{"id":5755,"date":"2024-03-18T15:00:11","date_gmt":"2024-03-18T06:00:11","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=5755"},"modified":"2025-03-20T15:45:35","modified_gmt":"2025-03-20T06:45:35","slug":"%e5%8f%82%e8%80%83%ef%bc%9asympy-plotting-backends-%e3%81%a7%e5%88%9d%e7%ad%89%e9%96%a2%e6%95%b0%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\/%e5%8f%82%e8%80%83%ef%bc%9a%e5%88%9d%e7%ad%89%e9%96%a2%e6%95%b0%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%82%92%e6%8f%8f%e3%81%8f\/%e5%8f%82%e8%80%83%ef%bc%9asympy-plotting-backends-%e3%81%a7%e5%88%9d%e7%ad%89%e9%96%a2%e6%95%b0%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\uff1aSymPy Plotting Backends \u3067\u521d\u7b49\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\uff08Plot functions \u7de8\uff09"},"content":{"rendered":"

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\u30e2\u30b8\u30e5\u30fc\u30eb\u306e import \u3068\u3044\u304f\u3064\u304b\u306e\u8a2d\u5b9a<\/h3>\n

Python \u306e SymPy + SymPy Plotting Backends (SPB) \u3067\u521d\u7b49\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3002\u95a2\u6570\u306f\u5168\u3066 SymPy \u306e\u95a2\u6570\u3092\u4f7f\u3046\u3002NumPy \u306f\u4f7f\u308f\u306a\u3044\u65b9\u91dd\u3067\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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In\u00a0[1]:<\/div>\n
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from<\/span> sympy.abc<\/span> import<\/span> *<\/span>\r\nfrom<\/span> sympy<\/span> import<\/span> *<\/span>\r\n# SymPy Plotting Backends<\/span>\r\nfrom<\/span> spb<\/span> import<\/span> *<\/span>\r\n\r\n# \u03c0<\/span>\r\nPi<\/span> =<\/span> float<\/span>(<\/span>pi<\/span>)<\/span>\r\n\r\n# \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# \u30b0\u30e9\u30d5\u3092\u63cf\u304f\u305f\u3081\u3067\u306f\u306a\u304f\u30c7\u30d5\u30a9\u30eb\u30c8\u8a2d\u5b9a\u306e\u305f\u3081<\/span>\r\nimport<\/span> matplotlib.pyplot<\/span> as<\/span> plt<\/span>\r\n# font \u306e\u8a2d\u5b9a<\/span>\r\nplt<\/span>.<\/span>rcParams<\/span>[<\/span>'font.family'<\/span>]<\/span> =<\/span> 'serif'<\/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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\u3079\u304d\u95a2\u6570<\/h3>\n
\u307e\u305a\uff0c$y = x^{-1}$ \u306e\u30b0\u30e9\u30d5\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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plot<\/span>(<\/span>1<\/span>\/<\/span>x<\/span>,<\/span> (<\/span>x<\/span>,<\/span> -<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> \r\n     xlim<\/span> =<\/span> (<\/span>-<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> ylim<\/span> =<\/span> (<\/span>-<\/span>10<\/span>,<\/span> 10<\/span>))<\/span>;<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$y=x^{-1}$ \u306e\u30b0\u30e9\u30d5\u306e $x\uff1d0$ \u4ed8\u8fd1\uff0c$y \\rightarrow -\\infty$ \u3068 $y \\rightarrow +\\infty$ \u3092\u7e26\u306e\u76f4\u7dda\u3067\u3064\u306a\u3044\u3067\u3057\u307e\u3046\u3002<\/p>\n
\u4e0d\u9023\u7d9a\u70b9\u3092\u3064\u306a\u3052\u306a\u3044\u5bfe\u7b56<\/h4>\n
detect_poles=True<\/code> \u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u3064\u3051\u3066\uff0c\u3055\u3089\u306b n<\/code> \u306e\u5024\u3092\u5927\u304d\u3081\u306b\u3059\u308b\u3068\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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plot<\/span>(<\/span>1<\/span>\/<\/span>x<\/span>,<\/span> (<\/span>x<\/span>,<\/span> -<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> \r\n     xlim<\/span> =<\/span> (<\/span>-<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> ylim<\/span> =<\/span> (<\/span>-<\/span>10<\/span>,<\/span> 10<\/span>),<\/span> \r\n     detect_poles<\/span> =<\/span> True<\/span>,<\/span> n<\/span> =<\/span> 1e4<\/span>)<\/span>;<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$y = x^{-2}, \\ x^{-1}, \\ x^2, \\ x^3$ \u306e\u30b0\u30e9\u30d5\u4f8b\u3002$y = x^{-1}$ \u306e\u4e0d\u9023\u7d9a\u70b9\u3092\u3064\u306a\u3052\u306a\u3044\u3088\u3046\u306b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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plot<\/span>(<\/span>x<\/span>**<\/span>(<\/span>-<\/span>2<\/span>),<\/span> x<\/span>**<\/span>(<\/span>-<\/span>1<\/span>),<\/span> x<\/span>**<\/span>2<\/span>,<\/span> x<\/span>**<\/span>3<\/span>,<\/span> (<\/span>x<\/span>,<\/span> -<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> \r\n     xlim<\/span> =<\/span> (<\/span>-<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> ylim<\/span> =<\/span> (<\/span>-<\/span>10<\/span>,<\/span> 10<\/span>),<\/span> size<\/span> =<\/span> (<\/span>6.4<\/span>,<\/span> 6.4<\/span>),<\/span>\r\n     detect_poles<\/span> =<\/span> True<\/span>,<\/span> n<\/span> =<\/span> 1e4<\/span>)<\/span>;<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4ee5\u4e0b\u3067\u306f\u300c\u53c2\u8003\uff1a\u521d\u7b49\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/a>\u300d\u30b7\u30ea\u30fc\u30ba\u306e\u4ed6\u306e\u30da\u30fc\u30b8\u306e\u898b\u3066\u304f\u308c\u306b\u5408\u308f\u305b\u3066\uff0c\u3044\u304f\u3064\u304b\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3057\u3066\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u4f8b\u3092\u7d39\u4ecb\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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p<\/span> =<\/span> plot<\/span>((<\/span>x<\/span>**<\/span>(<\/span>-<\/span>2<\/span>),<\/span> '$x^{-2}$'<\/span>),<\/span> \r\n         (<\/span>x<\/span>**<\/span>(<\/span>-<\/span>1<\/span>),<\/span> '$x^{-1}$'<\/span>),<\/span>\r\n         (<\/span>x<\/span>**<\/span>2<\/span>,<\/span> '$x^2$'<\/span>),<\/span>\r\n         (<\/span>x<\/span>**<\/span>3<\/span>,<\/span> '$x^3$'<\/span>),<\/span> (<\/span>x<\/span>,<\/span> -<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> \r\n         xlim<\/span> =<\/span> (<\/span>-<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> ylim<\/span> =<\/span> (<\/span>-<\/span>10<\/span>,<\/span> 10<\/span>),<\/span> \r\n         detect_poles<\/span> =<\/span> True<\/span>,<\/span> n<\/span> =<\/span> 1e4<\/span>,<\/span> \r\n         size<\/span> =<\/span> (<\/span>6.4<\/span>,<\/span> 6.4<\/span>),<\/span> show<\/span> =<\/span> False<\/span>)<\/span>\r\n\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> p<\/span>.<\/span>fig<\/span>,<\/span> p<\/span>.<\/span>ax<\/span>\r\nfig<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\n\r\n# x \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_xticks<\/span>([<\/span>i<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>)])<\/span>\r\nax<\/span>.<\/span>set_xlabel<\/span>(<\/span>'$x$'<\/span>,<\/span> fontsize<\/span> =<\/span> 12<\/span>)<\/span>\r\n# y <\/span>\r\nax<\/span>.<\/span>set_ylabel<\/span>(<\/span>''<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306f dotted \u306b<\/span>\r\nax<\/span>.<\/span>grid<\/span>(<\/span>ls<\/span> =<\/span> ':'<\/span>)<\/span>\r\n# x\u8ef8 y\u8ef8\u306f dashed \u306b<\/span>\r\nax<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/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>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\n\r\nax<\/span>.<\/span>legend<\/span>(<\/span>fontsize<\/span> =<\/span> 12<\/span>);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$\\displaystyle y = \\sqrt{x}, \\ \\frac{1}{\\sqrt{x}}$ \u306e\u30b0\u30e9\u30d5\u4f8b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[6]:<\/div>\n
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# x = 0 \u306f\u9664\u304f<\/span>\r\np<\/span> =<\/span> plot<\/span>((<\/span>sqrt<\/span>(<\/span>x<\/span>),<\/span> '$<\/span>\\\\<\/span>sqrt<\/span>{x}<\/span>$'<\/span>,<\/span> (<\/span>x<\/span>,<\/span> 0<\/span>,<\/span> 5<\/span>)),<\/span> \r\n         (<\/span>1<\/span>\/<\/span>sqrt<\/span>(<\/span>x<\/span>),<\/span> '$1\/<\/span>\\\\<\/span>sqrt<\/span>{x}<\/span>$'<\/span>,<\/span> (<\/span>x<\/span>,<\/span> 0.0001<\/span>,<\/span> 5<\/span>)),<\/span> \r\n         xlim<\/span> =<\/span> (<\/span>0<\/span>,<\/span> 5<\/span>),<\/span> ylim<\/span> =<\/span> (<\/span>0<\/span>,<\/span> 5<\/span>),<\/span> \r\n         size<\/span> =<\/span> (<\/span>6.4<\/span>,<\/span> 4.8<\/span>),<\/span> show<\/span> =<\/span> False<\/span>)<\/span>\r\n\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> p<\/span>.<\/span>fig<\/span>,<\/span> p<\/span>.<\/span>ax<\/span>\r\nfig<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\n\r\n# x <\/span>\r\nax<\/span>.<\/span>set_xlabel<\/span>(<\/span>'$x$'<\/span>,<\/span> fontsize<\/span> =<\/span> 12<\/span>)<\/span>\r\n# y <\/span>\r\nax<\/span>.<\/span>set_ylabel<\/span>(<\/span>''<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306f dotted \u306b<\/span>\r\nax<\/span>.<\/span>grid<\/span>(<\/span>ls<\/span> =<\/span> ':'<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>legend<\/span>(<\/span>fontsize<\/span> =<\/span> 12<\/span>);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6307\u6570\u95a2\u6570<\/h3>\n
$y = e^{-x}, \\ e^x$ \u306e\u30b0\u30e9\u30d5\u4f8b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[7]:<\/div>\n
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p<\/span> =<\/span> plot<\/span>(<\/span>exp<\/span>(<\/span>-<\/span>x<\/span>),<\/span> exp<\/span>(<\/span>x<\/span>),<\/span> (<\/span>x<\/span>,<\/span> -<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> \r\n         xlim<\/span> =<\/span> (<\/span>-<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> ylim<\/span> =<\/span> (<\/span>-<\/span>1<\/span>,<\/span> 30<\/span>),<\/span> \r\n         size<\/span> =<\/span> (<\/span>6.4<\/span>,<\/span> 4.8<\/span>),<\/span> show<\/span> =<\/span> False<\/span>)<\/span>\r\n\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> p<\/span>.<\/span>fig<\/span>,<\/span> p<\/span>.<\/span>ax<\/span>\r\nfig<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\n\r\n# x \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_xticks<\/span>([<\/span>i<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>)])<\/span>\r\nax<\/span>.<\/span>set_xlabel<\/span>(<\/span>'$x$'<\/span>,<\/span> fontsize<\/span> =<\/span> 12<\/span>)<\/span>\r\n# y <\/span>\r\nax<\/span>.<\/span>set_ylabel<\/span>(<\/span>''<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306f dotted \u306b<\/span>\r\nax<\/span>.<\/span>grid<\/span>(<\/span>ls<\/span> =<\/span> ':'<\/span>)<\/span>\r\n# x\u8ef8 y\u8ef8\u306f dashed \u306b<\/span>\r\nax<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/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>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\n\r\nax<\/span>.<\/span>legend<\/span>(<\/span>fontsize<\/span> =<\/span> 14<\/span>);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4e09\u89d2\u95a2\u6570<\/h3>\n
$ y = \\sin x, \\ \\cos x, \\ \\tan x $ \u306e\u30b0\u30e9\u30d5\u4f8b\u3002$\\tan x$ \u306e\u4e0d\u9023\u7d9a\u70b9\u306e\u51e6\u7406\u3068\uff0c$x$ \u8ef8\u306e\u76ee\u76db\u3092 $\\pi\/2$ \u3054\u3068\u306b\u3057\u3066\u30e9\u30d9\u30eb\u3092\u3064\u3051\u308b\u4f8b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[8]:<\/div>\n
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p<\/span> =<\/span> plot<\/span>((<\/span>sin<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>sin x$\"<\/span>),<\/span> \r\n         (<\/span>cos<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>cos x$\"<\/span>),<\/span> \r\n         (<\/span>tan<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>tan x$\"<\/span>),<\/span> (<\/span>x<\/span>,<\/span> -<\/span>2<\/span>*<\/span>pi<\/span>,<\/span> 2<\/span>*<\/span>pi<\/span>+<\/span>1<\/span>),<\/span> \r\n         xlim<\/span> =<\/span> (<\/span>-<\/span>2<\/span>*<\/span>pi<\/span>,<\/span> 2<\/span>*<\/span>pi<\/span>+<\/span>1<\/span>),<\/span> ylim<\/span> =<\/span> (<\/span>-<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> \r\n         size<\/span> =<\/span> (<\/span>6.4<\/span>,<\/span> 6.4<\/span>),<\/span> show<\/span>=<\/span>False<\/span>,<\/span>\r\n         # \u4e0d\u9023\u7d9a\u70b9\u3092\u3064\u306a\u3052\u306a\u3044\u5bfe\u7b56<\/span>\r\n         detect_poles<\/span> =<\/span> True<\/span>)<\/span>\r\n\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> p<\/span>.<\/span>fig<\/span>,<\/span> p<\/span>.<\/span>ax<\/span>\r\nfig<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\n\r\n# x \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_xticks<\/span>(<\/span>\r\n    [<\/span>i<\/span>*<\/span>Pi<\/span>\/<\/span>2<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>4<\/span>,<\/span> 5<\/span>)],<\/span> \r\n    [<\/span>\"$-2 \\pi$\"<\/span>,<\/span> \"$-3 \\pi\/2$\"<\/span>,<\/span> \"$-\\pi$\"<\/span>,<\/span> \"$-\\pi\/2$\"<\/span>,<\/span>\"$0$\"<\/span>,<\/span>\r\n     \"$\\pi\/2$\"<\/span>,<\/span> \"$\\pi$\"<\/span>,<\/span> \"$3 \\pi\/2$\"<\/span>,<\/span> \"$2 \\pi$\"<\/span>])<\/span>\r\nax<\/span>.<\/span>set_xlabel<\/span>(<\/span>'$x$'<\/span>,<\/span> fontsize<\/span> =<\/span> 12<\/span>)<\/span>\r\n# y \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_yticks<\/span>([<\/span>i<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>)])<\/span>\r\nax<\/span>.<\/span>set_ylabel<\/span>(<\/span>''<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306f dotted \u3067<\/span>\r\nplt<\/span>.<\/span>grid<\/span>(<\/span>ls<\/span> =<\/span> ':'<\/span>)<\/span>\r\n# x\u8ef8 y\u8ef8 \u306f dashed \u3067<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>legend<\/span>(<\/span>fontsize<\/span> =<\/span> 12<\/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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\u9006\u4e09\u89d2\u95a2\u6570<\/h3>\n
$y = \\sin^{-1} x = \\arcsin x =$ asin(x)<\/code> \u306e\u5b9a\u7fa9\u57df\u306f $-1 \\leq x \\leq 1$
\n$y = \\cos^{-1} x = \\arccos x =$ acos(x)<\/code> \u306e\u5b9a\u7fa9\u57df\u306f $-1 \\leq x \\leq 1$
\n$y = \\tan^{-1} x = \\arctan x =$ atan(x)<\/code> \u306e\u5b9a\u7fa9\u57df\u306f $-\\infty < x < \\infty$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[9]:<\/div>\n
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p<\/span> =<\/span> plot<\/span>((<\/span>asin<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>arcsin x$\"<\/span>),<\/span> \r\n         (<\/span>acos<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>arccos x$\"<\/span>),<\/span> (<\/span>x<\/span>,<\/span> -<\/span>1<\/span>,<\/span> 1<\/span>),<\/span> \r\n         xlim<\/span> =<\/span> (<\/span>-<\/span>1<\/span>,<\/span> 1<\/span>),<\/span> ylim<\/span>=<\/span>(<\/span>-<\/span>0.5<\/span>,<\/span> 1<\/span>),<\/span> show<\/span> =<\/span> False<\/span>)<\/span>\r\n\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> p<\/span>.<\/span>fig<\/span>,<\/span> p<\/span>.<\/span>ax<\/span>\r\nfig<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\n\r\n# x \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_xticks<\/span>([<\/span>0.2<\/span>*<\/span>i<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>)])<\/span>\r\nax<\/span>.<\/span>set_xlabel<\/span>(<\/span>'$x$'<\/span>,<\/span> fontsize<\/span> =<\/span> 12<\/span>)<\/span>\r\n# y \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_yticks<\/span>(<\/span>\r\n    [<\/span>i<\/span>*<\/span>Pi<\/span>\/<\/span>4<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>2<\/span>,<\/span> 5<\/span>)],<\/span> \r\n    [<\/span>\"$-\\pi\/2$\"<\/span>,<\/span> \"\"<\/span>,<\/span> \"$0$\"<\/span>,<\/span> \"\"<\/span>,<\/span> \"$\\pi\/2$\"<\/span>,<\/span> \"\"<\/span>,<\/span> \"$\\pi$\"<\/span>])<\/span>\r\nax<\/span>.<\/span>set_ylabel<\/span>(<\/span>''<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306f dotted \u3067<\/span>\r\nplt<\/span>.<\/span>grid<\/span>(<\/span>ls<\/span> =<\/span> ':'<\/span>)<\/span>\r\n# x\u8ef8 y\u8ef8 \u306f dashed \u3067<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>legend<\/span>(<\/span>fontsize<\/span>=<\/span>12<\/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[10]:<\/div>\n
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p<\/span> =<\/span> plot<\/span>(<\/span>atan<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>arctan x$\"<\/span>,<\/span> (<\/span>x<\/span>,<\/span> -<\/span>30<\/span>,<\/span> 30<\/span>),<\/span> \r\n         xlim<\/span> =<\/span> (<\/span>-<\/span>30<\/span>,<\/span> 30<\/span>),<\/span> ylim<\/span>=<\/span>(<\/span>-<\/span>pi<\/span>\/<\/span>2<\/span>,<\/span> pi<\/span>\/<\/span>2<\/span>),<\/span> show<\/span> =<\/span> False<\/span>)<\/span>\r\n\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> p<\/span>.<\/span>fig<\/span>,<\/span> p<\/span>.<\/span>ax<\/span>\r\nfig<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\n\r\n# x <\/span>\r\nax<\/span>.<\/span>set_xlabel<\/span>(<\/span>'$x$'<\/span>,<\/span> fontsize<\/span> =<\/span> 12<\/span>)<\/span>\r\n# y \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_yticks<\/span>(<\/span>\r\n    [<\/span>i<\/span>*<\/span>Pi<\/span>\/<\/span>4<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>2<\/span>,<\/span> 3<\/span>)],<\/span> \r\n    [<\/span>\"$-\\pi\/2$\"<\/span>,<\/span> \"$-\\pi\/4$\"<\/span>,<\/span> \"$0$\"<\/span>,<\/span> \"$\\pi\/4$\"<\/span>,<\/span> \"$\\pi\/2$\"<\/span>])<\/span>\r\nax<\/span>.<\/span>set_ylabel<\/span>(<\/span>''<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306f dotted \u3067<\/span>\r\nplt<\/span>.<\/span>grid<\/span>(<\/span>ls<\/span> =<\/span> ':'<\/span>)<\/span>\r\n# x\u8ef8 y\u8ef8 \u306f dashed \u3067<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>legend<\/span>(<\/span>fontsize<\/span>=<\/span>12<\/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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3\u3064\u306e\u9006\u4e09\u89d2\u95a2\u6570\u3092\u4e00\u7dd2\u306b\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[11]:<\/div>\n
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p<\/span> =<\/span> plot<\/span>((<\/span>asin<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>arcsin x$\"<\/span>,<\/span> (<\/span>x<\/span>,<\/span> -<\/span>1<\/span>,<\/span> 1<\/span>)),<\/span> \r\n         (<\/span>acos<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>arccos x$\"<\/span>,<\/span> (<\/span>x<\/span>,<\/span> -<\/span>1<\/span>,<\/span> 1<\/span>)),<\/span> \r\n         (<\/span>atan<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>arctan x$\"<\/span>,<\/span> (<\/span>x<\/span>,<\/span> -<\/span>10<\/span>,<\/span> 10<\/span>)),<\/span> \r\n         xlim<\/span> =<\/span> (<\/span>-<\/span>10<\/span>,<\/span> 10<\/span>),<\/span> ylim<\/span> =<\/span> (<\/span>-<\/span>pi<\/span>\/<\/span>2<\/span>,<\/span> pi<\/span>),<\/span> \r\n         size<\/span> =<\/span> (<\/span>6.4<\/span>,<\/span> 4.8<\/span>),<\/span> show<\/span> =<\/span> False<\/span>)<\/span>\r\n\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> p<\/span>.<\/span>fig<\/span>,<\/span> p<\/span>.<\/span>ax<\/span>\r\nfig<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\n\r\n# x \u306e\u76ee\u76db<\/span>\r\nxticl<\/span> =<\/span> []<\/span>\r\nfor<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>10<\/span>,<\/span> 11<\/span>,<\/span> 2<\/span>):<\/span>\r\n    xticl<\/span>.<\/span>append<\/span>(<\/span>str<\/span>(<\/span>i<\/span>))<\/span>\r\n    xticl<\/span>.<\/span>append<\/span>(<\/span>\"\"<\/span>)<\/span>\r\nax<\/span>.<\/span>set_xticks<\/span>([<\/span>i<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>10<\/span>,<\/span> 11<\/span>)],<\/span> xticl<\/span>[:<\/span>-<\/span>1<\/span>])<\/span>\r\nax<\/span>.<\/span>set_xlabel<\/span>(<\/span>'$x$'<\/span>,<\/span> fontsize<\/span> =<\/span> 12<\/span>)<\/span>\r\n# y \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_yticks<\/span>(<\/span>\r\n    [<\/span>i<\/span>*<\/span>Pi<\/span>\/<\/span>4<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>2<\/span>,<\/span> 5<\/span>)],<\/span> \r\n    [<\/span>\"$-\\pi\/2$\"<\/span>,<\/span> \"\"<\/span>,<\/span> \"$0$\"<\/span>,<\/span> \"\"<\/span>,<\/span> \"$\\pi\/2$\"<\/span>,<\/span> \"\"<\/span>,<\/span> \"$\\pi$\"<\/span>])<\/span>\r\nax<\/span>.<\/span>set_ylabel<\/span>(<\/span>''<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306f dotted \u3067<\/span>\r\nplt<\/span>.<\/span>grid<\/span>(<\/span>ls<\/span> =<\/span> ':'<\/span>)<\/span>\r\n# x\u8ef8 y\u8ef8 \u306f dashed \u3067<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>legend<\/span>(<\/span>fontsize<\/span>=<\/span>12<\/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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\u53cc\u66f2\u7dda\u95a2\u6570<\/h3>\n
$y = \\sinh x, \\ \\cosh x, \\ \\tanh x$ \u306e\u30b0\u30e9\u30d5\u4f8b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[12]:<\/div>\n
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p<\/span> =<\/span> plot<\/span>((<\/span>sinh<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>sinh x$\"<\/span>),<\/span> \r\n         (<\/span>cosh<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>cosh x$\"<\/span>),<\/span> (<\/span>x<\/span>,<\/span> -<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> \r\n         xlim<\/span> =<\/span> (<\/span>-<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> ylim<\/span> =<\/span> (<\/span>-<\/span>50<\/span>,<\/span> 50<\/span>),<\/span> show<\/span> =<\/span> False<\/span>)<\/span>\r\n\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> p<\/span>.<\/span>fig<\/span>,<\/span> p<\/span>.<\/span>ax<\/span>\r\nfig<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\n\r\n# x \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_xticks<\/span>([<\/span>i<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>)])<\/span>\r\nax<\/span>.<\/span>set_xlabel<\/span>(<\/span>'$x$'<\/span>,<\/span> fontsize<\/span> =<\/span> 12<\/span>)<\/span>\r\n# y <\/span>\r\nax<\/span>.<\/span>set_ylabel<\/span>(<\/span>''<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306f dotted \u3067<\/span>\r\nplt<\/span>.<\/span>grid<\/span>(<\/span>ls<\/span> =<\/span> ':'<\/span>)<\/span>\r\n# x\u8ef8 y\u8ef8 \u306f dashed \u3067<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>legend<\/span>(<\/span>fontsize<\/span>=<\/span>12<\/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[13]:<\/div>\n
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p<\/span> =<\/span> plot<\/span>((<\/span>tanh<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>tanh x$\"<\/span>),<\/span> (<\/span>x<\/span>,<\/span> -<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> legend<\/span> =<\/span> True<\/span>,<\/span>\r\n         xlim<\/span> =<\/span> (<\/span>-<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> ylim<\/span>=<\/span>(<\/span>-<\/span>1<\/span>,<\/span> 1<\/span>),<\/span> show<\/span> =<\/span> False<\/span>)<\/span>\r\n\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> p<\/span>.<\/span>fig<\/span>,<\/span> p<\/span>.<\/span>ax<\/span>\r\nfig<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\n\r\n# x \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_xticks<\/span>([<\/span>i<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>)])<\/span>\r\nax<\/span>.<\/span>set_xlabel<\/span>(<\/span>'$x$'<\/span>,<\/span> fontsize<\/span> =<\/span> 12<\/span>)<\/span>\r\n# y \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_yticks<\/span>([<\/span>0.2<\/span>*<\/span>i<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>)])<\/span>\r\nax<\/span>.<\/span>set_ylabel<\/span>(<\/span>''<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306f dotted \u3067<\/span>\r\nplt<\/span>.<\/span>grid<\/span>(<\/span>ls<\/span> =<\/span> ':'<\/span>)<\/span>\r\n# x\u8ef8 y\u8ef8 \u306f dashed \u3067<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>legend<\/span>(<\/span>fontsize<\/span>=<\/span>12<\/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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3\u3064\u306e\u53cc\u66f2\u7dda\u95a2\u6570\u3092\u4e00\u7dd2\u306b\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[14]:<\/div>\n
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p<\/span> =<\/span> plot<\/span>((<\/span>sinh<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>sinh x$\"<\/span>),<\/span> \r\n         (<\/span>cosh<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>cosh x$\"<\/span>),<\/span> \r\n         (<\/span>tanh<\/span>(<\/span>x<\/span>),<\/span> \"$<\/span>\\\\<\/span>tanh x$\"<\/span>),<\/span> (<\/span>x<\/span>,<\/span> -<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> \r\n         xlim<\/span> =<\/span> (<\/span>-<\/span>5<\/span>,<\/span> 5<\/span>),<\/span> ylim<\/span> =<\/span> (<\/span>-<\/span>10<\/span>,<\/span> 10<\/span>),<\/span> \r\n         size<\/span> =<\/span> (<\/span>6.4<\/span>,<\/span> 6.4<\/span>),<\/span> show<\/span> =<\/span> False<\/span>)<\/span>\r\n\r\nfig<\/span>,<\/span> ax<\/span> =<\/span> p<\/span>.<\/span>fig<\/span>,<\/span> p<\/span>.<\/span>ax<\/span>\r\nfig<\/span>.<\/span>tight_layout<\/span>()<\/span>\r\n\r\n# x \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_xticks<\/span>([<\/span>i<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>)])<\/span>\r\nax<\/span>.<\/span>set_xlabel<\/span>(<\/span>'$x$'<\/span>,<\/span> fontsize<\/span> =<\/span> 12<\/span>)<\/span>\r\n# y \u306e\u76ee\u76db<\/span>\r\nax<\/span>.<\/span>set_yticks<\/span>([<\/span>i<\/span> for<\/span> i<\/span> in<\/span> range<\/span>(<\/span>-<\/span>10<\/span>,<\/span> 11<\/span>)])<\/span>\r\nax<\/span>.<\/span>set_ylabel<\/span>(<\/span>''<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\uff08\u683c\u5b50\u7dda\uff09\u306f dotted \u3067<\/span>\r\nplt<\/span>.<\/span>grid<\/span>(<\/span>ls<\/span> =<\/span> ':'<\/span>)<\/span>\r\n# x\u8ef8 y\u8ef8 \u306f dashed \u3067<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> c<\/span>=<\/span>'k'<\/span>,<\/span> ls<\/span> =<\/span> '--'<\/span>,<\/span> lw<\/span>=<\/span>0.5<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>legend<\/span>(<\/span>fontsize<\/span>=<\/span>12<\/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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\u9006\u53cc\u66f2\u7dda\u95a2\u6570<\/h3>\n
$ y = \\sinh^{-1} x = \\mbox{arsinh}\\ x = $ np.arcsinh(x)<\/code> \u306e\u5b9a\u7fa9\u57df\u306f $ -\\infty < x < \\infty$<\/p>\n
$ y = \\cosh^{-1} x = \\mbox{arcosh}\\ x = $ np.arccosh(x)<\/code> \u306e\u5b9a\u7fa9\u57df\u306f $ 1 \\leq x < \\infty$<\/p>\n
$ y = \\tanh^{-1} x = \\mbox{artanh}\\ x = $ np.arctanh(x)<\/code> \u306e\u5b9a\u7fa9\u57df\u306f $ -1 < x < 1$<\/p>\n