{"id":3619,"date":"2022-08-31T10:37:22","date_gmt":"2022-08-31T01:37:22","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=3619"},"modified":"2023-03-28T17:59:35","modified_gmt":"2023-03-28T08:59:35","slug":"palette-%e3%81%a7%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e8%89%b2%e3%82%92%e5%a4%89%e3%81%88%e3%81%a6-gnuplot-%e3%81%a7%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%ef%bc%88%e9%9b%bb%e5%a0%b4","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3619\/","title":{"rendered":"palette \u3067\u30d9\u30af\u30c8\u30eb\u306e\u8272\u3092\u5909\u3048\u3066 gnuplot \u3067\u96fb\u5834\u30fb\u78c1\u5834\u3092\u63cf\u304f"},"content":{"rendered":"

\u5148\u65e5\uff0c\u300cgnuplot \u3067\u30d9\u30af\u30c8\u30eb\u5834\uff08\u96fb\u5834\u30fb\u78c1\u5834\uff09\u3092\u63cf\u304f<\/a>\u300d\u3067\u63cf\u3044\u3066\u307f\u305f\u304c\uff0c\u3044\u308d\u3044\u308d\u691c\u7d22\u3059\u308b\u3068 palette \u3067\u30d9\u30af\u30c8\u30eb\u306e\u8272\u3092\uff08\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306b\u5408\u308f\u305b\u3066\uff09\u53ef\u5909\u306b\u3067\u304d\u308b\u3088\u3046\u306a\u306e\u3067\uff0c\u5099\u5fd8\u9332\u3068\u3057\u3066\u3002<\/p>\n

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\u70b9\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834 $\\boldsymbol{E}$<\/h3>\n

\u4f4d\u7f6e $\\boldsymbol{r}_1$ \u306b\u3042\u308b\u70b9\u96fb\u8377 $q_1$ \u304c\u3064\u304f\u308b\u96fb\u5834\u30d9\u30af\u30c8\u30eb $\\boldsymbol{E}$ \u306f<\/p>\n

\\begin{eqnarray}
\n\\boldsymbol{E}
\n&=& \\frac{q_1}{4\\pi \\varepsilon_0} \\frac{\\boldsymbol{r} – \\boldsymbol{r}_1}{|\\boldsymbol{r} – \\boldsymbol{r}_1|^3}\\end{eqnarray}<\/p>\n

$z=0$ \u306e $xy$ \u5e73\u9762\u30672\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u5834\u3092\u63cf\u304f\u3002<\/p>\n

$$\\boldsymbol{r} = (x, y, 0), \\quad \\boldsymbol{r}_1 = (x_1, y_1, 0)$$$$E_x = s \\frac{x-x_1}{\\left((x-x_1)^2 + (y-y_1)^2\\right)^{3\/2}}$$$$E_y = s \\frac{y-y_1}{\\left((x-x_1)^2 + (y-y_1)^2\\right)^{3\/2}}$$<\/p>\n

$s$ \u306f $\\mbox{scaling}$ \u4fc2\u6570\u3002\u5b9f\u969b\u306e\u63cf\u753b\u306e\u969b\u306b\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u3092\u5fae\u8abf\u6574\u3059\u308b\u4fc2\u6570\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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# \u96fb\u5834 E<\/span>\r\nEx<\/span>(x, y) =<\/span> scaling<\/span> *<\/span> x<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>)<\/span>\r\nEy<\/span>(x, y) =<\/span> scaling<\/span> *<\/span> y<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>)<\/span>\r\n\r\n# \u96fb\u5834 E \u306e\u5927\u304d\u3055\u306f\u8ddd\u96e2\u306e2\u4e57\u306b\u53cd\u6bd4\u4f8b<\/span>\r\nE<\/span>(x, y) =<\/span> 1.<\/span>\/<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>\r\n\r\nreset<\/span>\r\nunset<\/span> xtics<\/span>\r\nunset<\/span> ytics<\/span>\r\nunset<\/span> border<\/span>\r\n\r\n# special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n# urange, vrange \u3067\u63cf\u753b\u7bc4\u56f2\u306e\u8a2d\u5b9a<\/span>\r\nset<\/span> urange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> vrange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> size<\/span> ratio<\/span> 1<\/span>\r\n\r\n# x \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\nset<\/span> samples<\/span> 13<\/span>\r\n# y \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\nset<\/span> isosamples<\/span> 13<\/span>\r\n\r\n# \u77e2\u5370\u306e\u9577\u3055\u8abf\u6574\u7528<\/span>\r\nscaling<\/span> =<\/span> 0.2<\/span>\r\n\r\n# \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u9752\u4e38\u3068 +<\/span>\r\nx1<\/span> =<\/span> 0<\/span>\r\ny1<\/span> =<\/span> 1<\/span>\r\nset<\/span> label<\/span> 1<\/span> point<\/span> pt<\/span> 6<\/span> ps<\/span> 1.5<\/span> lc<\/span> \"blue\"<\/span> at<\/span> x1<\/span>,<\/span> y1<\/span>\r\nset<\/span> label<\/span> 2<\/span> center<\/span> at<\/span> first<\/span> x1<\/span>,<\/span> y1<\/span> \"+\"<\/span> tc<\/span> \"blue\"<\/span>\r\n\r\nset<\/span> title<\/span> \"\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\"<\/span>\r\n\r\n# colorbox \u3092\u975e\u8868\u793a\u306b<\/span>\r\nunset<\/span> colorbox<\/span>\r\n# palette \u306e cublehelix \u3067\u306e\u8a2d\u5b9a\u4f8b\uff1a <\/span>\r\n# start 0: blue, 1: red, 2: green<\/span>\r\n# cycles 0 \u3067\u540c\u4e00\u8272\u306e\u6fc3\u6de1\u306e\u307f\u306b<\/span>\r\n# saturation 3 \u304c\u597d\u307f<\/span>\r\n# negative \u3067\u5f37\u3044\u3068\u3053\u308d\u304c\u6fc3\u304f\u306a\u308b<\/span>\r\nset<\/span> palette<\/span> cubehelix<\/span> start<\/span> 0<\/span> cycles<\/span> 0<\/span> saturation<\/span> 3<\/span> negative<\/span>\r\n\r\n# using \u59cb\u70b9\u306ex : \u59cb\u70b9\u306ey : \u30d9\u30af\u30c8\u30eb\u306ex\u6210\u5206 : \u30d9\u30af\u30c8\u30eb\u306ey\u6210\u5206 : variable color \u60c5\u5831<\/span>\r\nplot<\/span> \"++\"<\/span> u<\/span> 1<\/span>:<\/span>2<\/span>:<\/span>(<\/span>Ex<\/span>(<\/span>$<\/span>1<\/span>-<\/span>x1<\/span>,<\/span>$<\/span>2<\/span>-<\/span>y1<\/span>))<\/span>:<\/span>(<\/span>Ey<\/span>(<\/span>$<\/span>1<\/span>-<\/span>x1<\/span>,<\/span>$<\/span>2<\/span>-<\/span>y1<\/span>))<\/span>:<\/span>(<\/span>log<\/span>(<\/span>E<\/span>(<\/span>$<\/span>1<\/span>-<\/span>x1<\/span>,<\/span>$<\/span>2<\/span>-<\/span>y1<\/span>)))<\/span> \\\r\n     w<\/span> vec<\/span> notitle<\/span> lw<\/span> 4<\/span> lc<\/span> palette<\/span> filled<\/span> head<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$\\boldsymbol{E}$ \u306e\u5411\u304d\u3092\u8868\u3059\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u5834<\/h3>\n
\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\u4e0a\u56f3\u306e\u3088\u3046\u306b\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u304c\u5927\u304d\u304f\u5909\u5316\u3059\u308b\u3002\u3053\u308c\u306f\u3053\u308c\u3067\u6b63\u3057\u3044\u306e\u3060\u304c\uff0c\u898b\u3084\u3059\u304f\u3059\u308b\u305f\u3081\u306b\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b $\\boldsymbol{E}$ \u306e\u5411\u304d\u3092\u8868\u3059\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u5834\uff08\u5927\u304d\u3055\u304c $1$\uff09\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
$$\\hat{\\boldsymbol{E}} \\equiv \\frac{\\boldsymbol{E}}{\\sqrt{\\boldsymbol{E}\\cdot\\boldsymbol{E}}} =
\n\\frac{\\boldsymbol{r} – \\boldsymbol{r}_1}{|\\boldsymbol{r} – \\boldsymbol{r}_1|}$$$$\\hat{E}_x = s \\frac{x-x_1}{\\sqrt{(x-x_1)^2 + (y-y_1)^2}}$$$$\\hat{E}_y = s \\frac{y-y_1}{\\sqrt{(x-x_1)^2 + (y-y_1)^2}}$$<\/p>\n
$s$ \u306f $\\mbox{scaling}$ \u4fc2\u6570\u3002\u5b9f\u969b\u306e\u63cf\u753b\u306e\u969b\u306b\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u3092\u5fae\u8abf\u6574\u3059\u308b\u4fc2\u6570\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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# \u96fb\u5834 E<\/span>\r\nEx<\/span>(x, y) =<\/span> x<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>)<\/span>\r\nEy<\/span>(x, y) =<\/span> y<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>)<\/span>\r\n# \u96fb\u5834 E \u306e\u5927\u304d\u3055<\/span>\r\nE<\/span>(x, y) =<\/span> sqrt<\/span>(<\/span>Ex<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>**<\/span>2<\/span> +<\/span> Ey<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>**<\/span>2<\/span>)<\/span>\r\n# \u898f\u683c\u5316\u3055\u308c\u305f hat E<\/span>\r\nhEx<\/span>(x, y) =<\/span> scaling<\/span> *<\/span> Ex<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\/<\/span>E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\nhEy<\/span>(x, y) =<\/span> scaling<\/span> *<\/span> Ey<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\/<\/span>E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\n\r\nreset<\/span>\r\nunset<\/span> xtics<\/span>\r\nunset<\/span> ytics<\/span>\r\nunset<\/span> border<\/span>\r\n\r\n# special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n# urange, vrange \u3067\u63cf\u753b\u7bc4\u56f2\u306e\u8a2d\u5b9a<\/span>\r\nset<\/span> urange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> vrange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> size<\/span> ratio<\/span> 1<\/span>\r\n\r\n# x \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\nset<\/span> samples<\/span> 19<\/span>\r\n# y \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\nset<\/span> isosamples<\/span> 19<\/span>\r\n\r\n# \u77e2\u5370\u306e\u9577\u3055\u8abf\u6574\u7528<\/span>\r\nscaling<\/span> =<\/span> 0.2<\/span>\r\n\r\n# \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u9752\u4e38\u3068 +<\/span>\r\nx1<\/span> =<\/span> 0<\/span>\r\ny1<\/span> =<\/span> 1<\/span>\r\nset<\/span> label<\/span> 1<\/span> point<\/span> pt<\/span> 6<\/span> ps<\/span> 1.5<\/span> lc<\/span> \"blue\"<\/span> at<\/span> x1<\/span>,<\/span> y1<\/span>\r\nset<\/span> label<\/span> 2<\/span> center<\/span> at<\/span> first<\/span> x1<\/span>,<\/span> y1<\/span> \"+\"<\/span> tc<\/span> \"blue\"<\/span>\r\n\r\nset<\/span> title<\/span> \"\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\"<\/span>\r\nunset<\/span> colorbox<\/span>\r\nset<\/span> palette<\/span> cubehelix<\/span> start<\/span> 0<\/span> cycles<\/span> 0<\/span> saturation<\/span> 3<\/span> negative<\/span>\r\n\r\nplot<\/span> \"++\"<\/span> u<\/span> 1<\/span>:<\/span>2<\/span>:<\/span>(<\/span>hEx<\/span>(<\/span>$<\/span>1<\/span>-<\/span>x1<\/span>,<\/span>$<\/span>2<\/span>-<\/span>y1<\/span>))<\/span>:<\/span>(<\/span>hEy<\/span>(<\/span>$<\/span>1<\/span>-<\/span>x1<\/span>,<\/span>$<\/span>2<\/span>-<\/span>y1<\/span>))<\/span>:<\/span>(<\/span>log<\/span>(<\/span>E<\/span>(<\/span>$<\/span>1<\/span>-<\/span>x1<\/span>,<\/span>$<\/span>2<\/span>-<\/span>y1<\/span>)))<\/span> \\\r\n     w<\/span> vec<\/span> notitle<\/span>  lw<\/span> 4<\/span> lc<\/span> palette<\/span> filled<\/span> head<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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# \u96fb\u5834 E<\/span>\r\nEx<\/span>(x, y) =<\/span> -<\/span>(<\/span>x<\/span>-<\/span>x2<\/span>)<\/span>\/<\/span>(<\/span>sqrt<\/span>((<\/span>x<\/span>-<\/span>x2<\/span>)<\/span>**<\/span>2<\/span> +<\/span> (<\/span>y<\/span>-<\/span>y2<\/span>)<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>)<\/span>\r\nEy<\/span>(x, y) =<\/span> -<\/span>(<\/span>y<\/span>-<\/span>y2<\/span>)<\/span>\/<\/span>(<\/span>sqrt<\/span>((<\/span>x<\/span>-<\/span>x2<\/span>)<\/span>**<\/span>2<\/span> +<\/span> (<\/span>y<\/span>-<\/span>y2<\/span>)<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>)<\/span>\r\n# \u96fb\u5834 E \u306e\u5927\u304d\u3055<\/span>\r\nE<\/span>(x, y) =<\/span> sqrt<\/span>(<\/span>Ex<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>**<\/span>2<\/span> +<\/span> Ey<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>**<\/span>2<\/span>)<\/span>\r\n# \u898f\u683c\u5316\u3055\u308c\u305f hat E<\/span>\r\nhEx<\/span>(x, y) =<\/span> scaling<\/span> *<\/span> Ex<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\/<\/span>E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\nhEy<\/span>(x, y) =<\/span> scaling<\/span> *<\/span> Ey<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\/<\/span>E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\n\r\nreset<\/span>\r\nunset<\/span> xtics<\/span>\r\nunset<\/span> ytics<\/span>\r\nunset<\/span> border<\/span>\r\n\r\n# special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n# urange, vrange \u3067\u63cf\u753b\u7bc4\u56f2\u306e\u8a2d\u5b9a<\/span>\r\nset<\/span> urange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> vrange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> size<\/span> ratio<\/span> 1<\/span>\r\n\r\n# x \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\nset<\/span> samples<\/span> 19<\/span>\r\n# y \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\nset<\/span> isosamples<\/span> 19<\/span>\r\n\r\n# \u77e2\u5370\u306e\u9577\u3055\u8abf\u6574\u7528<\/span>\r\nscaling<\/span> =<\/span> 0.2<\/span>\r\n\r\n# \u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u8d64\u4e38\u3068 -<\/span>\r\nx2<\/span> =<\/span> 0<\/span>\r\ny2<\/span> =<\/span> -1<\/span>\r\nset<\/span> label<\/span> 3<\/span> point<\/span> pt<\/span> 6<\/span> ps<\/span> 1.5<\/span> lc<\/span> \"red\"<\/span> at<\/span> x2<\/span>,<\/span> y2<\/span>\r\nset<\/span> label<\/span> 4<\/span> center<\/span> at<\/span> first<\/span> x2<\/span>,<\/span> y2<\/span> \"-\"<\/span> tc<\/span> \"red\"<\/span>\r\n\r\nset<\/span> title<\/span> \"\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\"<\/span>\r\nunset<\/span> colorbox<\/span>\r\nset<\/span> palette<\/span> cubehelix<\/span> start<\/span> 1<\/span> cycles<\/span> 0<\/span> saturation<\/span> 3<\/span> negative<\/span>\r\n\r\nplot<\/span> \"++\"<\/span> u<\/span> 1<\/span>:<\/span>2<\/span>:<\/span>(<\/span>hEx<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>))<\/span>:<\/span>(<\/span>hEy<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>))<\/span>:<\/span>(<\/span>log<\/span>(<\/span>E<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>)))<\/span> \\\r\n     w<\/span> vec<\/span> notitle<\/span> lc<\/span> palette<\/span> lw<\/span> 4<\/span> filled<\/span> head<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6b63\u96fb\u8377\u3068\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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In [4]:<\/div>\n
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# \u96fb\u5834 E<\/span>\r\nEx<\/span>(x, y) =<\/span> x<\/span>\/<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>\r\nEy<\/span>(x, y) =<\/span> y<\/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\u96fb\u8377\u3068\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834<\/span>\r\nE2x<\/span>(x, y) =<\/span> Ex<\/span>(<\/span>x<\/span>-<\/span>x1<\/span>,<\/span> y<\/span>-<\/span>y1<\/span>)<\/span> -<\/span> Ex<\/span>(<\/span>x<\/span>-<\/span>x2<\/span>,<\/span> y<\/span>-<\/span>y2<\/span>)<\/span>\r\nE2y<\/span>(x, y) =<\/span> Ey<\/span>(<\/span>x<\/span>-<\/span>x1<\/span>,<\/span> y<\/span>-<\/span>y1<\/span>)<\/span> -<\/span> Ey<\/span>(<\/span>x<\/span>-<\/span>x2<\/span>,<\/span> y<\/span>-<\/span>y2<\/span>)<\/span>\r\n# \u96fb\u5834\u306e\u5927\u304d\u3055<\/span>\r\nE<\/span>(x, y) =<\/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# \u898f\u683c\u5316\u3055\u308c\u305f hat E<\/span>\r\nhE2x<\/span>(x, y) =<\/span> scaling<\/span> *<\/span> E2x<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\/<\/span>E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\nhE2y<\/span>(x, y) =<\/span> scaling<\/span> *<\/span> E2y<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\/<\/span>E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\n\r\nreset<\/span>\r\nunset<\/span> xtics<\/span>\r\nunset<\/span> ytics<\/span>\r\nunset<\/span> border<\/span>\r\n\r\n# special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n# urange, vrange \u3067\u63cf\u753b\u7bc4\u56f2\u306e\u8a2d\u5b9a<\/span>\r\nset<\/span> urange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> vrange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> size<\/span> ratio<\/span> 1<\/span>\r\n\r\n# x \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\nset<\/span> samples<\/span> 19<\/span>\r\n# y \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\nset<\/span> isosamples<\/span> 19<\/span>\r\n\r\n# \u77e2\u5370\u306e\u9577\u3055\u8abf\u6574\u7528<\/span>\r\nscaling<\/span> =<\/span> 0.2<\/span>\r\n\r\n# \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u9752\u4e38\u3068 +<\/span>\r\nx1<\/span> =<\/span> 0<\/span>\r\ny1<\/span> =<\/span> 1<\/span>\r\nset<\/span> label<\/span> 1<\/span> point<\/span> pt<\/span> 6<\/span> ps<\/span> 1.5<\/span> lc<\/span> \"blue\"<\/span> at<\/span> x1<\/span>,<\/span> y1<\/span>\r\nset<\/span> label<\/span> 2<\/span> center<\/span> at<\/span> first<\/span> x1<\/span>,<\/span> y1<\/span> \"+\"<\/span> tc<\/span> \"blue\"<\/span>\r\n\r\n# \u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u8d64\u4e38\u3068 -<\/span>\r\nx2<\/span> =<\/span> 0<\/span>\r\ny2<\/span> =<\/span> -1<\/span>\r\nset<\/span> label<\/span> 3<\/span> point<\/span> pt<\/span> 6<\/span> ps<\/span> 1.5<\/span> lc<\/span> \"red\"<\/span> at<\/span> x2<\/span>,<\/span> y2<\/span>\r\nset<\/span> label<\/span> 4<\/span> center<\/span> at<\/span> first<\/span> x2<\/span>,<\/span> y2<\/span> \"-\"<\/span> tc<\/span> \"red\"<\/span>\r\n\r\nset<\/span> title<\/span> \"\u6b63\u96fb\u8377\u3068\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\"<\/span>\r\nunset<\/span> colorbox<\/span>\r\nset<\/span> palette<\/span> cubehelix<\/span> start<\/span> 2<\/span> cycles<\/span> 0<\/span> saturation<\/span> 3<\/span> negative<\/span>\r\nplot<\/span> \"++\"<\/span> u<\/span> 1<\/span>:<\/span>2<\/span>:<\/span>(<\/span>hE2x<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>))<\/span>:<\/span>(<\/span>hE2y<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>))<\/span>:<\/span>(<\/span>log<\/span>(<\/span>E<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>)))<\/span> \\\r\n     w<\/span> vec<\/span> notitle<\/span> lc<\/span> palette<\/span> lw<\/span> 4<\/span> filled<\/span> head<\/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\u53cc\u6975\u5b50\u304c\u3064\u304f\u308b\u96fb\u5834<\/h3>\n
$$\\boldsymbol{E} = 3 \\frac{\\boldsymbol{r}\\cdot\\boldsymbol{p}}{r^5} \\boldsymbol{r}
\n– \\frac{\\boldsymbol{p}}{r^3}$$<\/p>\n
$\\boldsymbol{p} = (0, 1, 0), \\quad z = 0$ \u3068\u3057\u3066<\/p>\n
\\begin{eqnarray}
\nE_x &=& \\frac{3}{\\left( x^2 + y^2 \\right)^{5\/2}} x y \\\\
\nE_y &=& \\frac{3}{\\left( x^2 + y^2 \\right)^{5\/2}} y^2 – \\frac{1}{\\left( x^2 + y^2 \\right)^{3\/2}} \\\\
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\u96fb\u6c17\u53cc\u6975\u5b50\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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In [5]:<\/div>\n
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# \u96fb\u5834 E<\/span>\r\nEx<\/span>(x, y) =<\/span> 3.<\/span>*<\/span> x<\/span>*<\/span>y<\/span>\/<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>5<\/span> \r\nEy<\/span>(x, y) =<\/span> 3.<\/span>*<\/span> y<\/span>*<\/span>y<\/span>\/<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>5<\/span> -<\/span> 1.<\/span>\/<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>3<\/span>\r\n\r\n# \u898f\u683c\u5316\u3055\u308c\u305f hat E<\/span>\r\nE<\/span>(x, y) =<\/span> sqrt<\/span>(<\/span>Ex<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>**<\/span>2<\/span> +<\/span> Ey<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>**<\/span>2<\/span>)<\/span>\r\nhEx<\/span>(x,y) =<\/span> scaling<\/span> *<\/span> Ex<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\/<\/span>E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\nhEy<\/span>(x,y) =<\/span> scaling<\/span> *<\/span> Ey<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\/<\/span>E<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\n\r\nreset<\/span>\r\nunset<\/span> xtics<\/span>\r\nunset<\/span> ytics<\/span>\r\nunset<\/span> border<\/span>\r\nset<\/span> zeroaxis<\/span>\r\n\r\n# special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n# urange, vrange \u3067\u8a2d\u5b9a<\/span>\r\nset<\/span> urange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> vrange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> size<\/span> ratio<\/span> 1<\/span>\r\n\r\n# x \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\nset<\/span> samples<\/span> 19<\/span>\r\n# y \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\nset<\/span> isosamples<\/span> 19<\/span>\r\n\r\nscaling<\/span> =<\/span> 0.15<\/span>\r\n\r\n# \u96fb\u6c17\u53cc\u6975\u5b50 p<\/span>\r\nset<\/span> arrow<\/span> 1<\/span> from<\/span> 0<\/span>,<\/span> -0<\/span>.2<\/span> to<\/span> 0<\/span>,<\/span> 0.2<\/span> filled<\/span> head<\/span> lw<\/span> 5<\/span> lc<\/span> \"red\"<\/span> lt<\/span> 1<\/span>\r\n\r\nset<\/span> title<\/span> \"\u96fb\u6c17\u53cc\u6975\u5b50\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\"<\/span>\r\nunset<\/span> colorbox<\/span>\r\nset<\/span> palette<\/span> cubehelix<\/span> start<\/span> 0<\/span> cycles<\/span> 0<\/span> saturation<\/span> 3<\/span> negative<\/span>\r\n\r\nplot<\/span> \"++\"<\/span> u<\/span> 1<\/span>:<\/span>2<\/span>:<\/span>(<\/span>hEx<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>))<\/span>:<\/span>(<\/span>hEy<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>))<\/span>:<\/span>(<\/span>log<\/span>(<\/span>E<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>)))<\/span>\\\r\n     w<\/span> vec<\/span> notitle<\/span> lc<\/span> palette<\/span> lw<\/span> 4<\/span> filled<\/span> head<\/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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\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834 $\\boldsymbol{B}$<\/h3>\n
$$\\boldsymbol{B} = \\frac{\\boldsymbol{I}\\times\\boldsymbol{\\rho}}{\\rho^2}$$$$ \\boldsymbol{I} = (0, 0, I), \\quad \\boldsymbol{\\rho} = (x, y, 0)$$\\begin{eqnarray}
\nB_x &=& – \\frac{ I y}{x^2 + y^2} \\\\
\nB_y &=& \\frac{ I x}{x^2 + y^2}
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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In [6]:<\/div>\n
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# \u78c1\u5834 B<\/span>\r\nBx<\/span>(x, y) =<\/span> -<\/span> scaling<\/span> *<\/span> y<\/span>\/<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>\r\nBy<\/span>(x, y) =<\/span>   scaling<\/span> *<\/span> x<\/span>\/<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>\r\n# \u78c1\u5834 B \u306e\u5927\u304d\u3055<\/span>\r\nB<\/span>(x, y) =<\/span> 1.<\/span>\/<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>\r\n\r\nreset<\/span>\r\nunset<\/span> xtics<\/span>\r\nunset<\/span> ytics<\/span>\r\nunset<\/span> border<\/span>\r\nset<\/span> zeroaxis<\/span>\r\n\r\n# special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n# urange, vrange \u3067\u8a2d\u5b9a<\/span>\r\nset<\/span> urange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> vrange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> size<\/span> ratio<\/span> 1<\/span>\r\n\r\n# x \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\nset<\/span> samples<\/span> 19<\/span>\r\n# y \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\nset<\/span> isosamples<\/span> 19<\/span>\r\n\r\nscaling<\/span> =<\/span> 0.25<\/span>\r\n\r\n# \u96fb\u7dda\u306e\u4f4d\u7f6e<\/span>\r\nset<\/span> label<\/span> 1<\/span> point<\/span> pt<\/span> 6<\/span> ps<\/span> 1.5<\/span> lc<\/span> \"blue\"<\/span> at<\/span> 0<\/span>,<\/span> 0<\/span>\r\nset<\/span> label<\/span> 2<\/span> center<\/span> at<\/span> first<\/span> 0<\/span>,<\/span>0<\/span> \"+\"<\/span> tc<\/span> \"blue\"<\/span>\r\n\r\nset<\/span> title<\/span> \"\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834\"<\/span>\r\nunset<\/span> colorbox<\/span>\r\nset<\/span> palette<\/span> cubehelix<\/span> start<\/span> 1<\/span> cycles<\/span> 0<\/span> saturation<\/span> 3<\/span> negative<\/span>\r\n\r\nplot<\/span> \"++\"<\/span> u<\/span> 1<\/span>:<\/span>2<\/span>:<\/span>(<\/span>Bx<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>))<\/span>:<\/span>(<\/span>By<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>))<\/span>:<\/span>(<\/span>log<\/span>(<\/span>B<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>)))<\/span>\\\r\n     w<\/span> vec<\/span> notitle<\/span> lw<\/span> 4<\/span> lc<\/span> palette<\/span> filled<\/span> head<\/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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\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834\u306e\u5411\u304d<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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In [7]:<\/div>\n
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# \u78c1\u5834 B<\/span>\r\nBx<\/span>(x, y) =<\/span> -<\/span> y<\/span>\/<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>\r\nBy<\/span>(x, y) =<\/span>   x<\/span>\/<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>)<\/span>\r\n# \u78c1\u5834 B \u306e\u5927\u304d\u3055<\/span>\r\nB<\/span>(x, y) =<\/span> sqrt<\/span>(<\/span>Bx<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>**<\/span>2<\/span> +<\/span> By<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>**<\/span>2<\/span>)<\/span>\r\n# \u898f\u683c\u5316\u3055\u308c\u305f hat B<\/span>\r\nhBx<\/span>(x, y) =<\/span> scaling<\/span> *<\/span> Bx<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\/<\/span>B<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\nhBy<\/span>(x, y) =<\/span> scaling<\/span> *<\/span> By<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\/<\/span>B<\/span>(<\/span>x<\/span>,<\/span> y<\/span>)<\/span>\r\n\r\nreset<\/span>\r\nunset<\/span> xtics<\/span>\r\nunset<\/span> ytics<\/span>\r\nunset<\/span> border<\/span>\r\nset<\/span> zeroaxis<\/span>\r\n# \u8868\u793a\u7bc4\u56f2\u306e\u8a2d\u5b9a<\/span>\r\nset<\/span> size<\/span> ratio<\/span> 1<\/span>\r\n\r\n# special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n# urange, vrange \u3067\u8a2d\u5b9a<\/span>\r\nset<\/span> urange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\nset<\/span> vrange<\/span> [<\/span>-3<\/span>:<\/span>3<\/span>]<\/span>\r\n\r\nset<\/span> samples<\/span> 19<\/span>\r\nset<\/span> isosamples<\/span> 19<\/span>\r\n\r\nscaling<\/span> =<\/span> 0.2<\/span>\r\n\r\n# \u96fb\u7dda\u306e\u4f4d\u7f6e<\/span>\r\nset<\/span> label<\/span> 1<\/span> point<\/span> pt<\/span> 6<\/span> ps<\/span> 1.5<\/span> lc<\/span> \"blue\"<\/span> at<\/span> 0<\/span>,<\/span> 0<\/span>\r\nset<\/span> label<\/span> 2<\/span> center<\/span> at<\/span> first<\/span> 0<\/span>,<\/span>0<\/span> \"+\"<\/span> tc<\/span> \"blue\"<\/span>\r\n\r\nset<\/span> title<\/span> \"\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834\u306e\u5411\u304d\"<\/span>\r\nunset<\/span> colorbox<\/span>\r\nset<\/span> palette<\/span> cubehelix<\/span> start<\/span> 1<\/span> cycles<\/span> 0<\/span> saturation<\/span> 3<\/span> negative<\/span>\r\n\r\nplot<\/span> \"++\"<\/span> u<\/span> 1<\/span>:<\/span>2<\/span>:<\/span>(<\/span>hBx<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>))<\/span>:<\/span>(<\/span>hBy<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>))<\/span>:<\/span>(<\/span>log<\/span>(<\/span>B<\/span>(<\/span>$<\/span>1<\/span>,<\/span>$<\/span>2<\/span>)))<\/span> \\\r\n     w<\/span> vec<\/span> notitle<\/span> lw<\/span> 4<\/span> lc<\/span> palette<\/span> filled<\/span> head<\/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":"
\u5148\u65e5\uff0c\u300cgnuplot \u3067\u30d9\u30af\u30c8\u30eb\u5834\uff08\u96fb\u5834\u30fb\u78c1\u5834\uff09\u3092\u63cf\u304f\u300d\u3067\u63cf\u3044\u3066\u307f\u305f\u304c\uff0c\u3044\u308d\u3044\u308d\u691c\u7d22\u3059\u308b\u3068 palette \u3067\u30d9\u30af\u30c8\u30eb\u306e\u8272\u3092\uff08\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306b\u5408\u308f\u305b\u3066\uff09\u53ef\u5909\u306b\u3067\u304d\u308b\u3088\u3046\u306a\u306e\u3067\uff0c\u5099\u5fd8\u9332\u3068\u3057\u3066\u3002<\/p>
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