{"id":5016,"date":"2025-01-21T12:00:09","date_gmt":"2025-01-21T03:00:09","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=5016"},"modified":"2025-01-23T10:19:33","modified_gmt":"2025-01-23T01:19:33","slug":"scipy-%e3%81%a7%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/scipy-%e3%81%a7%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81\/","title":{"rendered":"SciPy \u3066\u3099\u5358\u632f\u308a\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u304b\u3089\u5468\u671f\u3092\u6c42\u3081\u308b"},"content":{"rendered":"<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u304b\u3089\u5f97\u3089\u308c\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u304b\u3089\uff0cPython \u306e SciPy \u3068 NumPy \u3092\u4f7f\u3063\u3066\uff08\u304b\u3064 SymPy \u306f\u4f7f\u308f\u305a\u306b\uff09\u6570\u5024\u7a4d\u5206\u306b\u3088\u3063\u3066\u5468\u671f\u3092\u6c42\u3081\u308b\u3002\u5c0e\u51fa\u306b\u3064\u3044\u3066\u306f\u4ee5\u4e0b\u3092\u53c2\u7167\uff1a<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/\">\u5358\u632f\u308a\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u304b\u3089\u5468\u671f\u3092\u6c42\u3081\u308b\u6e96\u5099<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<p><!--more--><\/p>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u30e9\u30a4\u30d6\u30e9\u30ea\u306e-import\">\u30e9\u30a4\u30d6\u30e9\u30ea\u306e import<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># NumPy \u3082\u4f7f\u3044\u307e\u3059<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">numpy<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">np<\/span>\r\n\r\n<span class=\"c1\"># \u6570\u5024\u7a4d\u5206 scipy.integrate.quad()<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">scipy.integrate<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">quad<\/span>\r\n\r\n<span class=\"c1\"># \u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206 K(m)<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">scipy.special<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">ellipk<\/span>\r\n\r\n<span class=\"c1\"># Matplotlib \u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">matplotlib.pyplot<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">plt<\/span>\r\n\r\n<span class=\"c1\"># \u4ee5\u4e0b\u306f\u30b0\u30e9\u30d5\u3092 SVG \u3067 Notebook \u306b\u30a4\u30f3\u30e9\u30a4\u30f3\u8868\u793a\u3055\u305b\u308b\u8a2d\u5b9a<\/span>\r\n<span class=\"o\">%<\/span><span class=\"k\">config<\/span> InlineBackend.figure_formats = ['svg']\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5e73\u65b9\u6839\u3084\u4e09\u89d2\u95a2\u6570\u306a\u3069\u306f NumPy \u306e\u95a2\u6570 <code>np.sqrt()<\/code>\uff0c<code>np.cos()<\/code>\uff0c<code>np.sin()<\/code> \u306a\u3069\u3092\u4f7f\u3044\u307e\u3059\u3002<code>scipy.integrate.quad()<\/code> \u306b\u3064\u3044\u3066\u306f\u6388\u696d\u3067\u7c21\u5358\u306a\u8aac\u660e\u3092\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/python-%e3%81%a7%e6%95%b0%e5%80%a4%e8%a7%a3%e6%9e%90\/python-%e3%81%ae-scipy-%e3%81%a7%e6%95%b0%e5%80%a4%e8%a7%a3%e6%9e%90\/#SciPy-2\">SciPy \u306b\u3088\u308b\u6570\u5024\u7a4d\u5206<\/a><\/li>\n<\/ul>\n<p>\u6570\u5024\u8a08\u7b97\u306b\u9650\u308b\u3053\u3068\u306b\u3057\uff0cSymPy \u306e\u95a2\u6570\u3092\u6df7\u5728\u3055\u305b\u306a\u3044\u3053\u3068\u306b\u3057\u3066\uff0cNumPy \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570\u3084\u5b9a\u6570\u306e\u307f\u3092\u4f7f\u3046\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"SciPy-\u306e-quad()-\u3067\u6570\u5024\u7a4d\u5206\u3059\u308b\">SciPy \u306e <code>quad()<\/code> \u3067\u6570\u5024\u7a4d\u5206\u3059\u308b<\/h3>\n<p>\u632f\u5e45 $\\theta_0$ \u306e\u5358\u632f\u308a\u5b50\u306e\u5468\u671f $T_p$ \u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\nT_p(\\theta_0) &amp;=&amp;<br \/>\n\\frac{2}{\\pi} \\int_{0}^{\\theta_0} \\frac{1}{\\sqrt{2(\\cos\\theta-\\cos\\theta_0)}}d\\theta \\\\<br \/>\n&amp;=&amp;<br \/>\n\\frac{\\sqrt{2}}{\\pi} \\int_{0}^{\\theta_0} \\frac{1}{\\sqrt{\\cos\\theta-\\cos\\theta_0}}d\\theta<br \/>\n\\end{eqnarray}<\/p>\n<p>\u7a4d\u5206\u90e8\u5206\u306f\u6570\u5024\u7a4d\u5206 <code>scipy.integrate.quad()<\/code> \u3092\u4f7f\u3046\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$\\theta = \\theta_0$ \u3067\u88ab\u7a4d\u5206\u95a2\u6570\u306e\u5206\u6bcd\u306f\u30bc\u30ed\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u306e\u3067\uff0c\u4f55\u304b\u30a8\u30e9\u30fc\u3067\u3082\u8d77\u3053\u308b\u306e\u304b\u3068\u601d\u3044\u304d\u3084\uff0c<code>scipy.integrate.quad()<\/code> \u306f\u5927\u5909\u512a\u79c0\u3067\u4f55\u4e8b\u3082\u306a\u304b\u3063\u305f\u304b\u306e\u3088\u3046\u306b\u6570\u5024\u7a4d\u5206\u3057\u3066\u3057\u307e\u3044\u307e\u3059\uff01<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><code>quad()<\/code> \u306f (<strong>\u7a4d\u5206\u306e\u8fd1\u4f3c<\/strong>, <strong>\u898b\u7a4d\u3082\u3089\u308c\u305f\u8fd1\u4f3c\u306e\u7d76\u5bfe\u8aa4\u5dee<\/strong>) \u306e2\u3064\u306e\u6570\u5024\u3092\u8fd4\u3057\u307e\u3059\u3002<\/p>\n<h4 id=\"SciPy-\u306e-quad()-\u3067-Tp1(th0)\">SciPy \u306e <code>quad()<\/code> \u3067 <code>Tp1(th0)<\/code><\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u88ab\u7a4d\u5206\u95a2\u6570\u306e\u5b9a\u7fa9<\/span>\r\n<span class=\"c1\"># quad() \u3092\u4f7f\u3046\u5834\u5408\u306f\u7a4d\u5206\u5909\u6570\u540d\u306f x \u6c7a\u3081\u6253\u3061<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">f1<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta0<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">pi<\/span><span class=\"o\">*<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">-<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">theta0<\/span><span class=\"p\">)))<\/span>\r\n\r\n<span class=\"c1\"># \u5468\u671f Tp1(theta0) \u306e\u5b9a\u7fa9<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">Tp1<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"sd\">\"\"\"\u5ea6\u3067\u4e0e\u3048\u3089\u308c\u305f\u632f\u5e45 th \u304b\u3089<\/span>\r\n<span class=\"sd\">       \u898f\u683c\u5316\u3055\u308c\u305f\u5358\u632f\u308a\u5b50\u306e\u898f\u683c\u5316\u3055\u308c\u305f\u5468\u671f\u3092\u6c42\u3081\u308b\"\"\"<\/span>\r\n    <span class=\"c1\"># \u5ea6\u3067\u4e0e\u3048\u3089\u308c\u305f th \u304b\u3089\u30e9\u30b8\u30a2\u30f3\u3078\u5909\u63db<\/span>\r\n    <span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">radians<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">ans<\/span> <span class=\"o\">=<\/span> <span class=\"n\">quad<\/span><span class=\"p\">(<\/span><span class=\"n\">f1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta0<\/span><span class=\"p\">,<\/span> <span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"n\">theta0<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"c1\"># <\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">ans<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30bb\u30eb\u306e\u5148\u982d\u306b <code>%%time<\/code> \u3092\u66f8\u304f\u3068\uff0c\u30bb\u30eb\u306e\u5b9f\u884c\uff08\u8a08\u7b97\uff09\u306b\u304b\u304b\u3063\u305f\u6642\u9593\u3092\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span> \r\n\r\n<span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">radians<\/span><span class=\"p\">(<\/span><span class=\"mi\">80<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">quad<\/span><span class=\"p\">(<\/span><span class=\"n\">f1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta0<\/span><span class=\"p\">,<\/span> <span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"n\">theta0<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 762 \u00b5s, sys: 656 \u00b5s, total: 1.42 ms\r\nWall time: 1.42 ms\r\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[3]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>(1.137492559922196, 7.409517444045832e-11)<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\uff08SymPy \u306e\u95a2\u6570\u3067\u5b9a\u7fa9\u3057\u305f\u5834\u5408\u3068\u304f\u3089\u3079\u3066\uff09\u5727\u5012\u7684\u306b\u77ed\u3044\u6642\u9593\u3067\u8a08\u7b97\u3057\u3066\u304f\u308c\u307e\u3059\u3002\u305f\u3060\u3057\uff0c\u3053\u306e\u307e\u307e\u3060\u3068\uff0c\uff08\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u7aef\u70b9\u3067\u767a\u6563\u3059\u308b\u3068\u3044\u3046\u554f\u984c\u3082\u3042\u308a\uff09\u8aa4\u5dee\u304c $10^{-11}$ \u7a0b\u5ea6\u3042\u308a\u307e\u3059\u3002<\/p>\n<p><code>quad()<\/code> \u306e\u7cbe\u5ea6\u306b\u95a2\u3059\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u306f <code>epsabs<\/code> \u3068 <code>epsrel<\/code> \u3067\u3059\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a2d\u5b9a\u3057\u3066\u307f\u308b\u3068&#8230;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span> \r\n\r\n<span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">radians<\/span><span class=\"p\">(<\/span><span class=\"mi\">80<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">quad<\/span><span class=\"p\">(<\/span><span class=\"n\">f1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta0<\/span><span class=\"p\">,<\/span> <span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"n\">theta0<\/span><span class=\"p\">,<\/span> <span class=\"n\">epsabs<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1e-12<\/span><span class=\"p\">,<\/span> <span class=\"n\">epsrel<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1e-12<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 2.4 ms, sys: 0 ns, total: 2.4 ms\r\nWall time: 2.4 ms\r\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[4]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>(1.1374925599236223, 1.106226221736506e-12)<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u7d76\u5bfe\u8aa4\u5dee\u306f\u5c0f\u3055\u304f\u306a\u308a\u307e\u3059\u304c\uff0c<code>theta0<\/code> \u306e\u5024\u306b\u3088\u3063\u3066\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u8b66\u544a\u304c\u51fa\u308b\u3088\u3046\u306a\u306e\u3067\uff0c\u3042\u307e\u308a\u3044\u3058\u3089\u306a\u3044\u3053\u3068\u306b\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span> \r\n\r\n<span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">radians<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">quad<\/span><span class=\"p\">(<\/span><span class=\"n\">f1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta0<\/span><span class=\"p\">,<\/span> <span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"n\">theta0<\/span><span class=\"p\">,<\/span> <span class=\"n\">epsabs<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1e-12<\/span><span class=\"p\">,<\/span> <span class=\"n\">epsrel<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1e-12<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 4.88 ms, sys: 748 \u00b5s, total: 5.63 ms\r\nWall time: 5.52 ms\r\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stderr output_text\">\n<pre>&lt;timed exec&gt;:2: IntegrationWarning: The algorithm does not converge.  Roundoff error is detected\r\n  in the extrapolation table.  It is assumed that the requested tolerance\r\n  cannot be achieved, and that the returned result (if full_output = 1) is \r\n  the best which can be obtained.\r\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[5]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>(1.000019039198938, 3.466740692258108e-10)<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u632f\u5e45<\/span>\r\n<span class=\"n\">th0s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">+<\/span> <span class=\"p\">[<\/span><span class=\"mi\">10<\/span><span class=\"o\">*<\/span><span class=\"n\">i<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span><span class=\"mi\">10<\/span><span class=\"p\">)]<\/span>\r\n<span class=\"c1\"># \u5468\u671f<\/span>\r\n<span class=\"n\">Tp1s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n<span class=\"c1\"># \u5404\u632f\u5e45\u3054\u3068\u306e\u5468\u671f<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th0<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">th0s<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"n\">Tp1s<\/span> <span class=\"o\">+=<\/span> <span class=\"p\">[<\/span><span class=\"n\">Tp1<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)]<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'\u03b8_0 = <\/span><span class=\"si\">%2d<\/span><span class=\"s1\">\u00b0 \u306e\u3068\u304d\uff0c'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">th0<\/span><span class=\"p\">,<\/span> <span class=\"n\">end<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">''<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'\u5468\u671f T = <\/span><span class=\"si\">%10.8f<\/span><span class=\"s1\">'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">Tp1s<\/span><span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>\u03b8_0 =  1\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.00001904\r\n\u03b8_0 = 10\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.00190719\r\n\u03b8_0 = 20\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.00766903\r\n\u03b8_0 = 30\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.01740880\r\n\u03b8_0 = 40\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.03134052\r\n\u03b8_0 = 50\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.04978296\r\n\u03b8_0 = 60\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.07318201\r\n\u03b8_0 = 70\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.10214491\r\n\u03b8_0 = 80\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.13749256\r\n\u03b8_0 = 90\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.18034060\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"Tp1(th0)-\u306e\u30b0\u30e9\u30d5\uff1aax-\u7de8\"><code>Tp1(th0)<\/code> \u306e\u30b0\u30e9\u30d5\uff1aax \u7de8<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><code>ax.***<\/code> \u306e\u307f\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002<\/p>\n<p>Python \u306e Matplotlib \u306b\u3088\u308b\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u306f\uff0c<code>plt.***<\/code> \u3068\u3044\u3046\u95a2\u6570\u306e\u307f\u3092\u4f7f\u3063\u305f <strong>plt (pyplot) \u6d41<\/strong>\uff08pyplot \u30a4\u30f3\u30bf\u30fc\u30d5\u30a7\u30fc\u30b9\u3068\u3082\uff09\u3068\uff0c<code>ax.***<\/code> \u3068\u3044\u3046\u95a2\u6570\u306e\u307f\u3092\u4f7f\u3063\u305f <strong>ax \u6d41<\/strong>\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u6307\u5411\u30a4\u30f3\u30bf\u30fc\u30d5\u30a7\u30fc\u30b9\u3068\u3082\uff09\u306e2\u3064\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p><code>ax.***<\/code> \u306e\u307f\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u3059\u308b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u306b\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/python-%e3%81%a7%e3%82%b0%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90\/matplotlib-%e3%81%a7%e3%82%b0%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90%ef%bc%9aax-%e7%b7%a8\/\">Matplotlib \u3067\u30b0\u30e9\u30d5\u4f5c\u6210\uff1aax \u7de8<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># ax \u3092\u4f7f\u3046\u969b\u306e\u6700\u521d\u306e\u304a\u307e\u3058\u306a\u3044<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u306b\u632f\u5e45 th0s, \u7e26\u8ef8\u306b\u5468\u671f Tp1s<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">scatter<\/span><span class=\"p\">(<\/span><span class=\"n\">th0s<\/span><span class=\"p\">,<\/span> <span class=\"n\">Tp1s<\/span><span class=\"p\">,<\/span> <span class=\"n\">s<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u5358\u632f\u308a\u5b50\u306e\u632f\u5e45\u3068\u5468\u671f\"<\/span><span class=\"p\">);<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u632f\u5e45 \u03b8 (\u00b0)\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u5468\u671f T\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlim<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">91<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.98<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.2<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">(<\/span><span class=\"nb\">list<\/span><span class=\"p\">(<\/span><span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span><span class=\"mi\">91<\/span><span class=\"p\">,<\/span><span class=\"mi\">10<\/span><span class=\"p\">)))<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-10036\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/axPFURI-01.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"Tp1(th0)-\u306e\u30b0\u30e9\u30d5\uff1aplt-\u7de8\"><code>Tp1(th0)<\/code> \u306e\u30b0\u30e9\u30d5\uff1aplt \u7de8<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><code>plt.***<\/code> \u306e\u307f\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002<\/p>\n<p>Python \u306e Matplotlib \u306b\u3088\u308b\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u306f\uff0c<code>plt.***<\/code> \u3068\u3044\u3046\u95a2\u6570\u306e\u307f\u3092\u4f7f\u3063\u305f <strong>plt (pyplot) \u6d41<\/strong>\uff08pyplot \u30a4\u30f3\u30bf\u30fc\u30d5\u30a7\u30fc\u30b9\u3068\u3082\uff09\u3068\uff0c<code>ax.***<\/code> \u3068\u3044\u3046\u95a2\u6570\u306e\u307f\u3092\u4f7f\u3063\u305f <strong>ax \u6d41<\/strong>\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u6307\u5411\u30a4\u30f3\u30bf\u30fc\u30d5\u30a7\u30fc\u30b9\u3068\u3082\uff09\u306e2\u3064\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p><code>plt.***<\/code> \u306e\u307f\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u3059\u308b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u306b\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/python-%e3%81%a7%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/matplotlib-%e3%81%a7%e3%82%b0%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90\/\">Matplotlib \u3067\u30b0\u30e9\u30d5\u4f5c\u6210\uff1aplt \u7de8<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u6a2a\u8ef8\u306b\u632f\u5e45 th0s, \u7e26\u8ef8\u306b\u5468\u671f Tp1s<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">scatter<\/span><span class=\"p\">(<\/span><span class=\"n\">th0s<\/span><span class=\"p\">,<\/span> <span class=\"n\">Tp1s<\/span><span class=\"p\">,<\/span> <span class=\"n\">s<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u5358\u632f\u308a\u5b50\u306e\u632f\u5e45\u3068\u5468\u671f\"<\/span><span class=\"p\">);<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u632f\u5e45 \u03b8 (\u00b0)\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u5468\u671f T\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlim<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">91<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">ylim<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.98<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.2<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xticks<\/span><span class=\"p\">(<\/span><span class=\"nb\">list<\/span><span class=\"p\">(<\/span><span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span><span class=\"mi\">91<\/span><span class=\"p\">,<\/span><span class=\"mi\">10<\/span><span class=\"p\">)))<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-10037\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/pltPFURI-01.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u767a\u6563\u3057\u306a\u3044\u3088\u3046\u306b\u5909\u6570\u5909\u63db\u3057\u3066\u7f6e\u63db\u7a4d\u5206\">\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u767a\u6563\u3057\u306a\u3044\u3088\u3046\u306b\u5909\u6570\u5909\u63db\u3057\u3066\u7f6e\u63db\u7a4d\u5206<\/h3>\n<p><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/#1\">\u3053\u306e\u3078\u3093<\/a>\u306b\u307e\u3068\u3081\u3066\u3044\u308b\u3088\u3046\u306b\uff0c\u5909\u6570\u5909\u63db\u306b\u3088\u3063\u3066<br \/>\n\\begin{eqnarray}<br \/>\n\\int_0^{\\theta_0} \\frac{1}{\\sqrt{2(\\cos\\theta-\\cos\\theta_0)}} d\\theta<br \/>\n&amp;=&amp;<br \/>\n\\int_0^{\\pi\/2} \\frac{dt}{\\sqrt{1 -k^2 \\sin^2 t}}, \\\\ \\quad k &amp;\\equiv&amp; \\sin\\frac{\\theta_0}{2}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u66f8\u3051\u308b\u3002\u3053\u306e\u5f62\u306b\u3059\u308b\u3068\uff0c\u7a4d\u5206\u7bc4\u56f2\u5185\u3067\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u767a\u6563\u3059\u308b\u3053\u3068\u3082\u306a\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"SciPy-\u306e-quad()-\u3067-Tp2(th0)\">SciPy \u306e <code>quad()<\/code> \u3067 <code>Tp2(th0)<\/code><\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u88ab\u7a4d\u5206\u95a2\u6570\u306e\u5b9a\u7fa9<\/span>\r\n<span class=\"c1\"># quad() \u3092\u4f7f\u3046\u5834\u5408\u306f\u7a4d\u5206\u5909\u6570\u540d\u306f x \u6c7a\u3081\u6253\u3061<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">f2<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta0<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">k<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">theta0<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"mi\">2<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">pi<\/span> <span class=\"o\">*<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">k<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"k\">def<\/span> <span class=\"nf\">Tp2<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">radians<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">ans<\/span> <span class=\"o\">=<\/span> <span class=\"n\">quad<\/span><span class=\"p\">(<\/span><span class=\"n\">f2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"n\">theta0<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"c1\"># \u7a4d\u5206\u5024\u306e\u307f\u3092 ans[0] \u3092\u304b\u3048\u3059<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">ans<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">radians<\/span><span class=\"p\">(<\/span><span class=\"mi\">80<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">quad<\/span><span class=\"p\">(<\/span><span class=\"n\">f2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"n\">theta0<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 166 \u00b5s, sys: 0 ns, total: 166 \u00b5s\r\nWall time: 171 \u00b5s\r\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[10]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>(1.137492559923922, 1.3208745240142514e-13)<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u767a\u6563\u3057\u306a\u3044\u3088\u3046\u306b\u5909\u6570\u5909\u63db\u3057\u3066\u304b\u3089 <code>quad()<\/code> \u3067\u6570\u5024\u7a4d\u5206\u3059\u308b\u3068\uff0c\u8aa4\u5dee\u304c\u5c0f\u3055\u304f\uff0c\u3088\u308a\u77ed\u6642\u9593\u3067\u5b9f\u884c\u3057\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206\u3092\u4f7f\u3046\">\u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206\u3092\u4f7f\u3046<\/h3>\n<p><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/#1\">\u3053\u306e\u3078\u3093<\/a>\u306b\u307e\u3068\u3081\u3066\u3044\u308b\u3088\u3046\u306b\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206<\/strong><\/span> $K(k)$ \u3092\u4f7f\u3046\u3068\uff0c\u632f\u5e45 $\\theta_0$ \u306e\u5358\u632f\u308a\u5b50\u306e\u5468\u671f $T_p$ \u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\nT_p(\\theta_0) &amp;=&amp;<br \/>\n\\frac{2}{\\pi} \\int_{0}^{\\theta_0} \\frac{1}{\\sqrt{2(\\cos\\theta-\\cos\\theta_0)}}d\\theta \\\\<br \/>\n&amp;=&amp; \\frac{2}{\\pi} K(k) \\\\<br \/>\n&amp;\\equiv&amp; \\frac{2}{\\pi}\\int_0^{\\pi\/2} \\frac{dt}{\\sqrt{1-k^2 \\sin^2 t}}, \\quad k \\equiv \\sin\\frac{\\theta_0}{2}<br \/>\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"SciPy-\u306e-ellipk(m)-\u3067-Tp3(th0)\">SciPy \u306e <code>ellipk(m)<\/code> \u3067 <code>Tp3(th0)<\/code><\/h4>\n<p>\u3042\u308a\u304c\u305f\u3044\u3053\u3068\u306b\uff0cSciPy \u3067\u306f<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206<\/strong><\/span>\u304c\u4f7f\u3048\u308b\u3002 \u30de\u30cb\u30e5\u30a2\u30eb\u306f\u4ee5\u4e0b\u3092\u53c2\u7167\uff1a<\/p>\n<ul>\n<li><a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.special.ellipk.html\">scipy.special.ellipk &#8211; SciPy Manual<\/a><\/li>\n<\/ul>\n<p><code>ellipk(m)<\/code> $\\displaystyle = K(m) \\equiv \\int_0^{\\frac{\\pi}{2}}\\frac{1}{\\sqrt{1 -m \\sin^2 x}} dx$\u3002$m \\equiv k^2$ \u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3002<\/p>\n<p><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206<\/strong><\/span> <code>scipy.special.ellipk(m)<\/code> \u3092\u4f7f\u3063\u3066\uff0c\u632f\u5e45 $\\theta_0$ \u306e\u5358\u632f\u308a\u5b50\u306e\u5468\u671f $T_p$ \u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3059\u308b\u3002\uff08$m = k^2$ \u306b\u6ce8\u610f\u3002\uff09<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[11]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"k\">def<\/span> <span class=\"nf\">Tp3<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">radians<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">m<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">theta0<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"mi\">2<\/span><span class=\"o\">\/<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">pi<\/span><span class=\"o\">*<\/span><span class=\"n\">ellipk<\/span><span class=\"p\">(<\/span><span class=\"n\">m<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">Tp3<\/span><span class=\"p\">(<\/span><span class=\"mi\">80<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 32 \u00b5s, sys: 23 \u00b5s, total: 55 \u00b5s\r\nWall time: 60.8 \u00b5s\r\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[12]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>1.137492559923922<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u25cb\u7df4\u7fd2\uff1a\u8aa4\u5dee\u3068\u8a08\u7b97\u6642\u9593\u306e\u8a55\u4fa1\">\u25cb\u7df4\u7fd2\uff1a\u8aa4\u5dee\u3068\u8a08\u7b97\u6642\u9593\u306e\u8a55\u4fa1<\/h3>\n<p><code>Tp1(th0)<\/code>, <code>Tp2(th0)<\/code>, <code>Tp3(th0)<\/code>\u306e\u8aa4\u5dee\u304a\u3088\u3073\u8a08\u7b97\u6642\u9593\u3092\u8abf\u3079\u308b\u3002<\/p>\n<p><code>th0 = 80<\/code> \u306e\u5834\u5408\u306b\u306f\u3059\u3067\u306b\u51fa\u3057\u3066\u3044\u308b\u3002\u4ed6\u306e\u89d2\u5ea6\u306b\u3064\u3044\u3066\u3082\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[13]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">Tp1s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th0<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">th0s<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"n\">Tp1s<\/span> <span class=\"o\">+=<\/span> <span class=\"p\">[<\/span><span class=\"n\">Tp1<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 12.5 ms, sys: 367 \u00b5s, total: 12.9 ms\r\nWall time: 12.6 ms\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[14]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">Tp2s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th0<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">th0s<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"n\">Tp2s<\/span> <span class=\"o\">+=<\/span> <span class=\"p\">[<\/span><span class=\"n\">Tp2<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 472 \u00b5s, sys: 337 \u00b5s, total: 809 \u00b5s\r\nWall time: 813 \u00b5s\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[15]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">Tp3s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th0<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">th0s<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"n\">Tp3s<\/span> <span class=\"o\">+=<\/span> <span class=\"p\">[<\/span><span class=\"n\">Tp3<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 40 \u00b5s, sys: 29 \u00b5s, total: 69 \u00b5s\r\nWall time: 72 \u00b5s\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[16]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">th0s<\/span><span class=\"p\">)):<\/span>\r\n    <span class=\"n\">th0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">th0s<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'Tp1(<\/span><span class=\"si\">%2d<\/span><span class=\"s1\">)=<\/span><span class=\"si\">%.15f<\/span><span class=\"s1\">'<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">,<\/span> <span class=\"n\">Tp1s<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]))<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'Tp2(<\/span><span class=\"si\">%2d<\/span><span class=\"s1\">)=<\/span><span class=\"si\">%.15f<\/span><span class=\"s1\">'<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">,<\/span> <span class=\"n\">Tp2s<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]))<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'Tp3(<\/span><span class=\"si\">%2d<\/span><span class=\"s1\">)=<\/span><span class=\"si\">%.15f<\/span><span class=\"s1\">'<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">,<\/span> <span class=\"n\">Tp3s<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]))<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">''<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>Tp1( 1)=1.000019039346868\r\nTp2( 1)=1.000019038921006\r\nTp3( 1)=1.000019038921006\r\n\r\nTp1(10)=1.001907188148492\r\nTp2(10)=1.001907188143217\r\nTp3(10)=1.001907188143217\r\n\r\nTp1(20)=1.007669025790702\r\nTp2(20)=1.007669025791545\r\nTp3(20)=1.007669025791545\r\n\r\nTp1(30)=1.017408797590877\r\nTp2(30)=1.017408797595956\r\nTp3(30)=1.017408797595956\r\n\r\nTp1(40)=1.031340519129575\r\nTp2(40)=1.031340519130037\r\nTp3(40)=1.031340519130037\r\n\r\nTp1(50)=1.049782960621919\r\nTp2(50)=1.049782960623032\r\nTp3(50)=1.049782960623032\r\n\r\nTp1(60)=1.073182007117023\r\nTp2(60)=1.073182007149364\r\nTp3(60)=1.073182007149365\r\n\r\nTp1(70)=1.102144909638314\r\nTp2(70)=1.102144909639270\r\nTp3(70)=1.102144909639270\r\n\r\nTp1(80)=1.137492559922196\r\nTp2(80)=1.137492559923922\r\nTp3(80)=1.137492559923922\r\n\r\nTp1(90)=1.180340599016056\r\nTp2(90)=1.180340599016096\r\nTp3(90)=1.180340599016096\r\n\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u304b\u3089\u5f97\u3089\u308c\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u304b\u3089\uff0cPython \u306e SciPy \u3068 NumPy \u3092\u4f7f\u3063\u3066\uff08\u304b\u3064 SymPy \u306f\u4f7f\u308f\u305a\u306b\uff09\u6570\u5024\u7a4d\u5206\u306b\u3088\u3063\u3066\u5468\u671f\u3092\u6c42\u3081\u308b\u3002\u5c0e\u51fa\u306b\u3064\u3044\u3066\u306f\u4ee5\u4e0b\u3092\u53c2\u7167\uff1a<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/scipy-%e3%81%a7%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n<ul>\n<li>\u5358\u632f\u308a\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u304b\u3089\u5468\u671f\u3092\u6c42\u3081\u308b\u6e96\u5099<\/li>\n<\/ul>\n","protected":false},"author":33,"featured_media":0,"parent":4976,"menu_order":20,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-5016","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5016","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=5016"}],"version-history":[{"count":25,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5016\/revisions"}],"predecessor-version":[{"id":10068,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5016\/revisions\/10068"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4976"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=5016"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}