{"id":1935,"date":"2019-06-24T17:25:52","date_gmt":"2019-06-24T08:25:52","guid":{"rendered":"https:\/\/www.bi.appi.keio.ac.jp\/?p=1935"},"modified":"2024-08-20T18:18:25","modified_gmt":"2024-08-20T09:18:25","slug":"%e5%9b%ba%e6%9c%89%e5%80%a4%e3%83%bb%e5%9b%ba%e6%9c%89%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%a8%e8%a1%8c%e5%88%97%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/www.bi.appi.keio.ac.jp\/?p=1935","title":{"rendered":"\u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3068\u884c\u5217\u5fae\u5206\u65b9\u7a0b\u5f0f"},"content":{"rendered":"\n

Google Colaboratory\u304c\u91cd\u3044\u306e\u3067\u7d50\u679c\u3060\u3051\u8f09\u305b\u307e\u3059\uff0e<\/p>\n\n\n\n

$\\displaystyle\\frac{dx_1(t)}{dt} = x_2(t)$
$\\displaystyle\\frac{dx_2(t)}{dt}=x_1(t)$
\u3067\u56fa\u6709\u5024\u306e1\u3064\u304c\u6b63\u30671\u3064\u304c\u8ca0\u306e\u5834\u5408<\/p>\n\n\n\n

import numpy as np\nimport matplotlib.pyplot as plt\nimport numpy.linalg as LA\nimport random\n\nA = np.array([[0, 1], [1, 0]])\nw, v = LA.eig(A)\nprint('\u56fa\u6709\u5024')\nprint(w)\nprint('\u56fa\u6709\u30d9\u30af\u30c8\u30eb')\nprint(v)\nx10 = 4\nx20 = 2\nt = np.arange(0.0, 2.0, 0.1)\nx10 = [random.uniform(-10, 10) for i in range(300)]\nx20 = [random.uniform(-10, 10) for i in range(300)]\n\nN = 22\nx = np.linspace(-10,  10,  N)\ny = np.linspace(-10,  10,  N)\n(xm, ym) = np.meshgrid(x, y)\ndxdt = ym\ndydt = xm\nnorm = (np.sqrt(dxdt**2 + dydt**2))\ndxdt2 = dxdt\/norm\ndydt2 = dydt\/norm\nplt.figure(figsize=(5, 5))\nplt.quiver(xm, ym, dxdt2, dydt2, angles='xy', scale_units='xy', scale=1)\nplt.xlim([-10, 10])\nplt.ylim([-10, 10])\nplt.xlabel('x1')\nplt.ylabel('x2')\nplt.show()\n\n# \u89e3\u6790\u89e3\nplt.figure(figsize=(5, 5))\nfor i in range(300):\n  c = LA.solve(v, np.array([x10[i], x20[i]]))\n  xxa = c[0] * np.exp(w[0]*t) * v[:,0].reshape(2, 1) +c[1] * np.exp(w[1]*t) * v[:,1].reshape(2, 1)\n  plt.plot(xxa[0,:], xxa[1,:], color='blue', alpha=0.2)\nplt.xlim([-10, 10])\nplt.ylim([-10, 10])\nplt.xlabel('x1')\nplt.ylabel('x2')\nplt.show()<\/pre>\n\n\n\n
\u56fa\u6709\u5024\n[ 1. -1.]\n\u56fa\u6709\u30d9\u30af\u30c8\u30eb\n[[ 0.70710678 -0.70710678]\n [ 0.70710678  0.70710678]]<\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n
$\\displaystyle\\frac{dx_1(t)}{dt} = -x_2(t)$
$\\displaystyle\\frac{dx_2(t)}{dt}=-x_1(t)$
\u3067\u56fa\u6709\u5024\u306e1\u3064\u304c\u6b63\u30671\u3064\u304c\u8ca0\u306e\u5834\u5408<\/p>\n\n\n\n
\u56fa\u6709\u5024\n[ 1. -1.]\n\u56fa\u6709\u30d9\u30af\u30c8\u30eb\n[[ 0.70710678  0.70710678]\n [-0.70710678  0.70710678]]<\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
Google Colaboratory\u304c\u91cd\u3044\u306e\u3067\u7d50\u679c\u3060\u3051\u8f09\u305b\u307e\u3059\uff0e $\\displaystyle\\frac{dx_1(t)}{dt} = x_2(t)$$\\displaystyle\\frac{dx_2(t)}{dt}=x … “\u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3068\u884c\u5217\u5fae\u5206\u65b9\u7a0b\u5f0f” \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-1935","post","type-post","status-publish","format-standard","hentry","category-9"],"_links":{"self":[{"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/1935","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1935"}],"version-history":[{"count":21,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/1935\/revisions"}],"predecessor-version":[{"id":2257,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/1935\/revisions\/2257"}],"wp:attachment":[{"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1935"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1935"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1935"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}