{"id":1300,"date":"2017-09-09T13:33:13","date_gmt":"2017-09-09T04:33:13","guid":{"rendered":"http:\/\/www.python.ambitious-engineer.com\/?p=1300"},"modified":"2018-02-25T13:47:19","modified_gmt":"2018-02-25T04:47:19","slug":"%e5%9f%ba%e6%9c%ac%e7%9a%84%e3%81%aa%e7%b7%9a%e5%bd%a2%e4%bb%a3%e6%95%b0%e8%a8%88%e7%ae%97-%e3%81%9d%e3%81%ae4-%e5%9b%ba%e6%9c%89%e5%80%a4","status":"publish","type":"post","link":"https:\/\/www.python.ambitious-engineer.com\/archives\/1300","title":{"rendered":"NumPy\u5165\u9580 \u57fa\u672c\u7684\u306a\u7dda\u5f62\u4ee3\u6570\u8a08\u7b97 \u305d\u306e4 \u56fa\u6709\u5024"},"content":{"rendered":"<p><script async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.0\/MathJax.js?config=TeX-AMS_CHTML\"><\/script><\/p>\n<h2>\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb<\/h2>\n<h3>\u56fa\u6709\u5024\u306e\u5fa9\u7fd2<\/h3>\n<p>\u56fa\u6709\u5024\u306e\u5fa9\u7fd2\u304b\u3089\u3067\u3059\u3002<\/p>\n<p>\u4ee5\u4e0b\u306en\u6b21\u306e\u6b63\u65b9\u884c\u5217\\( A \\)\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u305f\u3068\u3057\u307e\u3059\u3002<br \/>\n\\[<br \/>\n A = \\left(<br \/>\n    \\begin{array}{llll}<br \/>\n      a_{11} & a_{12} & \u2026 & a_{1n} \\\\<br \/>\n      a_{21} & a_{22} & \u2026 & a_{2n} \\\\<br \/>\n      : & : & \u2026 & : \\\\<br \/>\n      a_{n1} & a_{n2} & \u2026 & a_{nn}<br \/>\n    \\end{array}<br \/>\n  \\right)<br \/>\n\\]\n<p>\u3053\u306e\u884c\u5217\u306b\u5bfe\u3057\u3001<br \/>\n\\[<br \/>\nAx = \\lambda x<br \/>\n\\]\n\u3068\u306a\u308b\\( x \\neq 0 \\)\u304c\u5b58\u5728\u3059\u308b\u6642\u3001\\(\\lambda\\)\u3092\\( A \\)\u306e\u56fa\u6709\u5024\u3068\u547c\u3073\u307e\u3059\u3002\u307e\u305f\u3001\\( x \\)\u3092\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n<p>\u56fa\u6709\u5024\u3092\u81ea\u529b\u3067\u8a08\u7b97\u3059\u308b\u306b\u306f\u56fa\u6709\u65b9\u7a0b\u5f0f\u306e\u89e3\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u304c\u3001Numpy\u3067\u306flinalg.eig\u3067\u7b97\u51fa\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h3>linalg.eig<\/h3>\n<p>\u3067\u306f\u3055\u3063\u305d\u304f\u4f7f\u3063\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u4eca\u56de\u306f\u30b5\u30f3\u30d7\u30eb\u3068\u3057\u3066\u3001\uff13\u884c\uff13\u5217\u306e\u884c\u5217\u3092\u4f7f\u7528\u3057\u3066\u307f\u307e\u3059\u3002\u623b\u308a\u5024\u306fw\u3001v\u306e\uff12\u3064\u3067\u305d\u308c\u305e\u308c\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<pre class=\"brush: python; title: ; notranslate\" title=\"\">\r\nimport numpy as np\r\na = np.array([[2, 1, 1],[1, 2, 1],[1, 1, 2]])\r\n# array([[2, 1, 1],\r\n#        [1, 2, 1],\r\n#        [1, 1, 2]])\r\n\r\nw, v = np.linalg.eig(a)\r\nw\r\n# array([ 1.,  4.,  1.])\r\n\r\nv\r\n# array([[-0.81649658,  0.57735027,  0.381008  ],\r\n#        [ 0.40824829,  0.57735027, -0.81590361],\r\n#        [ 0.40824829,  0.57735027,  0.43489561]])\r\n# \r\n\r\n<\/pre>\n<p>\u56fa\u6709\u65b9\u7a0b\u5f0f\u304c\u91cd\u89e3\u3092\u6301\u3064\u5834\u5408\u3067\u3082\u3001linalg.eig\u306e\u623b\u308a\u5024\u306f\u91cd\u8907\u3057\u305f\u5024\u3092\u8fd4\u3059\u3068\u3044\u3046\u70b9\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4e0a\u306e\u884c\u5217\u306e\u56fa\u6709\u5024\u65b9\u7a0b\u5f0f\u306f\u3001\\( (\\lambda - 1)^2(\\lambda - 4) = 0 \\)\u30671\u306f\u91cd\u89e3\u3067\u3059\u304c\u3001w\u30671\u304c\uff12\u3064\u8fd4\u3055\u308c\u3066\u3044\u307e\u3059\u3002v\u3067w\u306e\u6dfb\u5b57\u306b\u5bfe\u5fdc\u3057\u305f\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u304c\u8fd4\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u691c\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u307e\u305a\u306f\u56fa\u6709\u5024\u304c\uff11\u306e\u5834\u5408\u3067\u3059\u3002\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306f\u4ee5\u4e0b\u306e\u5e73\u9762\u3068\u306a\u308a\u307e\u3059\u3002\uff08s\u3001t\u306f\u4efb\u610f\u306e\u6570\u3068\u3057\u307e\u3059\u3002\uff09<\/p>\n<p>\\[<br \/>\nx = s \\left(<br \/>\n    \\begin{array}{l}<br \/>\n      -0.81649658 \\\\<br \/>\n      0.40824829 \\\\<br \/>\n      0.40824829<br \/>\n    \\end{array}<br \/>\n  \\right)<br \/>\n  +<br \/>\n  t \\left(<br \/>\n    \\begin{array}{l}<br \/>\n      0.381008 \\\\<br \/>\n      -0.81590361 \\\\<br \/>\n      0.43489561<br \/>\n    \\end{array}<br \/>\n  \\right)<br \/>\n\\]\n<p>\u691c\u7b97\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<pre class=\"brush: python; title: ; notranslate\" title=\"\">\r\nl = w[0] # \u56fa\u6709\u50241\r\nx = np.array([v[:, 0], v[:, 2]]).T # \u56fa\u6709\u30d9\u30af\u30c8\u30eb\r\n\r\nnp.dot(a, x)\r\n# array([[-0.81649658,  0.381008  ],\r\n#        [ 0.40824829, -0.81590361],\r\n#        [ 0.40824829,  0.43489561]])\r\n\r\nl * x\r\n# array([[-0.81649658,  0.381008  ],\r\n#        [ 0.40824829, -0.81590361],\r\n#        [ 0.40824829,  0.43489561]])\r\n\r\n<\/pre>\n<p>\u5143\u306e\u884c\u5217\u3068\u56fa\u6709\u5024\u3001\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306e\u95a2\u4fc2\u304c\u793a\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n<p>\u6b21\u306b\u56fa\u6709\u5024\u304c4\u306e\u5834\u5408\u3067\u3059\u3002\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n<p>\\[<br \/>\n  x = t \\left(<br \/>\n    \\begin{array}{l}<br \/>\n      0.57735027 \\\\<br \/>\n      0.57735027 \\\\<br \/>\n      0.57735027<br \/>\n    \\end{array}<br \/>\n  \\right)<br \/>\n\\]\n<p>\u691c\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<pre class=\"brush: python; title: ; notranslate\" title=\"\">\r\nl = w[1] # \u56fa\u6709\u50244\r\nx = np.array([v[:, 1]]).T # \u56fa\u6709\u30d9\u30af\u30c8\u30eb\r\n\r\nnp.dot(a, x)\r\n# array([[ 2.30940108],\r\n#        [ 2.30940108],\r\n#        [ 2.30940108]])\r\n\r\nl * x\r\n# array([[ 2.30940108],\r\n#        [ 2.30940108],\r\n#        [ 2.30940108]])\r\n# \r\n<\/pre>\n<p>\u3053\u3061\u3089\u3082\u3084\u306f\u308a\u5143\u306e\u884c\u5217\u3068\u56fa\u6709\u5024\u3001\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306e\u95a2\u4fc2\u304c\u793a\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n<h2>\u88dc\u8db3<\/h2>\n<p>\u4e0a\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u624b\u3067\u8a08\u7b97\u3059\u308b\u3068\u30b7\u30f3\u30d7\u30eb\u306b\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff08\u3082\u3061\u308d\u3093\u8a08\u7b97\u65b9\u6cd5\u306b\u4f9d\u5b58\u3057\u307e\u3059\u304c\uff09\u3002<\/p>\n<p>\u56fa\u6709\u65b9\u7a0b\u5f0f<br \/>\n\\[<br \/>\n(\\lambda - 1)^2 (\\lambda - 4) = 0<br \/>\n\\]\n\u4e0a\u3092\u89e3\u304f\u3068<br \/>\n\\[<br \/>\n\\lambda = 1, 4<br \/>\n\\]\n<p>\\( \\lambda = 1 \\)\u306e\u5834\u5408\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb<\/p>\n<p>\\[<br \/>\nx = s \\left(<br \/>\n    \\begin{array}{l}<br \/>\n      -1 \\\\<br \/>\n      1 \\\\<br \/>\n      0<br \/>\n    \\end{array}<br \/>\n  \\right)<br \/>\n  +<br \/>\n  t \\left(<br \/>\n    \\begin{array}{l}<br \/>\n      -1 \\\\<br \/>\n      0 \\\\<br \/>\n      1<br \/>\n    \\end{array}<br \/>\n  \\right)<br \/>\n\\]\n<p>\\( \\lambda = 4 \\)\u306e\u5834\u5408\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb<\/p>\n<p>\\[<br \/>\nx = t \\left(<br \/>\n    \\begin{array}{l}<br \/>\n      1 \\\\<br \/>\n      1 \\\\<br \/>\n      1<br \/>\n    \\end{array}<br \/>\n  \\right)<br \/>\n\\]\n<p>\u30e6\u30cb\u30fc\u30af\u3067\u306f\u306a\u3044\u305f\u3081\u5f53\u7136\u3068\u3044\u3048\u3070\u5f53\u7136\u3067\u3059\u304c\u3001\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u304c\u6559\u79d1\u66f8\u901a\u308a\u306e\u5024\u3068\u306f\u7570\u306a\u308b\u70b9\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb \u56fa\u6709\u5024\u306e\u5fa9\u7fd2 \u56fa\u6709\u5024\u306e\u5fa9\u7fd2\u304b\u3089\u3067\u3059\u3002 \u4ee5\u4e0b\u306en\u6b21\u306e\u6b63\u65b9\u884c\u5217\\( A \\)\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u305f\u3068\u3057\u307e\u3059\u3002 \\[ A = \\left( \\begin{array}{llll} a_{11} &#038; a_{12}...<\/p>\n","protected":false},"author":1,"featured_media":1607,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[168],"tags":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.python.ambitious-engineer.com\/wp-json\/wp\/v2\/posts\/1300"}],"collection":[{"href":"https:\/\/www.python.ambitious-engineer.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.python.ambitious-engineer.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.python.ambitious-engineer.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.python.ambitious-engineer.com\/wp-json\/wp\/v2\/comments?post=1300"}],"version-history":[{"count":19,"href":"https:\/\/www.python.ambitious-engineer.com\/wp-json\/wp\/v2\/posts\/1300\/revisions"}],"predecessor-version":[{"id":3514,"href":"https:\/\/www.python.ambitious-engineer.com\/wp-json\/wp\/v2\/posts\/1300\/revisions\/3514"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.python.ambitious-engineer.com\/wp-json\/wp\/v2\/media\/1607"}],"wp:attachment":[{"href":"https:\/\/www.python.ambitious-engineer.com\/wp-json\/wp\/v2\/media?parent=1300"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.python.ambitious-engineer.com\/wp-json\/wp\/v2\/categories?post=1300"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.python.ambitious-engineer.com\/wp-json\/wp\/v2\/tags?post=1300"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}