0f\u88dc\u9593\u3001\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u306a\u3069\u306e 2 \u6b21\u5143\u88dc\u9593\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u3067\u306f\u30012 \u6b21\u5143\u88dc\u9593\u306e\u57fa\u672c\u7684\u306a\u624b\u9806\u3092\u7d39\u4ecb\u3059\u308b\u305f\u3081\u306b\u3001\u4f8b\u3068\u3057\u3066 2 \u6b21\u5143\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u3092\u53d6\u308a\u4e0a\u3052\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306e\u3088\u3046\u306a\u65e2\u77e5\u306e 2D \u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u306e\u30bb\u30c3\u30c8\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 1, 2, 3, 4, 5])\nz = np.array([[ 0,  1,  4,  9, 16, 25],\n              [ 1,  2,  5, 10, 17, 26],\n              [ 4,  5,  8, 13, 20, 29],\n              [ 9, 10, 13, 18, 25, 34],\n              [16, 17, 20, 25, 32, 41],\n              [25, 26, 29, 34, 41, 50]])\n<\/code><\/pre>\n\n\n\n<p>\u3053\u3053\u3067\u3001x \u3068 y \u306f\u72ec\u7acb\u5909\u6570\u306e 1 \u6b21\u5143\u914d\u5217\u3067\u3001z \u306f\u5f93\u5c5e\u5909\u6570\u306e 2 \u6b21\u5143\u914d\u5217\u3067\u3059\u3002<\/p>\n\n\n\n<p>2D \u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u306b\u306f interp2d() \u95a2\u6570\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import interpolate\n\nf = interpolate.interp2d(x, y, z, kind='cubic')\n<\/code><\/pre>\n\n\n\n<p>\u305d\u306e\u4e2d\u3067\u3001interp2d() \u95a2\u6570\u306f x\u3001y\u3001\u304a\u3088\u3073 z \u3092\u5165\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3068\u3057\u3066\u53d7\u3051\u53d6\u308a\u3001\u547c\u3073\u51fa\u3057\u53ef\u80fd\u306a\u88dc\u9593\u95a2\u6570 f \u3092\u8fd4\u3057\u307e\u3059\u3002kind \u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u88dc\u9593\u65b9\u6cd5\u3092\u6307\u5b9a\u3057\u3001\u3053\u3053\u3067\u306f 3 \u6b21\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u65b9\u6cd5\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001\u3053\u306e\u88dc\u9593\u95a2\u6570 f \u3092\u4f7f\u7528\u3057\u3066\u3001\u4efb\u610f\u306e (x, y) \u5024\u3067\u306e\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>print(f(2.5, 2.5))\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u30012 \u6b21\u5143\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u95a2\u6570 f \u3092\u4f7f\u7528\u3057\u3066 (x, y)=(2.5, 2.5) \u3067\u306e\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3057\u3001\u51fa\u529b\u7d50\u679c\u306f 7.675 \u3067\u3059\u3002<\/p>\n\n\n\n<p>2 \u6b21\u5143\u88dc\u9593\u6cd5\u306f 2 \u6b21\u5143\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u9593\u306e\u30b5\u30fc\u30d5\u30a7\u30b9\u88dc\u9593\u306b\u9069\u3057\u3066\u304a\u308a\u3001\u30d0\u30a4\u30ca\u30ea\u95a2\u6570\u306e\u4efb\u610f\u306e\u30dd\u30a4\u30f3\u30c8\u5024\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u9593\u306b\u8907\u6570\u306e\u72ec\u7acb\u5909\u6570\u307e\u305f\u306f\u5f93\u5c5e\u5909\u6570\u304c\u3042\u308b\u5834\u5408\u3001\u3053\u308c\u3089\u306e\u30c7\u30fc\u30bf\u3092\u51e6\u7406\u3059\u308b\u306b\u306f\u3001\u9ad8\u6b21\u5143\u306e\u88dc\u9593\u6cd5\u307e\u305f\u306f\u305d\u306e\u4ed6\u306e\u30c7\u30fc\u30bf\u51e6\u7406\u624b\u6cd5\u304c\u5fc5\u8981\u3067\u3059\u3002\u540c\u6642\u306b\u3001\u9069\u5207\u306a\u88dc\u9593\u65b9\u6cd5\u3068\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u9078\u629e\u3059\u308b\u3068\u3001\u88dc\u9593\u7d50\u679c\u306e\u7cbe\u5ea6\u3068\u4fe1\u983c\u6027\u306b\u3082\u5f71\u97ff\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u3001\u5b9f\u969b\u306e\u554f\u984c\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u9078\u629e\u304a\u3088\u3073\u8abf\u6574\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u4f8b\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044: \u30c7\u30fc\u30bf\u88dc\u9593\u306e\u5b9f\u88c5<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u3067\u306f\u30012 \u6b21\u5143\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u3092\u4f8b\u3068\u3057\u3066\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u88dc\u9593\u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u30c7\u30fc\u30bf\u88dc\u9593\u3092\u5b9f\u88c5\u3059\u308b\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306e\u3088\u3046\u306a\u65e2\u77e5\u306e 2D \u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u306e\u30bb\u30c3\u30c8\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\n\nx = np.array([0, 1, 2, 3, 4, 5])\ny = np.array([0, 1, 2, 3, 4, 5])\nz = np.array([[ 0,  1,  4,  9, 16, 25],\n              [ 1,  2,  5, 10, 17, 26],\n              [ 4,  5,  8, 13, 20, 29],\n              [ 9, 10, 13, 18, 25, 34],\n              [16, 17, 20, 25, 32, 41],\n              [25, 26, 29, 34, 41, 50]])\n<\/code><\/pre>\n\n\n\n<p>\u3053\u3053\u3067\u3001x \u3068 y \u306f\u72ec\u7acb\u5909\u6570\u306e 1 \u6b21\u5143\u914d\u5217\u3067\u3001z \u306f\u5f93\u5c5e\u5909\u6570\u306e 2 \u6b21\u5143\u914d\u5217\u3067\u3059\u3002<\/p>\n\n\n\n<p>2D \u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u306b\u306f interp2d() \u95a2\u6570\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import interpolate\n\nf = interpolate.interp2d(x, y, z, kind='cubic')\n<\/code><\/pre>\n\n\n\n<p>\u305d\u306e\u4e2d\u3067\u3001interp2d() \u95a2\u6570\u306f x\u3001y\u3001\u304a\u3088\u3073 z \u3092\u5165\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3068\u3057\u3066\u53d7\u3051\u53d6\u308a\u3001\u547c\u3073\u51fa\u3057\u53ef\u80fd\u306a\u88dc\u9593\u95a2\u6570 f \u3092\u8fd4\u3057\u307e\u3059\u3002kind \u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u88dc\u9593\u65b9\u6cd5\u3092\u6307\u5b9a\u3057\u3001\u3053\u3053\u3067\u306f 3 \u6b21\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u65b9\u6cd5\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001\u3053\u306e\u88dc\u9593\u95a2\u6570 f \u3092\u4f7f\u7528\u3057\u3066\u3001\u4efb\u610f\u306e (x, y) \u5024\u3067\u306e\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>print(f(2.5, 2.5))\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u30012 \u6b21\u5143\u30b9\u30d7\u30e9\u30a4\u30f3\u88dc\u9593\u95a2\u6570 f \u3092\u4f7f\u7528\u3057\u3066 (x, y)=(2.5, 2.5) \u3067\u306e\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3057\u3001\u51fa\u529b\u7d50\u679c\u306f 7.675 \u3067\u3059\u3002<\/p>\n\n\n\n<p>2 \u6b21\u5143\u88dc\u9593\u6cd5\u306f 2 \u6b21\u5143\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u9593\u306e\u30b5\u30fc\u30d5\u30a7\u30b9\u88dc\u9593\u306b\u9069\u3057\u3066\u304a\u308a\u3001\u30d0\u30a4\u30ca\u30ea\u95a2\u6570\u306e\u4efb\u610f\u306e\u30dd\u30a4\u30f3\u30c8\u5024\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u30c7\u30fc\u30bf \u30dd\u30a4\u30f3\u30c8\u9593\u306b\u8907\u6570\u306e\u72ec\u7acb\u5909\u6570\u307e\u305f\u306f\u5f93\u5c5e\u5909\u6570\u304c\u3042\u308b\u5834\u5408\u3001\u3053\u308c\u3089\u306e\u30c7\u30fc\u30bf\u3092\u51e6\u7406\u3059\u308b\u306b\u306f\u3001\u9ad8\u6b21\u5143\u306e\u88dc\u9593\u6cd5\u307e\u305f\u306f\u305d\u306e\u4ed6\u306e\u30c7\u30fc\u30bf\u51e6\u7406\u624b\u6cd5\u304c\u5fc5\u8981\u3067\u3059\u3002\u540c\u6642\u306b\u3001\u9069\u5207\u306a\u88dc\u9593\u65b9\u6cd5\u3068\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u9078\u629e\u3059\u308b\u3068\u3001\u88dc\u9593\u7d50\u679c\u306e\u7cbe\u5ea6\u3068\u4fe1\u983c\u6027\u306b\u3082\u5f71\u97ff\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u3001\u5b9f\u969b\u306e\u554f\u984c\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u9078\u629e\u304a\u3088\u3073\u8abf\u6574\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7dda\u5f62\u4ee3\u6570 scipy.linalg \u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e linalg \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u3001\u884c\u5217\u306e\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\u3001\u884c\u5217\u306e\u7279\u7570\u5024\u5206\u89e3\u3001\u884c\u5217\u306e LU \u5206\u89e3\u3001\u304a\u3088\u3073\u884c\u5217\u306e QR \u5206\u89e3\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u3055\u307e\u3056\u307e\u306a\u6570\u5b66\u304a\u3088\u3073\u5de5\u5b66\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u7dda\u5f62\u4ee3\u6570\u306e\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u7dda\u5f62\u4ee3\u6570\u95a2\u6570\u3092\u6b21\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5: Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e solve() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u6b21\u306b\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import linalg\n\na = np.array([[3, 2], [1, 4]])\nb = np.array([1, 2])\nx = linalg.solve(a, b)\n\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001linalg.solve() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb Ax=b \u3092\u89e3\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001A \u306f\u4fc2\u6570\u884c\u5217\u3001b \u306f\u5b9a\u6570\u30d9\u30af\u30c8\u30eb\u3001x \u306f\u672a\u77e5\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u51fa\u529b\u7d50\u679c\u306f\u3001\u65b9\u7a0b\u5f0f\u7cfb\u306e\u89e3\u3092\u8868\u3059 x=[-0.2 0.6] \u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97: Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e eig() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u884c\u5217\u306e\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>a = np.array([[1, 2], [2, 1]])\nw, v = linalg.eig(a)\n\nprint(w)\nprint(v)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001linalg.eig() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u884c\u5217 a \u306e\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001w \u306f\u56fa\u6709\u5024\u306e 1 \u6b21\u5143\u914d\u5217\u3001v \u306f\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306e 2 \u6b21\u5143\u914d\u5217\u3067\u3059\u3002\u51fa\u529b\u7d50\u679c\u306f w=[ 3. -1.] \u3067\u3001\u884c\u5217 a \u306e\u56fa\u6709\u5024\u304c 3 \u3068 -1 \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3001v=[[-0.70710678 -0.70710678], [ 0.70710678 -0.70710678]] \u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u793a\u3057\u307e\u3059\u3002\u30de\u30c8\u30ea\u30c3\u30af\u30b9<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>\u7279\u7570\u5024\u5206\u89e3: Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e svd() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u884c\u5217\u306e\u7279\u7570\u5024\u5206\u89e3\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u6b21\u306b\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>a = np.array([[1, 2], [3, 4], [5, 6]])\nu, s, vh = linalg.svd(a)\n\nprint(u)\nprint(s)\nprint(vh)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001linalg.svd() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u884c\u5217 a \u306e\u7279\u7570\u5024\u5206\u89e3\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001u \u306f\u5de6\u7279\u7570\u30d9\u30af\u30c8\u30eb\u306e\u884c\u5217\u3001s \u306f\u7279\u7570\u5024\u306e 1D \u914d\u5217\u3001vh \u306f\u6b21\u306e\u8ee2\u7f6e\u884c\u5217\u3067\u3059\u3002\u53f3\u7279\u7570\u30d9\u30af\u30c8\u30eb\u3002\u51fa\u529b\u7d50\u679c\u306f u=[[-0.2298477 -0.88346102 -0.40824829], [-0.52474482 -0.24078249 0.81649658], [-0.81964193 0.40189605 -0.40824829]] \u3068\u306a\u308a\u3001\u884c\u5217\u30d9\u30af\u30c8\u30eb\u3001s=[9.52551809 0.514300<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001linalg.lu() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u884c\u5217 a \u306e LU \u5206\u89e3\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001p \u306f\u884c\u7f6e\u63db\u884c\u5217\u3001l \u306f\u4e0b\u4e09\u89d2\u884c\u5217\u3001u \u306f\u4e0a\u4e09\u89d2\u884c\u5217\u3067\u3059\u3002\u51fa\u529b\u7d50\u679c\u306f p=[0 1 2] \u3067\u3001\u3053\u308c\u306f\u884c\u7f6e\u63db\u884c\u5217\u3092\u610f\u5473\u3057\u3001l=[[1. 0. 0. ], [0.4 1. 0. ], [0.2 0.12903226 1. ]] \u3067\u4e0b\u4e09\u89d2\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u884c\u5217\u3001u =[[ 5. 6. 7. ]\u3001[ 0. 0.2 0.4 ]\u3001[ 0. 0. -0.06451613]]\u3001\u4e0a\u4e09\u89d2\u884c\u5217\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e linalg \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u6570\u5b66\u304a\u3088\u3073\u5de5\u5b66\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u7dda\u5f62\u4ee3\u6570\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b\u8c4a\u5bcc\u306a\u7dda\u5f62\u4ee3\u6570\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u6b63\u78ba\u3067\u4fe1\u983c\u3067\u304d\u308b\u7d50\u679c\u3092\u5f97\u308b\u305f\u3081\u306b\u306f\u3001\u5b9f\u969b\u306e\u554f\u984c\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u9069\u5207\u306a\u95a2\u6570\u3068\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3092\u9078\u629e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u884c\u5217\u5206\u89e3\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u6559\u3048\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u5206\u89e3\u306f\u3001\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u8907\u6570\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306b\u5206\u89e3\u3059\u308b\u65b9\u6cd5\u3067\u3042\u308a\u3001\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u64cd\u4f5c\u3092\u7c21\u7d20\u5316\u3057\u305f\u308a\u3001\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u69cb\u9020\u60c5\u5831\u3092\u62bd\u51fa\u3057\u305f\u308a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u6570\u5b66\u304a\u3088\u3073\u5de5\u5b66\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u884c\u5217\u5206\u89e3\u306f\u975e\u5e38\u306b\u91cd\u8981\u306a\u30c4\u30fc\u30eb\u3067\u3042\u308a\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u305f\u308a\u3001\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u8a08\u7b97\u3057\u305f\u308a\u3001\u6700\u5c0f\u4e8c\u4e57\u554f\u984c\u3092\u89e3\u3044\u305f\u308a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e linalg \u30e2\u30b8\u30e5\u30fc\u30eb\u306f, \u3055\u307e\u3056\u307e\u306a\u884c\u5217\u5206\u89e3\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u307e\u3059. \u4ee5\u4e0b\u306b, \u3088\u304f\u4f7f\u308f\u308c\u308b\u884c\u5217\u5206\u89e3\u3092\u3044\u304f\u3064\u304b\u793a\u3057\u307e\u3059.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>LU \u5206\u89e3: LU \u5206\u89e3\u306f\u3001\u884c\u5217\u3092\u4e0b\u4e09\u89d2\u884c\u5217 L \u3068\u4e0a\u4e09\u89d2\u884c\u5217 U \u306e\u7a4d\u306b\u5206\u89e3\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u3092\u4f7f\u7528\u3057\u3066\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304d\u3001\u884c\u5217\u5f0f\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u6b21\u306e\u3088\u3046\u306b linalg.lu() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066 LU \u5206\u89e3\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import linalg\n\na = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\np, l, u = linalg.lu(a)\n\nprint(p)\nprint(l)\nprint(u)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001linalg.lu() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u884c\u5217 a \u306e LU \u5206\u89e3\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001p \u306f\u884c\u7f6e\u63db\u884c\u5217\u3001l \u306f\u4e0b\u4e09\u89d2\u884c\u5217\u3001u \u306f\u4e0a\u4e09\u89d2\u884c\u5217\u3067\u3059\u3002\u51fa\u529b\u7d50\u679c\u306f p=[[0. 1. 0.], [0. 0. 1.], [1. 0. 0.]] \u3067\u3001\u884c\u7f6e\u63db\u884c\u5217 l=[[1. 0. 0 . ] , [0.14285714 1. 0. ], [0.57142857 0.125 1. ]], \u4e0b\u4e09\u89d2\u884c\u5217\u3092\u8868\u3059, u=[[7. 8. 9. ], [0. 0.85714286 1.71428571], [0. 0. 0.125 ]] \u306f\u3001\u4e0a\u4e09\u89d2\u884c\u5217\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>QR \u5206\u89e3: QR \u5206\u89e3\u306f\u3001\u884c\u5217\u3092\u76f4\u4ea4\u884c\u5217 Q \u3068\u4e0a\u4e09\u89d2\u884c\u5217 R \u306e\u7a4d\u306b\u5206\u89e3\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u3092\u4f7f\u7528\u3057\u3066\u3001\u6700\u5c0f\u4e8c\u4e57\u554f\u984c\u3092\u8a08\u7b97\u3057\u3001\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u6b21\u306e\u3088\u3046\u306b linalg.qr() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066 QR \u5206\u89e3\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>a = np.array([[1, 2], [3, 4], [5, 6]])\nq, r = linalg.qr(a)\n\nprint(q)\nprint(r)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001linalg.qr() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u884c\u5217 a \u306e QR \u5206\u89e3\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001q \u306f\u76f4\u4ea4\u884c\u5217\u3001r \u306f\u4e0a\u4e09\u89d2\u884c\u5217\u3067\u3059\u3002\u51fa\u529b\u7d50\u679c\u306f q=[[-0.16903085 0.89708523 0.40824829], [-0.50709255 0.27602622 -0.81649658], [-0.84515425 -0.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>\u7279\u7570\u5024\u5206\u89e3: \u7279\u7570\u5024\u5206\u89e3\u3068\u306f\u3001\u884c\u5217\u3092\u5de6\u7279\u7570\u30d9\u30af\u30c8\u30eb\u884c\u5217 U\u3001\u7279\u7570\u5024\u884c\u5217 S\u3001\u53f3\u7279\u7570\u30d9\u30af\u30c8\u30eb\u884c\u5217 V \u306e\u7a4d\u306b\u5206\u89e3\u3059\u308b\u3053\u3068\u3067\u3001\u30c7\u30fc\u30bf\u306e\u6b21\u5143\u524a\u6e1b\u3068\u884c\u5217\u8fd1\u4f3c\u8868\u73fe\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u6b21\u306e\u3088\u3046\u306b linalg.svd() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u7279\u7570\u5024\u5206\u89e3\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\nu, s, vh = linalg.svd(a)\n\nprint(u)\nprint(s)\nprint(vh)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001linalg.svd() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u884c\u5217 a \u306e\u7279\u7570\u5024\u5206\u89e3\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001u \u306f\u5de6\u7279\u7570\u30d9\u30af\u30c8\u30eb\u884c\u5217\u3001s \u306f\u7279\u7570\u5024\u884c\u5217\u3001vh \u306f\u53f3\u7279\u7570\u30d9\u30af\u30c8\u30eb\u306e\u8ee2\u7f6e\u3067\u3059\u3002\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3002\u51fa\u529b\u7d50\u679c\u306f\u3001\u5de6\u7279\u7570\u30d9\u30af\u30c8\u30eb\u3092\u8868\u3059 u=[[-0.21483724 -0.88723069 0.40824829], [-0.52058739 -0.24964395 -0.81649658], [-0.82633753 0.38794278 0.40824829]] \u3067\u3059\u3002\u884c\u5217\u3001s=[1.68481034e+01 1.06836951e+00 2.22044605e -16]\u3001\u3053\u308c\u306f\u7279\u7570\u5024\u884c\u5217\u3092\u610f\u5473\u3057\u307e\u3059\u3002 8 -0.40824829] ]\u3001\u53f3\u7279\u7570\u884c\u5217\u306e\u8ee2\u7f6e\u3092\u8868\u3059\u30d9\u30af\u30c8\u30eb\u3002<\/p>\n\n\n\n<p>\u884c\u5217\u5206\u89e3\u3092\u4f7f\u7528\u3057\u3066\u3001\u884c\u5217\u6f14\u7b97\u3092\u7c21\u7d20\u5316\u3057\u305f\u308a\u3001\u884c\u5217\u306e\u69cb\u9020\u60c5\u5831\u3092\u62bd\u51fa\u3057\u305f\u308a\u3067\u304d\u307e\u3059\u304c\u3001\u3059\u3079\u3066\u306e\u884c\u5217\u3092\u5206\u89e3\u3067\u304d\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u540c\u6642\u306b\u3001\u9069\u5207\u306a\u5206\u89e3\u65b9\u6cd5\u3068\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u9078\u629e\u3059\u308b\u3068\u3001\u5206\u89e3\u7d50\u679c\u306e\u7cbe\u5ea6\u3068\u4fe1\u983c\u6027\u306b\u3082\u5f71\u97ff\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u3001\u5b9f\u969b\u306e\u554f\u984c\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u9078\u629e\u304a\u3088\u3073\u8abf\u6574\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9\u3092\u8a73\u3057\u304f\u6559\u3048\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u306f\u3001\u91cd\u8981\u306a\u7dda\u5f62\u4ee3\u6570\u306e\u554f\u984c\u3067\u3042\u308a\u3001\u901a\u5e38\u3001\u9006\u884c\u5217\u3001LU \u5206\u89e3\u3001QR \u5206\u89e3\u3001\u7279\u7570\u5024\u5206\u89e3\u306a\u3069\u306e\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e linalg \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001solve()\u3001inv()\u3001lstsq() \u306a\u3069\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u305f\u3081\u306e\u3055\u307e\u3056\u307e\u306a\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u305f\u3081\u306b\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u95a2\u6570\u3068\u30e1\u30bd\u30c3\u30c9\u3092\u6b21\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>solve() \u95a2\u6570: solve() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001Ax=b \u5f62\u5f0f\u306e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001A \u306f\u4fc2\u6570\u884c\u5217\u3001b \u306f\u5b9a\u6570\u30d9\u30af\u30c8\u30eb\u3001x \u306f\u672a\u77e5\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u4f8b\u3048\u3070\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import linalg\n\na = np.array([[3, 2], [1, 4]])\nb = np.array([1, 2])\nx = linalg.solve(a, b)\n\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001linalg.solve() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb Ax=b \u3092\u89e3\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001A \u306f\u4fc2\u6570\u884c\u5217\u3001b \u306f\u5b9a\u6570\u30d9\u30af\u30c8\u30eb\u3001x \u306f\u672a\u77e5\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u51fa\u529b\u7d50\u679c\u306f\u3001\u65b9\u7a0b\u5f0f\u7cfb\u306e\u89e3\u3092\u8868\u3059 x=[-0.2 0.6] \u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>inv() \u95a2\u6570: inv() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u884c\u5217\u306e\u9006\u884c\u5217\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u305f\u3081\u3001\u9006\u884c\u5217\u3092\u4f7f\u7528\u3057\u3066\u4e00\u6b21\u65b9\u7a0b\u5f0f\u7cfb\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>a = np.array([[1, 2], [3, 4]])\na_inv = linalg.inv(a)\nb = np.array([5, 6])\nx = a_inv.dot(b)\n\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001linalg.inv() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u884c\u5217 a \u306e\u9006\u884c\u5217\u3092\u89e3\u304d\u3001\u6b21\u306b\u9006\u884c\u5217\u3092\u4f7f\u7528\u3057\u3066\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb Ax=b \u3092\u89e3\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001A \u306f\u4fc2\u6570\u884c\u5217\u3001b \u306f\u5b9a\u6570\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002 \u3001x \u306f\u672a\u77e5\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u51fa\u529b\u306f\u3001\u9023\u7acb\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u8868\u3059 x=[-4.4.] \u3067\u3059\u3002<\/p>\n\n\n\n<p>\u9006\u884c\u5217\u3092\u4f7f\u7528\u3057\u3066\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u65b9\u6cd5\u306f\u3001\u901a\u5e38\u3001LU \u5206\u89e3\u3084 QR \u5206\u89e3\u306a\u3069\u3092\u4f7f\u7528\u3059\u308b\u3088\u308a\u3082\u6642\u9593\u304c\u304b\u304b\u308a\u3001\u9006\u884c\u5217\u304c\u5b58\u5728\u3057\u306a\u3044\u304b\u3001\u4e00\u610f\u3067\u3042\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u305f\u3081\u3001\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\u3002\u6700\u9069\u306a\u65b9\u6cd5\u306b\u306f\u306a\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>lstsq() \u95a2\u6570: lstsq() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001Ax=b \u5f62\u5f0f\u306e\u6700\u5c0f\u4e8c\u4e57\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001A \u306f\u4fc2\u6570\u884c\u5217\u3001b \u306f\u5b9a\u6570\u30d9\u30af\u30c8\u30eb\u3001x \u306f\u672a\u77e5\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u4f8b\u3048\u3070\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>a = np.array([[1, 2], [3, 4], [5, 6]])\nb = np.array([7, 8, 9])\nx, residuals, rank, s = linalg.lstsq(a, b)\n\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001linalg.lstsq() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u6700\u5c0f\u4e8c\u4e57\u554f\u984c Ax=b \u3092\u89e3\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001A \u306f\u4fc2\u6570\u884c\u5217\u3001b \u306f\u5b9a\u6570\u30d9\u30af\u30c8\u30eb\u3001x \u306f\u672a\u77e5\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u51fa\u529b\u306f x=[-1.94444444 2.38888889] \u3067\u3001\u3053\u308c\u306f\u554f\u984c\u306e\u6700\u5c0f\u4e8c\u4e57\u89e3\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb\u3092\u89e3\u304f\u3053\u3068\u306f\u3001\u6570\u5b66\u304a\u3088\u3073\u5de5\u5b66\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u4e00\u822c\u7684\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u3057\u304b\u3057\u3001\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u30b5\u30a4\u30ba\u3068\u69cb\u9020\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u89e3\u6cd5\u306e\u52b9\u7387\u3068\u7cbe\u5ea6\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u305f\u3081\u3001\u7279\u5b9a\u306e\u554f\u984c\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u9078\u629e\u304a\u3088\u3073\u8abf\u6574\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li>LU \u5206\u89e3\u6cd5: LU \u5206\u89e3\u306f\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u305f\u3081\u306b\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u65b9\u6cd5\u3067\u3059. \u4fc2\u6570\u884c\u5217 A \u306f\u3001\u4e0b\u4e09\u89d2\u884c\u5217 L \u3068\u4e0a\u4e09\u89d2\u884c\u5217 U \u306e\u7a4d\u306b\u5206\u89e3\u3067\u304d\u308b\u305f\u3081\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306f\u5206\u89e3\u306b\u3088\u3063\u3066\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059.&nbsp;Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u4fc2\u6570\u884c\u5217\u306e LU \u5206\u89e3\u306f\u3001\u6b21\u306e\u3088\u3046\u306b linalg.lu_factor() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>a = np.array([[3, 2], [1, 4]])\nlu, piv = linalg.lu_factor(a)\nb = np.array([1, 2])\nx = linalg.lu_solve((lu, piv), b)\n\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001linalg.lu_factor() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u4fc2\u6570\u884c\u5217 a \u306e LU \u5206\u89e3\u3092\u8a08\u7b97\u3057\u3001\u6b21\u306b linalg.lu_solve() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb Ax=b \u3092\u89e3\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001A \u306f\u4fc2\u6570\u884c\u5217\u3067\u3059\u3002 \u3001b \u306f\u5b9a\u6570\u30d9\u30af\u30c8\u30eb\u3001x \u306f\u672a\u77e5\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u51fa\u529b\u7d50\u679c\u306f\u3001\u65b9\u7a0b\u5f0f\u7cfb\u306e\u89e3\u3092\u8868\u3059 x=[-0.2 0.6] \u3067\u3059\u3002<\/p>\n\n\n\n<p>LU \u5206\u89e3\u6cd5\u306f\u3001\u524d\u51e6\u7406\u306b\u3088\u3063\u3066\u89e3\u306e\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u8907\u6570\u306e\u7570\u306a\u308b\u5b9a\u6570\u30d9\u30af\u30c8\u30eb\u3092\u6301\u3064\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n<li>QR\u5206\u89e3\u6cd5\uff1aQR\u5206\u89e3\u306f\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u305f\u3081\u306b\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u3082\u30461\u3064\u306e\u65b9\u6cd5\u3067\u3059.\u4fc2\u6570\u884c\u5217A\u306f\u3001\u76f4\u4ea4\u884c\u5217Q\u3068\u4e0a\u4e09\u89d2\u884c\u5217R\u306e\u7a4d\u306b\u5206\u89e3\u3067\u304d\u308b\u305f\u3081\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306f\u5206\u89e3\u306b\u3088\u3063\u3066\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059.&nbsp;Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u4fc2\u6570\u884c\u5217\u306e QR \u5206\u89e3\u306f\u3001\u6b21\u306e\u3088\u3046\u306b linalg.qr() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>a = np.array([[3, 2], [1, 4]])\nq, r = linalg.qr(a)\nb = np.array([1, 2])\nx = linalg.solve_triangular(r, np.dot(q.T, b))\n\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001linalg.qr() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u4fc2\u6570\u884c\u5217 a \u306e QR \u5206\u89e3\u3092\u8a08\u7b97\u3057\u3001\u6b21\u306b linalg.solve_triangular() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb Ax=b \u3092\u89e3\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001A \u306f\u4fc2\u6570\u884c\u5217\u3067\u3059\u3002 \u3001b \u306f\u5b9a\u6570\u30d9\u30af\u30c8\u30eb\u3001x \u306f\u672a\u77e5\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u51fa\u529b\u7d50\u679c\u306f\u3001\u65b9\u7a0b\u5f0f\u7cfb\u306e\u89e3\u3092\u8868\u3059 x=[-0.2 0.6] \u3067\u3059\u3002<\/p>\n\n\n\n<p>QR \u5206\u89e3\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u7279\u7570\u4fc2\u6570\u884c\u5217\u306e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u3001\u524d\u51e6\u7406\u306b\u3088\u3063\u3066\u89e3\u6cd5\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u4f8b\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044: System of Linear Equations Solving<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u3066\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb\u3092\u89e3\u304f\u4f8b\u3067\u3059\u3002\u3053\u308c\u306b\u306f\u3001solve() \u95a2\u6570\u3068 LU \u5206\u89e3\u30e1\u30bd\u30c3\u30c9\u3092\u4f7f\u7528\u3057\u3066\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb\u3092\u89e3\u304f\u3053\u3068\u3082\u542b\u307e\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>solve() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb\u3092\u89e3\u304d\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import linalg\n\n# \u5b9a\u4e49\u7cfb\u6570\u77e9\u9635A\u548c\u5e38\u6570\u5411\u91cfb\na = np.array([[3, 2], [1, 4]])\nb = np.array([1, 2])\n\n# \u4f7f\u7528solve()\u51fd\u6570\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\nx = linalg.solve(a, b)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e linalg.solve() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb Ax=b \u3092\u89e3\u304d\u307e\u3059\u3002\u4fc2\u6570\u884c\u5217 A \u306f 3 2, 1 4 \u3067\u3001\u5b9a\u6570\u30d9\u30af\u30c8\u30eb b \u306f 1, 2 \u3067\u3059\u3002\u51fa\u529b\u7d50\u679c\u306f\u3001\u65b9\u7a0b\u5f0f\u7cfb\u306e\u89e3\u3092\u8868\u3059 x=[-0.2 0.6] \u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>LU\u5206\u89e3\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u4e00\u6b21\u65b9\u7a0b\u5f0f\u7cfb\u3092\u89e3\u304f\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import linalg\n\n# \u5b9a\u4e49\u7cfb\u6570\u77e9\u9635A\u548c\u5e38\u6570\u5411\u91cfb\na = np.array([[3, 2], [1, 4]])\nb = np.array([1, 2])\n\n# \u4f7f\u7528LU\u5206\u89e3\u65b9\u6cd5\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\nlu, piv = linalg.lu_factor(a)\nx = linalg.lu_solve((lu, piv), b)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint(x)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e linalg.lu_factor() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u4fc2\u6570\u884c\u5217 A \u306e LU \u5206\u89e3\u3092\u8a08\u7b97\u3057\u3001\u6b21\u306b linalg.lu_solve() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u7dda\u5f62\u65b9\u7a0b\u5f0f\u7cfb Ax=b \u3092\u89e3\u304d\u307e\u3059\u3002\u4fc2\u6570\u884c\u5217 A \u306f 3 2, 1 4 \u3067\u3001\u5b9a\u6570\u30d9\u30af\u30c8\u30eb b \u306f 1, 2 \u3067\u3059\u3002\u51fa\u529b\u7d50\u679c\u306f\u3001\u65b9\u7a0b\u5f0f\u7cfb\u306e\u89e3\u3092\u8868\u3059 x=[-0.2 0.6] \u3067\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u3089 2 \u3064\u306e\u65b9\u6cd5\u306e\u7d50\u679c\u306f\u540c\u3058\u3067\u3059\u304c\u3001LU \u5206\u89e3\u6cd5\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u6700\u521d\u306e\u5206\u89e3\u3067 1 \u56de\u3060\u3051\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u8907\u6570\u306e\u7570\u306a\u308b\u5b9a\u6570\u30d9\u30af\u30c8\u30eb\u3092\u6301\u3064\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u306e\u306b\u3088\u308a\u9069\u3057\u3066\u3044\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u306f\u5206\u89e3\u7d50\u679c\u3092\u76f4\u63a5\u4f7f\u7528\u3067\u304d\u308b\u305f\u3081\u3001\u8a08\u7b97\u6642\u9593\u3068\u30b9\u30da\u30fc\u30b9\u3092\u7bc0\u7d04\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u4fe1\u53f7\u51e6\u7406 scipy.signal \u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u4fe1\u53f7\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3001\u30b9\u30da\u30af\u30c8\u30eb\u89e3\u6790\u3001\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3001\u30a6\u30a7\u30fc\u30d6\u30ec\u30c3\u30c8\u5909\u63db\u3001\u4fe1\u53f7\u751f\u6210\u3001\u4fe1\u53f7\u5909\u8abf\u3001\u30ce\u30a4\u30ba\u751f\u6210\u306a\u3069\u306e\u6a5f\u80fd\u3092\u542b\u3080\u3001\u3055\u307e\u3056\u307e\u306a\u4fe1\u53f7\u51e6\u7406\u6a5f\u80fd\u3068\u30c4\u30fc\u30eb\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u4fe1\u53f7\u51e6\u7406\u95a2\u6570\u3068\u30c4\u30fc\u30eb\u3092\u6b21\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30d5\u30a3\u30eb\u30bf\u30fc\u6a5f\u80fd: \u4fe1\u53f7\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u7573\u307f\u8fbc\u307f\u30d5\u30a3\u30eb\u30bf\u30fc\u3001\u5dee\u5206\u30d5\u30a3\u30eb\u30bf\u30fc\u3001\u30e1\u30c7\u30a3\u30a2\u30f3 \u30d5\u30a3\u30eb\u30bf\u30fc\u3001\u30ab\u30eb\u30de\u30f3 \u30d5\u30a3\u30eb\u30bf\u30fc\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u30d5\u30a3\u30eb\u30bf\u30fc\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u305d\u306e\u4e2d\u3067\u3001\u7573\u307f\u8fbc\u307f\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3068\u5fae\u5206\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306f\u4fe1\u53f7\u306e\u5e73\u6ed1\u5316\u3068\u30a8\u30c3\u30b8\u691c\u51fa\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u3001\u30e1\u30c7\u30a3\u30a2\u30f3 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306f\u4fe1\u53f7\u306e\u30ce\u30a4\u30ba\u3092\u9664\u53bb\u3059\u308b\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u3001\u30ab\u30eb\u30de\u30f3 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306f\u4fe1\u53f7\u306e\u72b6\u614b\u3068\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u63a8\u5b9a\u3059\u308b\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import signal\n\n# \u5b9a\u4e49\u4fe1\u53f7\nt = np.linspace(0, 1, 1000)\ny = np.sin(2 * np.pi * 5 * t) + np.random.normal(size=1000)\n\n# \u4f7f\u7528\u4e2d\u503c\u6ee4\u6ce2\u51fd\u6570\u53bb\u9664\u566a\u58f0\ny_medfilt = signal.medfilt(y, kernel_size=21)\n\n# \u4f7f\u7528\u5dee\u5206\u6ee4\u6ce2\u51fd\u6570\u68c0\u6d4b\u4fe1\u53f7\u8fb9\u7f18\ny_diff = np.abs(signal.convolve(y, [-1, 1], mode='valid'))\n\n# \u8f93\u51fa\u7ed3\u679c\nplt.figure(figsize=(10, 4))\nplt.plot(t, y, label='Original signal')\nplt.plot(t, y_medfilt, label='Median filter')\nplt.plot(t[1:], y_diff, label='Edge detection')\nplt.legend()\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e signal.medfilt() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u30ce\u30a4\u30ba\u3092\u542b\u3080\u6b63\u5f26\u6ce2\u4fe1\u53f7\u306b\u5bfe\u3057\u3066\u30e1\u30c7\u30a3\u30a2\u30f3 \u30d5\u30a3\u30eb\u30bf\u30fc\u51e6\u7406\u3092\u5b9f\u884c\u3057\u3066\u30ce\u30a4\u30ba\u3092\u9664\u53bb\u3057\u3001\u6b21\u306b signal.convolve() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066 1 \u6b21\u5dee\u5206\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u4fe1\u53f7\u306e\u30a8\u30c3\u30b8\u3092\u691c\u51fa\u3057\u307e\u3059\u3002\u51fa\u529b\u7d50\u679c\u3092\u6b21\u306e\u56f3\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/13\/ZfxK8BL32ojzX4I.png\" alt=\"signal_processing_example.png\"\/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u30b9\u30da\u30af\u30c8\u30eb\u5206\u6790\u6a5f\u80fd\uff1a\u4fe1\u53f7\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u30d1\u30ef\u30fc\u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u63a8\u5b9a\u3001\u81ea\u5df1\u76f8\u95a2\u6a5f\u80fd\u3001\u76f8\u4e92\u76f8\u95a2\u6a5f\u80fd\u3001\u30d4\u30fc\u30af\u5468\u6ce2\u6570\u691c\u51fa\u3001\u30b9\u30da\u30af\u30c8\u30eb\u5e73\u5766\u5ea6\u691c\u51fa\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u30b9\u30da\u30af\u30c8\u30eb\u5206\u6790\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u305d\u306e\u4e2d\u3067\u3082\u3001\u30d1\u30ef\u30fc\u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u63a8\u5b9a\u306f\u4fe1\u53f7\u306e\u5468\u6ce2\u6570\u5206\u5e03\u3068\u5468\u671f\u6027\u306e\u5206\u6790\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u3001\u81ea\u5df1\u76f8\u95a2\u95a2\u6570\u3068\u76f8\u4e92\u76f8\u95a2\u95a2\u6570\u306f\u4fe1\u53f7\u306e\u30de\u30c3\u30c1\u30f3\u30b0\u3068\u30a2\u30e9\u30a4\u30e1\u30f3\u30c8\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u3001\u30d4\u30fc\u30af\u5468\u6ce2\u6570\u691c\u51fa\u3068\u30b9\u30da\u30af\u30c8\u30eb\u5e73\u5766\u5ea6\u691c\u51fa\u306f\u4fe1\u53f7\u7279\u5fb4\u62bd\u51fa\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u305d\u3057\u3066\u5206\u985e\u3002\u4f8b\u3048\u3070\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import signal\n\n# \u5b9a\u4e49\u4fe1\u53f7\nt = np.linspace(0, 1, 1000)\ny = np.sin(2 * np.pi * 5 * t) + np.sin(2 * np.pi * 10 * t) + np.random.normal(size=1000)\n\n# \u4f7f\u7528welch\u51fd\u6570\u8ba1\u7b97\u529f\u7387\u8c31\u5bc6\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u6e96\u5099\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u7533\u3057\u8a33\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u524d\u306e\u56de\u7b54\u306b\u8aa4\u308a\u304c\u3042\u308a\u307e\u3057\u305f. \u30a6\u30a7\u30eb\u30c1\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u30d1\u30ef\u30fc \u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u63a8\u5b9a\u5024\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059. \u30b3\u30fc\u30c9\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import signal\n\n# \u5b9a\u4e49\u4fe1\u53f7\nt = np.linspace(0, 1, 1000)\ny = np.sin(2 * np.pi * 5 * t) + np.sin(2 * np.pi * 10 * t) + np.random.normal(size=1000)\n\n# \u4f7f\u7528welch\u51fd\u6570\u8ba1\u7b97\u529f\u7387\u8c31\u5bc6\u5ea6\u4f30\u8ba1\nf, pxx = signal.welch(y, fs=1000, nperseg=256)\n\n# \u8f93\u51fa\u7ed3\u679c\nplt.figure(figsize=(6, 4))\nplt.plot(f, pxx)\nplt.xlabel('Frequency [Hz]')\nplt.ylabel('PSD [V**2\/Hz]')\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e signal.welch() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30012 \u3064\u306e\u6b63\u5f26\u6ce2\u3068\u30ce\u30a4\u30ba\u3092\u542b\u3080\u4fe1\u53f7\u306e\u30d1\u30ef\u30fc \u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u3092\u63a8\u5b9a\u3057\u3001\u4fe1\u53f7\u306e\u5468\u6ce2\u6570\u5206\u5e03\u3068\u5468\u671f\u6027\u3092\u5206\u6790\u3057\u307e\u3059\u3002\u51fa\u529b\u7d50\u679c\u3092\u6b21\u306e\u56f3\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/dyHLf6pcW7VvOKS.png\" alt=\"signal_processing_example_2.png\"\/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u6a5f\u80fd: \u4fe1\u53f7\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u9ad8\u901f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3001\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3001\u9006\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3001\u30d2\u30eb\u30d9\u30eb\u30c8\u5909\u63db\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u305d\u306e\u4e2d\u3067\u3001\u9ad8\u901f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306f\u4fe1\u53f7\u306e\u30b9\u30da\u30af\u30c8\u30eb\u5206\u5e03\u3068\u5468\u671f\u6027\u3092\u8fc5\u901f\u306b\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u3001\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306f\u96e2\u6563\u4fe1\u53f7\u306e\u30b9\u30da\u30af\u30c8\u30eb\u5206\u6790\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u3001\u9006\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306f\u5468\u6ce2\u6570\u9818\u57df\u4fe1\u53f7\u3092\u6642\u9593\u9818\u57df\u4fe1\u53f7\u306b\u5909\u63db\u3059\u308b\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u30cf\u30eb\u30d9\u30eb\u30c8\u5909\u63db\u306f\u3001\u4fe1\u53f7\u306e\u30a8\u30f3\u30d9\u30ed\u30fc\u30d7\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import signal\n\n# \u5b9a\u4e49\u4fe1\u53f7\nt = np.linspace(0, 1, 1000)\ny = np.sin(2 * np.pi * 5 * t) + np.random.normal(size=1000)\n\n# \u4f7f\u7528fft\u51fd\u6570\u8ba1\u7b97\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\ny_fft = np.fft.fft(y)\nfreq = np.fft.fftfreq(y.size, 1\/1000)\n\n# \u8f93\u51fa\u7ed3\u679c\nplt.figure(figsize=(6, 4))\nplt.plot(freq, np.abs(y_fft))\nplt.xlabel('Frequency [Hz]')\nplt.ylabel('Amplitude [V]')\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e np.fft.fft() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u6b63\u5f26\u6ce2\u3068\u30ce\u30a4\u30ba\u3092\u542b\u3080\u4fe1\u53f7\u306b\u5bfe\u3057\u3066\u9ad8\u901f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u5b9f\u884c\u3057\u3001\u4fe1\u53f7\u306e\u30b9\u30da\u30af\u30c8\u30eb\u5206\u5e03\u3068\u5468\u671f\u6027\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u51fa\u529b\u7d50\u679c\u3092\u6b21\u306e\u56f3\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/LTucrZ8sXtBy3So.png\" alt=\"signal_processing_example_3.png\"\/><\/figure>\n\n\n\n<p>\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u95a2\u6570\u306f\u3001\u4fe1\u53f7\u3092\u51e6\u7406\u3059\u308b\u3068\u304d\u306b\u30bc\u30ed \u30d1\u30c7\u30a3\u30f3\u30b0\u3068\u4fe1\u53f7\u306e\u524d\u51e6\u7406\u3092\u5b9f\u884c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u30d5\u30a3\u30eb\u30bf\u8a2d\u8a08\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u30d5\u30a3\u30eb\u30bf\u306f\u3001\u4fe1\u53f7\u5185\u306e\u7279\u5b9a\u306e\u5468\u6ce2\u6570\u6210\u5206\u3092\u9664\u53bb\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u30b7\u30b9\u30c6\u30e0\u3067\u3001\u7279\u5b9a\u306e\u5468\u6ce2\u6570\u7bc4\u56f2\u5185\u306e\u4fe1\u53f7\u6210\u5206\u3092\u901a\u904e\u3055\u305b\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u4ed6\u306e\u5468\u6ce2\u6570\u306e\u4fe1\u53f7\u6210\u5206\u3092\u9664\u53bb\u3067\u304d\u307e\u3059\u3002\u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08\u3068\u306f\u3001\u7279\u5b9a\u306e\u4fe1\u53f7\u8981\u4ef6\u3068\u6027\u80fd\u6307\u6a19\u306b\u5f93\u3063\u3066\u9069\u5207\u306a\u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3059\u308b\u3053\u3068\u3092\u6307\u3057\u3001\u901a\u5e38\u3001\u9069\u5207\u306a\u30d5\u30a3\u30eb\u30bf\u30fc \u30bf\u30a4\u30d7\u306e\u9078\u629e\u3001\u30d5\u30a3\u30eb\u30bf\u30fc \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u6c7a\u5b9a\u3001\u30d5\u30a3\u30eb\u30bf\u30fc\u56de\u8def\u306e\u8a2d\u8a08\u306a\u3069\u306e\u624b\u9806\u304c\u542b\u307e\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u30b7\u30b0\u30ca\u30eb \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001FIR \u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08\u3001IIR \u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08\u3001\u30d0\u30bf\u30fc\u30ef\u30fc\u30b9 \u30d5\u30a3\u30eb\u30bf\u30fc\u3001\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5 \u30d5\u30a3\u30eb\u30bf\u30fc\u3001\u30c7\u30b8\u30bf\u30eb \u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08\u6a5f\u80fd\u3068\u30c4\u30fc\u30eb\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08\u95a2\u6570\u3068\u30c4\u30fc\u30eb\u306e\u4e00\u90e8\u3092\u4ee5\u4e0b\u306b\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>FIR \u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08: \u4fe1\u53f7\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001firwin\u3001remez\u3001kaiser \u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a FIR \u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u306e\u3046\u3061\u3001firwin \u95a2\u6570\u306f\u7a93\u95a2\u6570\u6cd5\u3092\u4f7f\u7528\u3057\u3066 FIR \u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u3001remez \u95a2\u6570\u306f\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3092\u4f7f\u7528\u3057\u3066 FIR \u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u3001kaiser \u95a2\u6570\u306f\u30ab\u30a4\u30b6\u30fc\u7a93\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066 FIR \u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import signal\n\n# \u8bbe\u8ba1\u4e00\u4e2a\u5e26\u901aFIR\u6ee4\u6ce2\u5668\nfs = 1000\nf1 = 20\nf2 = 50\nN = 101\n\nb = signal.firwin(N, [f1, f2], pass_zero=False, fs=fs)\n\n# \u8f93\u51fa\u7ed3\u679c\nplt.figure(figsize=(6, 4))\nplt.plot(b)\nplt.xlabel('Sample number')\nplt.ylabel('Amplitude')\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e signal.firwin() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30d0\u30f3\u30c9\u30d1\u30b9 FIR \u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001N \u306f\u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u6b21\u6570\u3001[f1, f2] \u306f\u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u901a\u904e\u5e2f\u57df\u5883\u754c\u5468\u6ce2\u6570\u3001pass_zero=False \u306f no \u3092\u610f\u5473\u3057\u307e\u3059\u3002 \u3001fs \u306f\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0 \u30ec\u30fc\u30c8\u3067\u3059\u3002\u51fa\u529b\u7d50\u679c\u3092\u6b21\u306e\u56f3\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/ojJ5zThYSBLDf1a.png\" alt=\"filter_design_example_1.png\"\/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>IIR \u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08: \u30b7\u30b0\u30ca\u30eb \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001butter\u3001cheby1\u3001cheby2\u3001ellip \u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a IIR \u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u95a2\u6570 butter \u306f\u30d0\u30bf\u30fc\u30ef\u30fc\u30b9 \u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u3001\u95a2\u6570 cheby1 \u306f\u7b2c 1 \u578b\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5 \u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u3001\u95a2\u6570 cheby2 \u306f\u7b2c 2 \u578b\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5 \u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u3001\u95a2\u6570 ellip \u306f\u6955\u5186\u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import signal\n\n# \u8bbe\u8ba1\u4e00\u4e2a\u4f4e\u901aIIR\u6ee4\u6ce2\u5668\nfs = 1000\nfc = 100\nN = 4\n\nb, a = signal.butter(N, fc, 'low', fs=fs)\n\n# \u8f93\u51fa\u7ed3\u679c\nw, h = signal.freqz(b, a)\nplt.figure(figsize=(\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"6\">\n<li>\u30c7\u30b8\u30bf\u30eb \u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08: \u4fe1\u53f7\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001firwin2\u3001remezord\u3001firpm \u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u30c7\u30b8\u30bf\u30eb \u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08\u6a5f\u80fd\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002\u305d\u306e\u4e2d\u3067\u3001\u95a2\u6570 firwin2 \u306f\u5468\u6ce2\u6570\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u6cd5\u3092\u4f7f\u7528\u3057\u3066 FIR \u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u3001\u95a2\u6570 remezord \u306f\u6700\u5c0f\u304a\u3088\u3073\u6700\u5927\u30ea\u30c3\u30d7\u30eb\u3092\u4f7f\u7528\u3057\u3066 FIR \u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u3001\u95a2\u6570 firpm \u306f\u6700\u5c0f\u304a\u3088\u3073\u6700\u5927\u30ea\u30c3\u30d7\u30eb\u3092\u4f7f\u7528\u3057\u3066 FIR \u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\uff1a<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import signal\n\n# \u8bbe\u8ba1\u4e00\u4e2a\u6570\u5b57\u4f4e\u901a\u6ee4\u6ce2\u5668\nfs = 1000\nfc = 100\nN = 51\n\nb = signal.firwin2(N, [0, fc, fc*1.2, 0.5*fs], [1, 1, 0, 0], fs=fs)\n\n# \u8f93\u51fa\u7ed3\u679c\nw, h = signal.freqz(b)\nplt.figure(figsize=(6, 4))\nplt.plot(w\/np.pi*fs\/2, 20*np.log10(np.abs(h)))\nplt.xlabel('Frequency [Hz]')\nplt.ylabel('Magnitude [dB]')\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e signal.firwin2() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30c7\u30b8\u30bf\u30eb \u30ed\u30fc\u30d1\u30b9 \u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001N \u306f\u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u6b21\u6570\u3067\u3001[0, fc, fc*1.2, 0.5*fs] \u306f\u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u901a\u904e\u5e2f\u57df\u3067\u3059\u3002\u5883\u754c\u5468\u6ce2\u6570 [1, 1, 0, 0] \u306f\u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u901a\u904e\u5e2f\u57df\u3068\u963b\u6b62\u5e2f\u57df\u306e\u30b2\u30a4\u30f3\u5024\u3001fs \u306f\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0 \u30ec\u30fc\u30c8\u3067\u3059\u3002\u51fa\u529b\u7d50\u679c\u3092\u6b21\u306e\u56f3\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/hC9ZLRljB5Ov14J.png\" alt=\"filter_design_example_3.png\"\/><\/figure>\n\n\n\n<p>\u4e0a\u8a18\u306f\u3001\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u30d5\u30a3\u30eb\u30bf\u30fc\u8a2d\u8a08\u6a5f\u80fd\u3068\u30c4\u30fc\u30eb\u306e\u4e00\u90e8\u3067\u3059.\u3053\u308c\u3089\u306e\u6a5f\u80fd\u3068\u30c4\u30fc\u30eb\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u5b9f\u969b\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u9069\u5207\u306a\u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u3001\u4fe1\u53f7\u3092\u52b9\u679c\u7684\u306b\u30d5\u30a3\u30eb\u30bf\u30fc\u51e6\u7406\u304a\u3088\u3073\u51e6\u7406\u3067\u304d\u307e\u3059.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u4fe1\u53f7\u89e3\u6790\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u4fe1\u53f7\u5206\u6790\u3068\u306f\u3001\u4fe1\u53f7\u306e\u6027\u8cea\u3068\u7279\u6027\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u4fe1\u53f7\u3092\u5206\u6790\u304a\u3088\u3073\u51e6\u7406\u3059\u308b\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002\u4fe1\u53f7\u89e3\u6790\u306b\u306f\u591a\u304f\u306e\u5074\u9762\u304c\u542b\u307e\u308c\u307e\u3059\u304c\u3001\u305d\u306e\u4e2d\u3067\u3082\u3088\u308a\u91cd\u8981\u306a\u3082\u306e\u306b\u306f\u3001\u6642\u9593\u9818\u57df\u89e3\u6790\u3001\u5468\u6ce2\u6570\u9818\u57df\u89e3\u6790\u3001\u304a\u3088\u3073\u6642\u9593-\u5468\u6ce2\u6570\u9818\u57df\u89e3\u6790\u304c\u542b\u307e\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6642\u9593\u9818\u57df\u89e3\u6790: \u6642\u9593\u9818\u57df\u89e3\u6790\u3068\u306f\u3001\u30bf\u30a4\u30df\u30f3\u30b0 \u30c0\u30a4\u30a2\u30b0\u30e9\u30e0\u3001\u81ea\u5df1\u76f8\u95a2\u95a2\u6570\u3001\u76f8\u4e92\u76f8\u95a2\u95a2\u6570\u3001\u304a\u3088\u3073\u30a8\u30cd\u30eb\u30ae\u30fc \u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u3092\u542b\u3080\u3001\u7d4c\u6642\u7684\u306a\u4fe1\u53f7\u5909\u5316\u306e\u89e3\u6790\u3092\u6307\u3057\u307e\u3059\u3002\u30bf\u30a4\u30e0\u30c9\u30e1\u30a4\u30f3\u89e3\u6790\u306f\u3001\u4fe1\u53f7\u306e\u6ce2\u5f62\u3001\u5468\u671f\u3001\u632f\u5e45\u306a\u3069\u306e\u60c5\u5831\u3092\u660e\u3089\u304b\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u30bf\u30a4\u30df\u30f3\u30b0\u306e\u5224\u65ad\u3084\u4fe1\u53f7\u306e\u51e6\u7406\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u5468\u6ce2\u6570\u30c9\u30e1\u30a4\u30f3\u5206\u6790: \u5468\u6ce2\u6570\u30c9\u30e1\u30a4\u30f3\u5206\u6790\u3068\u306f\u3001\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3001\u30d1\u30ef\u30fc\u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u3001\u30d5\u30a3\u30eb\u30bf\u30fc\u306a\u3069\u3092\u542b\u3080\u3001\u5468\u6ce2\u6570\u306b\u304a\u3051\u308b\u4fe1\u53f7\u306e\u7279\u6027\u306e\u5206\u6790\u3092\u6307\u3057\u307e\u3059\u3002\u5468\u6ce2\u6570\u30c9\u30e1\u30a4\u30f3\u5206\u6790\u306f\u3001\u4fe1\u53f7\u306e\u5468\u6ce2\u6570\u5206\u5e03\u3001\u5468\u671f\u6027\u3001\u9ad8\u8abf\u6ce2\u3001\u304a\u3088\u3073\u305d\u306e\u4ed6\u306e\u60c5\u5831\u3092\u660e\u3089\u304b\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3084\u30ce\u30a4\u30ba\u9664\u53bb\u306a\u3069\u306e\u4fe1\u53f7\u51e6\u7406\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u6642\u9593-\u5468\u6ce2\u6570\u30c9\u30e1\u30a4\u30f3\u5206\u6790: \u6642\u9593-\u5468\u6ce2\u6570\u30c9\u30e1\u30a4\u30f3\u5206\u6790\u306f\u3001\u77ed\u6642\u9593\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3068\u30a6\u30a7\u30fc\u30d6\u30ec\u30c3\u30c8\u5909\u63db\u3092\u542b\u3080\u3001\u6642\u9593\u3068\u5468\u6ce2\u6570\u306b\u304a\u3051\u308b\u4fe1\u53f7\u306e\u7279\u6027\u306e\u7d50\u5408\u5206\u6790\u3092\u6307\u3057\u307e\u3059\u3002\u6642\u9593-\u5468\u6ce2\u6570\u30c9\u30e1\u30a4\u30f3\u5206\u6790\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u671f\u9593\u3068\u5468\u6ce2\u6570\u671f\u9593\u306b\u304a\u3051\u308b\u4fe1\u53f7\u306e\u5909\u5316\u3068\u7279\u6027\u3092\u660e\u3089\u304b\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u8907\u96d1\u306a\u4fe1\u53f7\u5206\u6790\u3068\u4fe1\u53f7\u306e\u7279\u5fb4\u62bd\u51fa\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30b7\u30b0\u30ca\u30eb \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3001\u30d1\u30ef\u30fc \u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u63a8\u5b9a\u3001\u81ea\u5df1\u76f8\u95a2\u95a2\u6570\u3001\u76f8\u4e92\u76f8\u95a2\u95a2\u6570\u3001\u77ed\u6642\u9593\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3001\u30a6\u30a7\u30fc\u30d6\u30ec\u30c3\u30c8\u5909\u63db\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u4fe1\u53f7\u89e3\u6790\u30c4\u30fc\u30eb\u3068\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import signal\n\n# \u751f\u6210\u4e00\u4e2a\u542b\u6709\u4e24\u4e2a\u6b63\u5f26\u6ce2\u548c\u566a\u58f0\u7684\u4fe1\u53f7\nt = np.linspace(0, 1, 1000)\ny = np.sin(2*np.pi*5*t) + np.sin(2*np.pi*10*t) + np.random.normal(size=1000)\n\n# \u8ba1\u7b97\u4fe1\u53f7\u7684\u529f\u7387\u8c31\u5bc6\u5ea6\u4f30\u8ba1\nf, Pxx = signal.welch(y, fs=1000)\n\n# \u8ba1\u7b97\u4fe1\u53f7\u7684\u81ea\u76f8\u5173\u51fd\u6570\u548c\u4e92\u76f8\u5173\u51fd\u6570\ncorr_y = signal.correlate(y, y, mode='full')\ncorr_y1_y2 = signal.correlate(y1, y2, mode='full')\n\n# \u8fdb\u884c\u77ed\u65f6\u5085\u91cc\u53f6\u53d8\u6362\nf, t, Zxx = signal.stft(y, fs=1000, nperseg=256)\n\n# \u8fdb\u884c\u5c0f\u6ce2\u53d8\u6362\ncA, cD = pywt.dwt(y, 'db2')\n\n# \u8f93\u51fa\u7ed3\u679c\nplt.figure(figsize=(8, 10))\nplt.subplot(511)\nplt.plot(t, y)\nplt.xlabel('Time [s]')\nplt.ylabel('Amplitude')\nplt.subplot(512)\nplt.plot(f, Pxx)\nplt.xlabel('Frequency [Hz]')\nplt.ylabel('PSD [V**2\/Hz]')\nplt.subplot(513)\nplt.plot(corr_y)\nplt.xlabel('Lag')\nplt.ylabel\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>&#8216;Autocorrelation&#8217;) plt.subplot(514) plt.plot(corr_y1_y2) plt.xlabel(&#8216;Lag&#8217;) plt.ylabel(&#8216;\u76f8\u4e92\u76f8\u95a2&#8217;) plt.subplot(515) plt.pcolormesh(t, f, np. abs(Zxx), vmin=0, vmax=amp) plt.xlabel(&#8216;\u6642\u9593 [s]&#8217;) plt.ylabel(&#8216;\u5468\u6ce2\u6570 [Hz]&#8217;) plt.colorbar() plt.show()<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">diff\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>\n\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528Scipy\u5e93\u4e2d\u7684signal\u6a21\u5757\u4e2d\u7684\u591a\u4e2a\u51fd\u6570\u5bf9\u4fe1\u53f7\u8fdb\u884c\u4e86\u65f6\u57df\u5206\u6790\u3001\u9891\u57df\u5206\u6790\u3001\u65f6\u9891\u57df\u5206\u6790\uff0c\u5176\u4e2d\uff1a\n\n- \u4f7f\u7528signal.welch()\u51fd\u6570\u8ba1\u7b97\u4fe1\u53f7\u7684\u529f\u7387\u8c31\u5bc6\u5ea6\u4f30\u8ba1\uff0c\u53ef\u4ee5\u5f97\u5230\u4fe1\u53f7\u5728\u4e0d\u540c\u9891\u7387\u6bb5\u5185\u7684\u80fd\u91cf\u5206\u5e03\u60c5\u51b5\uff1b\n\n- \u4f7f\u7528signal.correlate()\u51fd\u6570\u8ba1\u7b97\u4fe1\u53f7\u7684\u81ea\u76f8\u5173\u51fd\u6570\u548c\u4e92\u76f8\u5173\u51fd\u6570\uff0c\u53ef\u4ee5\u5f97\u5230\u4fe1\u53f7\u7684\u5468\u671f\u6027\u548c\u76f8\u5173\u6027\u4fe1\u606f\uff1b\n\n- \u4f7f\u7528signal.stft()\u51fd\u6570\u8fdb\u884c\u77ed\u65f6\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u53ef\u4ee5\u5f97\u5230\u4fe1\u53f7\u5728\u4e0d\u540c\u65f6\u95f4\u548c\u9891\u7387\u6bb5\u5185\u7684\u9891\u8c31\u4fe1\u606f\uff1b\n\n- \u4f7f\u7528pywt.dwt()\u51fd\u6570\u8fdb\u884c\u5c0f\u6ce2\u53d8\u6362\uff0c\u53ef\u4ee5\u5f97\u5230\u4fe1\u53f7\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u7684\u9891\u8c31\u4fe1\u606f\u3002\n\n\u4ee5\u4e0a\u662f\u4e00\u4e9b\u5e38\u7528\u7684\u4fe1\u53f7\u5206\u6790\u51fd\u6570\u548c\u5de5\u5177\uff0c\u4f7f\u7528\u8fd9\u4e9b\u51fd\u6570\u548c\u5de5\u5177\u53ef\u4ee5\u5bf9\u4fe1\u53f7\u8fdb\u884c\u6df1\u5165\u7684\u5206\u6790\u548c\u5904\u7406\uff0c\u6709\u52a9\u4e8e\u63d0\u53d6\u4fe1\u53f7\u7684\u7279\u5f81\u548c\u4fe1\u606f\u3002\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u4f8b\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044: \u4fe1\u53f7\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306e\u5b9f\u88c5<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30b7\u30b0\u30ca\u30eb \u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u3001\u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u4f7f\u7528\u3057\u3066\u30b7\u30b0\u30ca\u30eb\u3092\u30d5\u30a3\u30eb\u30bf\u30fc\u51e6\u7406\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u307e\u3059\u3002\u5177\u4f53\u7684\u306a\u624b\u9806\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6b63\u5f26\u6ce2\u4fe1\u53f7\u306b\u30db\u30ef\u30a4\u30c8 \u30ac\u30a6\u30b9 \u30ce\u30a4\u30ba\u3092\u52a0\u3048\u305f\u3082\u306e\u306a\u3069\u3001\u30ce\u30a4\u30ba\u306e\u591a\u3044\u4fe1\u53f7\u3092\u751f\u6210\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nfrom scipy import signal\n\n# \u751f\u6210\u4e00\u4e2a\u542b\u6709\u566a\u58f0\u7684\u4fe1\u53f7\nt = np.linspace(0, 1, 1000)\ny = np.sin(2*np.pi*50*t) + np.random.normal(size=1000)\n<\/code><\/pre>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u30ab\u30c3\u30c8\u30aa\u30d5\u5468\u6ce2\u6570\u304c 20 Hz \u306e FIR \u30d5\u30a3\u30eb\u30bf\u30fc\u306a\u3069\u3001\u30c7\u30b8\u30bf\u30eb \u30ed\u30fc\u30d1\u30b9 \u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u8a2d\u8a08\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code># \u8bbe\u8ba1\u4e00\u4e2a\u6570\u5b57\u4f4e\u901a\u6ee4\u6ce2\u5668\nfs = 1000\nfc = 20\nN = 51\n\nb = signal.firwin2(N, [0, fc, fc*1.2, 0.5*fs], [1, 1, 0, 0], fs=fs)\n<\/code><\/pre>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>\u30d5\u30a3\u30eb\u30bf\u30fc\u3092\u4f7f\u7528\u3057\u3066\u4fe1\u53f7\u3092\u30d5\u30a3\u30eb\u30bf\u30fc\u51e6\u7406\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code># \u4f7f\u7528\u6ee4\u6ce2\u5668\u8fdb\u884c\u6ee4\u6ce2\ny_filtered = signal.lfilter(b, 1, y)\n<\/code><\/pre>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li>\u5143\u306e\u4fe1\u53f7\u3068\u30d5\u30a3\u30eb\u30bf\u30fc\u51e6\u7406\u3055\u308c\u305f\u4fe1\u53f7\u306e\u6642\u9593\u9818\u57df\u6ce2\u5f62\u3068\u5468\u6ce2\u6570\u9818\u57df\u30b9\u30da\u30af\u30c8\u30eb\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code># \u7ed8\u5236\u539f\u59cb\u4fe1\u53f7\u548c\u6ee4\u6ce2\u540e\u7684\u4fe1\u53f7\u7684\u65f6\u57df\u6ce2\u5f62\u548c\u9891\u57df\u8c31\nf, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 6))\nax1.plot(t, y, 'b-', linewidth=1, label='Original signal')\nax1.plot(t, y_filtered, 'r-', linewidth=2, label='Filtered signal')\nax1.legend(loc='best')\nax1.set_xlabel('Time [s]')\nax1.set_ylabel('Amplitude')\nax1.set_title('Signal Filtering')\n\nfrequencies, power_spectrum = signal.periodogram(y, fs)\nax2.semilogy(frequencies, power_spectrum, 'b-', linewidth=1, label='Original signal')\nfrequencies, power_spectrum = signal.periodogram(y_filtered, fs)\nax2.semilogy(frequencies, power_spectrum, 'r-', linewidth=2, label='Filtered signal')\nax2.legend(loc='best')\nax2.set_xlabel('Frequency [Hz]')\nax2.set_ylabel('Power Spectrum')\nax2.set_title('Frequency Domain')\n\nplt.tight_layout()\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u6700\u7d42\u7d50\u679c\u306f\u3001\u6b21\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/hpbVM5Hy8xdj7la.png\" alt=\"signal_filtering_example.png\"\/><\/figure>\n\n\n\n<p>\u7d50\u679c\u304b\u3089\u3001\u30ed\u30fc\u30d1\u30b9 \u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u51e6\u7406\u5f8c\u3001\u4fe1\u53f7\u306e\u9ad8\u5468\u6ce2\u30ce\u30a4\u30ba\u304c\u52b9\u679c\u7684\u306b\u9664\u53bb\u3055\u308c\u3001\u30d5\u30a3\u30eb\u30bf\u30fc\u51e6\u7406\u3055\u308c\u305f\u4fe1\u53f7\u304c\u3088\u308a\u6ed1\u3089\u304b\u306b\u306a\u308a\u3001\u30b9\u30da\u30af\u30c8\u30eb\u304c 50 Hz \u4ed8\u8fd1\u306b\u3088\u308a\u96c6\u4e2d\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u753b\u50cf\u51e6\u7406 scipy.ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u753b\u50cf\u51e6\u7406\u3068\u306f\u3001\u60c5\u5831\u3068\u7279\u5fb4\u3092\u53d6\u5f97\u3059\u308b\u305f\u3081\u306b\u30c7\u30b8\u30bf\u30eb\u753b\u50cf\u3092\u51e6\u7406\u304a\u3088\u3073\u5206\u6790\u3059\u308b\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3001\u5f62\u614b\u5b66\u7684\u51e6\u7406\u3001\u753b\u50cf\u5909\u63db\u3001\u7279\u5fb4\u62bd\u51fa\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u753b\u50cf\u51e6\u7406\u6a5f\u80fd\u3068\u30c4\u30fc\u30eb\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6a5f\u80fd\u3068\u30c4\u30fc\u30eb\u306e\u4f7f\u3044\u65b9\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0: ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u30ac\u30a6\u30b9 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3001\u30e1\u30c7\u30a3\u30a2\u30f3 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3001\u6700\u5927\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3001\u6700\u5c0f\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u3001\u753b\u50cf\u306b\u5bfe\u3057\u3066\u5e73\u6ed1\u5316\u3001\u30ce\u30a4\u30ba\u9664\u53bb\u3001\u304a\u3088\u3073\u305d\u306e\u4ed6\u306e\u51e6\u7406\u3092\u5b9f\u884c\u3057\u3066\u3001\u753b\u50cf\u306e\u54c1\u8cea\u3068\u8996\u899a\u52b9\u679c\u3092\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u5f62\u614b\u5b66\u7684\u51e6\u7406: ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u6d78\u98df\u3001\u81a8\u5f35\u3001\u958b\u9589\u64cd\u4f5c\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u5f62\u614b\u5b66\u7684\u51e6\u7406\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u3001\u753b\u50cf\u306b\u5bfe\u3057\u3066 2 \u5024\u5316\u3001\u30bb\u30b0\u30e1\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u3001\u5857\u308a\u3064\u3076\u3057\u306a\u3069\u306e\u51e6\u7406\u3092\u5b9f\u884c\u3057\u3066\u3001\u753b\u50cf\u306e\u54c1\u8cea\u3068\u51e6\u7406\u52b9\u679c\u3092\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u753b\u50cf\u5909\u63db: ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u30a2\u30d5\u30a3\u30f3\u5909\u63db\u3001\u900f\u8996\u5909\u63db\u3001\u56de\u8ee2\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u753b\u50cf\u5909\u63db\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u3001\u753b\u50cf\u306b\u5bfe\u3057\u3066\u5e73\u884c\u79fb\u52d5\u3001\u56de\u8ee2\u3001\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u306a\u3069\u306e\u5909\u63db\u3092\u5b9f\u884c\u3057\u3066\u3001\u753b\u50cf\u306e\u5f62\u72b6\u3084\u8996\u899a\u52b9\u679c\u3092\u5909\u66f4\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u7279\u5fb4\u62bd\u51fa: ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u30a8\u30c3\u30b8\u691c\u51fa\u3001\u30b3\u30fc\u30ca\u30fc\u691c\u51fa\u3001\u8f2a\u90ed\u62bd\u51fa\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u7279\u5fb4\u62bd\u51fa\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u8a8d\u8b58\u3068\u5206\u985e\u306b\u5f79\u7acb\u3064\u7279\u5b9a\u306e\u7279\u5fb4\u3092\u753b\u50cf\u304b\u3089\u62bd\u51fa\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4ee5\u4e0b\u3067\u306f\u3001\u753b\u50cf\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306e\u4f8b\u3092\u4f7f\u7528\u3057\u3066\u3001ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u4f7f\u7528\u65b9\u6cd5\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>from scipy import ndimage\nimport matplotlib.pyplot as plt\nimport numpy as np\n\n# \u8bfb\u53d6\u4e00\u5f20\u7070\u5ea6\u56fe\u50cf\nimg = plt.imread('lena.png')\ngray = np.dot(img[...,:3], [0.299, 0.587, 0.114])\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u9ad8\u65af\u6ee4\u6ce2\nsigma = 3\nfiltered = ndimage.gaussian_filter(gray, sigma)\n\n# \u663e\u793a\u7ed3\u679c\nfig, ax = plt.subplots(1, 2, figsize=(8, 4))\nax[0].imshow(gray, cmap=plt.cm.gray)\nax[0].axis('off')\nax[0].set_title('Original Image')\nax[1].imshow(filtered, cmap=plt.cm.gray)\nax[1].axis('off')\nax[1].set_title('Gaussian Filtered Image, $\\sigma$=' + str(sigma))\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u30b0\u30ec\u30fc\u30b9\u30b1\u30fc\u30eb \u30a4\u30e1\u30fc\u30b8\u3092\u8aad\u307f\u53d6\u308a\u3001ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u30ac\u30a6\u30b9 \u30d5\u30a3\u30eb\u30bf\u30fc\u95a2\u6570 ndimage.gaussian_filter() \u3092\u4f7f\u7528\u3057\u3066\u30a4\u30e1\u30fc\u30b8\u3092\u5e73\u6ed1\u5316\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u6bd4\u8f03\u306e\u305f\u3081\u306b\u5143\u306e\u753b\u50cf\u3068\u30d5\u30a3\u30eb\u30bf\u30fc\u51e6\u7406\u3055\u308c\u305f\u753b\u50cf\u3092\u4e00\u7dd2\u306b\u63cf\u753b\u3057\u307e\u3059\u3002\u7d50\u679c\u3092\u4e0b\u306e\u56f3\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>![\u753b\u50cf\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306e\u4f8b.png](&nbsp;<a href=\"https:\/\/i.loli.net\/2022\/01\/17\/TGRmMSyBtk\">https:\/\/i.loli.net\/2022\/01\/17\/TGRmMSyBtk<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u7d50\u679c\u304b\u3089\u3001\u30ac\u30a6\u30b9 \u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u51e6\u7406\u5f8c\u3001\u753b\u50cf\u5185\u306e\u30ce\u30a4\u30ba\u304c\u52b9\u679c\u7684\u306b\u9664\u53bb\u3055\u308c\u3001\u30d5\u30a3\u30eb\u30bf\u30fc\u51e6\u7406\u3055\u308c\u305f\u753b\u50cf\u304c\u3088\u308a\u6ed1\u3089\u304b\u306b\u306a\u308a\u3001\u7d30\u90e8\u304c\u3088\u308a\u660e\u78ba\u306b\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u306e\u4f8b\u3067\u306f\u3001ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u3067\u57fa\u672c\u7684\u306a\u753b\u50cf\u51e6\u7406\u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u307e\u3059. \u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u30cb\u30fc\u30ba\u3092\u6e80\u305f\u3059\u305f\u3081\u306b\u753b\u50cf\u306b\u5bfe\u3057\u3066\u3055\u307e\u3056\u307e\u306a\u51e6\u7406\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u753b\u50cf\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u753b\u50cf\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3068\u306f\u3001\u30c7\u30b8\u30bf\u30eb\u753b\u50cf\u3092\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3057\u3066\u3001\u30ce\u30a4\u30ba\u9664\u53bb\u3001\u5e73\u6ed1\u5316\u3001\u5f37\u5316\u3001\u304a\u3088\u3073\u305d\u306e\u4ed6\u306e\u52b9\u679c\u3092\u5b9f\u73fe\u3059\u308b\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002\u4e00\u822c\u7684\u306a\u753b\u50cf\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u65b9\u6cd5\u306b\u306f\u3001\u5e73\u5747\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3001\u30ac\u30a6\u30b9 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3001\u30e1\u30c7\u30a3\u30a2\u30f3 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3001\u30d0\u30a4\u30e9\u30c6\u30e9\u30eb \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306a\u3069\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u65b9\u6cd5\u306b\u306f\u305d\u308c\u305e\u308c\u7279\u5fb4\u304c\u3042\u308a\u3001\u5b9f\u969b\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u9069\u5207\u306a\u65b9\u6cd5\u3092\u9078\u629e\u3057\u3066\u51e6\u7406\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5e73\u5747\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0: \u5e73\u5747\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306f\u6700\u3082\u5358\u7d14\u306a\u753b\u50cf\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u65b9\u6cd5\u306e 1 \u3064\u3067\u3001\u753b\u50cf\u306e\u5e73\u6ed1\u5316\u3092\u5b9f\u73fe\u3059\u308b\u305f\u3081\u306b\u3001\u4e2d\u5fc3\u30d4\u30af\u30bb\u30eb\u306e\u5024\u3092\u8fd1\u96a3\u306e\u30d4\u30af\u30bb\u30eb\u306e\u5e73\u5747\u5024\u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\u3044\u3046\u8003\u3048\u65b9\u3067\u3059\u3002\u5e73\u5747\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306e\u6b20\u70b9\u306f\u3001\u30a8\u30c3\u30b8\u3068\u8a73\u7d30\u60c5\u5831\u3092\u7c21\u5358\u306b\u7834\u68c4\u3067\u304d\u308b\u3053\u3068\u3067\u3059\u3002<\/li>\n\n\n\n<li>\u30ac\u30a6\u30b9 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0: \u30ac\u30a6\u30b9 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306f\u3001\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u753b\u50cf\u306e\u5e73\u6ed1\u5316\u65b9\u6cd5\u3067\u3059. \u305d\u306e\u57fa\u672c\u7684\u306a\u8003\u3048\u65b9\u306f\u3001\u30ac\u30a6\u30b9\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u8fd1\u508d\u306e\u30d4\u30af\u30bb\u30eb\u3092\u91cd\u307f\u4ed8\u3051\u304a\u3088\u3073\u5e73\u5747\u5316\u3057\u3001\u753b\u50cf\u306e\u5e73\u6ed1\u5316\u3092\u5b9f\u73fe\u3059\u308b\u3053\u3068\u3067\u3059.&nbsp;\u30ac\u30a6\u30b9 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306f\u3001\u753b\u50cf\u306e\u8a73\u7d30\u3092\u4fdd\u6301\u3057\u306a\u304c\u3089\u9ad8\u5468\u6ce2\u30ce\u30a4\u30ba\u3092\u52b9\u679c\u7684\u306b\u9664\u53bb\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u30e1\u30c7\u30a3\u30a2\u30f3 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0: \u30e1\u30c7\u30a3\u30a2\u30f3 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306f\u975e\u7dda\u5f62\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u624b\u6cd5\u3067\u3001\u753b\u50cf\u306e\u30ce\u30a4\u30ba\u9664\u53bb\u3092\u5b9f\u73fe\u3059\u308b\u305f\u3081\u306b\u3001\u4e2d\u5fc3\u30d4\u30af\u30bb\u30eb\u306e\u5024\u3092\u8fd1\u96a3\u306e\u30d4\u30af\u30bb\u30eb\u306e\u4e2d\u592e\u5024\u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\u3044\u3046\u8003\u3048\u65b9\u3067\u3059\u3002\u30e1\u30b8\u30a2\u30f3 \u30d5\u30a3\u30eb\u30bf\u30fc\u51e6\u7406\u306f\u3001\u3054\u307e\u5869\u30ce\u30a4\u30ba\u3084\u30a4\u30f3\u30d1\u30eb\u30b9 \u30ce\u30a4\u30ba\u306a\u3069\u306e\u96e2\u6563\u30ce\u30a4\u30ba\u306e\u51e6\u7406\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u30d0\u30a4\u30e9\u30c6\u30e9\u30eb \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0: \u30d0\u30a4\u30e9\u30c6\u30e9\u30eb \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306f\u3001\u30a8\u30c3\u30b8\u3092\u4fdd\u5b58\u3059\u308b\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u65b9\u6cd5\u3067\u3059. \u305d\u306e\u57fa\u672c\u7684\u306a\u8003\u3048\u65b9\u306f\u3001\u753b\u50cf\u3092\u7dad\u6301\u3057\u306a\u304c\u3089\u30ac\u30a6\u30b9 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306b\u57fa\u3065\u3044\u3066\u3001\u30d4\u30af\u30bb\u30eb\u9593\u306e\u8ddd\u96e2\u306e\u5e73\u5747\u3068\u30b0\u30ec\u30fc\u5024\u306b\u91cd\u307f\u4ed8\u3051\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u753b\u50cf\u306e\u5e73\u6ed1\u5316\u3092\u5b9f\u73fe\u3059\u308b\u3053\u3068\u3067\u3059. \u30a8\u30c3\u30b8\u3068\u30c7\u30a3\u30c6\u30fc\u30eb\u60c5\u5831\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4ee5\u4e0b\u3067\u306f\u3001\u30ac\u30a6\u30b9 \u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306e\u4f8b\u3092\u4f7f\u7528\u3057\u3066\u3001\u753b\u50cf\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u306e\u5b9f\u88c5\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import misc, ndimage\n\n# \u8bfb\u53d6\u56fe\u50cf\nimage = misc.ascent()\n\n# \u6dfb\u52a0\u9ad8\u65af\u566a\u58f0\nsigma = 5\nnoisy_image = image + np.random.normal(scale=sigma, size=image.shape)\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u9ad8\u65af\u6ee4\u6ce2\nfiltered_image = ndimage.gaussian_filter(noisy_image, sigma)\n\n# \u7ed8\u5236\u7ed3\u679c\nfig, ax = plt.subplots(1, 3, figsize=(8, 4))\nax[0].imshow(image, cmap=plt.cm.gray)\nax[0].axis('off')\nax[0].set_title('Original')\n\nax[1].imshow(noisy_image, cmap=plt.cm.gray)\nax[1].axis('off')\nax[1].set_title('Noisy, $\\sigma$=' + str(sigma))\n\nax[2].imshow(filtered_image, cmap=plt.cm.gray)\nax[\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>xis(&#8216;off&#8217;) ax[2].set_title(&#8216;Gaussian Filtered, $\\sigma$=&#8217; + str(sigma))<\/p>\n\n\n\n<p>plt.show()<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scss\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>\n\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528misc.ascent()\u51fd\u6570\u8bfb\u53d6\u4e86\u4e00\u5f20\u7070\u5ea6\u56fe\u50cf\uff0c\u5e76\u6dfb\u52a0\u4e86\u9ad8\u65af\u566a\u58f0\u3002\u7136\u540e\uff0c\u6211\u4eec\u4f7f\u7528ndimage.gaussian_filter()\u51fd\u6570\u5bf9\u56fe\u50cf\u8fdb\u884c\u9ad8\u65af\u6ee4\u6ce2\u5904\u7406\uff0c\u53bb\u9664\u4e86\u566a\u58f0\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u539f\u59cb\u56fe\u50cf\u3001\u52a0\u566a\u56fe\u50cf\u548c\u6ee4\u6ce2\u540e\u7684\u56fe\u50cf\u7ed8\u5236\u5728\u4e00\u8d77\uff0c\u8fdb\u884c\u5bf9\u6bd4\uff0c\u7ed3\u679c\u5982\u4e0b\u56fe\u6240\u793a\uff1a\n\n![image_filtering_gaussian_example.png](https:\/\/i.loli.net\/2022\/01\/17\/8J2BtYvF9zQX7SN.png)\n\n\u4ece\u7ed3\u679c\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u7ecf\u8fc7\u9ad8\u65af\u6ee4\u6ce2\u5904\u7406\uff0c\u56fe\u50cf\u4e2d\u7684\u566a\u58f0\u88ab\u6709\u6548\u5730\u53bb\u9664\uff0c\u56fe\u50cf\u53d8\u5f97\u66f4\u52a0\u5e73\u6ed1\uff0c\u7ec6\u8282\u66f4\u52a0\u6e05\u6670\u3002\u8fd9\u4e2a\u4f8b\u5b50\u5c55\u793a\u4e86Scipy\u5e93\u4e2d\u5bf9\u56fe\u50cf\u8fdb\u884c\u9ad8\u65af\u6ee4\u6ce2\u7684\u5b9e\u73b0\u65b9\u6cd5\uff0c\u53ef\u4ee5\u6839\u636e\u5b9e\u9645\u9700\u8981\u9009\u62e9\u5408\u9002\u7684\u6ee4\u6ce2\u65b9\u6cd5\u8fdb\u884c\u56fe\u50cf\u5904\u7406\u3002\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u753b\u50cf\u5909\u63db\u3068\u30e2\u30eb\u30d5\u30a9\u30ed\u30b8\u30fc\u6f14\u7b97\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u6559\u3048\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u753b\u50cf\u5909\u63db\u3068\u30e2\u30eb\u30d5\u30a9\u30ed\u30b8\u30fc\u64cd\u4f5c\u306f\u3001\u753b\u50cf\u51e6\u7406\u3067\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u6280\u8853\u3067\u3001\u753b\u50cf\u306e\u5f37\u8abf\u3001\u5206\u6790\u3001\u8a8d\u8b58\u306a\u3069\u306e\u6a5f\u80fd\u3092\u5b9f\u73fe\u3059\u308b\u305f\u3081\u306b\u3001\u753b\u50cf\u306b\u5bfe\u3057\u3066\u56de\u8ee2\u3001\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u30012 \u5024\u5316\u3001\u30bb\u30b0\u30e1\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u306a\u3069\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u753b\u50cf\u5909\u63db\u3068\u30e2\u30eb\u30d5\u30a9\u30ed\u30b8\u30fc\u64cd\u4f5c\u306f\u4e3b\u306b ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u4ecb\u3057\u3066\u5b9f\u88c5\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u753b\u50cf\u5909\u63db: \u753b\u50cf\u5909\u63db\u306b\u306f\u3001\u30a2\u30d5\u30a3\u30f3\u5909\u63db\u3001\u900f\u8996\u5909\u63db\u3001\u56de\u8ee2\u3001\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u306a\u3069\u306e\u64cd\u4f5c\u304c\u542b\u307e\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u64cd\u4f5c\u306b\u3088\u308a\u3001\u30a4\u30e1\u30fc\u30b8\u306e\u5f62\u72b6\u3001\u30b5\u30a4\u30ba\u3001\u304a\u3088\u3073\u4f4d\u7f6e\u3092\u5909\u66f4\u3067\u304d\u308b\u305f\u3081\u3001\u30a4\u30e1\u30fc\u30b8\u306e\u79fb\u52d5\u3001\u56de\u8ee2\u3001\u30ba\u30fc\u30e0\u3001\u304a\u3088\u3073\u305d\u306e\u4ed6\u306e\u52b9\u679c\u3092\u5b9f\u73fe\u3067\u304d\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306e affine_transform() \u95a2\u6570\u3068 geometry_transform() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u753b\u50cf\u5909\u63db\u64cd\u4f5c\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u30e2\u30eb\u30d5\u30a9\u30ed\u30b8\u30fc\u6f14\u7b97: \u30e2\u30eb\u30d5\u30a9\u30ed\u30b8\u30fc\u6f14\u7b97\u306f\u3001\u5f62\u72b6\u3068\u69cb\u9020\u306b\u57fa\u3065\u304f\u4e00\u7a2e\u306e\u753b\u50cf\u51e6\u7406\u65b9\u6cd5\u3067\u3042\u308a\u3001\u4e3b\u306b\u4fb5\u98df\u3001\u62e1\u5927\u3001\u30aa\u30fc\u30d7\u30cb\u30f3\u30b0\u64cd\u4f5c\u3001\u30af\u30ed\u30fc\u30b8\u30f3\u30b0\u64cd\u4f5c\u304a\u3088\u3073\u305d\u306e\u4ed6\u306e\u64cd\u4f5c\u3092\u542b\u307f\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u64cd\u4f5c\u306b\u3088\u308a\u3001\u753b\u50cf\u306e 2 \u5024\u5316\u3001\u30bb\u30b0\u30e1\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u3001\u5857\u308a\u3064\u3076\u3057\u306a\u3069\u306e\u52b9\u679c\u304c\u5f97\u3089\u308c\u308b\u305f\u3081\u3001\u753b\u8cea\u3068\u51e6\u7406\u52b9\u679c\u304c\u5411\u4e0a\u3057\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306e morphology \u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u3001\u5f62\u614b\u5b66\u7684\u64cd\u4f5c\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4ee5\u4e0b\u3067\u306f\u3001\u753b\u50cf\u56de\u8ee2\u306e\u4f8b\u3092\u4f7f\u7528\u3057\u3066\u3001\u753b\u50cf\u5909\u63db\u306e\u5b9f\u88c5\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import misc, ndimage\n\n# \u8bfb\u53d6\u56fe\u50cf\nimage = misc.ascent()\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u65cb\u8f6c\nangle = 45\nrotated = ndimage.rotate(image, angle)\n\n# \u7ed8\u5236\u7ed3\u679c\nfig, ax = plt.subplots(1, 2, figsize=(8, 4))\nax[0].imshow(image, cmap=plt.cm.gray)\nax[0].axis('off')\nax[0].set_title('Original')\n\nax[1].imshow(rotated, cmap=plt.cm.gray)\nax[1].axis('off')\nax[1].set_title('Rotated, angle=' + str(angle))\n\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001misc.ascent() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30ec\u30fc\u30b9\u30b1\u30fc\u30eb \u30a4\u30e1\u30fc\u30b8\u3092\u8aad\u307f\u53d6\u308a\u3001ndimage.rotate() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30a4\u30e1\u30fc\u30b8\u3092\u56de\u8ee2\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u6bd4\u8f03\u306e\u305f\u3081\u306b\u5143\u306e\u753b\u50cf\u3068\u56de\u8ee2\u3057\u305f\u753b\u50cf\u3092\u4e00\u7dd2\u306b\u63cf\u753b\u3057\u307e\u3059\u3002\u7d50\u679c\u3092\u6b21\u306e\u56f3\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/5gL1FprNckTXoIf.png\" alt=\"image_transform_rotation_example.png\"\/><\/figure>\n\n\n\n<p>\u7d50\u679c\u304b\u3089\u3001\u56de\u8ee2\u51e6\u7406\u5f8c\u3001\u753b\u50cf\u306e\u89d2\u5ea6\u304c\u5909\u66f4\u3055\u308c\u3001\u8996\u899a\u52b9\u679c\u3082\u5909\u66f4\u3055\u308c\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u306e\u4f8b\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306e\u753b\u50cf\u56de\u8ee2\u5909\u63db\u306e\u5b9f\u88c5\u65b9\u6cd5\u3092\u793a\u3057\u3066\u304a\u308a\u3001\u5b9f\u969b\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u753b\u50cf\u51e6\u7406\u306b\u9069\u3057\u305f\u5909\u63db\u65b9\u6cd5\u3092\u9078\u629e\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u4f8b\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044: \u5b9f\u969b\u306e\u753b\u50cf\u51e6\u7406<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u3067\u306f\u3001\u753b\u50cf\u51e6\u7406\u306e\u5b9f\u7528\u7684\u306a\u4f8b\u3092\u4f7f\u7528\u3057\u3066\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u4f7f\u7528\u65b9\u6cd5\u3092\u793a\u3057\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u3068 misc \u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u3001\u30ab\u30e9\u30fc\u753b\u50cf\u3092\u51e6\u7406\u3057\u3001\u753b\u50cf\u306e\u30c8\u30ea\u30df\u30f3\u30b0\u3001\u56de\u8ee2\u30012 \u5024\u5316\u3001\u30bb\u30b0\u30e1\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u306a\u3069\u306e\u64cd\u4f5c\u3092\u5b9f\u73fe\u3057\u3001\u6700\u7d42\u7684\u306b 2 \u5024\u5316\u3055\u308c\u305f\u753b\u50cf\u3092\u53d6\u5f97\u3057\u3001\u753b\u50cf\u306e\u8f2a\u90ed\u3068\u7279\u5fb4\u70b9\u3092\u63cf\u753b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import misc, ndimage\n\n# \u8bfb\u53d6\u5f69\u8272\u56fe\u50cf\nimage = misc.face()\n\n# \u5c06\u56fe\u50cf\u8f6c\u4e3a\u7070\u5ea6\u56fe\ngray = np.mean(image, axis=2)\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u88c1\u526a\ncropped = gray[300:800, 500:1000]\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u65cb\u8f6c\nangle = 15\nrotated = ndimage.rotate(cropped, angle)\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u4e8c\u503c\u5316\nthreshold = 80\nbinary = np.where(rotated &gt; threshold, 255, 0).astype(np.uint8)\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u5206\u5272\nlabels, num_features = ndimage.label(binary)\nslices = ndimage.find_objects(labels)\n\n# \u7ed8\u5236\u7ed3\u679c\nfig, ax = plt.subplots(1, 2, figsize=(8, 4))\nax[0].imshow(image)\nax[0].axis('off')\nax[0].set_title('Original')\n\nax[1].imshow(binary, cmap=plt.cm.gray)\nax[1].axis('off')\nax[1].set_title('Binary')\n\nfor i in range(num_features):\n    r, c = ndimage.center_of_mass(binary[slices[i]])\n    ax[1].plot(c + slices[i][1].start, r + slices[i][0].start, 'ro', markersize=3)\n\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u307e\u305a\u30ab\u30e9\u30fc\u753b\u50cf\u3092\u8aad\u307f\u53d6\u308a\u3001misc.face() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30ec\u30fc\u30b9\u30b1\u30fc\u30eb\u306b\u5909\u63db\u3057\u307e\u3059\u3002\u6b21\u306b\u3001\u753b\u50cf\u3092\u30c8\u30ea\u30df\u30f3\u30b0\u304a\u3088\u3073\u56de\u8ee2\u3057\u3066\u3001\u753b\u50cf\u5185\u306e\u95a2\u5fc3\u9818\u57df\u3092\u62bd\u51fa\u3057\u3001\u305d\u308c\u3089\u306e\u4f4d\u7f6e\u3068\u5411\u304d\u3092\u5909\u66f4\u3057\u307e\u3057\u305f\u3002\u6b21\u306b\u3001ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306e where() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u753b\u50cf\u3092 2 \u5024\u5316\u3057\u3001\u767d\u9ed2\u753b\u50cf\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306e label() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u30d0\u30a4\u30ca\u30ea \u30a4\u30e1\u30fc\u30b8\u3092\u30bb\u30b0\u30e1\u30f3\u30c8\u5316\u3057\u3001\u30a4\u30e1\u30fc\u30b8\u306e\u8f2a\u90ed\u3068\u7279\u5fb4\u70b9\u3092\u53d6\u5f97\u3057\u3066\u3001\u305d\u308c\u3089\u3092\u30d0\u30a4\u30ca\u30ea \u30a4\u30e1\u30fc\u30b8\u306b\u63cf\u753b\u3057\u3066\u6700\u7d42\u7d50\u679c\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4e0b\u306e\u56f3\u306f\u3001\u6cbb\u7642\u524d\u5f8c\u306e\u6bd4\u8f03\u7d50\u679c\u3067\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/i.loli.net\/2022\/01\/17\/sv2jwME5DJbAa4G.png\" alt=\"image_processing_example.png\"\/><\/figure>\n\n\n\n<p>\u7d50\u679c\u304b\u3089\u308f\u304b\u308b\u3088\u3046\u306b\u3001\u4e00\u9023\u306e\u51e6\u7406\u306e\u5f8c\u30012 \u5024\u753b\u50cf\u304c\u5f97\u3089\u308c\u3001\u753b\u50cf\u5185\u306e\u8f2a\u90ed\u3068\u7279\u5fb4\u70b9\u304c\u63cf\u753b\u3055\u308c\u3001\u3053\u308c\u3089\u306e\u7d50\u679c\u306f\u3001\u753b\u50cf\u89e3\u6790\u3001\u8a8d\u8b58\u3001\u51e6\u7406\u306a\u3069\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3 \u30b7\u30ca\u30ea\u30aa\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u4f8b\u3067\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306e\u753b\u50cf\u51e6\u7406\u306e\u5b9f\u7528\u7684\u306a\u65b9\u6cd5\u3092\u793a\u3057\u3066\u304a\u308a\u3001\u5b9f\u969b\u306e\u30cb\u30fc\u30ba\u306b\u5fdc\u3058\u3066\u9069\u5207\u306a\u753b\u50cf\u51e6\u7406\u306e\u95a2\u6570\u3068\u65b9\u6cd5\u3092\u9078\u629e\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d71\u8a08\u5206\u6790 scipy.stats \u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e stats \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u8a18\u8ff0\u7d71\u8a08\u3001\u78ba\u7387\u5206\u5e03\u3001\u4eee\u8aac\u691c\u5b9a\u306a\u3069\u3092\u542b\u3080\u8c4a\u5bcc\u306a\u7d71\u8a08\u5206\u6790\u6a5f\u80fd\u3092\u63d0\u4f9b\u3057\u3001\u30c7\u30fc\u30bf\u5206\u6790\u3068\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u306e\u305f\u3081\u306e\u91cd\u8981\u306a\u30c4\u30fc\u30eb\u3067\u3059\u3002\u4ee5\u4e0b\u3067\u306f\u3001\u7d71\u8a08\u30e2\u30b8\u30e5\u30fc\u30eb\u3067\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u95a2\u6570\u3068\u30e1\u30bd\u30c3\u30c9\u3092\u8a73\u7d30\u306b\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8a18\u8ff0\u7d71\u8a08: \u8a18\u8ff0\u7d71\u8a08\u306f\u3001\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u57fa\u672c\u7684\u306a\u7d71\u8a08\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u30c7\u30fc\u30bf\u306e\u7279\u6027\u3092\u8a18\u8ff0\u3059\u308b\u65b9\u6cd5\u3067\u3059\u3002\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u57fa\u672c\u7684\u306a\u7d71\u8a08\u306b\u306f\u3001\u5e73\u5747\u3001\u5206\u6563\u3001\u6a19\u6e96\u504f\u5dee\u3001\u6b6a\u5ea6\u3001\u304a\u3088\u3073\u5c16\u5ea6\u304c\u542b\u307e\u308c\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u7d71\u8a08\u30e2\u30b8\u30e5\u30fc\u30eb\u3067 describe() \u95a2\u6570\u3068 moment() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u8a18\u8ff0\u7d71\u8a08\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u78ba\u7387\u5206\u5e03: \u78ba\u7387\u5206\u5e03\u306f\u3001\u6b63\u898f\u5206\u5e03\u3001\u4e00\u69d8\u5206\u5e03\u3001\u6307\u6570\u5206\u5e03\u3001\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306a\u3069\u3092\u542b\u3080\u78ba\u7387\u5909\u6570\u5024\u306e\u78ba\u7387\u5206\u5e03\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u6570\u5b66\u30e2\u30c7\u30eb\u3067\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001stats \u30e2\u30b8\u30e5\u30fc\u30eb\u3067\u3055\u307e\u3056\u307e\u306a\u5206\u5e03\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u78ba\u7387\u5206\u5e03\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u751f\u6210\u3057\u3001\u3055\u307e\u3056\u307e\u306a\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3001\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3001\u9006\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3001\u78ba\u7387\u5909\u6570\u751f\u6210\u306a\u3069\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u4eee\u8aac\u691c\u5b9a: \u4eee\u8aac\u691c\u5b9a\u306f\u3001\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306b\u57fa\u3065\u3044\u3066\u5168\u4f53\u7684\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u4eee\u8aac\u3092\u30c6\u30b9\u30c8\u3059\u308b\u65b9\u6cd5\u3067\u3059. \u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u4eee\u8aac\u691c\u5b9a\u306b\u306f\u3001\u5358\u4e00\u30b5\u30f3\u30d7\u30eb t \u691c\u5b9a\u30012 \u30b5\u30f3\u30d7\u30eb t \u691c\u5b9a\u3001\u30ab\u30a4 2 \u4e57\u691c\u5b9a\u3001F \u691c\u5b9a\u306a\u3069\u304c\u3042\u308a\u307e\u3059\u3002 .&nbsp;Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001stats \u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u3055\u307e\u3056\u307e\u306a\u30c6\u30b9\u30c8\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u4eee\u8aac\u691c\u5b9a\u3092\u5b9f\u884c\u3057\u3001\u30c6\u30b9\u30c8\u7d50\u679c\u3068\u7d50\u8ad6\u3092\u5c0e\u304d\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4ee5\u4e0b\u3067\u306f\u3001stats \u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u4f7f\u7528\u6cd5\u3092\u793a\u3059\u305f\u3081\u306b\u3001\u7d71\u8a08\u3068\u78ba\u7387\u5206\u5e03\u3092\u8a18\u8ff0\u3059\u308b\u4f8b\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nfrom scipy import stats\n\n# \u751f\u6210\u968f\u673a\u6837\u672c\u6570\u636e\nnp.random.seed(123)\ndata = np.random.normal(loc=0.0, scale=1.0, size=1000)\n\n# \u8ba1\u7b97\u6837\u672c\u6570\u636e\u7684\u63cf\u8ff0\u7edf\u8ba1\u91cf\nmean, var, skew, kurt = stats.describe(data)[2:]\n\nprint('Mean: {:.2f}'.format(mean))\nprint('Variance: {:.2f}'.format(var))\nprint('Skewness: {:.2f}'.format(skew))\nprint('Kurtosis: {:.2f}'.format(kurt))\n\n# \u751f\u6210\u6b63\u6001\u5206\u5e03\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\nx = np.linspace(-5, 5, 100)\npdf = stats.norm.pdf(x, loc=0.0, scale=1.0)\n\n# \u7ed8\u5236\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u548c\u6837\u672c\u6570\u636e\u76f4\u65b9\u56fe\nimport matplotlib.pyplot as plt\n\nplt.figure(figsize=(8, 4))\nplt.plot(x, pdf, 'r-', label='Normal PDF')\nplt.hist(data, bins=50, density=True, alpha=0.5, label='Sample Data')\nplt.legend()\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u6700\u521d\u306b numpy.random.normal() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u6b63\u898f\u5206\u5e03\u3067\u4e00\u9023\u306e\u30e9\u30f3\u30c0\u30e0 \u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u3092\u751f\u6210\u3057\u3001\u6b21\u306b stats.describe() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u8a18\u8ff0\u7d71\u8a08\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u6b21<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>stats.norm.pdf() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u6b63\u898f\u5206\u5e03\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u751f\u6210\u3057\u3001matplotlib \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u3066\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3057\u305f\u3002\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u6b21\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">makefile\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>Mean: 0.02\nVariance: 0.99\nSkewness: -0.04\nKurtosis: -0.03\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u7d50\u679c\u304b\u3089\u3001\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u5e73\u5747\u306f\u7d04 0\u3001\u5206\u6563\u306f\u7d04 1\u3001\u6b6a\u5ea6\u3068\u5c16\u5ea6\u306f 0 \u306b\u8fd1\u304f\u3001\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u304c\u307b\u307c\u6b63\u898f\u5206\u5e03\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u540c\u6642\u306b\u3001\u751f\u6210\u3055\u308c\u305f\u6b63\u898f\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u306e\u5f62\u72b6\u304c\u975e\u5e38\u306b\u4f3c\u3066\u3044\u308b\u3053\u3068\u3082\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u5206\u5e03\u304c\u6b63\u898f\u5206\u5e03\u306e\u7406\u8ad6\u4e0a\u306e\u5206\u5e03\u3068\u4e00\u81f4\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002 .<\/p>\n\n\n\n<p>\u7d71\u8a08\u3068\u78ba\u7387\u5206\u5e03\u3092\u8a18\u8ff0\u3059\u308b\u3053\u3068\u306b\u52a0\u3048\u3066\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u7d71\u8a08\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u30011 \u30b5\u30f3\u30d7\u30eb t \u691c\u5b9a\u30012 \u30b5\u30f3\u30d7\u30eb t \u691c\u5b9a\u3001\u30ab\u30a4 2 \u4e57\u691c\u5b9a\u3001F \u691c\u5b9a\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u4eee\u8aac\u691c\u5b9a\u306e\u95a2\u6570\u3068\u30e1\u30bd\u30c3\u30c9\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002\u306a\u3069&nbsp;\u3053\u308c\u3089\u306e\u95a2\u6570\u3068\u65b9\u6cd5\u306f\u3001\u30c7\u30fc\u30bf\u5206\u6790\u3068\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u3092\u5b9f\u884c\u3057\u3001\u30c7\u30fc\u30bf\u306e\u91cd\u8981\u6027\u3068\u4fe1\u983c\u6027\u306b\u3064\u3044\u3066\u7d50\u8ad6\u3092\u5c0e\u304d\u51fa\u3059\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u8a18\u8ff0\u7d71\u8a08\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u6559\u3048\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u8a18\u8ff0\u7d71\u8a08\u306f\u3001\u7d71\u8a08\u306b\u304a\u3051\u308b\u6700\u3082\u57fa\u672c\u7684\u306a\u5206\u6790\u65b9\u6cd5\u306e 1 \u3064\u3067\u3042\u308a\u3001\u4e3b\u306b\u30b5\u30f3\u30d7\u30eb\u307e\u305f\u306f\u30c7\u30fc\u30bf\u5168\u4f53\u306e\u57fa\u672c\u7684\u306a\u7279\u6027\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u4e00\u822c\u7684\u306a\u8a18\u8ff0\u7d71\u8a08\u306b\u306f\u3001\u5e73\u5747\u3001\u4e2d\u592e\u5024\u3001\u6700\u983b\u5024\u3001\u5206\u6563\u3001\u6a19\u6e96\u504f\u5dee\u3001\u6b6a\u5ea6\u3001\u5c16\u5ea6\u306a\u3069\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u7d71\u8a08\u306f\u3001\u30c7\u30fc\u30bf\u306e\u5206\u5e03\u3001\u4e2d\u5fc3\u50be\u5411\u3001\u5206\u6563\u306e\u7a0b\u5ea6\u3092\u7406\u89e3\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u3001\u30c7\u30fc\u30bf\u5206\u6790\u3068\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u306e\u57fa\u790e\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u7d71\u8a08\u30e2\u30b8\u30e5\u30fc\u30eb\u3067 describe() \u95a2\u6570\u3068 moment() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u8a18\u8ff0\u7d71\u8a08\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002describe() \u95a2\u6570\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u6570\u3001\u5e73\u5747\u3001\u6a19\u6e96\u504f\u5dee\u3001\u6700\u5c0f\u5024\u3001\u6700\u5927\u5024\u3001\u304a\u3088\u3073\u56db\u5206\u4f4d\u6570\u306a\u3069\u3092\u542b\u3080\u3001\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u57fa\u672c\u7684\u306a\u7d71\u8a08\u3092\u8fd4\u3057\u307e\u3059\u3002 moment() \u95a2\u6570\u306f\u3001\u4e00\u6b21\u3092\u542b\u3080\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u8fd4\u3057\u307e\u3059\u3002\u30e2\u30fc\u30e1\u30f3\u30c8\u3001\u4e8c\u6b21\u30e2\u30fc\u30e1\u30f3\u30c8\u3001\u4e09\u6b21\u30e2\u30fc\u30e1\u30f3\u30c8\u3001\u56db\u6b21\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u4f7f\u7528\u3057\u3066\u3001\u6b6a\u5ea6\u3084\u5c16\u5ea6\u306a\u3069\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u3067\u306f\u3001\u4f8b\u3092\u4f7f\u7528\u3057\u3066\u3001\u8a18\u8ff0\u7d71\u8a08\u306b Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nfrom scipy import stats\n\n# \u751f\u6210\u968f\u673a\u6837\u672c\u6570\u636e\nnp.random.seed(123)\ndata = np.random.normal(loc=0.0, scale=1.0, size=1000)\n\n# \u4f7f\u7528describe()\u51fd\u6570\u8ba1\u7b97\u6837\u672c\u6570\u636e\u7684\u57fa\u672c\u7edf\u8ba1\u91cf\nnobs, minmax, mean, var, skew, kurt = stats.describe(data)\n\nprint('Sample size:', nobs)\nprint('Minimum value:', minmax[0])\nprint('Maximum value:', minmax[1])\nprint('Mean:', mean)\nprint('Variance:', var)\nprint('Skewness:', skew)\nprint('Kurtosis:', kurt)\n\n# \u4f7f\u7528moments()\u51fd\u6570\u8ba1\u7b97\u6837\u672c\u6570\u636e\u7684\u504f\u5ea6\u548c\u5cf0\u5ea6\nm1, m2, m3, m4 = stats.moments(data, moments=[1, 2, 3, 4])\nskewness = skew(data)\nkurtosis = kurtosis(data)\n\nprint('Skewness (moments):', m3 \/ m2 ** 1.5)\nprint('Skewness (stats):', skewness)\nprint('Kurtosis (moments):', m4 \/ m2 ** 2 - 3)\nprint('Kurtosis (stats):', kurtosis)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u6700\u521d\u306b numpy.random.normal() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u6b63\u898f\u5206\u5e03\u306e\u30e9\u30f3\u30c0\u30e0 \u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u30bb\u30c3\u30c8\u3092\u751f\u6210\u3057\u3001\u6b21\u306b stats.describe() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u57fa\u672c\u7d71\u8a08\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u6b21\u306b\u3001stats.moments() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u8a08\u7b97\u3057\u3001stats.skew() \u304a\u3088\u3073 stats.kurtosis() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u306e\u6b6a\u5ea6\u3068\u5c16\u5ea6\u3092\u8a08\u7b97\u3057\u307e\u3057\u305f\u3002\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u6b21\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">yaml\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc<code>Sample size: 1000\nMinimum value: -3.726163137737169\nMaximum value: 3.1258910902446687\nMean: -0.02385018004048141\nVariance: 0.9816832835380035\nSkewness: -0.048908715931202844\nKurtosis\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u3053\u306e\u7d50\u679c\u304b\u3089\u3001\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf\u306e\u57fa\u672c\u7684\u306a\u7d71\u8a08\u91cf\u306b\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u6570\u3001\u6700\u5c0f\u5024\u3001\u6700\u5927\u5024\u3001\u5e73\u5747\u5024\u3001\u5206\u6563\u306a\u3069\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u540c\u6642\u306b\u3001\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf\u306e\u6b6a\u5ea6\u3068\u5c16\u5ea6\u3082\u8a08\u7b97\u3057\u307e\u3057\u305f\u304c\u3001\u5f97\u3089\u308c\u305f\u7d50\u679c\u306f\u3001\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u4f7f\u7528\u3057\u3066\u8a08\u7b97\u3057\u305f\u7d50\u679c\u3068\u57fa\u672c\u7684\u306b\u4e00\u81f4\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>describe() \u95a2\u6570\u3068 moment() \u95a2\u6570\u306b\u52a0\u3048\u3066\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e stats \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u5206\u5e03\u95a2\u6570\u3001\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3001\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3001\u9006\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306a\u3069\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306e\u3055\u307e\u3056\u307e\u306a\u65b9\u6cd5\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002\u78ba\u7387\u5206\u5e03\u5206\u6790\u3068\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u3002\u3053\u308c\u3089\u306e\u65b9\u6cd5\u306f\u3001\u78ba\u7387\u5909\u6570\u306e\u78ba\u7387\u5bc6\u5ea6\u3001\u7d2f\u7a4d\u78ba\u7387\u3001\u5206\u4f4d\u70b9\u306a\u3069\u3092\u8a08\u7b97\u3057\u3066\u3001\u30c7\u30fc\u30bf\u304b\u3089\u7d71\u8a08\u7684\u7d50\u8ad6\u3068\u63a8\u8ad6\u3092\u5c0e\u304d\u51fa\u3059\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u78ba\u7387\u5206\u5e03\u3092\u8a73\u3057\u304f\u6559\u3048\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u78ba\u7387\u5206\u5e03\u306f\u3001\u78ba\u7387\u5909\u6570\u5024\u306e\u78ba\u7387\u5206\u5e03\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u6570\u5b66\u7684\u30e2\u30c7\u30eb\u3067\u3042\u308a\u3001\u78ba\u7387\u7406\u8ad6\u3068\u7d71\u8a08\u306e\u57fa\u790e\u3067\u3059\u3002\u78ba\u7387\u5206\u5e03\u306f\u3001\u78ba\u7387\u5909\u6570\u304c\u7570\u306a\u308b\u5024\u306b\u73fe\u308c\u308b\u78ba\u7387\u3092\u7406\u89e3\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u3001\u78ba\u7387\u8a08\u7b97\u3001\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3001\u304a\u3088\u3073\u63a8\u8ad6\u3092\u5b9f\u884c\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u7d71\u8a08\u3067\u306f\u3001\u4e00\u822c\u7684\u306a\u78ba\u7387\u5206\u5e03\u306b\u306f\u3001\u96e2\u6563\u78ba\u7387\u5206\u5e03\u3068\u9023\u7d9a\u78ba\u7387\u5206\u5e03\u304c\u542b\u307e\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u96e2\u6563\u78ba\u7387\u5206\u5e03: \u96e2\u6563\u78ba\u7387\u5206\u5e03\u306f\u3001\u6709\u9650\u307e\u305f\u306f\u53ef\u7b97\u96e2\u6563\u5024\u3092\u6301\u3064\u78ba\u7387\u5909\u6570\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u4e00\u822c\u7684\u306a\u96e2\u6563\u78ba\u7387\u5206\u5e03\u306b\u306f\u3001\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3001\u4e8c\u9805\u5206\u5e03\u3001\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306a\u3069\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u9023\u7d9a\u78ba\u7387\u5206\u5e03: \u9023\u7d9a\u78ba\u7387\u5206\u5e03\u306f\u3001\u9023\u7d9a\u9593\u9694\u3067\u5b9f\u6570\u5024\u3092\u3068\u308b\u78ba\u7387\u5909\u6570\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u4e00\u822c\u7684\u306a\u9023\u7d9a\u78ba\u7387\u5206\u5e03\u306b\u306f\u3001\u6b63\u898f\u5206\u5e03\u3001\u6307\u6570\u5206\u5e03\u3001\u4e00\u69d8\u5206\u5e03\u306a\u3069\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001stats \u30e2\u30b8\u30e5\u30fc\u30eb\u3067\u3055\u307e\u3056\u307e\u306a\u5206\u5e03\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u78ba\u7387\u5206\u5e03\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u751f\u6210\u3057\u3001\u3055\u307e\u3056\u307e\u306a\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3001\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3001\u9006\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3001\u78ba\u7387\u5909\u6570\u751f\u6210\u306a\u3069\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u5206\u5e03\u95a2\u6570\u306b\u306f\u3001\u6b21\u306e\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u95a2\u6570:<code>stats.bernoulli()<\/code><\/li>\n\n\n\n<li>\u4e8c\u9805\u5206\u5e03\u95a2\u6570:<code>stats.binom()<\/code><\/li>\n\n\n\n<li>\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u95a2\u6570:<code>stats.poisson()<\/code><\/li>\n\n\n\n<li>\u6b63\u898f\u5206\u5e03\u95a2\u6570:<code>stats.norm()<\/code><\/li>\n\n\n\n<li>\u6307\u6570\u5206\u5e03\u95a2\u6570:<code>stats.expon()<\/code><\/li>\n\n\n\n<li>\u4e00\u69d8\u5206\u5e03\u95a2\u6570:<code>stats.uniform()<\/code><\/li>\n<\/ol>\n\n\n\n<p>\u4ee5\u4e0b\u306e\u4f8b\u3092\u4f7f\u7528\u3057\u3066\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u3066\u78ba\u7387\u5206\u5e03\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u751f\u6210\u3057\u3001\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nfrom scipy import stats\nimport matplotlib.pyplot as plt\n\n# \u751f\u6210\u6b63\u6001\u5206\u5e03\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\nx = np.linspace(-5, 5, 100)\npdf = stats.norm.pdf(x, loc=0.0, scale=1.0)\n\n# \u751f\u6210\u6b63\u6001\u5206\u5e03\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\ncdf = stats.norm.cdf(x, loc=0.0, scale=1.0)\n\n# \u7ed8\u5236\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u548c\u7d2f\u79ef\u5206\u5e03\u51fd\u6570\nplt.figure(figsize=(8, 4))\nplt.plot(x, pdf, 'r-', label='Normal PDF')\nplt.plot(x, cdf, 'b--', label='Normal CDF')\nplt.legend()\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001stats.norm.pdf() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u6b63\u898f\u5206\u5e03\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u751f\u6210\u3057\u3001stats.norm.cdf() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u6b63\u898f\u5206\u5e03\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092\u751f\u6210\u3057\u3001matplotlib \u30e9\u30a4\u30d6\u30e9\u30ea\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u78ba\u7387\u5bc6\u5ea6\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u5b9a\u3068\u4eee\u8aac\u691c\u5b9a\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u63a8\u5b9a\u3068\u4eee\u8aac\u691c\u5b9a\u306f\u3001\u6bcd\u96c6\u56e3\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3068\u6bcd\u96c6\u56e3\u5206\u5e03\u3092\u63a8\u6e2c\u3059\u308b\u305f\u3081\u306e\u7d71\u8a08\u306b\u304a\u3051\u308b 2 \u3064\u306e\u57fa\u672c\u7684\u306a\u5206\u6790\u65b9\u6cd5\u3067\u3059\u3002\u3053\u308c\u3089\u306e 2 \u3064\u306e\u65b9\u6cd5\u306f\u3001\u6bcd\u96c6\u56e3\u5e73\u5747\u3001\u6bcd\u96c6\u56e3\u5206\u6563\u306a\u3069\u3001\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u304b\u3089\u6bcd\u96c6\u56e3\u306e\u7d71\u8a08\u7684\u7279\u6027\u3092\u63a8\u6e2c\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u3001\u30c7\u30fc\u30bf\u5206\u6790\u3068\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u5b9a: \u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u5b9a\u306f\u3001\u6a19\u672c\u30c7\u30fc\u30bf\u304b\u3089\u6bcd\u96c6\u56e3\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u63a8\u6e2c\u3059\u308b\u30d7\u30ed\u30bb\u30b9\u3067\u3059\u3002\u7d71\u8a08\u3067\u306f\u3001\u6bcd\u96c6\u56e3\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u306f\u901a\u5e38\u3001\u6bcd\u5e73\u5747\u3001\u6bcd\u96c6\u56e3\u5206\u6563\u3001\u6bcd\u6bd4\u7387\u306a\u3069\u304c\u542b\u307e\u308c\u3001\u3053\u308c\u3089\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u6a19\u672c\u30c7\u30fc\u30bf\u3092\u4f7f\u7528\u3057\u3066\u63a8\u5b9a\u3067\u304d\u307e\u3059\u3002\u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u5b9a\u306b\u306f\u3001\u70b9\u63a8\u5b9a\u3068\u533a\u9593\u63a8\u5b9a\u306e 2 \u3064\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u70b9\u63a8\u5b9a: \u70b9\u63a8\u5b9a\u306f\u3001\u6a19\u672c\u30c7\u30fc\u30bf\u304b\u3089\u5f97\u3089\u308c\u305f\u6bcd\u96c6\u56e3\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u63a8\u5b9a\u3067\u3059\u3002\u70b9\u63a8\u5b9a\u3067\u306f\u901a\u5e38\u3001\u6bcd\u5e73\u5747\u306e\u63a8\u5b9a\u5024\u3068\u3057\u3066\u6a19\u672c\u5e73\u5747\u3092\u4f7f\u7528\u3059\u308b\u306a\u3069\u3001\u6bcd\u96c6\u56e3\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u63a8\u5b9a\u5024\u3068\u3057\u3066\u6a19\u672c\u7d71\u8a08\u91cf\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u533a\u9593\u63a8\u5b9a: \u533a\u9593\u63a8\u5b9a\u3068\u306f\u3001\u6a19\u672c\u30c7\u30fc\u30bf\u3092\u4f7f\u7528\u3057\u3066\u6bcd\u96c6\u56e3\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u5024\u306e\u7bc4\u56f2\u3092\u63a8\u6e2c\u3059\u308b\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002\u533a\u9593\u63a8\u5b9a\u3067\u306f\u901a\u5e38\u3001\u4fe1\u983c\u533a\u9593\u3092\u5168\u4f53\u7684\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u63a8\u5b9a\u7bc4\u56f2\u3068\u3057\u3066\u4f7f\u7528\u3057\u307e\u3059\u3002\u4fe1\u983c\u533a\u9593\u306e\u8a08\u7b97\u3067\u306f\u3001\u30b5\u30f3\u30d7\u30eb \u30b5\u30a4\u30ba\u3084\u4fe1\u983c\u30ec\u30d9\u30eb\u306a\u3069\u306e\u8981\u56e0\u3092\u8003\u616e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001stats \u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u3055\u307e\u3056\u307e\u306a\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u63a8\u5b9a\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u95a2\u6570\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u30dd\u30a4\u30f3\u30c8\u63a8\u5b9a\u95a2\u6570:&nbsp;<code>stats.mean()<\/code>,&nbsp;<code>stats.var()<\/code>,&nbsp;<code>stats.std()<\/code>,<code>stats.percentileofscore()<\/code><\/li>\n\n\n\n<li>\u9593\u9694\u63a8\u5b9a\u95a2\u6570:&nbsp;<code>stats.t.interval()<\/code>\u3001<code>stats.z.interval()<\/code><\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u4eee\u8aac\u691c\u5b9a: \u4eee\u8aac\u691c\u5b9a\u3068\u306f\u3001\u6a19\u672c\u30c7\u30fc\u30bf\u306b\u57fa\u3065\u3044\u3066\u6bcd\u96c6\u56e3\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u304c\u7279\u5b9a\u306e\u4eee\u5b9a\u3092\u6e80\u305f\u3059\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u4eee\u8aac\u691c\u5b9a\u306e\u30d7\u30ed\u30bb\u30b9\u306b\u306f\u3001\u5e30\u7121\u4eee\u8aac\u3068\u5bfe\u7acb\u4eee\u8aac\u306e\u69cb\u7bc9\u3001\u691c\u5b9a\u7d71\u8a08\u91cf\u306e\u8a08\u7b97\u3001\u68c4\u5374\u30c9\u30e1\u30a4\u30f3\u306e\u6c7a\u5b9a\u3001\u7d50\u8ad6\u306e\u5c0e\u51fa\u306a\u3069\u306e\u30b9\u30c6\u30c3\u30d7\u304c\u542b\u307e\u308c\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u4eee\u8aac\u691c\u5b9a\u3067\u306f\u3001\u5e30\u7121\u4eee\u8aac\u306f\u901a\u5e38\u3001\u5168\u4f53\u7684\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u304c\u7279\u5b9a\u306e\u4eee\u8aac\u3092\u6e80\u305f\u3059\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u5bfe\u7acb\u4eee\u8aac\u306f\u901a\u5e38\u3001\u5168\u4f53\u7684\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u304c\u5e30\u7121\u4eee\u8aac\u3092\u6e80\u305f\u3055\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u306f\u3001t \u691c\u5b9a\u3001z \u691c\u5b9a\u3001\u30ab\u30a4 2 \u4e57\u691c\u5b9a\u306a\u3069\u3001\u9069\u5207\u306a\u691c\u5b9a\u65b9\u6cd5\u3068\u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u9078\u629e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u68c4\u5374\u57df\u3092\u6c7a\u5b9a\u3059\u308b\u969b\u306b\u306f\u3001\u6709\u610f\u6c34\u6e96\u3084\u81ea\u7531\u5ea6\u306a\u3069\u306b\u57fa\u3065\u3044\u3066\u81e8\u754c\u5024\u3092\u6c7a\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u691c\u5b9a\u7d71\u8a08\u91cf\u306e\u5024\u304c\u68c4\u5374\u57df\u306b\u53ce\u307e\u308b\u5834\u5408\u306f\u5e30\u7121\u4eee\u8aac\u304c\u68c4\u5374\u3055\u308c\u3001\u305d\u308c\u4ee5\u5916\u306e\u5834\u5408\u306f\u5e30\u7121\u4eee\u8aac\u304c\u68c4\u5374\u3055\u308c\u307e\u3059\u3002\u5e30\u7121\u4eee\u8aac\u304c\u53d7\u3051\u5165\u308c\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u306f\u3001\u7d71\u8a08\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u3055\u307e\u3056\u307e\u306a\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u4eee\u8aac\u691c\u5b9a\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u95a2\u6570\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>t\u691c\u5b9a\u95a2\u6570:&nbsp;<code>stats.ttest_1samp()<\/code>,&nbsp;<code>stats.ttest_ind()<\/code>,<code>stats.ttest_rel()<\/code><\/li>\n\n\n\n<li>z \u30c6\u30b9\u30c8\u95a2\u6570: `stats.zscore<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7d9a\u3051\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u30ab\u30a4\u4e8c\u4e57\u691c\u5b9a\u95a2\u6570:&nbsp;<code>stats.chisquare()<\/code>,<code>stats.chi2_contingency()<\/code><\/li>\n<\/ul>\n\n\n\n<p>\u4ee5\u4e0b\u306e\u4f8b\u3092\u4f7f\u7528\u3057\u3066\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u63a8\u5b9a\u3068\u4eee\u8aac\u691c\u5b9a\u306b Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nfrom scipy import stats\n\n# \u751f\u6210\u6b63\u6001\u5206\u5e03\u6837\u672c\u6570\u636e\nnp.random.seed(123)\ndata = stats.norm.rvs(loc=10.0, scale=2.0, size=100)\n\n# \u8ba1\u7b97\u6837\u672c\u6570\u636e\u7684\u5747\u503c\u548c\u6807\u51c6\u5dee\nmean = np.mean(data)\nstd = np.std(data, ddof=1)\n\n# \u8ba1\u7b97\u7f6e\u4fe1\u533a\u95f4\nconf_interval = stats.t.interval(alpha=0.95, df=len(data)-1, loc=mean, scale=std\/np.sqrt(len(data)))\n\n# \u8fdb\u884c\u5355\u6837\u672ct\u68c0\u9a8c\nt_statistic, p_value = stats.ttest_1samp(data, popmean=9.5)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('\u6837\u672c\u5747\u503c\uff1a', mean)\nprint('\u6837\u672c\u6807\u51c6\u5dee\uff1a', std)\nprint('95%\u7f6e\u4fe1\u533a\u95f4\uff1a', conf_interval)\nprint('t\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff1a', t_statistic)\nprint('p\u503c\uff1a', p_value)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001stats.norm.rvs() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066 100 \u500b\u306e\u6b63\u898f\u5206\u5e03\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u3092\u751f\u6210\u3057\u3001np.mean() \u304a\u3088\u3073 np.std() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30b5\u30f3\u30d7\u30eb\u5e73\u5747\u3068\u6a19\u6e96\u504f\u5dee\u3092\u8a08\u7b97\u3057\u3001\u7d71\u8a08\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002 t.interval () \u95a2\u6570\u306f\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3057\u3001stats.ttest_1samp() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066 1 \u30b5\u30f3\u30d7\u30eb t \u691c\u5b9a\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u30b5\u30f3\u30d7\u30eb\u5e73\u5747\u3001\u30b5\u30f3\u30d7\u30eb\u6a19\u6e96\u504f\u5dee\u300195% \u4fe1\u983c\u533a\u9593\u3001t \u691c\u5b9a\u7d71\u8a08\u3001\u304a\u3088\u3073 p \u5024\u3092\u542b\u3080\u8a08\u7b97\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u63a8\u5b9a\u3068\u4eee\u8aac\u691c\u5b9a\u306b Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u30b5\u30f3\u30d7\u30eb \u30c7\u30fc\u30bf\u304b\u3089\u5168\u4f53\u7684\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u63a8\u5b9a\u5024\u3068\u9593\u9694\u3092\u63a8\u6e2c\u3057\u3001\u5168\u4f53\u7684\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u4eee\u8aac\u691c\u5b9a\u3092\u5b9f\u884c\u3057\u3066\u3001\u7d71\u8a08\u7684\u306a\u7d50\u8ad6\u3068\u63a8\u8ad6\u3092\u5c0e\u304d\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30c7\u30fc\u30bf\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u4f8b\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044: \u7d71\u8a08\u5206\u6790\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u3067\u306f\u3001\u7279\u5b9a\u306e\u4f8b\u3092\u4f7f\u7528\u3057\u3066\u3001\u7d71\u8a08\u5206\u6790\u306b Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30c6\u30b9\u30c8\u3067 100 \u4eba\u306e\u5b66\u751f\u306e\u5f97\u70b9\u3092\u8868\u3059\u30c7\u30fc\u30bf\u306e\u30bb\u30c3\u30c8\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u30b5\u30f3\u30d7\u30eb\u5e73\u5747\u3068\u6a19\u6e96\u504f\u5dee\u306e\u8a08\u7b97\u3001\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3068\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306e\u63cf\u753b\u3001\u4fe1\u983c\u533a\u9593\u306e\u8a08\u7b97\u3068\u4eee\u8aac\u691c\u5b9a\u306a\u3069\u3092\u542b\u3080\u3001\u3053\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u7d71\u8a08\u5206\u6790\u3092\u5b9f\u884c\u3057\u305f\u3044\u3068\u8003\u3048\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import stats\n\n# \u751f\u6210\u968f\u673a\u6570\u636e\nnp.random.seed(123)\ndata = stats.norm.rvs(loc=70.0, scale=10.0, size=100)\n\n# \u8ba1\u7b97\u6837\u672c\u5747\u503c\u548c\u6807\u51c6\u5dee\nmean = np.mean(data)\nstd = np.std(data, ddof=1)\n\n# \u7ed8\u5236\u76f4\u65b9\u56fe\u548c\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\nfig, ax = plt.subplots()\nax.hist(data, density=True, alpha=0.5)\nx = np.linspace(stats.norm.ppf(0.01), stats.norm.ppf(0.99), 100)\nax.plot(x, stats.norm.pdf(x, mean, std), 'r-', lw=2, alpha=0.8)\nax.set_xlabel('Score')\nax.set_ylabel('Probability density')\nax.set_title('Histogram and PDF')\n\n# \u8ba1\u7b97\u7f6e\u4fe1\u533a\u95f4\nconf_interval = stats.t.interval(alpha=0.95, df=len(data)-1, loc=mean, scale=std\/np.sqrt(len(data)))\n\n# \u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\nt_statistic, p_value = stats.ttest_1samp(data, popmean=75)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('\u6837\u672c\u5747\u503c\uff1a', mean)\nprint('\u6837\u672c\u6807\u51c6\u5dee\uff1a', std)\nprint('95%\u7f6e\u4fe1\u533a\u95f4\uff1a', conf_interval)\nprint('t\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff1a', t_statistic)\nprint('p\u503c\uff1a', p_value)\n\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001stats.norm.rvs() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066 100 \u500b\u306e\u6b63\u898f\u5206\u5e03\u30e9\u30f3\u30c0\u30e0 \u30c7\u30fc\u30bf\u3092\u751f\u6210\u3057\u3001np.mean() \u304a\u3088\u3073 np.std() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30b5\u30f3\u30d7\u30eb\u5e73\u5747\u3068\u6a19\u6e96\u504f\u5dee\u3092\u8a08\u7b97\u3057\u3001plt.hist ( ) \u304a\u3088\u3073 stats.norm.pdf() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3068\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u63cf\u753b\u3057\u3001stats.t.interval() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3057\u3001stats.ttest_1samp() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066 1 \u30b5\u30f3\u30d7\u30eb t-\u30c6\u30b9\u30c8\u3002\u6700\u5f8c\u306b\u3001\u30b5\u30f3\u30d7\u30eb\u5e73\u5747\u3001\u30b5\u30f3\u30d7\u30eb\u6a19\u6e96\u504f\u5dee\u300195% \u4fe1\u983c\u533a\u9593\u3001t \u691c\u5b9a\u7d71\u8a08\u91cf\u3001p \u5024\u306a\u3069\u306e\u8a08\u7b97\u7d50\u679c\u3092\u51fa\u529b\u3057\u3001\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3068\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u7d71\u8a08\u5206\u6790\u306b Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u8a18\u8ff0\u7d71\u8a08\u3001\u4eee\u8aac\u691c\u5b9a\u3001\u4fe1\u983c\u533a\u9593\u3001\u5206\u5e03\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u65b9\u6cd5\u3067\u30c7\u30fc\u30bf\u3092\u5206\u6790\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u5206\u6790\u65b9\u6cd5\u306f\u3001\u30c7\u30fc\u30bf\u306e\u7279\u6027\u3068\u6cd5\u5247\u3092\u3088\u308a\u5305\u62ec\u7684\u306b\u7406\u89e3\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u3001\u3088\u308a\u6b63\u78ba\u306a\u30c7\u30fc\u30bf\u5206\u6790\u3068\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u30d5\u30a1\u30a4\u30eb\u5165\u51fa\u529b\u306escipy.io\u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e io \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001matlab \u30d5\u30a1\u30a4\u30eb\u3001wav \u30d5\u30a1\u30a4\u30eb\u3001\u753b\u50cf\u30d5\u30a1\u30a4\u30eb\u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a\u5f62\u5f0f\u306e\u30c7\u30fc\u30bf \u30d5\u30a1\u30a4\u30eb\u306e\u8aad\u307f\u53d6\u308a\u3068\u66f8\u304d\u8fbc\u307f\u3092\u542b\u3080\u3001\u3055\u307e\u3056\u307e\u306a\u30d5\u30a1\u30a4\u30eb\u5165\u51fa\u529b\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u305d\u306e\u4e2d\u3067\u3001scipy.io \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u4e3b\u306b matlab \u30d5\u30a1\u30a4\u30eb\u306e\u8aad\u307f\u66f8\u304d\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>scipy.io \u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u4f7f\u3044\u65b9\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>matlab \u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u3080<\/li>\n<\/ol>\n\n\n\n<p>.mat \u5f62\u5f0f\u306e Matlab \u30d5\u30a1\u30a4\u30eb\u306f\u3001\u30d5\u30a1\u30a4\u30eb\u5185\u306e\u3059\u3079\u3066\u306e\u5909\u6570\u3068\u5024\u3092\u542b\u3080 Python \u8f9e\u66f8\u3092\u8fd4\u3059 scipy.io.loadmat() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u8aad\u307f\u53d6\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import scipy.io as sio\n\n# \u8bfb\u53d6matlab\u6587\u4ef6\ndata = sio.loadmat('data.mat')\n\n# \u83b7\u53d6\u53d8\u91cf\nx = data['x']\ny = data['y']\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('x:', x)\nprint('y:', y)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001sio.loadmat() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u300cdata.mat\u300d\u3068\u3044\u3046\u540d\u524d\u306e matlab \u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u53d6\u308a\u3001\u305d\u306e\u4e2d\u306e\u5909\u6570 x \u3068 y \u3092 Python \u5909\u6570\u306b\u4fdd\u5b58\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u8aad\u307f\u53d6\u308a\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>matlab \u30d5\u30a1\u30a4\u30eb\u306b\u66f8\u304d\u8fbc\u3080<\/li>\n<\/ol>\n\n\n\n<p>You can use the scipy.io.savemat() function to write Python variables to a matlab file in .mat format. \u3053\u306e\u95a2\u6570\u306f\u5f15\u6570\u3068\u3057\u3066\u8f9e\u66f8\u3092\u53d7\u3051\u53d6\u308a\u3001\u8f9e\u66f8\u306e\u30ad\u30fc\u306f\u5909\u6570\u540d\u3067\u3001\u5024\u306f\u5024\u3067\u3059\u3002\u5909\u6570\u306e\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import scipy.io as sio\n\n# \u5b9a\u4e49\u6570\u636e\nx = [1, 2, 3, 4]\ny = [5, 6, 7, 8]\n\n# \u5199\u5165matlab\u6587\u4ef6\nsio.savemat('data.mat', {'x': x, 'y': y})\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u30012 \u3064\u306e Python \u5909\u6570 x \u3068 y \u3092\u5b9a\u7fa9\u3057\u3001sio.savemat() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u3053\u308c\u3089 2 \u3064\u306e\u5909\u6570\u3092\u300cdata.mat\u300d\u3068\u3044\u3046\u540d\u524d\u306e matlab \u30d5\u30a1\u30a4\u30eb\u306b\u66f8\u304d\u8fbc\u307f\u307e\u3059\u3002<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e io \u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001wav \u30d5\u30a1\u30a4\u30eb\u3084\u753b\u50cf\u30d5\u30a1\u30a4\u30eb\u306a\u3069\u306e\u8aad\u307f\u66f8\u304d\u306a\u3069\u3001\u4ed6\u306e\u5f62\u5f0f\u306e\u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u66f8\u304d\u3059\u308b\u305f\u3081\u306e\u95a2\u6570\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u306e\u4f7f\u7528\u306f\u3001matlab \u30d5\u30a1\u30a4\u30eb\u306e\u8aad\u307f\u66f8\u304d\u306b\u4f3c\u3066\u3044\u307e\u3059\u3002\u5b9f\u969b\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u5fc5\u8981\u306b\u5fdc\u3058\u3066\u30c7\u30fc\u30bf\u3092\u8aad\u307f\u66f8\u304d\u3059\u308b\u9069\u5207\u306a\u95a2\u6570\u3092\u9078\u629e\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u30d5\u30a1\u30a4\u30eb\u306e\u8aad\u307f\u66f8\u304d\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u30c7\u30fc\u30bf\u5206\u6790\u3084\u79d1\u5b66\u6280\u8853\u8a08\u7b97\u306b\u304a\u3044\u3066\u3001\u30c7\u30fc\u30bf\u306e\u8aad\u307f\u66f8\u304d\u306f\u975e\u5e38\u306b\u91cd\u8981\u306a\u90e8\u5206\u3067\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306f\u3001\u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u3001\u30d0\u30a4\u30ca\u30ea \u30d5\u30a1\u30a4\u30eb\u3001matlab \u30d5\u30a1\u30a4\u30eb\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u5f62\u5f0f\u306e\u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u66f8\u304d\u3067\u304d\u308b\u3001\u3055\u307e\u3056\u307e\u306a\u30c7\u30fc\u30bf\u306e\u8aad\u307f\u66f8\u304d\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30c7\u30fc\u30bf\u306e\u8aad\u307f\u66f8\u304d\u306b Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3059\u308b\u65b9\u6cd5\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30c6\u30ad\u30b9\u30c8\u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u3080<\/li>\n<\/ol>\n\n\n\n<p>\u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e numpy.loadtxt() \u95a2\u6570\u307e\u305f\u306f pandas \u30e9\u30a4\u30d6\u30e9\u30ea\u306e pandas.read_csv() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u8aad\u307f\u53d6\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>numpy.loadtxt() \u95a2\u6570\u306f\u3001\u30d7\u30ec\u30fc\u30f3 \u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u53d6\u308a\u3001\u305d\u308c\u3092 NumPy \u914d\u5217\u306b\u5909\u63db\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\n\n# \u8bfb\u53d6\u6570\u636e\u6587\u4ef6\ndata = np.loadtxt('data.txt', delimiter=',')\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Data:', data)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001np.loadtxt() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u30b3\u30f3\u30de\u3067\u533a\u5207\u3089\u308c\u305f\u300cdata.txt\u300d\u3068\u3044\u3046\u540d\u524d\u306e\u30d7\u30ec\u30fc\u30f3 \u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u53d6\u308a\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306f\u3001\u30d5\u30a1\u30a4\u30eb\u5185\u306e\u30c7\u30fc\u30bf\u3092\u8868\u3059 NumPy \u914d\u5217\u3092\u8fd4\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u8aad\u307f\u53d6\u308a\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>pandas.read_csv() \u95a2\u6570\u306f\u3001\u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u3092 CSV \u5f62\u5f0f\u3067\u8aad\u307f\u53d6\u308a\u3001Pandas DataFrame \u306b\u5909\u63db\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import pandas as pd\n\n# \u8bfb\u53d6\u6570\u636e\u6587\u4ef6\ndata = pd.read_csv('data.csv')\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Data:', data)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u300cdata.csv\u300d\u3068\u3044\u3046 CSV \u5f62\u5f0f\u306e\u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u3092 pd.read_csv() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u8aad\u307f\u53d6\u308a\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306f\u3001\u30d5\u30a1\u30a4\u30eb\u5185\u306e\u30c7\u30fc\u30bf\u3092\u8868\u3059 Pandas DataFrame \u3092\u8fd4\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u8aad\u307f\u53d6\u308a\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u30c6\u30ad\u30b9\u30c8\u30d5\u30a1\u30a4\u30eb\u306b\u66f8\u304d\u8fbc\u3080<\/li>\n<\/ol>\n\n\n\n<p>numpy.savetxt() \u95a2\u6570\u307e\u305f\u306f pandas.DataFrame.to_csv() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u30c7\u30fc\u30bf\u3092\u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u306b\u66f8\u304d\u8fbc\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>numpy.savetxt() \u95a2\u6570\u306f\u3001NumPy \u914d\u5217\u3092\u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u306b\u66f8\u304d\u8fbc\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\n\n# \u5b9a\u4e49\u6570\u636e\ndata = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n\n# \u5199\u5165\u6570\u636e\u6587\u4ef6\nnp.savetxt('data.txt', data, delimiter=',')\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Data saved to data.txt')\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001np.savetxt() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001NumPy \u914d\u5217\u3092\u300cdata.txt\u300d\u3068\u3044\u3046\u540d\u524d\u306e\u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u306b\u30b3\u30f3\u30de\u3067\u533a\u5207\u3063\u3066\u66f8\u304d\u8fbc\u307f\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u66f8\u304d\u8fbc\u307f\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>pandas.DataFrame.to_csv() \u95a2\u6570\u306f\u3001Pandas DataFrame \u3092 CSV \u5f62\u5f0f\u306e\u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u306b\u66f8\u304d\u8fbc\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import pandas as pd\n\n# \u5b9a\u4e49\u6570\u636e\ndata = pd.DataFrame({'A': [1, 2, 3], 'B': [4, 5, 6], 'C': [7, 8, 9]})\n\n# \u5199\u5165\u6570\u636e\u6587\u4ef6\ndata.to_csv('data.csv', index=False)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Data saved to data.csv')\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001data.to_csv() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001Pandas DataFrame \u3092\u300cdata.csv\u300d\u3068\u3044\u3046\u540d\u524d\u306e CSV \u5f62\u5f0f\u306e\u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u306b\u66f8\u304d\u8fbc\u307f\u307e\u3059\u3002\u3053\u3053\u3067\u3001index=False \u306f\u3001\u884c\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u51fa\u529b\u3055\u308c\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u66f8\u304d\u8fbc\u307f\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30c7\u30fc\u30bf\u306e\u8aad\u307f\u53d6\u308a\u3068\u66f8\u304d\u8fbc\u307f\u306b Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u3055\u307e\u3056\u307e\u306a\u5f62\u5f0f\u306e\u30c7\u30fc\u30bf \u30d5\u30a1\u30a4\u30eb\u3092\u7c21\u5358\u306b\u8aad\u307f\u66f8\u304d\u3067\u304d\u3001\u30c7\u30fc\u30bf\u3092 NumPy \u914d\u5217\u307e\u305f\u306f Pandas DataFrame \u306b\u7c21\u5358\u306b\u5909\u63db\u3057\u3066\u3001\u305d\u306e\u5f8c\u306e\u30c7\u30fc\u30bf\u5206\u6790\u3068\u51e6\u7406\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u4f8b\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044: \u30d5\u30a1\u30a4\u30eb\u306b\u5bfe\u3059\u308b\u8aad\u307f\u53d6\u308a\u64cd\u4f5c\u3068\u66f8\u304d\u8fbc\u307f\u64cd\u4f5c<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u3066\u30c7\u30fc\u30bf\u306e\u8aad\u307f\u53d6\u308a\u3068\u66f8\u304d\u8fbc\u307f\u3092\u884c\u3046\u65b9\u6cd5\u3092\u793a\u3059\u305f\u3081\u306b\u3001\u30d5\u30a1\u30a4\u30eb\u306e\u8aad\u307f\u53d6\u308a\u3068\u66f8\u304d\u8fbc\u307f\u64cd\u4f5c\u306e\u4f8b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>\u6b21\u306e\u30c7\u30fc\u30bf\u3092\u542b\u3080\u300cdata.txt\u300d\u3068\u3044\u3046\u540d\u524d\u306e\u30d7\u30ec\u30fc\u30f3 \u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc<code>1,2,3\n4,5,6\n7,8,9\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u30d5\u30a1\u30a4\u30eb\u3092 NumPy \u914d\u5217\u306b\u8aad\u307f\u8fbc\u307f\u3001\u305d\u306e\u5e73\u5747\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u6b21\u306b\u3001\u8a08\u7b97\u7d50\u679c\u3092\u300cresult.txt\u300d\u3068\u3044\u3046\u5225\u306e\u30d7\u30ec\u30fc\u30f3 \u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u306b\u66f8\u304d\u8fbc\u307f\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u793a\u3055\u308c\u307e\u3059:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\n\n# \u8bfb\u53d6\u6570\u636e\u6587\u4ef6\ndata = np.loadtxt('data.txt', delimiter=',')\n\n# \u8ba1\u7b97\u5e73\u5747\u503c\nmean = np.mean(data)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Data:', data)\nprint('Mean:', mean)\n\n# \u5199\u5165\u7ed3\u679c\u6587\u4ef6\nwith open('result.txt', 'w') as f:\n    f.write('Mean: {}'.format(mean))\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Result saved to result.txt')\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u6700\u521d\u306b np.loadtxt() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u30b3\u30f3\u30de\u3067\u533a\u5207\u3089\u308c\u305f\u300cdata.txt\u300d\u3068\u3044\u3046\u540d\u524d\u306e\u30d7\u30ec\u30fc\u30f3 \u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u53d6\u308a\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306f\u3001\u30d5\u30a1\u30a4\u30eb\u5185\u306e\u30c7\u30fc\u30bf\u3092\u8868\u3059 NumPy \u914d\u5217\u3092\u8fd4\u3057\u307e\u3059\u3002\u6b21\u306b\u3001np.mean() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3053\u306e\u914d\u5217\u306e\u5e73\u5747\u3092\u8a08\u7b97\u3057\u3001\u8aad\u307f\u53d6\u308a\u7d50\u679c\u3068\u8a08\u7b97\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001Python \u306e\u7d44\u307f\u8fbc\u307f\u306e with \u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u3092\u4f7f\u7528\u3057\u3066\u3001\u300cresult.txt\u300d\u3068\u3044\u3046\u540d\u524d\u306e\u30c6\u30ad\u30b9\u30c8 \u30d5\u30a1\u30a4\u30eb\u3092\u958b\u304d\u3001\u8a08\u7b97\u7d50\u679c\u3092\u30d5\u30a1\u30a4\u30eb\u306b\u66f8\u304d\u8fbc\u307f\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u66f8\u304d\u8fbc\u307f\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u4f8b\u304b\u3089\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u3066\u30c7\u30fc\u30bf\u3092\u8aad\u307f\u66f8\u304d\u3059\u308b\u306e\u306f\u975e\u5e38\u306b\u4fbf\u5229\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059.Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u5f62\u5f0f\u306e\u30c7\u30fc\u30bf \u30d5\u30a1\u30a4\u30eb\u3092\u7c21\u5358\u306b\u8aad\u307f\u66f8\u304d\u3057\u3001\u305d\u306e\u5f8c\u306e\u30c7\u30fc\u30bf\u5206\u6790\u3068\u51e6\u7406\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u5171\u901a\u6a5f\u80fd\u3068\u88cf\u6280\u306e\u7279\u6b8a\u6a5f\u80fd\u3092\u8a73\u3057\u304f\u6559\u3048\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306f\u3001\u79d1\u5b66\u8a08\u7b97\u3001\u30c7\u30fc\u30bf\u5206\u6790\u3001\u4fe1\u53f7\u51e6\u7406\u3001\u304a\u3088\u3073\u305d\u306e\u4ed6\u306e\u5206\u91ce\u5411\u3051\u306e\u591a\u304f\u306e\u4e00\u822c\u7684\u306a\u95a2\u6570\u3068\u30c8\u30ea\u30c3\u30af\u306e\u7279\u6b8a\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u3067\u306f\u3001\u3053\u306e 2 \u7a2e\u985e\u306e\u6a5f\u80fd\u3092\u500b\u5225\u306b\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5171\u901a\u6a5f\u80fd<\/li>\n<\/ol>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u95a2\u6570\u306b\u306f\u3001\u6b21\u306e\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6570\u5b66\u95a2\u6570: \u4e09\u89d2\u95a2\u6570\u3001\u6307\u6570\u95a2\u6570\u3001\u5bfe\u6570\u95a2\u6570\u3001\u7d2f\u4e57\u95a2\u6570\u306a\u3069\u3092\u542b\u3080<\/li>\n\n\n\n<li>\u7dda\u5f62\u4ee3\u6570\u95a2\u6570: \u9006\u884c\u5217\u3001\u884c\u5217\u89e3\u3001\u884c\u5217\u56fa\u6709\u5024\u3001\u884c\u5217\u884c\u5217\u5f0f\u306a\u3069\u3092\u542b\u3080<\/li>\n\n\n\n<li>\u88dc\u9593\u6a5f\u80fd\uff1a\u4e00\u6b21\u5143\u88dc\u9593\u3001\u4e8c\u6b21\u5143\u88dc\u9593\u306a\u3069\u3092\u542b\u3080<\/li>\n\n\n\n<li>\u6700\u9069\u5316\u95a2\u6570: \u7dda\u5f62\u8a08\u753b\u6cd5\u3001\u975e\u7dda\u5f62\u8a08\u753b\u6cd5\u3001\u5927\u57df\u7684\u6700\u9069\u5316\u306a\u3069\u3092\u542b\u3080<\/li>\n\n\n\n<li>\u7d71\u8a08\u95a2\u6570: \u78ba\u7387\u5206\u5e03\u3001\u8a18\u8ff0\u7d71\u8a08\u3001\u4eee\u8aac\u691c\u5b9a\u306a\u3069\u3092\u542b\u3080<\/li>\n\n\n\n<li>\u4fe1\u53f7\u51e6\u7406\u6a5f\u80fd: \u30d5\u30a3\u30eb\u30bf\u8a2d\u8a08\u3001\u30b9\u30da\u30af\u30c8\u30eb\u63a8\u5b9a\u3001\u6ce2\u5f62\u51e6\u7406\u306a\u3069\u3092\u542b\u3080<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u308c\u3089\u306e\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u6a5f\u80fd\u306b\u3088\u308a\u3001\u79d1\u5b66\u8a08\u7b97\u3001\u30c7\u30fc\u30bf\u5206\u6790\u3001\u4fe1\u53f7\u51e6\u7406\u306a\u3069\u306e\u30bf\u30b9\u30af\u306e\u5b9f\u73fe\u304c\u5927\u5e45\u306b\u7c21\u7d20\u5316\u3055\u308c\u3001\u4f5c\u696d\u52b9\u7387\u304c\u5411\u4e0a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u30c8\u30ea\u30c3\u30af\u7279\u6b8a\u6a5f\u80fd<\/li>\n<\/ol>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e Trick \u7279\u6b8a\u95a2\u6570\u306b\u306f\u6b21\u306e\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u30d9\u30c3\u30bb\u30eb\u95a2\u6570: \u632f\u52d5\u3001\u6ce2\u52d5\u3001\u653e\u5c04\u306a\u3069\u306e\u554f\u984c\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u8d85\u5e7e\u4f55\u95a2\u6570: \u4e0d\u5747\u4e00\u306a\u5206\u5e03\u306e\u554f\u984c\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u30d5\u30a7\u30eb\u30de\u30fc\u95a2\u6570: \u97f3\u6ce2\u306e\u4f1d\u642c\u554f\u984c\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u6955\u5186\u95a2\u6570: \u661f\u306e\u8ecc\u9053\u3001\u96fb\u6c17\u529b\u5b66\u3001\u6d41\u4f53\u529b\u5b66\u3001\u305d\u306e\u4ed6\u306e\u554f\u984c\u306e\u8a08\u7b97\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u30ac\u30f3\u30de\u95a2\u6570: \u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3001\u7d71\u8a08\u5206\u5e03\u95a2\u6570\u3001\u304a\u3088\u3073\u305d\u306e\u4ed6\u306e\u554f\u984c\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u308c\u3089\u306e\u30b9\u30ad\u30eb\u3068\u7279\u6b8a\u306a\u6a5f\u80fd\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u7279\u6b8a\u306a\u554f\u984c\u306b\u5bfe\u51e6\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u7269\u7406\u5b66\u3001\u6570\u5b66\u3001\u5de5\u5b66\u3001\u5929\u6587\u5b66\u306a\u3069\u306e\u5206\u91ce\u3067\u5e45\u5e83\u3044\u7528\u9014\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3064\u307e\u308a\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u95a2\u6570\u3068\u30c8\u30ea\u30c3\u30af\u306e\u7279\u6b8a\u95a2\u6570\u306f\u5b9f\u7528\u7684\u306a\u4fa1\u5024\u304c\u9ad8\u304f\u3001\u79d1\u5b66\u8005\u3001\u30a8\u30f3\u30b8\u30cb\u30a2\u3001\u30c7\u30fc\u30bf \u30a2\u30ca\u30ea\u30b9\u30c8\u304c\u8907\u96d1\u306a\u79d1\u5b66\u8a08\u7b97\u3001\u30c7\u30fc\u30bf\u5206\u6790\u3001\u4fe1\u53f7\u51e6\u7406\u3001\u304a\u3088\u3073\u305d\u306e\u4ed6\u306e\u30bf\u30b9\u30af\u3092\u3088\u308a\u7c21\u5358\u306b\u89e3\u6c7a\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u7a93\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u6559\u3048\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u4fe1\u53f7\u51e6\u7406\u306e\u5206\u91ce\u3067\u306f\u3001\u4fe1\u53f7\u306e\u6642\u9593\u5206\u89e3\u80fd\u3092\u7dad\u6301\u3057\u306a\u304c\u3089\u3001\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306b\u304a\u3051\u308b\u30b9\u30da\u30af\u30c8\u30eb\u6f0f\u308c\u306e\u554f\u984c\u3092\u8efd\u6e1b\u3059\u308b\u305f\u3081\u306b\u3001\u6642\u7cfb\u5217\u306e\u30c7\u30fc\u30bf\u3092\u91cd\u307f\u4ed8\u3051\u3059\u308b\u305f\u3081\u306b\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u304c\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u4fe1\u53f7\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u3001\u4fe1\u53f7\u51e6\u7406\u3001\u30b9\u30da\u30af\u30c8\u30eb\u63a8\u5b9a\u3001\u304a\u3088\u3073\u305d\u306e\u4ed6\u306e\u5206\u91ce\u5411\u3051\u306e\u3055\u307e\u3056\u307e\u306a\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u306e\u539f\u7406\u306f\u3001\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u306b\u91cd\u307f\u4fc2\u6570\u3092\u8ffd\u52a0\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u901a\u5e38\u306f 0 \u304b\u3089 1 \u307e\u3067\u306e\u95a2\u6570\u3067\u3059\u3002\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u306e\u5f62\u72b6\u306f\u3001\u30c7\u30fc\u30bf\u306e\u91cd\u307f\u4ed8\u3051\u65b9\u6cd5\u3092\u6c7a\u5b9a\u3057\u307e\u3059. \u305f\u3068\u3048\u3070\u3001\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3067\u306f\u3001\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u4fe1\u53f7\u306e\u30b9\u30da\u30af\u30c8\u30eb\u6f0f\u308c\u3092\u6e1b\u3089\u3057\u3001\u5468\u6ce2\u6570\u5206\u89e3\u80fd\u3092\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059.<\/p>\n\n\n\n<p>\u4e00\u822c\u7684\u306a\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u306b\u306f\u6b21\u306e\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u77e9\u5f62\u7a93: \u6700\u3082\u5358\u7d14\u306a\u7a93\u95a2\u6570\u3001\u3064\u307e\u308a\u5358\u4f4d\u30d1\u30eb\u30b9\u306b\u306f\u3001\u91cd\u307f\u304c\u7b49\u3057\u3044\u3068\u3044\u3046\u6027\u8cea\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u30cf\u30df\u30f3\u30b0 \u30a6\u30a3\u30f3\u30c9\u30a6: \u9577\u65b9\u5f62\u306e\u30a6\u30a3\u30f3\u30c9\u30a6\u306b\u57fa\u3065\u3044\u3066\u3001\u4f59\u5f26\u95a2\u6570\u4fc2\u6570\u304c\u8ffd\u52a0\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30b9\u30da\u30af\u30c8\u30eb\u306e\u30e1\u30a4\u30f3 \u30ed\u30fc\u30d6\u3092\u5f31\u3081\u308b\u512a\u308c\u305f\u6a5f\u80fd\u3092\u5099\u3048\u3066\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u30cf\u30cb\u30f3\u30b0 \u30a6\u30a3\u30f3\u30c9\u30a6: \u30cf\u30df\u30f3\u30b0 \u30a6\u30a3\u30f3\u30c9\u30a6\u306b\u57fa\u3065\u3044\u3066\u3001\u3088\u308a\u591a\u304f\u306e\u4f59\u5f26\u95a2\u6570\u4fc2\u6570\u304c\u4f7f\u7528\u3055\u308c\u3001\u30e1\u30a4\u30f3 \u30ed\u30fc\u30d6\u306e\u6e1b\u8870\u80fd\u529b\u304c\u5411\u4e0a\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u30d6\u30e9\u30c3\u30af\u30de\u30f3 \u30a6\u30a3\u30f3\u30c9\u30a6: \u30cf\u30df\u30f3\u30b0 \u30a6\u30a3\u30f3\u30c9\u30a6\u306b\u57fa\u3065\u3044\u3066\u3001\u4f59\u5f26\u95a2\u6570\u4fc2\u6570\u3068\u7dda\u5f62\u52fe\u914d\u4fc2\u6570\u304c\u8ffd\u52a0\u3055\u308c\u3001\u6e1b\u8870\u80fd\u529b\u304c\u5411\u4e0a\u3057\u3001\u30b5\u30a4\u30c9\u30ed\u30fc\u30d6\u304c\u4f4e\u304f\u306a\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u30ec\u30a4\u30ba\u30c9 \u30b3\u30b5\u30a4\u30f3 \u30a6\u30a3\u30f3\u30c9\u30a6 (\u30b3\u30b5\u30a4\u30f3 \u30a6\u30a3\u30f3\u30c9\u30a6): \u30cf\u30cb\u30f3\u30b0 \u30a6\u30a3\u30f3\u30c9\u30a6\u306b\u4f3c\u3066\u3044\u307e\u3059\u304c\u3001\u3088\u308a\u591a\u304f\u306e\u30b3\u30b5\u30a4\u30f3\u95a2\u6570\u4fc2\u6570\u3068\u30b5\u30a4\u30f3\u95a2\u6570\u4fc2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u30b5\u30a4\u30c9\u30ed\u30fc\u30d6\u6e1b\u8870\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<p>Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30b7\u30b0\u30ca\u30eb \u30e2\u30b8\u30e5\u30fc\u30eb\u306b\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u306e\u5b9f\u88c5\u304c\u7528\u610f\u3055\u308c\u3066\u304a\u308a\u3001\u5fc5\u8981\u306b\u5fdc\u3058\u3066\u9069\u5207\u306a\u30a6\u30a3\u30f3\u30c9\u30a6\u95a2\u6570\u3092\u9078\u629e\u3067\u304d\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u30b3\u30fc\u30c9\u306f\u3001\u30cf\u30df\u30f3\u30b0 \u30a6\u30a3\u30f3\u30c9\u30a6\u3092\u4f7f\u7528\u3057\u3066\u4fe1\u53f7\u306b\u91cd\u307f\u3092\u4ed8\u3051\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nfrom scipy import signal\n\n# \u751f\u6210\u4fe1\u53f7\nt = np.linspace(0, 1, 1000, endpoint=False)\nx = np.sin(2 * np.pi * 10 * t) + np.sin(2 * np.pi * 20 * t)\n\n# \u5e94\u7528\u6c49\u660e\u7a97\nwindow = signal.hamming(51)\nxw = x[:51] * window\n\n# \u663e\u793a\u7ed3\u679c\nimport matplotlib.pyplot as plt\n\nplt.plot(x[:51], 'b', label='Original')\nplt.plot(xw, 'r', label='Hamming window')\nplt.legend()\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001np.sin() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066 2 \u3064\u306e\u6b63\u5f26\u6ce2\u3067\u69cb\u6210\u3055\u308c\u308b\u4fe1\u53f7\u3092\u751f\u6210\u3057\u307e\u3057\u305f\u3002\u6b21\u306b\u3001signal.hamming() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066 51 \u30dd\u30a4\u30f3\u30c8\u306e\u30cf\u30df\u30f3\u30b0 \u30a6\u30a3\u30f3\u30c9\u30a6\u3092\u751f\u6210\u3057\u3001\u4fe1\u53f7\u306b\u91cd\u307f\u3092\u4ed8\u3051\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u4fe1\u53f7\u306e\u6700\u521d\u306e 51 \u30dd\u30a4\u30f3\u30c8\u3067\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u4f8b\u3092\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044: Scipy \u30e6\u30fc\u30c6\u30a3\u30ea\u30c6\u30a3\u95a2\u6570<\/p>\n\n\n\n<p>Scipy \u306e\u30e6\u30fc\u30c6\u30a3\u30ea\u30c6\u30a3\u95a2\u6570\u306e\u4f8b\u3092\u6319\u3052\u3066\u3001\u79d1\u5b66\u8a08\u7b97\u3068\u30c7\u30fc\u30bf\u51e6\u7406\u306b Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>float \u306e 1000 \u8981\u7d20\u914d\u5217\u3092\u542b\u3080\u300cdata.txt\u300d\u3068\u3044\u3046\u30c7\u30fc\u30bf \u30d5\u30a1\u30a4\u30eb\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u914d\u5217\u3092\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db (DFT) \u3057\u3001\u305d\u306e\u30d1\u30ef\u30fc \u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6 (PSD) \u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u6b21\u306b\u3001\u30d1\u30ef\u30fc \u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u3092\u30b0\u30e9\u30d5\u3068\u3057\u3066\u30d7\u30ed\u30c3\u30c8\u3057\u3001\u305d\u306e\u30d4\u30fc\u30af\u5468\u6ce2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u793a\u3055\u308c\u307e\u3059:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.fft import fft, fftfreq\nfrom scipy.signal import welch\n\n# \u8bfb\u53d6\u6570\u636e\u6587\u4ef6\ndata = np.loadtxt('data.txt')\n\n# \u8ba1\u7b97\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362\ndft = fft(data)\n\n# \u8ba1\u7b97\u529f\u7387\u8c31\u5bc6\u5ea6\nf, psd = welch(data)\n\n# \u7ed8\u5236\u529f\u7387\u8c31\u5bc6\u5ea6\u56fe\u5f62\nplt.semilogy(f, psd)\nplt.xlabel('Frequency')\nplt.ylabel('Power Spectral Density')\nplt.title('Power Spectral Density')\nplt.show()\n\n# \u8ba1\u7b97\u5cf0\u503c\u9891\u7387\nidx = np.argmax(psd)\npeak_freq = f[idx]\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Peak frequency:', peak_freq)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u6700\u521d\u306b np.loadtxt() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u300cdata.txt\u300d\u3068\u3044\u3046\u540d\u524d\u306e\u30c7\u30fc\u30bf \u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u53d6\u308a\u307e\u3059\u3002\u3053\u306e\u30d5\u30a1\u30a4\u30eb\u306b\u306f\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u306e 1000 \u8981\u7d20\u306e\u914d\u5217\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u6b21\u306b\u3001scipy.fft.fft() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3053\u306e\u914d\u5217\u306e\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u8a08\u7b97\u3057\u3001scipy.signal.welch() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u305d\u306e\u30d1\u30ef\u30fc \u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u3092\u8a08\u7b97\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001matplotlib \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u3066\u30d1\u30ef\u30fc \u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3001np.argmax() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30d1\u30ef\u30fc \u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u306e\u30d4\u30fc\u30af\u5468\u6ce2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3057\u305f\u3002\u6700\u5f8c\u306b\u3001\u8a08\u7b97\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306e\u8a08\u7b97\u3001\u30d1\u30ef\u30fc\u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u306e\u8a08\u7b97\u3001\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u30b9\u306e\u63cf\u753b\u306a\u3069\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u3066\u79d1\u5b66\u8a08\u7b97\u3068\u30c7\u30fc\u30bf\u51e6\u7406\u3092\u7c21\u5358\u306b\u5b9f\u884c\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u79d1\u5b66\u8a08\u7b97\u306e\u4f5c\u696d\u304c\u5927\u5e45\u306b\u7c21\u7d20\u5316\u3055\u308c\u3001\u30c7\u30fc\u30bf\u51e6\u7406\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u30b1\u30fc\u30b9 1 \u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044: \u30c7\u30fc\u30bf\u306e\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3068\u4e88\u6e2c<\/p>\n\n\n\n<p>\u30c7\u30fc\u30bf\u306e\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3068\u4e88\u6e2c\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u6a5f\u80fd\u306e 1 \u3064\u3067\u3059\u3002\u3053\u306e\u5834\u5408\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e curve_fit() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u5358\u7d14\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u9069\u5408\u3055\u305b\u3001\u9069\u5408\u7d50\u679c\u3092\u4f7f\u7528\u3057\u3066\u4e88\u6e2c\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>x \u5024\u3068 y \u5024\u306e\u30c7\u30fc\u30bf \u30da\u30a2\u3092\u542b\u3080\u300cdata.txt\u300d\u3068\u3044\u3046\u540d\u524d\u306e\u30c7\u30fc\u30bf \u30d5\u30a1\u30a4\u30eb\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30c7\u30fc\u30bf\u3092\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3057\u3001\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u7d50\u679c\u3092\u4f7f\u7528\u3057\u3066\u4e88\u6e2c\u3092\u884c\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u793a\u3055\u308c\u307e\u3059:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.optimize import curve_fit\n\n# \u8bfb\u53d6\u6570\u636e\u6587\u4ef6\ndata = np.loadtxt('data.txt')\n\n# \u5b9a\u4e49\u62df\u5408\u51fd\u6570\ndef func(x, a, b, c):\n    return a * np.exp(-b * x) + c\n\n# \u8fdb\u884c\u6570\u636e\u62df\u5408\npopt, pcov = curve_fit(func, data[:, 0], data[:, 1])\n\n# \u7ed8\u5236\u62df\u5408\u66f2\u7ebf\nx = np.linspace(0, 5, 100)\ny = func(x, *popt)\nplt.plot(data[:, 0], data[:, 1], 'ro', label='Data')\nplt.plot(x, y, 'b-', label='Fit')\nplt.legend()\nplt.show()\n\n# \u8fdb\u884c\u9884\u6d4b\nx_pred = np.linspace(5, 10, 50)\ny_pred = func(x_pred, *popt)\n\n# \u8f93\u51fa\u7ed3\u679c\nprint('Parameters:', popt)\nprint('Predicted values:', y_pred)\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u6700\u521d\u306b np.loadtxt() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001x \u5024\u3068 y \u5024\u306e\u30c7\u30fc\u30bf \u30da\u30a2\u3092\u542b\u3080\u300cdata.txt\u300d\u3068\u3044\u3046\u30c7\u30fc\u30bf \u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u53d6\u308a\u307e\u3059\u3002\u6b21\u306b\u30014 \u3064\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc x\u3001a\u3001b\u3001\u304a\u3088\u3073 c \u3092\u53d6\u308b\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u95a2\u6570 func() \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001a\u3001b\u3001\u304a\u3088\u3073 c \u306f\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0 \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001scipy.optimize.curve_fit() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30c7\u30fc\u30bf\u3092\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3057\u3001\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0 \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc popt \u3068\u5171\u5206\u6563\u884c\u5217 pcov \u3092\u53d6\u5f97\u3057\u307e\u3059\u3002\u6b21\u306b\u3001\u30d7\u30ed\u30c3\u30c8 \u30e9\u30a4\u30d6\u30e9\u30ea matplotlib \u3092\u4f7f\u7528\u3057\u3066\u751f\u30c7\u30fc\u30bf\u3068\u8fd1\u4f3c\u66f2\u7dda\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3001np.linspace() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u4e88\u6e2c\u7528\u306e 50 \u500b\u306e x \u5024\u3092\u751f\u6210\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u6700\u5f8c\u306b\u3001\u9069\u5408\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u4e88\u6e2c\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u30b1\u30fc\u30b9\u3092\u901a\u3058\u3066\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067 curve_fit() \u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u30c7\u30fc\u30bf\u306e\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3068\u4e88\u6e2c\u304c\u5bb9\u6613\u306b\u306a\u308a\u3001\u30c7\u30fc\u30bf\u306e\u7406\u89e3\u3068\u5206\u6790\u304c\u5411\u4e0a\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u30b1\u30fc\u30b9 2 \u306e\u753b\u50cf\u8a8d\u8b58\u3068\u51e6\u7406\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044<\/p>\n\n\n\n<p>\u753b\u50cf\u306e\u8a8d\u8b58\u3068\u51e6\u7406\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u3082\u3046 1 \u3064\u306e\u6a5f\u80fd\u3067\u3059\u3002\u3053\u306e\u5834\u5408\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u753b\u50cf\u3092\u51e6\u7406\u3057\u3001\u753b\u50cf\u8a8d\u8b58\u306b skimage \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u300cimage.png\u300d\u3068\u3044\u3046\u540d\u524d\u306e\u753b\u50cf\u30d5\u30a1\u30a4\u30eb\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u753b\u50cf\u3092 2 \u5024\u5316\u3057\u3001\u6570\u5b57\u8a8d\u8b58\u306e\u305f\u3081\u306b skimage \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u793a\u3055\u308c\u307e\u3059:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import ndimage\nfrom skimage import io, morphology, measure\n\n# \u8bfb\u53d6\u56fe\u50cf\u6587\u4ef6\nimg = io.imread('image.png')\n\n# \u5c06\u56fe\u50cf\u8f6c\u6362\u4e3a\u7070\u5ea6\u56fe\u50cf\ngray_img = np.mean(img, axis=-1)\n\n# \u8fdb\u884c\u4e8c\u503c\u5316\u5904\u7406\nbinary_img = gray_img &gt; 127\n\n# \u5bf9\u56fe\u50cf\u8fdb\u884c\u5f62\u6001\u5b66\u5904\u7406\nmorph_img = morphology.binary_opening(binary_img, morphology.square(3))\n\n# \u8fdb\u884c\u6570\u5b57\u8bc6\u522b\nlabel_img = measure.label(morph_img, connectivity=2)\nprops = measure.regionprops(label_img)\n\n# \u7ed8\u5236\u7ed3\u679c\u56fe\u50cf\nfig, ax = plt.subplots()\nax.imshow(img)\n\nfor prop in props:\n    y, x = prop.centroid\n    ax.text(x, y, str(prop.label), color='red', fontsize=12)\n\nax.set_axis_off()\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u307e\u305a\u3001skimage \u30e9\u30a4\u30d6\u30e9\u30ea\u306e io.imread() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u300cimage.png\u300d\u3068\u3044\u3046\u540d\u524d\u306e\u753b\u50cf\u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u53d6\u308a\u307e\u3059\u3002\u6b21\u306b\u3001np.mean() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3053\u306e\u753b\u50cf\u3092\u30b0\u30ec\u30fc\u30b9\u30b1\u30fc\u30eb\u753b\u50cf\u306b\u5909\u63db\u3057\u3001\u5358\u7d14\u306a\u3057\u304d\u3044\u5024\u51e6\u7406\u3092\u4f7f\u7528\u3057\u3066\u4e8c\u5024\u5316\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001scipy.ndimage \u30e2\u30b8\u30e5\u30fc\u30eb\u306e morphology.binary_opening() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u753b\u50cf\u3092\u5f62\u614b\u5b66\u7684\u306b\u51e6\u7406\u3057\u3001\u30ce\u30a4\u30ba\u3068\u5c0f\u3055\u306a\u30d6\u30ed\u30d6\u3092\u9664\u53bb\u3057\u307e\u3059\u3002\u6b21\u306b\u3001skimage \u30e9\u30a4\u30d6\u30e9\u30ea\u306e measure.label() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u51e6\u7406\u3055\u308c\u305f\u753b\u50cf\u306b\u30e9\u30d9\u30eb\u3092\u4ed8\u3051\u3001measure.regionprops() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30e9\u30d9\u30eb\u4ed8\u3051\u3055\u308c\u305f\u9818\u57df\u306e\u30d7\u30ed\u30d1\u30c6\u30a3 (\u4e2d\u5fc3\u4f4d\u7f6e\u3084\u30e9\u30d9\u30eb\u756a\u53f7\u306a\u3069) \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6700\u5f8c\u306b\u3001matplotlib \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u3066\u7d50\u679c\u306e\u753b\u50cf\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3001ax.text() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u753b\u50cf\u306e\u8a8d\u8b58\u7d50\u679c\u306b\u6ce8\u91c8\u3092\u4ed8\u3051\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u4e8b\u4f8b\u304b\u3089\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u753b\u50cf\u5909\u63db\u30012 \u5024\u5316\u3001\u5f62\u614b\u7d20\u51e6\u7406\u3001\u30c7\u30b8\u30bf\u30eb\u8a8d\u8b58\u306a\u3069\u306e\u753b\u50cf\u51e6\u7406\u3068\u5206\u6790\u3092\u7c21\u5358\u306b\u5b9f\u884c\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u3001\u753b\u50cf\u30c7\u30fc\u30bf\u3092\u3088\u308a\u9069\u5207\u306b\u5206\u6790\u304a\u3088\u3073\u51e6\u7406\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/edu.ujhb.org\/?p=1869\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/chat.openai.com\/_next\/image?url=https%3A%2F%2Flh3.googleusercontent.com%2Fa%2FAGNmyxbwVdnTP0E2eBqDrujRQjV-wFP12Thr4vFgysVv5A%3Ds96-c&amp;w=96&amp;q=75\" alt=\"gun tei\"\/><\/figure>\n\n\n\n<p>\u30b1\u30fc\u30b9 3 \u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044: \u4fe1\u53f7\u306e\u30ce\u30a4\u30ba\u9664\u53bb\u3068\u5206\u6790<\/p>\n\n\n\n<p>\u4fe1\u53f7\u306e\u30ce\u30a4\u30ba\u9664\u53bb\u3068\u5206\u6790\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u3082\u3046 1 \u3064\u306e\u6a5f\u80fd\u3067\u3059\u3002\u3053\u306e\u4f8b\u3067\u306f\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30b7\u30b0\u30ca\u30eb \u30e2\u30b8\u30e5\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u5358\u7d14\u306a\u30b7\u30b0\u30ca\u30eb\u306e\u30ce\u30a4\u30ba\u3092\u9664\u53bb\u3057\u3001\u30b9\u30da\u30af\u30c8\u30eb\u5206\u6790\u3092\u4f7f\u7528\u3057\u3066\u30b7\u30b0\u30ca\u30eb\u5206\u6790\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30ce\u30a4\u30ba\u3092\u542b\u3080\u4fe1\u53f7\u3092\u542b\u3080\u300csignal.txt\u300d\u3068\u3044\u3046\u30c7\u30fc\u30bf \u30d5\u30a1\u30a4\u30eb\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u4fe1\u53f7\u306e\u30ce\u30a4\u30ba\u3092\u9664\u53bb\u3057\u3001\u4fe1\u53f7\u5206\u6790\u306b\u30b9\u30da\u30af\u30c8\u30eb\u5206\u6790\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u793a\u3055\u308c\u307e\u3059:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">python\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\u3059\u308b<code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import signal\n\n# \u8bfb\u53d6\u6570\u636e\u6587\u4ef6\ndata = np.loadtxt('signal.txt')\n\n# \u4f7f\u7528\u4e2d\u503c\u6ee4\u6ce2\u8fdb\u884c\u53bb\u566a\nfiltered_data = signal.medfilt(data)\n\n# \u8ba1\u7b97\u529f\u7387\u8c31\u5bc6\u5ea6\nf, psd = signal.welch(filtered_data)\n\n# \u7ed8\u5236\u529f\u7387\u8c31\u5bc6\u5ea6\u56fe\u5f62\nplt.semilogy(f, psd)\nplt.xlabel('Frequency')\nplt.ylabel('Power Spectral Density')\nplt.title('Power Spectral Density')\nplt.show()\n<\/code><\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u6700\u521d\u306b np.loadtxt() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u30ce\u30a4\u30ba\u3092\u542b\u3080\u4fe1\u53f7\u3092\u542b\u3080\u300csignal.txt\u300d\u3068\u3044\u3046\u30c7\u30fc\u30bf \u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u53d6\u308a\u307e\u3059\u3002\u6b21\u306b\u3001scipy.signal \u30e2\u30b8\u30e5\u30fc\u30eb\u306e signal.medfilt() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3053\u306e\u4fe1\u53f7\u3092\u30e1\u30c7\u30a3\u30a2\u30f3 \u30d5\u30a3\u30eb\u30bf\u30fc\u51e6\u7406\u3057\u3001\u30ce\u30a4\u30ba\u3092\u9664\u53bb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001scipy.signal \u30e2\u30b8\u30e5\u30fc\u30eb\u306e signal.welch() \u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30d5\u30a3\u30eb\u30bf\u30fc\u51e6\u7406\u3055\u308c\u305f\u4fe1\u53f7\u306e\u30d1\u30ef\u30fc \u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u3092\u8a08\u7b97\u3057\u3001matplotlib \u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u3066\u30d1\u30ef\u30fc \u30b9\u30da\u30af\u30c8\u30eb\u5bc6\u5ea6\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u30b1\u30fc\u30b9\u304b\u3089\u3001Scipy \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u4fe1\u53f7\u51e6\u7406\u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u4fe1\u53f7\u306e\u30ce\u30a4\u30ba\u9664\u53bb\u3068\u5206\u6790\u3092\u7c21\u5358\u306b\u5b9f\u884c\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u4fe1\u53f7\u30c7\u30fc\u30bf\u306e\u7406\u89e3\u3068\u5206\u6790\u304c\u5411\u4e0a\u3057\u307e\u3059<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3082\u3089\u3048\u307e\u3059\u304b\u3002Scipy \u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2 &hellip; <\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[23],"tags":[],"class_list":["post-1947","post","type-post","status-publish","format-standard","hentry","category-material"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=\/wp\/v2\/posts\/1947","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1947"}],"version-history":[{"count":1,"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=\/wp\/v2\/posts\/1947\/revisions"}],"predecessor-version":[{"id":1949,"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=\/wp\/v2\/posts\/1947\/revisions\/1949"}],"wp:attachment":[{"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1947"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1947"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/edu.ujhb.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1947"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}