{"id":5607,"date":"2023-03-08T12:36:24","date_gmt":"2023-03-08T03:36:24","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=5607"},"modified":"2023-03-08T12:36:24","modified_gmt":"2023-03-08T03:36:24","slug":"%e5%8f%82%e8%80%83%ef%bc%9apython-%e3%81%ae-matplotlib-%e3%81%a7-sin-x-%e3%81%a8-x-%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%82%92%e6%8f%8f%e3%81%8f","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/%e4%b8%89%e8%a7%92%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86\/%e5%8f%82%e8%80%83%ef%bc%9apython-%e3%81%ae-matplotlib-%e3%81%a7-sin-x-%e3%81%a8-x-%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%82%92%e6%8f%8f%e3%81%8f\/","title":{"rendered":"\u53c2\u8003\uff1aPython \u306e Matplotlib \u3067 sin x \u3068 x \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f"},"content":{"rendered":"
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\u53c2\u8003\uff1agnuplot \u3067 sin x \u3068 x \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/a> \u306e Python \u7248\u3002Python \u306e Matplotlib \u3067 $y = \\sin x $ \u3068 $y = x$ \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3002<\/p>\n

$ |x| \\ll 1 $ \u3067\u306f2\u3064\u306e\u30b0\u30e9\u30d5\u306f\u307b\u3068\u3093\u3069\u91cd\u306a\u3063\u3066\u3044\u3066 $ \\sin x \\simeq x $ \u3059\u306a\u308f\u3061 $\\displaystyle \\frac{\\sin x}{x} \\simeq 1$ \u3067\u3042\u308b\u3053\u3068\u3092\u898b\u3066\u78ba\u304b\u3081\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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import<\/span> matplotlib.pyplot<\/span> as<\/span> plt<\/span>\r\nimport<\/span> numpy<\/span> as<\/span> np<\/span>\r\nimport<\/span> matplotlib.patches<\/span> as<\/span> patches<\/span>\r\n\r\n# \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>config<\/span> InlineBackend.figure_formats = ['svg']\r\n# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba<\/span>\r\nplt<\/span>.<\/span>rcParams<\/span>[<\/span>\"figure.figsize\"<\/span>]<\/span> =<\/span> (<\/span>6<\/span>,<\/span> 6<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$ – \\pi \\leq x \\leq \\pi$ \u306e\u7bc4\u56f2\u3067 $y = \\sin x$ \u3068 $ y = x$ \u3092\u30d7\u30ed\u30c3\u30c8\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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# \u6b21\u306b\u62e1\u5927\u8868\u793a\u3059\u308b\u90e8\u5206\u306e\u77e9\u5f62<\/span>\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> plt<\/span>.<\/span>subplots<\/span>()<\/span>\r\nax<\/span>.<\/span>add_patch<\/span>(<\/span>\r\n     patches<\/span>.<\/span>Rectangle<\/span>((<\/span>-<\/span>1<\/span>,<\/span> -<\/span>1<\/span>),<\/span> 2<\/span>,<\/span> 2<\/span>,<\/span>\r\n        edgecolor<\/span> =<\/span> 'orange'<\/span>,<\/span> linewidth<\/span> =<\/span> 1<\/span>,<\/span>\r\n        fill<\/span>=<\/span>False<\/span>      \r\n     )<\/span>\r\n)<\/span>\r\n\r\nx<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>-<\/span>np<\/span>.<\/span>pi<\/span>,<\/span> np<\/span>.<\/span>pi<\/span>,<\/span> 100<\/span>)<\/span>\r\n# \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>-<\/span>np<\/span>.<\/span>pi<\/span>,<\/span> np<\/span>.<\/span>pi<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>-<\/span>np<\/span>.<\/span>pi<\/span>,<\/span> np<\/span>.<\/span>pi<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>,<\/span> np<\/span>.<\/span>sin<\/span>(<\/span>x<\/span>),<\/span> color<\/span> =<\/span> \"red\"<\/span>,<\/span> linewidth<\/span> =<\/span> 2<\/span>,<\/span> label<\/span>=<\/span>\"sin x\"<\/span>)<\/span>\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>,<\/span> x<\/span>,<\/span> color<\/span> =<\/span> \"blue\"<\/span>,<\/span> linewidth<\/span> =<\/span> 1<\/span>,<\/span> label<\/span>=<\/span>\"x\"<\/span>)<\/span>\r\n\r\n# \u4e3b\u76ee\u76db\u306b\u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09<\/span>\r\nplt<\/span>.<\/span>grid<\/span>(<\/span>which<\/span>=<\/span>\"major\"<\/span>,<\/span> color<\/span>=<\/span>\"lightgray\"<\/span>,<\/span> ls<\/span>=<\/span>\"--\"<\/span>,<\/span> linewidth<\/span>=<\/span>0.5<\/span>)<\/span>\r\n# x\u8ef8 y\u8ef8<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> linewidth<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> linewidth<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>legend<\/span>();<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$ – 1 \\leq x \\leq 1$ \u306e\u7bc4\u56f2\u3067 $y = \\sin x$ \u3068 $ y = x$ \u3092\u30d7\u30ed\u30c3\u30c8\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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# \u6b21\u306b\u62e1\u5927\u8868\u793a\u3059\u308b\u90e8\u5206\u306e\u77e9\u5f62<\/span>\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> plt<\/span>.<\/span>subplots<\/span>()<\/span>\r\nax<\/span>.<\/span>add_patch<\/span>(<\/span>\r\n     patches<\/span>.<\/span>Rectangle<\/span>((<\/span>-<\/span>0.1<\/span>,<\/span> -<\/span>0.1<\/span>),<\/span> 0.2<\/span>,<\/span> 0.2<\/span>,<\/span>\r\n        edgecolor<\/span> =<\/span> 'orange'<\/span>,<\/span> linewidth<\/span> =<\/span> 1<\/span>,<\/span>\r\n        fill<\/span>=<\/span>False<\/span>      \r\n     )<\/span>\r\n)<\/span>\r\n\r\nx<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>-<\/span>1<\/span>,<\/span> 1<\/span>,<\/span> 100<\/span>)<\/span>\r\n# \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>-<\/span>1<\/span>,<\/span> 1<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>-<\/span>1<\/span>,<\/span> 1<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>,<\/span> np<\/span>.<\/span>sin<\/span>(<\/span>x<\/span>),<\/span> color<\/span> =<\/span> \"red\"<\/span>,<\/span> linewidth<\/span> =<\/span> 2<\/span>,<\/span> label<\/span>=<\/span>\"sin x\"<\/span>)<\/span>\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>,<\/span> x<\/span>,<\/span> color<\/span> =<\/span> \"blue\"<\/span>,<\/span> linewidth<\/span> =<\/span> 1<\/span>,<\/span> label<\/span>=<\/span>\"x\"<\/span>)<\/span>\r\n\r\n# \u4e3b\u76ee\u76db\u306b\u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09<\/span>\r\nplt<\/span>.<\/span>grid<\/span>(<\/span>which<\/span>=<\/span>\"major\"<\/span>,<\/span> color<\/span>=<\/span>\"lightgray\"<\/span>,<\/span> ls<\/span>=<\/span>\"--\"<\/span>,<\/span> linewidth<\/span>=<\/span>0.5<\/span>)<\/span>\r\n# x\u8ef8 y\u8ef8<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> linewidth<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> linewidth<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>legend<\/span>();<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$ – 0.1 \\leq x \\leq 0.1$ \u306e\u7bc4\u56f2\u3067 $y = \\sin x$ \u3068 $ y = x$ \u3092\u30d7\u30ed\u30c3\u30c8\u3002\u307b\u3068\u3093\u3069\u91cd\u306a\u3063\u3066\u3044\u3066\uff0c\u533a\u5225\u304c\u3064\u304d\u306b\u304f\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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x<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>-<\/span>0.1<\/span>,<\/span> 0.1<\/span>,<\/span> 100<\/span>)<\/span>\r\n# \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>-<\/span>0.1<\/span>,<\/span> 0.1<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>-<\/span>0.1<\/span>,<\/span> 0.1<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>,<\/span> np<\/span>.<\/span>sin<\/span>(<\/span>x<\/span>),<\/span> color<\/span> =<\/span> \"red\"<\/span>,<\/span> linewidth<\/span> =<\/span> 2<\/span>,<\/span> label<\/span>=<\/span>\"sin x\"<\/span>)<\/span>\r\nplt<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>,<\/span> x<\/span>,<\/span> color<\/span> =<\/span> \"blue\"<\/span>,<\/span> linewidth<\/span> =<\/span> 1<\/span>,<\/span> label<\/span>=<\/span>\"x\"<\/span>)<\/span>\r\n\r\n# \u4e3b\u76ee\u76db\u306b\u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09<\/span>\r\nplt<\/span>.<\/span>grid<\/span>(<\/span>which<\/span>=<\/span>\"major\"<\/span>,<\/span> color<\/span>=<\/span>\"lightgray\"<\/span>,<\/span> ls<\/span>=<\/span>\"--\"<\/span>,<\/span> linewidth<\/span>=<\/span>0.5<\/span>)<\/span>\r\n# x\u8ef8 y\u8ef8<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> linewidth<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> linewidth<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>legend<\/span>();<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u53c2\u8003\uff1agnuplot \u3067 sin x \u3068 x \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f \u306e Python \u7248\u3002Python \u306e Matplotlib \u3067 $y = \\sin x $ \u3068 $y = x$ \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3002<\/p>\n
$ |x| \\ll 1 $ \u3067\u306f2\u3064\u306e\u30b0\u30e9\u30d5\u306f\u307b\u3068\u3093\u3069\u91cd\u306a\u3063\u3066\u3044\u3066 $ \\sin x \\simeq x $ \u3059\u306a\u308f\u3061 $\\displaystyle \\frac{\\sin x}{x} \\simeq 1$ \u3067\u3042\u308b\u3053\u3068\u3092\u898b\u3066\u78ba\u304b\u3081\u308b\u3002<\/p>
\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":2096,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-5607","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t