{"id":10076,"date":"2025-01-24T13:54:23","date_gmt":"2025-01-24T04:54:23","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=10076"},"modified":"2025-01-24T13:54:23","modified_gmt":"2025-01-24T04:54:23","slug":"matplotlib-%e3%81%a71%e6%ac%a1%e5%85%83%e6%b3%a2%e5%8b%95%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%81%a8%e3%82%a2%e3%83%8b%e3%83%a1%e3%82%92%e3%81%a4%e3%81%8f%e3%82%8b","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e7%9c%9f%e7%a9%ba%e4%b8%ad%e3%81%ae%e3%83%9e%e3%82%af%e3%82%b9%e3%82%a6%e3%82%a7%e3%83%ab%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%a8%e9%9b%bb%e7%a3%81%e6%b3%a2\/matplotlib-%e3%81%a71%e6%ac%a1%e5%85%83%e6%b3%a2%e5%8b%95%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%81%a8%e3%82%a2%e3%83%8b%e3%83%a1%e3%82%92%e3%81%a4%e3%81%8f%e3%82%8b\/","title":{"rendered":"Matplotlib \u30671\u6b21\u5143\u6ce2\u52d5\u306e\u30b0\u30e9\u30d5\u3068\u30a2\u30cb\u30e1\u3092\u3064\u304f\u308b"},"content":{"rendered":"

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\u30e9\u30a4\u30d6\u30e9\u30ea\u306e import<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[1]:<\/div>\n
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import<\/span> numpy<\/span> as<\/span> np<\/span>\r\nimport<\/span> matplotlib.pyplot<\/span> as<\/span> plt<\/span>\r\nfrom<\/span> matplotlib.ticker<\/span> import<\/span> MultipleLocator<\/span>\r\n\r\nfrom<\/span> matplotlib.animation<\/span> import<\/span> FuncAnimation<\/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\r\n# mathtext font \u306e\u8a2d\u5b9a<\/span>\r\nplt<\/span>.<\/span>rcParams<\/span>[<\/span>'mathtext.fontset'<\/span>]<\/span> =<\/span> 'cm'<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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1\u6b21\u5143\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u306e\u89e3<\/h3>\n
1\u6b21\u5143\u6ce2\u52d5\u65b9\u7a0b\u5f0f<\/p>\n
$$\\left( \\frac{\\partial^2}{\\partial x^2} -\\frac{1}{v^2} \\frac{\\partial^2 }{\\partial t^2} \\right) f = 0$$<\/p>\n
\u306e\u89e3\u306f<\/p>\n
$$f(x, t) = F(x -vt) + G(x + vt)$$<\/p>\n
\u3053\u3053\u3067\uff0c$F(x -vt)$ \u306f $+x$ \u65b9\u5411\u306b\u9032\u3080\u6ce2\uff0c$G(x + vt)$ \u306f $-x$ \u65b9\u5411\u306b\u9032\u3080\u6ce2\u3092\u8868\u3059\u3002<\/p>\n
\u4f8b\u3068\u3057\u3066\uff0c$f(x, t) = \\sin (x -vt)$ \u3092 $v=1$ \u3068\u3057\u3066\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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def<\/span> f<\/span>(<\/span>x<\/span>,<\/span> t<\/span>):<\/span>\r\n    return<\/span> np<\/span>.<\/span>sin<\/span>(<\/span>x<\/span> -<\/span> t<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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# ax \u3092\u4f7f\u3046\u969b\u306e\u6700\u521d\u306e\u304a\u307e\u3058\u306a\u3044<\/span>\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> plt<\/span>.<\/span>subplots<\/span>()<\/span>\r\n\r\n# \u6a2a\u8ef8\u7e26\u8ef8\u306e ticks <\/span>\r\nax<\/span>.<\/span>set_xticks<\/span>([])<\/span>\r\nax<\/span>.<\/span>set_yticks<\/span>([])<\/span>\r\n\r\n# \u8868\u793a\u7bc4\u56f2<\/span>\r\nax<\/span>.<\/span>axis<\/span>([<\/span>-<\/span>10<\/span>,<\/span> 12<\/span>,<\/span>-<\/span>1.2<\/span>,<\/span> 1.3<\/span> ])<\/span>\r\n\r\n# \u77e2\u5370<\/span>\r\nax<\/span>.<\/span>quiver<\/span>([<\/span>float<\/span>(<\/span>np<\/span>.<\/span>pi<\/span>\/<\/span>2<\/span>-<\/span>2<\/span>*<\/span>np<\/span>.<\/span>pi<\/span>),<\/span> \r\n           float<\/span>(<\/span>np<\/span>.<\/span>pi<\/span>\/<\/span>2<\/span>),<\/span> \r\n           float<\/span>(<\/span>np<\/span>.<\/span>pi<\/span>\/<\/span>2<\/span>+<\/span>2<\/span>*<\/span>np<\/span>.<\/span>pi<\/span>)],<\/span> [<\/span>1.1<\/span>,<\/span>1.1<\/span>,<\/span>1.1<\/span>],<\/span> [<\/span>2<\/span>,<\/span>2<\/span>,<\/span>2<\/span>],<\/span> [<\/span>0<\/span>,<\/span>0<\/span>,<\/span>0<\/span>],<\/span> \r\n          # \u5168\u30d9\u30af\u30c8\u30eb\u306b\u8272\u3092\u4e00\u62ec\u6307\u5b9a<\/span>\r\n          color<\/span>=<\/span>\"black\"<\/span>,<\/span> \r\n          # \u4ee5\u4e0b\u306e3\u70b9\u30bb\u30c3\u30c8\u3092\u66f8\u304b\u306a\u3044\u3068\u81ea\u52d5\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u3055\u308c\u308b<\/span>\r\n          angles<\/span>=<\/span>'xy'<\/span>,<\/span> scale_units<\/span>=<\/span>'xy'<\/span>,<\/span> scale<\/span>=<\/span>1<\/span>)<\/span>\r\n\r\n# x\u8ef8 y\u8ef8\u306f dashed \u306b<\/span>\r\nax<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'gray'<\/span>,<\/span> ls<\/span>=<\/span>'--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\nax<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'gray'<\/span>,<\/span> ls<\/span>=<\/span>'--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\n\r\n# x\u306e\u7bc4\u56f2<\/span>\r\nx<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>-<\/span>10<\/span>,<\/span> 10<\/span>,<\/span> 200<\/span>)<\/span>\r\n\r\n# t = 0<\/span>\r\nax<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>,<\/span> f<\/span>(<\/span>x<\/span>,<\/span> 0<\/span>),<\/span> label<\/span> =<\/span> '$t = 0.0$'<\/span>,<\/span> \r\n        lw<\/span> =<\/span> 0.5<\/span>,<\/span> c<\/span> =<\/span> '#cccccc'<\/span>)<\/span>\r\n# t = 0.5<\/span>\r\nax<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>,<\/span> f<\/span>(<\/span>x<\/span>,<\/span> 0.5<\/span>),<\/span> label<\/span> =<\/span> '$t = 0.5$'<\/span>,<\/span> \r\n        lw<\/span> =<\/span> 0.7<\/span>,<\/span> c<\/span> =<\/span> '#888888'<\/span>)<\/span>\r\n# t = 1.0<\/span>\r\nax<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>,<\/span> f<\/span>(<\/span>x<\/span>,<\/span> 1.0<\/span>),<\/span> label<\/span> =<\/span> '$t = 1.0$'<\/span>,<\/span> \r\n        lw<\/span> =<\/span> 1<\/span>,<\/span> c<\/span> =<\/span> '#555555'<\/span>)<\/span>\r\n# t = 1.5<\/span>\r\nax<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>,<\/span> f<\/span>(<\/span>x<\/span>,<\/span> 1.5<\/span>),<\/span> label<\/span> =<\/span> '$t = 1.5$'<\/span>,<\/span> \r\n        lw<\/span> =<\/span> 1.5<\/span>,<\/span> c<\/span> =<\/span> '#000000'<\/span>)<\/span>\r\n\r\nax<\/span>.<\/span>set_title<\/span>(<\/span>r<\/span>'$f(x, t) = \\sin(x - v t)$'<\/span>)<\/span>\r\nax<\/span>.<\/span>set_xlabel<\/span>(<\/span>r<\/span>'$x \\quad \\rightarrow$'<\/span>)<\/span>\r\nax<\/span>.<\/span>legend<\/span>();<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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# ax \u3092\u4f7f\u3046\u969b\u306e\u6700\u521d\u306e\u304a\u307e\u3058\u306a\u3044<\/span>\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> plt<\/span>.<\/span>subplots<\/span>()<\/span>\r\n\r\ndef<\/span> func<\/span>(<\/span>i<\/span>):<\/span>\r\n    # \u524d\u306e frame \u3092\u6d88\u3059<\/span>\r\n    ax<\/span>.<\/span>cla<\/span>()<\/span>\r\n\r\n    # \u8868\u793a\u7bc4\u56f2<\/span>\r\n    ax<\/span>.<\/span>axis<\/span>([<\/span>-<\/span>10<\/span>,<\/span> 10<\/span>,<\/span> -<\/span>1.2<\/span>,<\/span> 1.2<\/span>])<\/span>\r\n    # \u6a2a\u8ef8\u76ee\u76db<\/span>\r\n    ax<\/span>.<\/span>set_xticks<\/span>([])<\/span>\r\n    # \u7e26\u8ef8\u76ee\u76db<\/span>\r\n    ax<\/span>.<\/span>set_yticks<\/span>([])<\/span>\r\n    ax<\/span>.<\/span>set_title<\/span>(<\/span>r<\/span>'$f(x, t) = \\sin(x - v t)$'<\/span>)<\/span>\r\n    ax<\/span>.<\/span>set_xlabel<\/span>(<\/span>r<\/span>'$x \\quad \\rightarrow$'<\/span>)<\/span>\r\n    ax<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'gray'<\/span>,<\/span> ls<\/span>=<\/span>'--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\n    ax<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'gray'<\/span>,<\/span> ls<\/span>=<\/span>'--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\n\r\n    t<\/span> =<\/span> 2<\/span>*<\/span>np<\/span>.<\/span>pi<\/span>\/<\/span>frames<\/span> *<\/span> i<\/span>\r\n    # x\u306e\u7bc4\u56f2<\/span>\r\n    x<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>-<\/span>10<\/span>,<\/span> 10<\/span>,<\/span> 200<\/span>)<\/span>\r\n\r\n    ax<\/span>.<\/span>plot<\/span>(<\/span>x<\/span>,<\/span> f<\/span>(<\/span>x<\/span>,<\/span> t<\/span>),<\/span> c<\/span> =<\/span> 'k'<\/span>)<\/span>\r\n\r\n# \u5909\u6570\u540d frames \u306f\u56fa\u5b9a\u3002<\/span>\r\n# \u8ecc\u9053\u5168\u4f53\u3092 frames \u500b\u306b\u5206\u5272\u3057\u3066\u30d1\u30e9\u30d1\u30e9\u30a2\u30cb\u30e1\u306b\u3002<\/span>\r\n# frames \u6570\u3092\u5897\u3084\u3057\uff0cinterval \u3092\u77ed\u304f\u3059\u308b\u3068\u6ed1\u3089\u304b\u306b\u3002<\/span>\r\nframes<\/span> =<\/span> 30<\/span>\r\nani<\/span> =<\/span> FuncAnimation<\/span>(<\/span>fig<\/span>,<\/span> func<\/span>,<\/span>  \r\n        # interval \u306f frame \u9593\u306e\u6642\u9593\u3092\u30df\u30ea\u79d2\u5358\u4f4d\u3067\u3002<\/span>\r\n        interval<\/span> =<\/span> 100<\/span>,<\/span> \r\n        # \u7aef\u70b9\u3082\u542b\u3081\u3066 frames \u500b\u306e\u30b3\u30de\u6570\u306b\u3057\u3066\u307f\u305f\u3002<\/span>\r\n        frames<\/span> =<\/span> range<\/span>(<\/span>frames<\/span>))<\/span>\r\n\r\n# \u52d5\u753b\u3092 jupyterhub \u306e\u30db\u30fc\u30e0\u306b mp4 \u30d5\u30a1\u30a4\u30eb\u3068\u3057\u3066\u4fdd\u5b58\u3002<\/span>\r\n# \u5c0f\u7dba\u9e97\u306a\u52d5\u753b\u306b\u3059\u308b\u305f\u3081\u306b\u89e3\u50cf\u5ea6 dpi \u3092\u8a2d\u5b9a<\/span>\r\nani<\/span>.<\/span>save<\/span>(<\/span>\"wave-anim01.mp4\"<\/span>,<\/span> dpi<\/span>=<\/span>288<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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