{"id":5175,"date":"2023-02-08T14:10:36","date_gmt":"2023-02-08T05:10:36","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=5175"},"modified":"2025-01-21T17:41:47","modified_gmt":"2025-01-21T08:41:47","slug":"scipy-%e3%81%a7%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%82%92%e8%aa%bf%e3%81%b9%e3%82%8b","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\/%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%82%92%e8%aa%bf%e3%81%b9%e3%82%8b%e6%ba%96%e5%82%99\/scipy-%e3%81%a7%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%82%92%e8%aa%bf%e3%81%b9%e3%82%8b\/","title":{"rendered":"SciPy \u3066\u3099\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u3092\u8abf\u3079\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>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u8ecc\u9053\u3092\uff0cPython \u306e SciPy \u3068 NumPy \u3092\u4f7f\u3063\u3066\uff08\u304b\u3064 SymPy \u3092\u4f7f\u308f\u305a\u306b\uff09\u8abf\u3079\u308b\u3002<\/p>\n<p>\u8a73\u7d30\u306f\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8<\/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\/%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%82%92%e8%aa%bf%e3%81%b9%e3%82%8b%e6%ba%96%e5%82%99\/#i-5\">\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u3092\u8abf\u3079\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=\"\u5fc5\u8981\u306a\u30e2\u30b8\u30e5\u30fc\u30eb\u306e-import\">\u5fc5\u8981\u306a\u30e2\u30b8\u30e5\u30fc\u30eb\u306e import<\/h3>\n<p>\u5fc5\u8981\u306a\u30e2\u30b8\u30e5\u30fc\u30eb\u3092 import \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[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># NumPy \u306e\u95a2\u6570\u3092\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<span class=\"c1\"># \u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">scipy.optimize<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">root_scalar<\/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\"># \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<h3 id=\"\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u89e3\">\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u89e3<\/h3>\n<p>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u659c\u65b9\u6295\u5c04\u306e\u89e3\u306f\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\nX &amp;=&amp; \\frac{1-e^{-b T}}{b} \\, \\cos\\theta \\\\<br \/>\nY &amp;=&amp; H + \\frac{1-e^{-b T}}{b} \\, \\sin\\theta + \\frac{1 &#8211; b T -e^{-b T}}{b^2}<br \/>\n\\end{eqnarray}<\/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[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u89d2\u5ea6 th \u306f\u5ea6\u3067 <\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">theta<\/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\">th<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"o\">*<\/span><span class=\"n\">T<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"n\">b<\/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\">theta<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># T -&gt; x \u306b\u3002\u3042\u3068\u3067 root_scalar \u3067\u4f7f\u3046\u305f\u3081\u3002<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">theta<\/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\">th<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">H<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"n\">b<\/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\">theta<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"o\">-<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"n\">b<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/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<h3 id=\"\u6ede\u7a7a\u6642\u9593-$T_1$\">\u6ede\u7a7a\u6642\u9593 $T_1$<\/h3>\n<p>$T = 0$ \u3067\u6253\u3061\u51fa\u3055\u308c\u305f\u7c92\u5b50\u304c\u5730\u9762 $Y=0$ \u306b\u843d\u3061\u308b\u307e\u3067\u306e\u6ede\u7a7a\u6642\u9593 $T_1$ \u306f\u4ee5\u4e0b\u3092\u6e80\u305f\u3059\u3002<\/p>\n<p>\\begin{eqnarray}<br \/>\nY(T_1, \\theta, H, b) &amp;=&amp; H + \\frac{1-e^{-b T_1}}{b} \\, \\sin\\theta + \\frac{1 &#8211; b T_1 -e^{-b T_1}}{b^2} = 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u306e\u5f0f\u306f $T_1$ \u306b\u3064\u3044\u3066\u8d85\u8d8a\u65b9\u7a0b\u5f0f\u3067\u3042\u308a\uff0c\u89e3\u6790\u7684\u306b\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002<\/p>\n<p>\u305d\u3053\u3067 Python \u3067\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\uff0c<code>scipy.optimize.root_scalar()<\/code> \u3092\u4f7f\u3046\u3002<\/p>\n<h3 id=\"\u6c34\u5e73\u5230\u9054\u8ddd\u96e2-$L$\">\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$<\/h3>\n<p>$Y(T_1, \\theta, H, b) =0$ \u306e\u6570\u5024\u89e3 $T_1(\\theta, H, b)$ \u304c\u6c42\u307e\u3063\u305f\u3089\uff0c\u3053\u306e\u6ede\u7a7a\u6642\u9593\u306e\u9593\u306e\u6c34\u5e73\u65b9\u5411\u306e\u5230\u9054\u8ddd\u96e2 $L$ \u306f\uff0c<\/p>\n<p>$$L = X(T_1(\\theta, H, b), \\theta, b)$$<\/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=\"k\">def<\/span> <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"c1\"># \u3069\u306e\u7bc4\u56f2\u3067 root_scalar \u3059\u308b\u304b\u3002\u3053\u3053\u3067\u306f 0.1 ~ 3.0 \u3068\u5e83\u3081\u306b <\/span>\r\n    <span class=\"n\">ans<\/span> <span class=\"o\">=<\/span> <span class=\"n\">root_scalar<\/span><span class=\"p\">(<\/span><span class=\"n\">Y<\/span><span class=\"p\">,<\/span> <span class=\"n\">bracket<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">3<\/span><span class=\"p\">],<\/span> <span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">))<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">ans<\/span><span class=\"o\">.<\/span><span class=\"n\">root<\/span>\r\n\r\n<span class=\"k\">def<\/span> <span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/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<h3 id=\"$H-=-0$-\u306e\u5834\u5408\u306e\u8ecc\u9053\">$H = 0$ \u306e\u5834\u5408\u306e\u8ecc\u9053<\/h3>\n<p>\u7a7a\u6c17\u62b5\u6297\u306e\u4fc2\u6570 $b=0.5$ \u306e\u5834\u5408\u306b\uff0c$\\theta = 45^{\\circ}$ \u524d\u5f8c\u306e\u89d2\u5ea6\u3067\u306e\u659c\u65b9\u6295\u5c04\u306e\u8ecc\u9053\u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n<p>\u3068\u308a\u3042\u3048\u305a\u306f $\\theta = 45^{\\circ}$ \u306e\u5834\u5408\u30921\u672c\uff0c\u30b0\u30e9\u30d5\u306b\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[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">th<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">45<\/span>\r\n<span class=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"n\">b<\/span> <span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span>\r\n\r\n<span class=\"c1\"># \u6642\u9593 T \u306e\u7bc4\u56f2\u3002\u6ede\u7a7a\u6642\u9593 T1 \u307e\u3067\u3002<\/span>\r\n<span class=\"n\">T_list<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"mi\">100<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/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-7492\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Scibtosha01.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<p>\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3057\u3066\u305d\u308c\u3089\u3057\u3044\u30b0\u30e9\u30d5\u306b\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=\"c1\"># \u03b8 = 45\u00b0 \u306e\u30b0\u30e9\u30d5<\/span>\r\n<span class=\"c1\"># \u5fc5\u8981\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6570\u5024\u8a2d\u5b9a<\/span>\r\n<span class=\"n\">th<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">45<\/span>\r\n<span class=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"n\">b<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.5<\/span>\r\n\r\n<span class=\"c1\"># \u6642\u9593 T \u306e\u7bc4\u56f2\u3002\u6ede\u7a7a\u6642\u9593 T1 \u307e\u3067\u3002<\/span>\r\n<span class=\"n\">T_list<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"mi\">100<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u306e\u6570\u5024\u306e\u6841\u6570\u3092\u63c3\u3048\u308b<\/span>\r\n<span class=\"n\">key<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"\u03b8 = <\/span><span class=\"si\">%2d<\/span><span class=\"s2\">\u00b0\"<\/span> <span class=\"o\">%<\/span> <span class=\"n\">th<\/span>\r\n\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"n\">key<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u30c9\u30c3\u30c8\u3067<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"X\"<\/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\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"b = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\">, H = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\"> \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\"<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\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=\"mf\">0.8<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.4<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.9<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">yticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"c1\"># \u7e26\u6a2a\u306e\u6bd4\uff0c\u30a2\u30b9\u30da\u30af\u30c8\u6bd4<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">gca<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">set_aspect<\/span><span class=\"p\">(<\/span><span class=\"s1\">'equal'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\u8868\u793a<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/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-7493\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Scibtosha02.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<p>$\\theta$ \u306e\u5024\u3092 $38^{\\circ}$ \u304b\u3089 $45^{\\circ}$ \u307e\u3067 $1^{\\circ}$ \u523b\u307f\u3067\u5909\u3048\u3066\uff0c\u8907\u6570\u306e\u66f2\u7dda\u3092\u4e00\u5ea6\u306b\u63cf\u304f\u4f8b\u3002<\/p>\n<p><code>for<\/code> \u3067\u7e70\u308a\u8fd4\u3057\u51e6\u7406\u3055\u305b\u3066\u307f\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\uff0c\u7d30\u304b\u3044\u3053\u3068\u3067\u3059\u304c\uff0c\u30b0\u30e9\u30d5\u306e\u6700\u9ad8\u70b9\u306f $\\theta$ \u306e\u5024\u304c\u5927\u304d\u3044\u3068\u304d\u3067\u3059\u306e\u3067\uff0c\u5148\u306b $45^{\\circ}$ \u304b\u3089\u63cf\u304d\u306f\u3058\u3081\u3066\uff0c$1^{\\circ}$ \u305a\u3064\u6e1b\u3089\u3057\u3066\u307f\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[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># for \u3067 1 \u305a\u3064\u6e1b\u3089\u3057\u3066\u3044\u304f\u4f8b 1<\/span>\r\n<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\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">end<\/span><span class=\"o\">=<\/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>5 4 3 2 1<\/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[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># for \u3067 1 \u305a\u3064\u6e1b\u3089\u3057\u3066\u3044\u304f\u4f8b 2<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">reversed<\/span><span class=\"p\">(<\/span><span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">6<\/span><span class=\"p\">)):<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">end<\/span><span class=\"o\">=<\/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>5 4 3 2 1 0<\/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[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"n\">b<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.5<\/span>\r\n\r\n<span class=\"c1\"># \u8907\u6570\u306e\u30b0\u30e9\u30d5\u3092\u4e00\u5ea6\u306b\u63cf\u304f\u5834\u5408\u306f...<\/span>\r\n<span class=\"c1\"># \u4ee5\u4e0b\u306e\u3088\u3046\u306b for \u30eb\u30fc\u30d7\u3067\u7e70\u308a\u8fd4\u3057\u51e6\u7406\u3055\u305b\u308c\u3070\u3088\u3044\u3002<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">th<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">45<\/span><span class=\"p\">,<\/span> <span class=\"mi\">37<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"c1\"># \u6642\u9593 T \u306e\u7bc4\u56f2\u3002\u6ede\u7a7a\u6642\u9593 T1 \u307e\u3067\u3002<\/span>\r\n    <span class=\"n\">T_list<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"mi\">100<\/span><span class=\"p\">)<\/span>\r\n\r\n    <span class=\"c1\"># \u51e1\u4f8b\u306e\u6570\u5024\u306e\u6841\u6570\u3092\u63c3\u3048\u308b<\/span>\r\n    <span class=\"n\">key<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"\u03b8 = <\/span><span class=\"si\">%2d<\/span><span class=\"s2\">\u00b0\"<\/span> <span class=\"o\">%<\/span> <span class=\"n\">th<\/span>\r\n\r\n    <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> \r\n             <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"n\">key<\/span><span class=\"p\">,<\/span> <span class=\"n\">linewidth<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.8<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u30c9\u30c3\u30c8\u3067<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"X\"<\/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\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"b = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\">, H = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\"> \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\"<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\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=\"mf\">0.8<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.4<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.9<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">yticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">gca<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">set_aspect<\/span><span class=\"p\">(<\/span><span class=\"s1\">'equal'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\u8868\u793a<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/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-7494\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Scibtosha03.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<p>\u843d\u4e0b\u70b9\u4ed8\u8fd1\u3092\u62e1\u5927\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[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"n\">b<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.5<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">th<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">45<\/span><span class=\"p\">,<\/span> <span class=\"mi\">37<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"c1\"># \u6642\u9593 T \u306e\u7bc4\u56f2\u3002\u6ede\u7a7a\u6642\u9593 T1 \u307e\u3067\u3002<\/span>\r\n    <span class=\"n\">T_list<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"mi\">100<\/span><span class=\"p\">)<\/span>\r\n\r\n    <span class=\"c1\"># \u51e1\u4f8b\u306e\u6570\u5024\u306e\u6841\u6570\u3092\u63c3\u3048\u308b<\/span>\r\n    <span class=\"n\">key<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"\u03b8 = <\/span><span class=\"si\">%2d<\/span><span class=\"s2\">\u00b0\"<\/span> <span class=\"o\">%<\/span> <span class=\"n\">th<\/span>\r\n\r\n    <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> \r\n             <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"n\">key<\/span><span class=\"p\">,<\/span> <span class=\"n\">linewidth<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.8<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u30c9\u30c3\u30c8\u3067<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"X\"<\/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\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"b = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\">, H = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\"> \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\"<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># \u843d\u4e0b\u70b9\u4ed8\u8fd1\u3092\u62e1\u5927\u8868\u793a<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlim<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.66<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.68<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.01<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\u8868\u793a<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/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-7495\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Scibtosha04.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<p>$b = 0.5$ \u306e\u5834\u5408\uff0c\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u306a\u308b\u306e\u306f $\\theta$ \u304c 39\u00b0 \u304b\u3089 40\u00b0 \u304f\u3089\u3044\u306e\u6642\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u3082\u3046\u5c11\u3057\u5b9a\u91cf\u7684\u306b\u6c42\u3081\u3066\u307f\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=\"\u6c34\u5e73\u5230\u9054\u8ddd\u96e2-$L$-\u306e\u30b0\u30e9\u30d5\">\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$ \u306e\u30b0\u30e9\u30d5<\/h3>\n<p>\u5b9a\u91cf\u7684\u306b\u8abf\u3079\u308b\u305f\u3081\u306b\uff0c\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 <code>L(th, H, b)<\/code> \u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n<p>\u4e0a\u3067\u5b9a\u7fa9\u3057\u305f <code>L(th, H, b)<\/code> \u3067\u306f\uff0c\u5f15\u6570 <code>th<\/code> \u306e\u90e8\u5206\u306b\u30ea\u30b9\u30c8 <code>th_list<\/code> \u3092\u5165\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u306e\u3067\uff0c\u5c11\u3057\u5de5\u592b\u3057\u3066\u307f\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[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"n\">b<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.5<\/span>\r\n\r\n<span class=\"n\">th_list<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">38<\/span><span class=\"p\">,<\/span> <span class=\"mi\">42<\/span><span class=\"p\">,<\/span> <span class=\"mi\">100<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">L_list<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">th_list<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"n\">L_list<\/span> <span class=\"o\">+=<\/span> <span class=\"p\">[<\/span><span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">th<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">)]<\/span>\r\n    \r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">th_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">L_list<\/span><span class=\"p\">);<\/span>\r\n    \r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u30c9\u30c3\u30c8\u3067<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u6295\u5c04\u89d2\u5ea6 \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\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 L\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"b = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\">, H = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\"> \u306e\u5834\u5408\u306e\u6295\u5c04\u89d2\u5ea6\u3068\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/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-7496\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Scibtosha05.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=\"\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u306a\u308b\u89d2\u5ea6-$\\theta_{\\rm-max}$-\u3092\u6570\u5024\u5fae\u5206\u3067\u6c42\u3081\u308b\">\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u306a\u308b\u89d2\u5ea6 $\\theta_{\\rm max}$ \u3092\u6570\u5024\u5fae\u5206\u3067\u6c42\u3081\u308b<\/h3>\n<p>$L(\\theta, H, b)$ \u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f $\\displaystyle \\frac{d L}{d \\theta} = 0$ \u3068\u306a\u308b\u89d2\u5ea6\u306e\u3068\u304d\u3067\u3059\u3002<\/p>\n<p>$L(\\theta, H, b)$ \u306f\u89e3\u6790\u7684\u306a\u95a2\u6570\u3068\u3057\u3066\u4e0e\u3048\u3089\u308c\u3066\u3044\u306a\u3044\u306e\u3067\uff0c\u3053\u3053\u3067\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6570\u5024\u5fae\u5206\u3067\u6c42\u3081\u308b\u3053\u3068\u306b\u3057\u307e\u3059\u3002<\/p>\n<p>$$\\frac{d L}{d \\theta} \\simeq \\frac{L(\\theta+\\delta, H, b)-L(\\theta-\\delta, H, b)}{2 \\delta}$$<\/p>\n<p>$\\displaystyle \\frac{d L}{d \\theta} = 0$ \u3068\u306a\u308b\u89d2\u5ea6 $\\theta$ \u3092\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u6570\u5024\u7684\u306b\u89e3\u304f <code>root_scalar()<\/code> \u3092\u4f7f\u3063\u3066\u6c42\u3081\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[11]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u6570\u5024\u5fae\u5206: delta \u306f\u5c0f\u3055\u3044\u307b\u3069\u3088\u3044\uff0c\u3068\u3044\u3046\u308f\u3051\u3067\u306f\u306a\u3044<\/span>\r\n<span class=\"c1\"># th -&gt; x \u306b<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">dL<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">delta<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"p\">(<\/span><span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">+<\/span><span class=\"n\">delta<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">-<\/span><span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">-<\/span><span class=\"n\">delta<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">delta<\/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=\"n\">b<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.5<\/span>\r\n<span class=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n\r\n<span class=\"c1\"># \u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3<\/span>\r\n<span class=\"c1\"># dL = 0 \u3068\u306a\u308b\u89d2\u5ea6\u3092 delta \u3092\u5909\u3048\u3066\u6c42\u3081\u308b<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">delta<\/span> <span class=\"ow\">in<\/span> <span class=\"p\">[<\/span><span class=\"mf\">1e-3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-6<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-7<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-8<\/span><span class=\"p\">]:<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"n\">root_scalar<\/span><span class=\"p\">(<\/span><span class=\"n\">dL<\/span><span class=\"p\">,<\/span> <span class=\"n\">bracket<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">38<\/span><span class=\"p\">,<\/span> <span class=\"mi\">42<\/span><span class=\"p\">],<\/span><span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span><span class=\"n\">delta<\/span><span class=\"p\">))<\/span><span class=\"o\">.<\/span><span class=\"n\">root<\/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>39.487609707324665\r\n39.48760970570406\r\n39.4876097136504\r\n39.48760970315897\r\n39.48761054464386\r\n39.487606095044356\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>\u4e0a\u306e\u7d50\u679c\u304b\u3089\uff0c<code>delta = 1e-4<\/code> \u306b\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u95a2\u6570\u3092\u5b9a\u7fa9\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[13]:<\/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\">thmax<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"sd\">\"\"\" \u9ad8\u3055 H \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u3067\u6700\u5927\u5230\u9054\u8ddd\u96e2\u306b\u306a\u308b\u89d2\u5ea6\uff08\u00b0\uff09<\/span>\r\n<span class=\"sd\">    \"\"\"<\/span>\r\n    <span class=\"n\">delta<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1e-4<\/span>\r\n    <span class=\"n\">ans<\/span> <span class=\"o\">=<\/span> <span class=\"n\">root_scalar<\/span><span class=\"p\">(<\/span><span class=\"n\">dL<\/span><span class=\"p\">,<\/span> <span class=\"n\">bracket<\/span><span class=\"o\">=<\/span><span class=\"p\">[<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span><span class=\"mi\">45<\/span><span class=\"p\">],<\/span> <span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span><span class=\"n\">delta<\/span><span class=\"p\">))<\/span><span class=\"o\">.<\/span><span class=\"n\">root<\/span>    \r\n    <span class=\"k\">return<\/span> <span class=\"n\">ans<\/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<h3 id=\"$H=0,-b-=-0.5$-\u306e\u5834\u5408\">$H=0, b = 0.5$ \u306e\u5834\u5408<\/h3>\n<h4 id=\"\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u6295\u5c04\u89d2\u5ea6\">\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u6295\u5c04\u89d2\u5ea6<\/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[14]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"n\">b<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.5<\/span>\r\n\r\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'b = <\/span><span class=\"si\">%.1f<\/span><span class=\"s1\">, H = <\/span><span class=\"si\">%.1f<\/span><span class=\"s1\"> \u306e\u3068\u304d'<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">))<\/span>\r\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'L \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6 \u03b8max \u306f <\/span><span class=\"si\">%.6f<\/span><span class=\"s1\">\u00b0'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">thmax<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">))<\/span>\r\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 Lmax \u306f <\/span><span class=\"si\">%.6f<\/span><span class=\"s1\">'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">thmax<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/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>b = 0.5, H = 0.0 \u306e\u3068\u304d\r\nL \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6 \u03b8max \u306f 39.487610\u00b0\r\n\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 Lmax \u306f 0.679421\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=\"\u8ecc\u9053\u306e\u30b0\u30e9\u30d5\">\u8ecc\u9053\u306e\u30b0\u30e9\u30d5<\/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[15]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u3042\u3089\u305f\u3081\u3066\u4f7f\u3046\u6570\u5024\u3092\u307e\u3068\u3081\u3066\u304a\u304f\u3002<\/span>\r\n<span class=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"n\">b<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.5<\/span>\r\n\r\n<span class=\"n\">thm<\/span> <span class=\"o\">=<\/span> <span class=\"n\">thmax<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># \u6642\u9593 T \u306e\u7bc4\u56f2\u3002\u6ede\u7a7a\u6642\u9593 T1 \u307e\u3067\u3002<\/span>\r\n<span class=\"n\">T_list<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"mi\">100<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u306e\u6570\u5024\u306e\u6841\u6570\u3092\u63c3\u3048\u308b<\/span>\r\n<span class=\"n\">key<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"b = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\">, \u03b8 = <\/span><span class=\"si\">%.4f<\/span><span class=\"s2\">\u00b0, Lmax = <\/span><span class=\"si\">%.4f<\/span><span class=\"s2\">\"<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"n\">key<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u30c9\u30c3\u30c8\u3067<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"X\"<\/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\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"H = <\/span><span class=\"si\">%.0f<\/span><span class=\"s2\"> \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span> <span class=\"o\">%<\/span> <span class=\"n\">H<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\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=\"mf\">0.8<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.4<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.9<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">yticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">gca<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">set_aspect<\/span><span class=\"p\">(<\/span><span class=\"s1\">'equal'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\u8868\u793a<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/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-7497\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Scibtosha06.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=\"\u554f\u984c-1\">\u554f\u984c 1<\/h3>\n<p>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u9ad8\u3055 $H=0$ \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u6295\u5c04\u89d2\u5ea6\u3068\uff0c\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u308f\u304b\u308b\u3088\u3046\u306a\u30b0\u30e9\u30d5\u3092\u6b21\u306e\u898f\u683c\u5316\u3055\u308c\u305f\u62b5\u6297\u4fc2\u6570 $b$ \u306e\u5834\u5408\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u3066\u63cf\u3051\u3002<\/p>\n<p>$$ b = 0.5, \\ 1.0, \\ 1.5, \\ 2.0$$<\/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=\"\u89e3\u7b54\u4f8b\">\u89e3\u7b54\u4f8b<\/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[16]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">b_list<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">2.0<\/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[17]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">H<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">b<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">b_list<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"c1\"># \u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u6295\u5c04\u89d2\u5ea6<\/span>\r\n    <span class=\"n\">thm<\/span> <span class=\"o\">=<\/span> <span class=\"n\">thmax<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">)<\/span>\r\n\r\n    <span class=\"c1\"># \u6642\u9593 T \u306e\u7bc4\u56f2\u3002\u6ede\u7a7a\u6642\u9593 T1 \u307e\u3067\u3002<\/span>\r\n    <span class=\"n\">T_list<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"mi\">100<\/span><span class=\"p\">)<\/span>\r\n\r\n    <span class=\"c1\"># \u51e1\u4f8b\u306e\u6570\u5024\u306e\u6841\u6570\u3092\u63c3\u3048\u308b<\/span>\r\n    <span class=\"n\">key<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"b = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\">, \u03b8max = <\/span><span class=\"si\">%.4f<\/span><span class=\"s2\">\u00b0, Lmax = <\/span><span class=\"si\">%.4f<\/span><span class=\"s2\">\"<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">))<\/span>\r\n\r\n    <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"n\">key<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u30c9\u30c3\u30c8\u3067<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"X\"<\/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\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"H = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\"> \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span> <span class=\"o\">%<\/span> <span class=\"n\">H<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\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=\"mf\">0.8<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.4<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.9<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">yticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">gca<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">set_aspect<\/span><span class=\"p\">(<\/span><span class=\"s1\">'equal'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\u8868\u793a<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/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-7498\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Scibtosha07.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=\"\u554f\u984c-2\">\u554f\u984c 2<\/h3>\n<p>\u554f\u984c 1 \u3067\uff0c$H = 0$ \u306e\u5834\u5408\uff0c\u7a7a\u6c17\u62b5\u6297\u304c\u306a\u3044\u3068\u304d\uff0c\u3064\u307e\u308a $b=0$ \u306e\u3068\u304d\u306b\u306f $\\theta=45^{\\circ}$ \u306e\u3068\u304d\u306b\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u306b\u306a\u308b\u304c\uff0c\u3053\u306e\u307e\u307e\u3067\u306f <code>b=0<\/code> \u306e\u5834\u5408\u306e\u30b0\u30e9\u30d5\u3092\u8ffd\u52a0\u3057\u3088\u3046\u3068\u3059\u308b\u3068\u30a8\u30e9\u30fc\u306b\u306a\u308b\u306f\u305a\u3067\u3042\u308b\u3002<\/p>\n<p>\u305d\u306e\u539f\u56e0\u3092\u3064\u304d\u3068\u3081\uff0c\u6539\u5584\u3057\uff0c$b = 0, 0.5, 1.0, 1.5$ \u306e\u5834\u5408\u306e\u30b0\u30e9\u30d5\u3092\u307e\u3068\u3081\u3066\u63cf\u3051\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[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre> \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<h3 id=\"\u554f\u984c-3\">\u554f\u984c 3<\/h3>\n<p>\u7a7a\u6c17\u62b5\u6297 $b = 0.5$ \u306e\u5834\u5408\u306e\u9ad8\u3055 $H$ \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u6295\u5c04\u89d2\u5ea6\u3068\uff0c\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u308f\u304b\u308b\u3088\u3046\u306a\u30b0\u30e9\u30d5\u3092\u6b21\u306e $H$ \u306e\u5834\u5408\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u3066\u63cf\u3051\u3002<\/p>\n<p>$$ H = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0$$<\/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=\"\u89e3\u7b54\u4f8b\">\u89e3\u7b54\u4f8b<\/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[18]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># NumPy \u306b\u983c\u3089\u306a\u3044\u65b9\u6cd5<\/span>\r\n<span class=\"n\">H_list<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"o\">\/<\/span><span class=\"mi\">10<\/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\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">11<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">)]<\/span>\r\n<span class=\"n\">H_list<\/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 output_prompt\">Out[18]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>[0.0, 0.2, 0.4, 0.6, 0.8, 1.0]<\/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[19]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># NumPy \u306b\u983c\u308b\u65b9\u6cd5 1<\/span>\r\n<span class=\"n\">H_list<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">6<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">H_list<\/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 output_prompt\">Out[19]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>array([0. , 0.2, 0.4, 0.6, 0.8, 1. ])<\/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[20]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># NumPy \u306b\u983c\u308b\u65b9\u6cd5 2<\/span>\r\n<span class=\"n\">H_list<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.1<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">H_list<\/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 output_prompt\">Out[20]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>array([0. , 0.2, 0.4, 0.6, 0.8, 1. ])<\/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[21]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">b<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.5<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">H<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">reversed<\/span><span class=\"p\">(<\/span><span class=\"n\">H_list<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"c1\"># \u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u6295\u5c04\u89d2\u5ea6<\/span>\r\n    <span class=\"n\">thm<\/span> <span class=\"o\">=<\/span> <span class=\"n\">thmax<\/span><span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">)<\/span>\r\n\r\n    <span class=\"c1\"># \u6642\u9593 T \u306e\u7bc4\u56f2\u3002\u6ede\u7a7a\u6642\u9593 T1 \u307e\u3067\u3002<\/span>\r\n    <span class=\"n\">T_list<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"mi\">100<\/span><span class=\"p\">)<\/span>\r\n\r\n    <span class=\"c1\"># \u51e1\u4f8b\u306e\u6570\u5024\u306e\u6841\u6570\u3092\u63c3\u3048\u308b<\/span>\r\n    <span class=\"c1\"># \u4e0a\u4ed8\u4e0b\u4ed8\u6dfb\u5b57\u306f $ \u3067\u631f\u3093\u3067 LaTeX \u5f62\u5f0f\u3067<\/span>\r\n    <span class=\"n\">key<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"H =<\/span><span class=\"si\">%.1f<\/span><span class=\"s2\">, \u03b8 =<\/span><span class=\"si\">%.4f<\/span><span class=\"s2\">\u00b0, Lmax =<\/span><span class=\"si\">%.4f<\/span><span class=\"s2\">\"<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">L<\/span><span class=\"p\">(<\/span><span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">))<\/span>\r\n\r\n    <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">T_list<\/span><span class=\"p\">,<\/span> <span class=\"n\">thm<\/span><span class=\"p\">,<\/span> <span class=\"n\">H<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"n\">key<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u30c9\u30c3\u30c8\u3067<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb\u3068\u30bf\u30a4\u30c8\u30eb<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"X\"<\/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\">\"Y\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"b = <\/span><span class=\"si\">%.1f<\/span><span class=\"s2\"> \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span> <span class=\"o\">%<\/span> <span class=\"n\">b<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\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=\"mf\">1.8<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.1<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.8<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.2<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">yticks<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">arange<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.1<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.2<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">gca<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">set_aspect<\/span><span class=\"p\">(<\/span><span class=\"s1\">'equal'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\u8868\u793a<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/span><span class=\"p\">(<\/span><span class=\"n\">prop<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s2\">\"size\"<\/span><span class=\"p\">:<\/span> <span class=\"s2\">\"small\"<\/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-7499\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Scibtosha08.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u8ecc\u9053\u3092\uff0cPython \u306e SciPy \u3068 NumPy \u3092\u4f7f\u3063\u3066\uff08\u304b\u3064 SymPy \u3092\u4f7f\u308f\u305a\u306b\uff09\u8abf\u3079\u308b\u3002<\/p>\n<p>\u8a73\u7d30\u306f\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8<\/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\/%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%82%92%e8%aa%bf%e3%81%b9%e3%82%8b%e6%ba%96%e5%82%99\/scipy-%e3%81%a7%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%82%92%e8%aa%bf%e3%81%b9%e3%82%8b\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n<ul>\n<li>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u3092\u8abf\u3079\u308b\u6e96\u5099<\/li>\n<\/ul>\n","protected":false},"author":33,"featured_media":0,"parent":5138,"menu_order":20,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-5175","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\/5175","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=5175"}],"version-history":[{"count":9,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5175\/revisions"}],"predecessor-version":[{"id":10054,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5175\/revisions\/10054"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5138"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=5175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}