{"id":6003,"date":"2023-10-23T11:30:12","date_gmt":"2023-10-23T02:30:12","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=6003"},"modified":"2023-10-23T11:34:54","modified_gmt":"2023-10-23T02:34:54","slug":"matplotlib-%e3%81%a7%e9%9b%bb%e5%a0%b4%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e6%96%b9%e5%90%91%e5%a0%b4%e3%82%92%e6%8f%8f%e3%81%8f","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/6003\/","title":{"rendered":"Matplotlib \u3067\u96fb\u5834\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u5834\u3092\u63cf\u304f"},"content":{"rendered":"

\u6b63\u8ca0\u306e\u70b9\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\u3092\u8868\u3059\u65b9\u5411\u5834\u3092 Python \u306e Matplotlib \u3067\u63cf\u304f\u3002
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\u6b63\u8ca0\u306e\u70b9\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834<\/h3>\n

$\\boldsymbol{r}_1$ \u306b\u3042\u308b\u6b63\u96fb\u8377 $q\\ (>0)$ \u3068\uff0c$\\boldsymbol{r}_2$ \u306b\u3042\u308b\u8ca0\u96fb\u8377 $-q$ \u304c\u3064\u304f\u308b\u96fb\u5834\u30d9\u30af\u30c8\u30eb $\\boldsymbol{E}$ \u306f<\/p>\n

\\begin{eqnarray}
\n\\boldsymbol{E}
\n&=& \\frac{q}{4\\pi \\varepsilon_0} \\frac{\\boldsymbol{r} – \\boldsymbol{r}_1}{|\\boldsymbol{r} – \\boldsymbol{r}_1|^3}
\n– \\frac{q}{4\\pi \\varepsilon_0} \\frac{\\boldsymbol{r} – \\boldsymbol{r}_2}{|\\boldsymbol{r} – \\boldsymbol{r}_2|^3}
\n\\end{eqnarray}<\/p>\n

$z=0$ \u306e $xy$ \u5e73\u9762\u30672\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u5834\u3092\u63cf\u304f\u3002\u9069\u5b9c\u7121\u6b21\u5143\u5316\u3092\u884c\u3044\uff0c
\n$\\displaystyle \\frac{q}{4\\pi \\varepsilon_0}\\rightarrow 1$ \u3068\u3059\u308b\u3002\u307e\u305f\uff0c<\/p>\n

$$\\boldsymbol{r} = (x, y, 0), \\quad \\boldsymbol{r}_1 = (0, 1, 0),
\n\\quad \\boldsymbol{r}_2 = (0, -1, 0)$$<\/p>\n

\u3068\u3059\u308b\u3068\uff0c<\/p>\n

$$E_x = \\frac{x}{\\left(x^2 + (y-1)^2\\right)^{3\/2}}-\\frac{x}{\\left(x^2 + (y+1)^2\\right)^{3\/2}}$$$$E_y = \\frac{y-1}{\\left(x^2 + (y-1)^2\\right)^{3\/2}}-
\n\\frac{y+1}{\\left(x^2 + (y+1)^2\\right)^{3\/2}}$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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$\\boldsymbol{E}$ \u306e\u5411\u304d\u3092\u8868\u3059\u65b9\u5411\u5834\uff08\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u5834\uff09<\/h3>\n

\u4e00\u822c\u306b\u30d9\u30af\u30c8\u30eb\u306f\u5927\u304d\u3055\u3068\u5411\u304d\u3092\u8868\u3059\u3002\u96fb\u5834 $\\boldsymbol{E}$ \u306e\u5927\u304d\u3055\u306f\u96fb\u8377\u304b\u3089\u306e\u8ddd\u96e2\u306e2\u4e57\u306b\u53cd\u6bd4\u4f8b\u3059\u308b\u306e\u3067\uff0c]\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u304c\u5927\u304d\u304f\u5909\u5316\u3059\u308b\u3002\u898b\u3084\u3059\u304f\u3059\u308b\u305f\u3081\u306b\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b $\\boldsymbol{E}$ \u306e\u5411\u304d\u3092\u8868\u3059\u65b9\u5411\u5834\uff0c\u3059\u306a\u308f\u3061\u5927\u304d\u3055\u304c $1$ \u306e\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u5834\u3092\u5b9a\u7fa9\u3057\u3066\uff0c\u30d9\u30af\u30c8\u30eb\u306e\u5411\u304d\u306e\u307f\u3092\u6b63\u3057\u304f\u63cf\u753b\u3059\u308b\u3002<\/p>\n

$$\\hat{\\boldsymbol{E}} \\equiv \\frac{\\boldsymbol{E}}{\\sqrt{\\boldsymbol{E}\\cdot\\boldsymbol{E}}}$$$$\\hat{E}_x = \\frac{E_x}{\\sqrt{E_x^2 + E_y^2}}$$$$\\hat{E}_y = \\frac{E_y}{\\sqrt{E_x^2 + E_y^2}}$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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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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# NumPy <\/span>\r\nimport<\/span> numpy<\/span> as<\/span> np<\/span>\r\n# Matplotlib <\/span>\r\nimport<\/span> matplotlib.pyplot<\/span> as<\/span> plt<\/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# \u30d5\u30a9\u30f3\u30c8\u8a2d\u5b9a<\/span>\r\nplt<\/span>.<\/span>rcParams<\/span>[<\/span>'font.family'<\/span>]<\/span> =<\/span> 'Noto Sans CJK JP'<\/span>\r\nplt<\/span>.<\/span>rcParams<\/span>[<\/span>'font.size'<\/span>]<\/span> =<\/span> 14<\/span>\r\nplt<\/span>.<\/span>rcParams<\/span>[<\/span>'xtick.labelsize'<\/span>]<\/span> =<\/span> 12<\/span>\r\nplt<\/span>.<\/span>rcParams<\/span>[<\/span>'ytick.labelsize'<\/span>]<\/span> =<\/span> 12<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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quiver()<\/code> \u3067\u96fb\u5834\u306e\u65b9\u5411\u5834\u3092\u63cf\u304f<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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\u96fb\u5834\u30d9\u30af\u30c8\u30eb\u306e\u5b9a\u7fa9<\/h4>\n
\u96fb\u5834\u30d9\u30af\u30c8\u30eb\u3092 x, y<\/code> \u306e2\u5909\u6570\u95a2\u6570\u3068\u3057\u3066\u5b9a\u7fa9\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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# 1\u500b\u306e\u70b9\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834<\/span>\r\ndef<\/span> Ex<\/span>(<\/span>x<\/span>,<\/span> y<\/span>):<\/span>\r\n    return<\/span> x<\/span>\/<\/span>np<\/span>.<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>\r\ndef<\/span> Ey<\/span>(<\/span>x<\/span>,<\/span> y<\/span>):<\/span>\r\n    return<\/span> y<\/span>\/<\/span>np<\/span>.<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>\r\n\r\n# \u6b63\u8ca0\u306e2\u500b\u306e\u70b9\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834<\/span>\r\ndef<\/span> E2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>):<\/span>\r\n    return<\/span> Ex<\/span>(<\/span>x<\/span>,<\/span> y<\/span>-<\/span>1<\/span>)<\/span> -<\/span> Ex<\/span>(<\/span>x<\/span>,<\/span> y<\/span>+<\/span>1<\/span>)<\/span>\r\ndef<\/span> E2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>):<\/span>\r\n    return<\/span> Ey<\/span>(<\/span>x<\/span>,<\/span> y<\/span>-<\/span>1<\/span>)<\/span> -<\/span> Ey<\/span>(<\/span>x<\/span>,<\/span> y<\/span>+<\/span>1<\/span>)<\/span>\r\n\r\n# \u6b63\u8ca0\u306e2\u500b\u306e\u70b9\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5927\u304d\u3055<\/span>\r\ndef<\/span> E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>):<\/span>\r\n    return<\/span> np<\/span>.<\/span>sqrt<\/span>(<\/span>E2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>**<\/span>2<\/span> +<\/span> E2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>**<\/span>2<\/span>)<\/span>\r\n\r\n# \u898f\u683c\u5316\u3055\u308c\u305f\u96fb\u5834\u30d9\u30af\u30c8\u30eb<\/span>\r\ndef<\/span> hE2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>):<\/span>\r\n    return<\/span> E2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\/<\/span>E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\ndef<\/span> hE2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>):<\/span>\r\n    return<\/span> E2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\/<\/span>E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30d9\u30af\u30c8\u30eb\u5834\u3092\u63cf\u304f<\/h4>\n
\u70b9\u96fb\u8377\u304c $y$ \u8ef8\u4e0a\u306b\u3042\u308b\u306e\u3067\uff0c\u30ea\u30b9\u30c8\u3092\u4f5c\u6210\u3059\u308b\u969b\uff0c\u30d9\u30af\u30c8\u30eb\u306e\u59cb\u70b9\u304c $y$ \u8ef8\u306b\u6765\u306a\u3044\u3088\u3046\u306b\u3057\u3066\u304a\u304f\u3002\uff08\u70b9\u96fb\u8377\u4e0a\u3067\u306f\u96fb\u5834\u306e\u5206\u6bcd\u304c\u30bc\u30ed\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u304b\u3089\u3002\uff09
\n\u4ee5\u4e0b\u306e\u4f8b\u3067\u306f\uff0c$x$ \u5ea7\u6a19\u306f<\/p>\n
$$-5.5, -4.5, \\cdots, -0.5, 0.5, \\cdots, 5.5$$<\/p>\n
\u3068\u306a\u308a\uff0c$y$ \u8ef8\u4e0a ($x = 0$) \u306b\u59cb\u70b9\u304c\u3053\u306a\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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x<\/span> =<\/span> y<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>-<\/span>5.5<\/span>,<\/span> 5.5<\/span>,<\/span> 12<\/span>)<\/span>\r\nx<\/span>,<\/span> y<\/span> =<\/span> np<\/span>.<\/span>meshgrid<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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plt.quiver()<\/code> \u306e\u66f8\u5f0f\u306f…<\/p>\n
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plt<\/span>.<\/span>quiver<\/span>(<\/span>\u59cb\u70b9\u306ex\u5ea7\u6a19<\/span>,<\/span> \u59cb\u70b9\u306ey\u5ea7\u6a19<\/span>,<\/span> \u30d9\u30af\u30c8\u30eb\u306ex\u6210\u5206<\/span>,<\/span> \u30d9\u30af\u30c8\u30eb\u306ey\u6210\u5206<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>6.4<\/span>,<\/span> 6.4<\/span>))<\/span>\r\n\r\n# \u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>-<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>-<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\u306e\u8868\u793a<\/span>\r\nplt<\/span>.<\/span>grid<\/span>()<\/span>\r\n\r\n# x \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\nplt<\/span>.<\/span>xticks<\/span>(<\/span>np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>,<\/span> 1<\/span>))<\/span>\r\n# y \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\nplt<\/span>.<\/span>yticks<\/span>(<\/span>np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>,<\/span> 1<\/span>))<\/span>\r\n\r\n# x, y \u3092\u59cb\u70b9\u3068\u3057\u305f\u30d9\u30af\u30c8\u30eb\u5834\u306e\u8868\u793a<\/span>\r\nplt<\/span>.<\/span>quiver<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> hE2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> hE2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>))<\/span>\r\n\r\n# \u5ff5\u306e\u305f\u3081\u306b\u5404\u30d9\u30af\u30c8\u30eb\u306e\u59cb\u70b9\u3092\u8d64\u70b9\u3067<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> c<\/span>=<\/span>'r'<\/span>,<\/span> s<\/span>=<\/span>5<\/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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pivot='mid'<\/code> \u30aa\u30d7\u30b7\u30e7\u30f3<\/h4>\n
pivot='mid'<\/code> \u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u4f7f\u3046\u3068\uff0c\u30d9\u30af\u30c8\u30eb\u306e\u771f\u3093\u4e2d\u3092\u4e2d\u5fc3\u306b\u3057\u3066\u30d9\u30af\u30c8\u30eb\u306e\u5411\u304d\u3092\u5909\u3048\u3066\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>6.4<\/span>,<\/span> 6.4<\/span>))<\/span>\r\n\r\n# \u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>-<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>-<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\u306e\u8868\u793a<\/span>\r\nplt<\/span>.<\/span>grid<\/span>()<\/span>\r\n\r\n# x \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\nplt<\/span>.<\/span>xticks<\/span>(<\/span>np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>,<\/span> 1<\/span>))<\/span>\r\n# y \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\nplt<\/span>.<\/span>yticks<\/span>(<\/span>np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>,<\/span> 1<\/span>))<\/span>\r\n\r\n# pivot = 'mid' \u3068\u3057\u305f\u30d9\u30af\u30c8\u30eb\u5834\u306e\u8868\u793a<\/span>\r\nplt<\/span>.<\/span>quiver<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> hE2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> hE2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> pivot<\/span> =<\/span> 'mid'<\/span>)<\/span>\r\n\r\n# \u5ff5\u306e\u305f\u3081\u306b\u5404\u30d9\u30af\u30c8\u30eb\u306epivot\u3092\u8d64\u70b9\u3067<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> c<\/span>=<\/span>'r'<\/span>,<\/span> s<\/span>=<\/span>5<\/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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\u70b9\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u30e9\u30d9\u30eb<\/h4>\n
\u6b63\u96fb\u8377\uff0c\u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u30e9\u30d9\u30eb\u3092\u3064\u3051\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[6]:<\/div>\n
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# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>6.4<\/span>,<\/span> 6.4<\/span>))<\/span>\r\n\r\n# \u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>-<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>-<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\u306e\u8868\u793a<\/span>\r\nplt<\/span>.<\/span>grid<\/span>()<\/span>\r\n\r\n# x \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\nplt<\/span>.<\/span>xticks<\/span>(<\/span>np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>,<\/span> 1<\/span>))<\/span>\r\n# y \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\nplt<\/span>.<\/span>yticks<\/span>(<\/span>np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>,<\/span> 1<\/span>))<\/span>\r\n\r\n# pivot = 'mid' \u3068\u3057\u305f\u30d9\u30af\u30c8\u30eb\u5834\u306e\u8868\u793a<\/span>\r\nplt<\/span>.<\/span>quiver<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> hE2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> hE2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> pivot<\/span> =<\/span> 'mid'<\/span>)<\/span>\r\n\r\n# \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u9752\u4e38\u3068 +<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>,<\/span> marker<\/span>=<\/span>'o'<\/span>,<\/span> \r\n            # size, color<\/span>\r\n            s<\/span> =<\/span> 200<\/span>,<\/span> c<\/span> =<\/span> 'white'<\/span>,<\/span>\r\n            edgecolors<\/span> =<\/span> 'blue'<\/span>,<\/span> linewidths<\/span> =<\/span> 2<\/span>)<\/span>\r\nplt<\/span>.<\/span>text<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>,<\/span> \"\uff0b\"<\/span>,<\/span> color<\/span> =<\/span> \"blue\"<\/span>,<\/span>\r\n         horizontalalignment<\/span> =<\/span> \"center\"<\/span>,<\/span> \r\n         verticalalignment<\/span> =<\/span> \"center\"<\/span>)<\/span>\r\n\r\n# \u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u8d64\u4e38\u3068 -<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>0<\/span>,<\/span> -<\/span>1<\/span>,<\/span> marker<\/span>=<\/span>'o'<\/span>,<\/span> \r\n            # size, color<\/span>\r\n            s<\/span> =<\/span> 200<\/span>,<\/span> c<\/span> =<\/span> 'white'<\/span>,<\/span>\r\n            edgecolors<\/span> =<\/span> 'red'<\/span>,<\/span> linewidths<\/span> =<\/span> 2<\/span>)<\/span>\r\nplt<\/span>.<\/span>text<\/span>(<\/span>0<\/span>,<\/span> -<\/span>1<\/span>,<\/span> \"\u30fc\"<\/span>,<\/span> color<\/span> =<\/span> \"red\"<\/span>,<\/span>\r\n         horizontalalignment<\/span> =<\/span> \"center\"<\/span>,<\/span> \r\n         verticalalignment<\/span> =<\/span> \"center\"<\/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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Colormap (cmap)<\/h4>\n
plt.quiver()<\/code> \u306e\u66f8\u5f0f\u30675\u756a\u76ee\u306e\u5f15\u6570\u3092\u8a2d\u5b9a\u3059\u308b\u3068\uff0c\u305d\u306e\u5927\u304d\u3055\u306b\u5fdc\u3058\u305f\u30ab\u30e9\u30fc\u30de\u30c3\u30d7\u304c\u4f7f\u3048\u308b\u3002<\/p>\n
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plt<\/span>.<\/span>quiver<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> vx<\/span>,<\/span> vy<\/span>,<\/span> C<\/span>,<\/span> cmap<\/span> =<\/span> ...<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n
\u4ee5\u4e0b\u306e\u4f8b\u3067\u306f\u96fb\u5834\u306e\u5927\u304d\u3055 E(x, y)<\/code> \u306b\u5fdc\u3058\u3066\u77e2\u5370\u306e\u8272\u304c\u5909\u5316\u3059\u308b\u3002
\n\u30ab\u30e9\u30fc\u30de\u30c3\u30d7 cmap = \"Blues\"<\/code> \u3092\u6307\u5b9a\u3057\u3066\u3044\u308b\u306e\u3067\uff0c\u96fb\u5834\u306e\u5f37\u3044\uff08E(x, y)<\/code> \u306e\u5024\u304c\u5927\u304d\u3044\uff09\u3068\u3053\u308d\u306f\u6fc3\u3044\u9752\u3067\uff0c\u5f31\u3044\uff08\u5024\u304c\u5c0f\u3055\u3044\uff09\u3068\u3053\u308d\u307b\u3069\u8584\u3044\u9752\u306b\u306a\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[7]:<\/div>\n
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# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>6.4<\/span>,<\/span> 6.4<\/span>))<\/span>\r\n\r\n# \u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>-<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>-<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\u306e\u8868\u793a<\/span>\r\nplt<\/span>.<\/span>grid<\/span>()<\/span>\r\n\r\n# x \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\nplt<\/span>.<\/span>xticks<\/span>(<\/span>np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>,<\/span> 1<\/span>))<\/span>\r\n# y \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\nplt<\/span>.<\/span>yticks<\/span>(<\/span>np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>,<\/span> 1<\/span>))<\/span>\r\n\r\n# \u96fb\u5834\u306e\u5927\u304d\u3055\u306b\u5fdc\u3058\u305f\u30ab\u30e9\u30fc\u30de\u30c3\u30d7\u306e\u8a2d\u5b9a<\/span>\r\nplt<\/span>.<\/span>quiver<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> hE2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> hE2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> \r\n           E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> cmap<\/span> =<\/span> \"Blues\"<\/span>,<\/span> pivot<\/span> =<\/span> 'mid'<\/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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cmap \u306e\u8272\u5473\uff0c\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u30fb\u592a\u3055\u306e\u8a2d\u5b9a<\/h4>\n
\u96fb\u8377\u306e\u4f4d\u7f6e\u304b\u3089\u96e2\u308c\u308b\u3068\uff0c\u96fb\u5834\u306e\u5927\u304d\u3055\u306f\u6025\u6fc0\u306b\u5c0f\u3055\u304f\u306a\u308b\u306e\u3067\uff0c\u3053\u306e\u307e\u307e\u3067\u306f\u8584\u304f\u3066\u307b\u3068\u3093\u3069\u898b\u3048\u306a\u3044\u30d9\u30af\u30c8\u30eb\u3070\u304b\u308a\u306b\u306a\u308b\u3002<\/p>\n
\u3053\u308c\u3060\u3068\u5c11\u3057\u5bc2\u3057\u3044\u306e\u3067\u30ab\u30e9\u30fc\u30de\u30c3\u30d7\u306e\u7bc4\u56f2\u3092\u8a2d\u5b9a\u3059\u308b clim<\/code> \u3092\u8abf\u6574\u3057\u3066\uff0c\u96e2\u308c\u305f\u4f4d\u7f6e\u306e\u30d9\u30af\u30c8\u30eb\u3082\u305d\u3053\u305d\u3053\u306e\u9752\u8272\u306b\u306a\u308b\u3088\u3046\u306b\u8abf\u6574\u3059\u308b\u3002<\/p>\n
\u4e0a\u8a18\u306e\u4f8b\u3067\u306f clim = (0, 2)<\/code> \u304f\u3089\u3044\u3067\u3042\u308d\u3046\u304b\u3089\uff0c\u30bc\u30ed\u306b\u8fd1\u3044\u5927\u304d\u3055\u3067\u3082\u8272\u304c\u3064\u304f\u3088\u3046\u306b\u624b\u63a2\u308a\u3067\u6570\u5024\u3092\u3044\u308c\u3066\u307f\u307e\u3059\u3002<\/p>\n
\u307e\u305f\uff0c\u30d9\u30af\u30c8\u30eb\u305d\u306e\u3082\u306e\u306e\u5927\u304d\u3055\u30fb\u592a\u3055\u3082\u5c11\u3057\u5909\u66f4\u3057\u3066\u307f\u308b\u3002\u66f8\u5f0f\u306f\u307e\u305a units='xy'<\/code> \u306a\u3069\u3068\u8a2d\u5b9a\u5f8c\uff0c\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u3092\u4f38\u3070\u3057\u305f\u3044\u306a\u3089 scale<\/code> \u306b\u3088\u308a\u5c0f\u3055\u3044\u5024\u3092\uff0c\u592a\u304f\u3057\u305f\u3044\u306a\u3089 width<\/code> \u306b\u3088\u308a\u5927\u304d\u3044\u5024\u3092\u3044\u308c\u307e\u3059\u3002\u3053\u308c\u3082\u624b\u63a2\u308a\u3067\u3044\u308c\u3066\u307f\u307e\u3057\u305f\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[8]:<\/div>\n
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# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>6.4<\/span>,<\/span> 6.4<\/span>))<\/span>\r\n\r\n# \u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>-<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>-<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\u306e\u8868\u793a<\/span>\r\nplt<\/span>.<\/span>grid<\/span>()<\/span>\r\n\r\n# x \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\nplt<\/span>.<\/span>xticks<\/span>(<\/span>np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>,<\/span> 1<\/span>))<\/span>\r\n# y \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\nplt<\/span>.<\/span>yticks<\/span>(<\/span>np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>,<\/span> 1<\/span>))<\/span>\r\n\r\n# <\/span>\r\nplt<\/span>.<\/span>quiver<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> hE2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> hE2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> \r\n           E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> cmap<\/span> =<\/span> \"Blues\"<\/span>,<\/span> pivot<\/span>=<\/span>'mid'<\/span>,<\/span> \r\n           # \u6570\u5024\u306f\u624b\u63a2\u308a\u3067<\/span>\r\n           clim<\/span>=<\/span>(<\/span>-<\/span>0.1<\/span>,<\/span> 0.8<\/span>),<\/span> \r\n           # units \u8a2d\u5b9a\u5f8c\uff0c\u9577\u3055\u306f scale, \u592a\u3055\u306f width \u3067<\/span>\r\n           units<\/span>=<\/span>'xy'<\/span>,<\/span> scale<\/span> =<\/span> 1<\/span>,<\/span> width<\/span>=<\/span>0.12<\/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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clim<\/code> \u3092\u624b\u63a2\u308a\u3067\u8a2d\u5b9a\u3059\u308b\u4ee5\u5916\u306e\u65b9\u6cd5\u3068\u3057\u3066\uff0c\u4ee5\u4e0b\u306e\u4f8b\u3067\u306f\u96fb\u5834\u306e\u5927\u304d\u3055\u305d\u306e\u3082\u306e\u3067\u306f\u306a\u304f\uff0c \u81ea\u7136\u5bfe\u6570 np.log(E(x, y))<\/code> \u306b\u5fdc\u3058\u3066\u77e2\u5370\u306e\u8272\u304c\u5909\u5316\u3059\u308b\u3088\u3046\u306b\u3057\u3066\u307f\u305f\u3002\u5927\u304d\u3055\u304c\u6025\u6fc0\u306b\u5909\u308f\u308b\u3088\u3046\u306a\u5834\u5408\u306b\u306f\uff0c\u5927\u304d\u3055\u305d\u306e\u3082\u306e\u3088\u308a\u3082\uff0cnp.log()<\/code> \u3084 np.sqrt()<\/code> \u306a\u3069\u3068\u4f7f\u3063\u3066\u5909\u5316\u3092\u7de9\u3084\u304b\u306b\u3059\u308b\u3068\u3044\u3046\u624b\u3082\u3042\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[9]:<\/div>\n
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# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>6.4<\/span>,<\/span> 6.4<\/span>))<\/span>\r\n\r\n# \u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>-<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>-<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>\r\n\r\n# \u30b0\u30ea\u30c3\u30c9\u306e\u8868\u793a<\/span>\r\nplt<\/span>.<\/span>grid<\/span>()<\/span>\r\n\r\n# x \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\nplt<\/span>.<\/span>xticks<\/span>(<\/span>np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>,<\/span> 1<\/span>))<\/span>\r\n# y \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\nplt<\/span>.<\/span>yticks<\/span>(<\/span>np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 6<\/span>,<\/span> 1<\/span>))<\/span>\r\n\r\n# <\/span>\r\nplt<\/span>.<\/span>quiver<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> hE2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> hE2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> \r\n           # E(x, y) \u3067\u306f\u306a\u304f log(E(x, y)) \u306b\u3057\u3066<\/span>\r\n           # \u5927\u304d\u3055\u306e\u5909\u5316\u3092\u7de9\u3084\u304b\u306b<\/span>\r\n           np<\/span>.<\/span>log<\/span>(<\/span>E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)),<\/span> cmap<\/span> =<\/span> \"Blues\"<\/span>,<\/span> pivot<\/span>=<\/span>'mid'<\/span>,<\/span> \r\n           # units \u8a2d\u5b9a\u5f8c\uff0c\u9577\u3055\u306f scale, \u592a\u3055\u306f width \u3067<\/span>\r\n           units<\/span>=<\/span>'xy'<\/span>,<\/span> scale<\/span> =<\/span> 1<\/span>,<\/span> width<\/span>=<\/span>0.12<\/span>);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4e00\u5fdc\u306e\u5b8c\u6210\u4f5c<\/h4>\n
\u4ee5\u4e0a\u306e\u8a2d\u5b9a\u3092\u307e\u3068\u3081\u3066\u307f\u305f\u306e\u304c\u4ee5\u4e0b\u306e\u4f8b\u3002\u5c11\u3057\u77ed\u3081\u306e\u30d9\u30af\u30c8\u30eb\u3092\u305f\u304f\u3055\u3093\u63cf\u3044\u3066\u307f\u305f\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[10]:<\/div>\n
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x<\/span> =<\/span> y<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>-<\/span>5.25<\/span>,<\/span> 5.25<\/span>,<\/span> 22<\/span>)<\/span>\r\nx<\/span>,<\/span> y<\/span> =<\/span> np<\/span>.<\/span>meshgrid<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\n\r\n# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>6.4<\/span>,<\/span> 6.4<\/span>))<\/span>\r\n\r\n# \u67a0\u3068\u7e26\u8ef8\u76ee\u76db\u3092\u975e\u8868\u793a\u306b<\/span>\r\nax<\/span> =<\/span> fig<\/span>.<\/span>add_subplot<\/span>()<\/span>\r\nax<\/span>.<\/span>axis<\/span>(<\/span>'off'<\/span>)<\/span>\r\n\r\n# \u8868\u793a\u7bc4\u56f2<\/span>\r\nplt<\/span>.<\/span>xlim<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 5<\/span>)<\/span>\r\nplt<\/span>.<\/span>ylim<\/span>(<\/span>-<\/span>5<\/span>,<\/span> 5<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>quiver<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> hE2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> hE2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> \r\n           # E(x, y) \u3067\u306f\u306a\u304f log(E(x, y)) \u306b\u3057\u3066<\/span>\r\n           # \u5927\u304d\u3055\u306e\u5909\u5316\u3092\u7de9\u3084\u304b\u306b<\/span>\r\n           np<\/span>.<\/span>log<\/span>(<\/span>E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)),<\/span> cmap<\/span> =<\/span> \"Blues\"<\/span>,<\/span> pivot<\/span>=<\/span>'mid'<\/span>,<\/span> \r\n           # units \u8a2d\u5b9a\u5f8c\uff0c\u9577\u3055\u306f scale, \u592a\u3055\u306f width \u3067<\/span>\r\n           units<\/span>=<\/span>'xy'<\/span>,<\/span> scale<\/span> =<\/span> 1.8<\/span>,<\/span> width<\/span>=<\/span>0.08<\/span>)<\/span>\r\n\r\n# \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u9752\u4e38\u3068 +<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>,<\/span> marker<\/span>=<\/span>'o'<\/span>,<\/span> \r\n            # size, color<\/span>\r\n            s<\/span> =<\/span> 200<\/span>,<\/span> c<\/span> =<\/span> 'white'<\/span>,<\/span>\r\n            edgecolors<\/span> =<\/span> 'blue'<\/span>,<\/span> linewidths<\/span> =<\/span> 2<\/span>)<\/span>\r\nplt<\/span>.<\/span>text<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>,<\/span> \"\uff0b\"<\/span>,<\/span> color<\/span> =<\/span> \"blue\"<\/span>,<\/span>\r\n         horizontalalignment<\/span> =<\/span> \"center\"<\/span>,<\/span> \r\n         verticalalignment<\/span> =<\/span> \"center\"<\/span>)<\/span>\r\n# \u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u8d64\u4e38\u3068 -<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>0<\/span>,<\/span> -<\/span>1<\/span>,<\/span> marker<\/span>=<\/span>'o'<\/span>,<\/span> \r\n            # size, color<\/span>\r\n            s<\/span> =<\/span> 200<\/span>,<\/span> c<\/span> =<\/span> 'white'<\/span>,<\/span>\r\n            edgecolors<\/span> =<\/span> 'red'<\/span>,<\/span> linewidths<\/span> =<\/span> 2<\/span>)<\/span>\r\nplt<\/span>.<\/span>text<\/span>(<\/span>0<\/span>,<\/span> -<\/span>1<\/span>,<\/span> \"\u30fc\"<\/span>,<\/span> color<\/span> =<\/span> \"red\"<\/span>,<\/span>\r\n         horizontalalignment<\/span> =<\/span> \"center\"<\/span>,<\/span> \r\n         verticalalignment<\/span> =<\/span> \"center\"<\/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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streamplot()<\/code> \u3067\u96fb\u6c17\u529b\u7dda\u3092\u63cf\u304f<\/h3>\n
streamplot()<\/code> \u3092\u4f7f\u3046\u3068\uff0c\u96fb\u5834\u30d9\u30af\u30c8\u30eb $\\boldsymbol{E}$ \u3092\u63a5\u30d9\u30af\u30c8\u30eb\u3068\u3059\u308b\u96fb\u6c17\u529b\u7dda\u3092\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n
\u4ee5\u4e0b\u306e\u4f8b\u3067\u306f\uff0c\u5358\u4f4d\u30d9\u30af\u30c8\u30eb $\\displaystyle \\frac{\\boldsymbol{E}}{\\sqrt{\\boldsymbol{E}\\cdot\\boldsymbol{E}}}$ \u3092\u63a5\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u3044\u308b\u3002\u307e\u305a\u306f\u30aa\u30d7\u30b7\u30e7\u30f3\u306a\u3057\u3067…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[11]:<\/div>\n
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# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>6.4<\/span>,<\/span> 6.4<\/span>))<\/span>\r\n\r\n# \u67a0\u3068\u7e26\u8ef8\u76ee\u76db\u3092\u975e\u8868\u793a\u306b<\/span>\r\nax<\/span> =<\/span> fig<\/span>.<\/span>add_subplot<\/span>()<\/span>\r\nax<\/span>.<\/span>axis<\/span>(<\/span>'off'<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>streamplot<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> hE2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> hE2y<\/span>(<\/span>x<\/span>,<\/span> y<\/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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\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u6307\u5b9a\u3057\u3066\u63cf\u304f\u4f8b\u3002\u96fb\u6c17\u529b\u7dda\u306f\u5207\u308c\u305f\u308a\u3057\u306a\u3044\u306e\u3067 broken_streamlines=False<\/code> \u3068\u3057\uff0c\u3042\u307e\u308a\u6df7\u96d1\u3057\u306a\u3044\u3088\u3046\u306b density<\/code> \u306e\u5024\u3092 1 \u3088\u308a\u5c0f\u3055\u304f\u3057\u3066\u307f\u308b\u3002\u307e\u305f\uff0c\u96fb\u6c17\u529b\u7dda\u3092\u300c\u5148\u306b\u300d\u63cf\u3044\u305f\u3042\u3068\u306b\u70b9\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u25cb\u3092\u63cf\u304f\u3088\u3046\u306b\u3059\u308b\u305f\u3081\uff0czorder = 0<\/code> \u3068\u3057\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[12]:<\/div>\n
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# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>6.4<\/span>,<\/span> 6.4<\/span>))<\/span>\r\n\r\n# \u67a0\u3068\u7e26\u8ef8\u76ee\u76db\u3092\u975e\u8868\u793a\u306b<\/span>\r\nax<\/span> =<\/span> fig<\/span>.<\/span>add_subplot<\/span>()<\/span>\r\nax<\/span>.<\/span>axis<\/span>(<\/span>'off'<\/span>)<\/span>\r\n\r\nplt<\/span>.<\/span>streamplot<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> hE2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> hE2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span>\r\n               # \u5404\u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a<\/span>\r\n               broken_streamlines<\/span> =<\/span> False<\/span>,<\/span> \r\n               density<\/span>=<\/span>0.3<\/span>,<\/span> \r\n               zorder<\/span> =<\/span> 0<\/span>,<\/span> \r\n               color<\/span> =<\/span> 'tab:blue'<\/span>);<\/span>\r\n\r\n# \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u9752\u4e38\u3068 +<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>,<\/span> marker<\/span>=<\/span>'o'<\/span>,<\/span> \r\n            # size, color<\/span>\r\n            s<\/span> =<\/span> 200<\/span>,<\/span> c<\/span> =<\/span> 'white'<\/span>,<\/span>\r\n            edgecolors<\/span> =<\/span> 'blue'<\/span>,<\/span> linewidths<\/span> =<\/span> 2<\/span>)<\/span>\r\nplt<\/span>.<\/span>text<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>,<\/span> \"\uff0b\"<\/span>,<\/span> color<\/span> =<\/span> \"blue\"<\/span>,<\/span>\r\n         horizontalalignment<\/span> =<\/span> \"center\"<\/span>,<\/span> \r\n         verticalalignment<\/span> =<\/span> \"center\"<\/span>)<\/span>\r\n\r\n# \u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u8d64\u4e38\u3068 -<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>0<\/span>,<\/span> -<\/span>1<\/span>,<\/span> marker<\/span>=<\/span>'o'<\/span>,<\/span> \r\n            # size, color<\/span>\r\n            s<\/span> =<\/span> 200<\/span>,<\/span> c<\/span> =<\/span> 'white'<\/span>,<\/span>\r\n            edgecolors<\/span> =<\/span> 'red'<\/span>,<\/span> linewidths<\/span> =<\/span> 2<\/span>)<\/span>\r\nplt<\/span>.<\/span>text<\/span>(<\/span>0<\/span>,<\/span> -<\/span>1<\/span>,<\/span> \"\u30fc\"<\/span>,<\/span> color<\/span> =<\/span> \"red\"<\/span>,<\/span>\r\n         horizontalalignment<\/span> =<\/span> \"center\"<\/span>,<\/span> \r\n         verticalalignment<\/span> =<\/span> \"center\"<\/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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contour()<\/code> \u3067\u7b49\u96fb\u4f4d\u9762\uff08\u7dda\uff09\u3092\u63cf\u304f<\/h3>\n
\u6b63\u8ca0\u306e\u70b9\u96fb\u8377\u304c\u3064\u304f\u308b\u9759\u96fb\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u306f\uff08\u9069\u5b9c\u7121\u6b21\u5143\u5316\u3092\u884c\u3063\u3066\uff09<\/p>\n
$$\\phi(x, y) = -\\frac{1}{\\sqrt{x^2 + (y-1)^2}}+\\frac{1}{\\sqrt{x^2 + (y+1)^2}}$$<\/p>\n
\u96fb\u5834\u30d9\u30af\u30c8\u30eb $\\boldsymbol{E}$ \u306f<\/p>\n
$$\\boldsymbol{E} = – \\nabla \\phi$$<\/p>\n
\u3067\u3042\u308b\u304b\u3089\uff0c$\\phi = \\mbox{const.}$ \u306e\u7b49\u96fb\u4f4d\u9762\uff08\u7dda\uff09\u306b\u5bfe\u3057\u3066\u96fb\u5834\u30d9\u30af\u30c8\u30eb $\\boldsymbol{E}$ \u306f\u76f4\u4ea4\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[13]:<\/div>\n
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# \u9759\u96fb\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb<\/span>\r\ndef<\/span> phi<\/span>(<\/span>x<\/span>,<\/span> y<\/span>):<\/span>\r\n    return<\/span> -<\/span>1<\/span>\/<\/span>np<\/span>.<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> (<\/span>y<\/span>-<\/span>1<\/span>)<\/span>**<\/span>2<\/span>)<\/span> +<\/span> 1<\/span>\/<\/span>np<\/span>.<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> (<\/span>y<\/span>+<\/span>1<\/span>)<\/span>**<\/span>2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[14]:<\/div>\n
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# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>6.4<\/span>,<\/span> 6.4<\/span>))<\/span>\r\n\r\n# \u67a0\u3068\u7e26\u8ef8\u76ee\u76db\u3092\u975e\u8868\u793a\u306b<\/span>\r\nax<\/span> =<\/span> fig<\/span>.<\/span>add_subplot<\/span>()<\/span>\r\nax<\/span>.<\/span>axis<\/span>(<\/span>'off'<\/span>)<\/span>\r\n\r\n# \u96fb\u5834\u30d9\u30af\u30c8\u30eb\u306e\u59cb\u70b9<\/span>\r\nx<\/span> =<\/span> y<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>-<\/span>5.5<\/span>,<\/span> 5.5<\/span>,<\/span> 12<\/span>)<\/span>\r\nx<\/span>,<\/span> y<\/span> =<\/span> np<\/span>.<\/span>meshgrid<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\n# \u96fb\u5834\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f<\/span>\r\nplt<\/span>.<\/span>quiver<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> hE2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> hE2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> \r\n           pivot<\/span> =<\/span> 'mid'<\/span>,<\/span> color<\/span>=<\/span>'tab:blue'<\/span>)<\/span>\r\n\r\n# contour \u306e meshgrid<\/span>\r\ndelta<\/span> =<\/span> 0.1<\/span>\r\nxrange<\/span> =<\/span> np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>6<\/span>,<\/span> 6<\/span>,<\/span> delta<\/span>)<\/span>\r\nyrange<\/span> =<\/span> np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>6<\/span>,<\/span> 6<\/span>,<\/span> delta<\/span>)<\/span>\r\nx<\/span>,<\/span> y<\/span> =<\/span> np<\/span>.<\/span>meshgrid<\/span>(<\/span>xrange<\/span>,<\/span> yrange<\/span>)<\/span>\r\n# \u7b49\u96fb\u4f4d\u9762\uff08\u7dda\uff09\u3092\u63cf\u304f<\/span>\r\nplt<\/span>.<\/span>contour<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> phi<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> \r\n            # \u7b49\u96fb\u4f4d\u7dda\u3092\u63cf\u304f phi(x, y) \u306e\u5024\u306e\u30ea\u30b9\u30c8<\/span>\r\n            [<\/span>-<\/span>1<\/span>,<\/span>  -<\/span>0.3<\/span>,<\/span> -<\/span>0.1<\/span>,<\/span> -<\/span>0.05<\/span>,<\/span> \r\n             0.05<\/span>,<\/span> 0.1<\/span>,<\/span> 0.3<\/span>,<\/span> 1<\/span>],<\/span> \r\n            # \u7b49\u96fb\u4f4d\u7dda\u306e\u8272\uff0c\u4eca\u56de\u306f\u5168\u3066\u540c\u8272\u306b<\/span>\r\n            colors<\/span>=<\/span>[<\/span>'lightgreen'<\/span>]<\/span>*<\/span>8<\/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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\u96fb\u6c17\u529b\u7dda\u3068\u7b49\u96fb\u4f4d\u9762\uff08\u7dda\uff09\u3092\u4e21\u65b9\u63cf\u304f<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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\u96fb\u6c17\u529b\u7dda\u3068\u7b49\u96fb\u4f4d\u9762\uff08\u7dda\uff09\u3092\u4e21\u65b9\u63cf\u3044\u3066\u307f\u308b\u3068\uff0c\u78ba\u304b\u306b\u96fb\u6c17\u529b\u7dda\u306f\u5e38\u306b\u7b49\u96fb\u4f4d\u9762\uff08\u7dda\uff09\u306b\u76f4\u4ea4\u3057\u3066\u3044\u308b\u3053\u3068\u304c\uff0c\u3088\u308a\u306f\u3063\u304d\u308a\u3068\u308f\u304b\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[15]:<\/div>\n
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# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>(<\/span>6.4<\/span>,<\/span> 6.4<\/span>))<\/span>\r\n\r\n# \u67a0\u3068\u7e26\u8ef8\u76ee\u76db\u3092\u975e\u8868\u793a\u306b<\/span>\r\nax<\/span> =<\/span> fig<\/span>.<\/span>add_subplot<\/span>()<\/span>\r\nax<\/span>.<\/span>axis<\/span>(<\/span>'off'<\/span>)<\/span>\r\n\r\n# \u96fb\u5834\u30d9\u30af\u30c8\u30eb\u306e\u59cb\u70b9<\/span>\r\nx<\/span> =<\/span> y<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>-<\/span>5.5<\/span>,<\/span> 5.5<\/span>,<\/span> 12<\/span>)<\/span>\r\nx<\/span>,<\/span> y<\/span> =<\/span> np<\/span>.<\/span>meshgrid<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\n# \u96fb\u6c17\u529b\u7dda\u3092\u63cf\u304f<\/span>\r\nplt<\/span>.<\/span>streamplot<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> hE2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> hE2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span>\r\n               broken_streamlines<\/span> =<\/span> False<\/span>,<\/span> \r\n               density<\/span>=<\/span>0.3<\/span>,<\/span> \r\n               zorder<\/span> =<\/span> 0<\/span>,<\/span> \r\n               color<\/span> =<\/span> 'tab:blue'<\/span>);<\/span>\r\n\r\n# \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u9752\u4e38\u3068 +<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>,<\/span> marker<\/span>=<\/span>'o'<\/span>,<\/span> \r\n            # size, color<\/span>\r\n            s<\/span> =<\/span> 200<\/span>,<\/span> c<\/span> =<\/span> 'white'<\/span>,<\/span>\r\n            edgecolors<\/span> =<\/span> 'blue'<\/span>,<\/span> linewidths<\/span> =<\/span> 2<\/span>)<\/span>\r\nplt<\/span>.<\/span>text<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>,<\/span> \"\uff0b\"<\/span>,<\/span> color<\/span> =<\/span> \"blue\"<\/span>,<\/span>\r\n         horizontalalignment<\/span> =<\/span> \"center\"<\/span>,<\/span> \r\n         verticalalignment<\/span> =<\/span> \"center\"<\/span>)<\/span>\r\n\r\n# \u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u8d64\u4e38\u3068 -<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>0<\/span>,<\/span> -<\/span>1<\/span>,<\/span> marker<\/span>=<\/span>'o'<\/span>,<\/span> \r\n            # size, color<\/span>\r\n            s<\/span> =<\/span> 200<\/span>,<\/span> c<\/span> =<\/span> 'white'<\/span>,<\/span>\r\n            edgecolors<\/span> =<\/span> 'red'<\/span>,<\/span> linewidths<\/span> =<\/span> 2<\/span>)<\/span>\r\nplt<\/span>.<\/span>text<\/span>(<\/span>0<\/span>,<\/span> -<\/span>1<\/span>,<\/span> \"\u30fc\"<\/span>,<\/span> color<\/span> =<\/span> \"red\"<\/span>,<\/span>\r\n         horizontalalignment<\/span> =<\/span> \"center\"<\/span>,<\/span> \r\n         verticalalignment<\/span> =<\/span> \"center\"<\/span>);<\/span>\r\n\r\n# contour \u306e meshgrid<\/span>\r\ndelta<\/span> =<\/span> 0.1<\/span>\r\nxrange<\/span> =<\/span> np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>6<\/span>,<\/span> 6<\/span>,<\/span> delta<\/span>)<\/span>\r\nyrange<\/span> =<\/span> np<\/span>.<\/span>arange<\/span>(<\/span>-<\/span>6<\/span>,<\/span> 6<\/span>,<\/span> delta<\/span>)<\/span>\r\nx<\/span>,<\/span> y<\/span> =<\/span> np<\/span>.<\/span>meshgrid<\/span>(<\/span>xrange<\/span>,<\/span> yrange<\/span>)<\/span>\r\n# \u7b49\u96fb\u4f4d\u9762\u3092\u63cf\u304f<\/span>\r\nplt<\/span>.<\/span>contour<\/span>(<\/span>x<\/span>,<\/span> y<\/span>,<\/span> phi<\/span>(<\/span>x<\/span>,<\/span> y<\/span>),<\/span> \r\n            # \u7b49\u96fb\u4f4d\u7dda\u3092\u63cf\u304f phi(x, y) \u306e\u5024\u306e\u30ea\u30b9\u30c8<\/span>\r\n            [<\/span>-<\/span>1<\/span>,<\/span>  -<\/span>0.3<\/span>,<\/span> -<\/span>0.1<\/span>,<\/span> -<\/span>0.05<\/span>,<\/span> \r\n             0.05<\/span>,<\/span> 0.1<\/span>,<\/span> 0.3<\/span>,<\/span> 1<\/span>],<\/span> \r\n            # \u7b49\u96fb\u4f4d\u7dda\u306e\u8272\uff0c\u4eca\u56de\u306f\u5168\u3066\u540c\u8272\u306b<\/span>\r\n            colors<\/span>=<\/span>[<\/span>'lightgreen'<\/span>]<\/span>*<\/span>8<\/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","protected":false},"excerpt":{"rendered":"
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\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[13,19],"tags":[],"class_list":["post-6003","post","type-post","status-publish","format-standard","hentry","category-matplotlib","category-19","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/6003","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/post"}],"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=6003"}],"version-history":[{"count":7,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/6003\/revisions"}],"predecessor-version":[{"id":6913,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/6003\/revisions\/6913"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=6003"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=6003"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=6003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}