{"id":3595,"date":"2022-08-29T13:49:02","date_gmt":"2022-08-29T04:49:02","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=3595"},"modified":"2023-03-28T17:59:51","modified_gmt":"2023-03-28T08:59:51","slug":"gnuplot-%e3%81%a7%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%82%92%e6%8f%8f%e3%81%8f","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3595\/","title":{"rendered":"gnuplot \u3067\u30d9\u30af\u30c8\u30eb\u5834\uff08\u96fb\u5834\u30fb\u78c1\u5834\uff09\u3092\u63cf\u304f"},"content":{"rendered":"<p>\u96fb\u78c1\u6c17\u5b66\u306e\u6388\u696d\u306e\u6e96\u5099\u3002<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e9%9d%99%e9%9b%bb%e5%a0%b4%ef%bc%9a%e9%9b%bb%e8%8d%b7%e5%af%86%e5%ba%a6%e3%81%8b%e3%82%89%e7%9b%b4%e6%8e%a5%e9%9b%bb%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/\" target=\"_blank\" rel=\"noopener\">\u9759\u96fb\u5834\uff1a\u96fb\u8377\u5bc6\u5ea6\u304b\u3089\u76f4\u63a5\u9759\u96fb\u5834\u3092\u6c42\u3081\u308b<\/a>\u300d<\/li>\n<\/ul>\n<p>gnuplot \u3067\u306f\uff0cspecial file-name &#8220;++&#8221; \u3092\u4f7f\u3046\u3068\uff0c\u30c7\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb\u3092\u4f5c\u3089\u305a\u306b\u30d9\u30af\u30c8\u30eb\u5834\u3092\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3061\u3087\u3063\u3068\u51fa\u6765\u4e0a\u304c\u308a\u304c\u3057\u3087\u307c\u3044\u304c\uff0c\u7c21\u5358\u306b\u30d9\u30af\u30c8\u30eb\u5834\u3092\u8868\u793a\u3067\u304d\u308b\u306e\u3067\u4f7f\u3063\u3066\u307f\u308b\u3002<!--more--><\/p>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u70b9\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834-$\\boldsymbol{E}$\">\u70b9\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834 $\\boldsymbol{E}$<\/h3>\n<p>\\begin{eqnarray}<br \/>\n\\boldsymbol{E}<br \/>\n&amp;=&amp; \\frac{q_1}{4\\pi \\varepsilon_0} \\frac{\\boldsymbol{r} &#8211; \\boldsymbol{r}_1}{|\\boldsymbol{r} &#8211; \\boldsymbol{r}_1|^3}\\end{eqnarray}<\/p>\n<p>$z=0$ \u306e $xy$ \u5e73\u9762\u30672\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u5834\u3092\u63cf\u304f\u3002<\/p>\n<p>$$\\boldsymbol{r} = (x, y, 0), \\quad \\boldsymbol{r}_1 = (x_1, y_1, 0)$$$$E_x = s \\frac{x-x_1}{\\left((x-x_1)^2 + (y-y_1)^2\\right)^{3\/2}}$$$$E_y = s \\frac{y-y_1}{\\left((x-x_1)^2 + (y-y_1)^2\\right)^{3\/2}}$$<\/p>\n<p>$s$ \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<ul>\n<li>\u53c2\u8003\uff1a\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e9%9d%99%e9%9b%bb%e5%a0%b4%ef%bc%9a%e9%9b%bb%e8%8d%b7%e5%af%86%e5%ba%a6%e3%81%8b%e3%82%89%e7%9b%b4%e6%8e%a5%e9%9b%bb%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/#i-2\" target=\"_blank\" rel=\"noopener\">\u70b9\u96fb\u8377\u306e\u96fb\u8377\u5bc6\u5ea6\u3068\u96fb\u5834<\/a>\u300d<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\">\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-gnuplot\">\n<pre><span class=\"c\"># \u96fb\u5834 E<\/span>\r\n<span class=\"nf\">Ex<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">Ey<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"n\">y<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">reset<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">xtics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">ytics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">border<\/span>\r\n\r\n<span class=\"c\"># \u8868\u793a\u7bc4\u56f2\u306e\u8a2d\u5b9a<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">xrange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">yrange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n\r\n<span class=\"c\"># special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n<span class=\"c\"># urange, vrange \u3067\u63cf\u753b\u7bc4\u56f2\u306e\u8a2d\u5b9a<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">urange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">vrange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">size<\/span> <span class=\"n\">ratio<\/span> <span class=\"mi\">1<\/span>\r\n\r\n<span class=\"c\"># x \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">samples<\/span> <span class=\"mi\">13<\/span>\r\n<span class=\"c\"># y \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">isosamples<\/span> <span class=\"mi\">13<\/span>\r\n\r\n<span class=\"nv\">scaling<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.2<\/span>\r\n\r\n<span class=\"c\"># \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u9752\u4e38\u3068 +<\/span>\r\n<span class=\"nv\">x1<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"nv\">y1<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">1<\/span> <span class=\"n\">point<\/span> <span class=\"n\">pt<\/span> <span class=\"mi\">6<\/span> <span class=\"n\">ps<\/span> <span class=\"mf\">1.5<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"blue\"<\/span> <span class=\"n\">at<\/span> <span class=\"n\">x1<\/span><span class=\"o\">,<\/span> <span class=\"n\">y1<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">2<\/span> <span class=\"n\">center<\/span> <span class=\"n\">at<\/span> <span class=\"n\">first<\/span> <span class=\"n\">x1<\/span><span class=\"o\">,<\/span> <span class=\"n\">y1<\/span> <span class=\"s\">\"+\"<\/span> <span class=\"n\">tc<\/span> <span class=\"s\">\"blue\"<\/span>\r\n\r\n<span class=\"k\">set<\/span> <span class=\"nb\">title<\/span> <span class=\"s\">\"\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\"<\/span>\r\n<span class=\"k\">plot<\/span> <span class=\"s\">\"++\"<\/span> <span class=\"nb\">using<\/span> <span class=\"mi\">1<\/span><span class=\"o\">:<\/span><span class=\"mi\">2<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">x1<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"o\">-<\/span><span class=\"n\">y1<\/span><span class=\"p\">))<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">x1<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"o\">-<\/span><span class=\"n\">y1<\/span><span class=\"p\">))<\/span> \\\r\n     <span class=\"nb\">w<\/span> <span class=\"n\">vec<\/span> <span class=\"nb\">notitle<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"blue\"<\/span> <span class=\"n\">lw<\/span> <span class=\"mf\">1.5<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3597 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/vec-fig01.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"$\\boldsymbol{E}$-\u306e\u5411\u304d\u3092\u8868\u3059\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u5834\">$\\boldsymbol{E}$ \u306e\u5411\u304d\u3092\u8868\u3059\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u5834<\/h3>\n<p>\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<p>$$\\hat{\\boldsymbol{E}} \\equiv \\frac{\\boldsymbol{E}}{\\sqrt{\\boldsymbol{E}\\cdot\\boldsymbol{E}}} =<br \/>\n\\frac{\\boldsymbol{r} &#8211; \\boldsymbol{r}_1}{|\\boldsymbol{r} &#8211; \\boldsymbol{r}_1|}$$$$\\hat{E}_x = s \\frac{x-x_1}{\\sqrt{(x-x_1)^2 + (y-y_1)^2}}$$$$\\hat{E}_y = s \\frac{y-y_1}{\\sqrt{(x-x_1)^2 + (y-y_1)^2}}$$<\/p>\n<p>$s$ \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<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\">\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-gnuplot\">\n<pre><span class=\"c\"># \u96fb\u5834 E<\/span>\r\n<span class=\"nf\">Ex<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">Ey<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">y<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c\"># \u898f\u683c\u5316\u3055\u308c\u305f hat E<\/span>\r\n<span class=\"nf\">E<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">hEx<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">hEy<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">reset<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">xtics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">ytics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">border<\/span>\r\n<span class=\"c\"># \u8868\u793a\u7bc4\u56f2\u306e\u8a2d\u5b9a<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">xrange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">yrange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n\r\n<span class=\"c\"># special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n<span class=\"c\"># urange, vrange \u3067\u63cf\u753b\u7bc4\u56f2\u306e\u8a2d\u5b9a<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">urange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">vrange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">size<\/span> <span class=\"n\">ratio<\/span> <span class=\"mi\">1<\/span>\r\n\r\n<span class=\"c\"># x \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">samples<\/span> <span class=\"mi\">13<\/span>\r\n<span class=\"c\"># y \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">isosamples<\/span> <span class=\"mi\">13<\/span>\r\n\r\n<span class=\"nv\">scaling<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.18<\/span>\r\n\r\n<span class=\"c\"># \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u9752\u4e38\u3068 +<\/span>\r\n<span class=\"nv\">x1<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"nv\">y1<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">1<\/span> <span class=\"n\">point<\/span> <span class=\"n\">pt<\/span> <span class=\"mi\">6<\/span> <span class=\"n\">ps<\/span> <span class=\"mf\">1.5<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"blue\"<\/span> <span class=\"n\">at<\/span> <span class=\"n\">x1<\/span><span class=\"o\">,<\/span> <span class=\"n\">y1<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">2<\/span> <span class=\"n\">center<\/span> <span class=\"n\">at<\/span> <span class=\"n\">first<\/span> <span class=\"n\">x1<\/span><span class=\"o\">,<\/span> <span class=\"n\">y1<\/span> <span class=\"s\">\"+\"<\/span> <span class=\"n\">tc<\/span> <span class=\"s\">\"blue\"<\/span>\r\n\r\n<span class=\"k\">set<\/span> <span class=\"nb\">title<\/span> <span class=\"s\">\"\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\"<\/span>\r\n<span class=\"k\">plot<\/span> <span class=\"s\">\"++\"<\/span> <span class=\"nb\">using<\/span> <span class=\"mi\">1<\/span><span class=\"o\">:<\/span><span class=\"mi\">2<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">hEx<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">x1<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"o\">-<\/span><span class=\"n\">y1<\/span><span class=\"p\">))<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">hEy<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">x1<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"o\">-<\/span><span class=\"n\">y1<\/span><span class=\"p\">))<\/span> \\\r\n     <span class=\"nb\">w<\/span> <span class=\"n\">vec<\/span> <span class=\"nb\">notitle<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"blue\"<\/span> <span class=\"n\">lw<\/span> <span class=\"mf\">1.5<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3599 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/vec-fig02.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\">\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-gnuplot\">\n<pre><span class=\"c\"># \u96fb\u5834 E<\/span>\r\n<span class=\"nf\">Ex<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"o\">-<\/span><span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">Ey<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"o\">-<\/span><span class=\"n\">y<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c\"># \u898f\u683c\u5316\u3055\u308c\u305f hat E<\/span>\r\n<span class=\"nf\">E<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">hEx<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">hEy<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">reset<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">xtics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">ytics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">border<\/span>\r\n\r\n<span class=\"c\"># special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n<span class=\"c\"># urange, vrange \u3067\u63cf\u753b\u7bc4\u56f2\u306e\u8a2d\u5b9a<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">urange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">vrange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">size<\/span> <span class=\"n\">ratio<\/span> <span class=\"mi\">1<\/span>\r\n\r\n<span class=\"c\"># x \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">samples<\/span> <span class=\"mi\">13<\/span>\r\n<span class=\"c\"># y \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">isosamples<\/span> <span class=\"mi\">13<\/span>\r\n\r\n<span class=\"nv\">scaling<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.18<\/span>\r\n\r\n<span class=\"c\"># \u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u8d64\u4e38\u3068 -<\/span>\r\n<span class=\"nv\">x2<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"nv\">y2<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">-1<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">3<\/span> <span class=\"n\">point<\/span> <span class=\"n\">pt<\/span> <span class=\"mi\">6<\/span> <span class=\"n\">ps<\/span> <span class=\"mf\">1.5<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"red\"<\/span> <span class=\"n\">at<\/span> <span class=\"n\">x2<\/span><span class=\"o\">,<\/span> <span class=\"n\">y2<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">4<\/span> <span class=\"n\">center<\/span> <span class=\"n\">at<\/span> <span class=\"n\">first<\/span> <span class=\"n\">x2<\/span><span class=\"o\">,<\/span> <span class=\"n\">y2<\/span> <span class=\"s\">\"-\"<\/span> <span class=\"n\">tc<\/span> <span class=\"s\">\"red\"<\/span>\r\n\r\n<span class=\"k\">set<\/span> <span class=\"nb\">title<\/span> <span class=\"s\">\"\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\"<\/span>\r\n<span class=\"k\">plot<\/span> <span class=\"s\">\"++\"<\/span> <span class=\"nb\">using<\/span> <span class=\"mi\">1<\/span><span class=\"o\">:<\/span><span class=\"mi\">2<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">hEx<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">x2<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"o\">-<\/span><span class=\"n\">y2<\/span><span class=\"p\">))<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">hEy<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">x2<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"o\">-<\/span><span class=\"n\">y2<\/span><span class=\"p\">))<\/span> \\\r\n     <span class=\"nb\">w<\/span> <span class=\"n\">vec<\/span> <span class=\"nb\">notitle<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"red\"<\/span> <span class=\"n\">lw<\/span> <span class=\"mf\">1.5<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3600 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/vec-fig03.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u6b63\u96fb\u8377\u3068\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\">\u6b63\u96fb\u8377\u3068\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d<\/h4>\n<ul>\n<li>\u53c2\u8003\uff1a\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e9%9d%99%e9%9b%bb%e5%a0%b4%ef%bc%9a%e9%9b%bb%e8%8d%b7%e5%af%86%e5%ba%a6%e3%81%8b%e3%82%89%e7%9b%b4%e6%8e%a5%e9%9b%bb%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/#2\" target=\"_blank\" rel=\"noopener\">2\u3064\u306e\u70b9\u96fb\u8377\u306b\u3088\u308b\u96fb\u5834<\/a>\u300d<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-gnuplot\">\n<pre><span class=\"c\"># \u96fb\u5834 E<\/span>\r\n<span class=\"nf\">Ex<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span>\r\n<span class=\"nf\">Ey<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">y<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span>\r\n\r\n<span class=\"c\"># \u6b63\u96fb\u8377\u3068\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834<\/span>\r\n<span class=\"nf\">E2x<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">-<\/span><span class=\"n\">x1<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"o\">-<\/span><span class=\"n\">y1<\/span><span class=\"p\">)<\/span> <span class=\"o\">-<\/span> <span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">-<\/span><span class=\"n\">x2<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"o\">-<\/span><span class=\"n\">y2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">E2y<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">-<\/span><span class=\"n\">x1<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"o\">-<\/span><span class=\"n\">y1<\/span><span class=\"p\">)<\/span> <span class=\"o\">-<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">-<\/span><span class=\"n\">x2<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"o\">-<\/span><span class=\"n\">y2<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c\"># \u898f\u683c\u5316\u3055\u308c\u305f hat E<\/span>\r\n<span class=\"nf\">E<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">E2x<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">E2y<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">hE2x<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">E2x<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">hE2y<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">E2y<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">reset<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">xtics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">ytics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">border<\/span>\r\n\r\n<span class=\"c\"># special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n<span class=\"c\"># urange, vrange \u3067\u63cf\u753b\u7bc4\u56f2\u306e\u8a2d\u5b9a<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">urange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">vrange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">size<\/span> <span class=\"n\">ratio<\/span> <span class=\"mi\">1<\/span>\r\n\r\n<span class=\"c\"># x \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">samples<\/span> <span class=\"mi\">17<\/span>\r\n<span class=\"c\"># y \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">isosamples<\/span> <span class=\"mi\">17<\/span>\r\n\r\n<span class=\"nv\">scaling<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.18<\/span>\r\n\r\n<span class=\"c\"># \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u9752\u4e38\u3068 +<\/span>\r\n<span class=\"nv\">x1<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"nv\">y1<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">1<\/span> <span class=\"n\">point<\/span> <span class=\"n\">pt<\/span> <span class=\"mi\">6<\/span> <span class=\"n\">ps<\/span> <span class=\"mf\">1.5<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"blue\"<\/span> <span class=\"n\">at<\/span> <span class=\"n\">x1<\/span><span class=\"o\">,<\/span> <span class=\"n\">y1<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">2<\/span> <span class=\"n\">center<\/span> <span class=\"n\">at<\/span> <span class=\"n\">first<\/span> <span class=\"n\">x1<\/span><span class=\"o\">,<\/span> <span class=\"n\">y1<\/span> <span class=\"s\">\"+\"<\/span> <span class=\"n\">tc<\/span> <span class=\"s\">\"blue\"<\/span>\r\n\r\n<span class=\"c\"># \u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e\u306b\u8d64\u4e38\u3068 -<\/span>\r\n<span class=\"nv\">x2<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"nv\">y2<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">-1<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">3<\/span> <span class=\"n\">point<\/span> <span class=\"n\">pt<\/span> <span class=\"mi\">6<\/span> <span class=\"n\">ps<\/span> <span class=\"mf\">1.5<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"red\"<\/span> <span class=\"n\">at<\/span> <span class=\"n\">x2<\/span><span class=\"o\">,<\/span> <span class=\"n\">y2<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">4<\/span> <span class=\"n\">center<\/span> <span class=\"n\">at<\/span> <span class=\"n\">first<\/span> <span class=\"n\">x2<\/span><span class=\"o\">,<\/span> <span class=\"n\">y2<\/span> <span class=\"s\">\"-\"<\/span> <span class=\"n\">tc<\/span> <span class=\"s\">\"red\"<\/span>\r\n\r\n<span class=\"k\">set<\/span> <span class=\"nb\">title<\/span> <span class=\"s\">\"\u6b63\u96fb\u8377\u3068\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\"<\/span>\r\n<span class=\"k\">plot<\/span> <span class=\"s\">\"++\"<\/span> <span class=\"nb\">using<\/span> <span class=\"mi\">1<\/span><span class=\"o\">:<\/span><span class=\"mi\">2<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">hE2x<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">hE2y<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span> \\\r\n     <span class=\"nb\">w<\/span> <span class=\"n\">vec<\/span> <span class=\"nb\">notitle<\/span> <span class=\"n\">lc<\/span> <span class=\"mi\">1<\/span> <span class=\"n\">lw<\/span> <span class=\"mf\">1.8<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3601 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/vec-fig04.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u96fb\u6c17\u53cc\u6975\u5b50\u304c\u3064\u304f\u308b\u96fb\u5834\">\u96fb\u6c17\u53cc\u6975\u5b50\u304c\u3064\u304f\u308b\u96fb\u5834<\/h3>\n<ul>\n<li>\u53c2\u8003\uff1a\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e9%9d%99%e9%9b%bb%e5%a0%b4%ef%bc%9a%e9%9b%bb%e8%8d%b7%e5%af%86%e5%ba%a6%e3%81%8b%e3%82%89%e7%9b%b4%e6%8e%a5%e9%9b%bb%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/#i-3\" target=\"_blank\" rel=\"noopener\">\u96fb\u6c17\u53cc\u6975\u5b50\u306b\u3088\u308b\u96fb\u5834<\/a>\u300d<\/li>\n<\/ul>\n<p>$$\\boldsymbol{E} = 3 \\frac{\\boldsymbol{r}\\cdot\\boldsymbol{p}}{r^5} \\boldsymbol{r}<br \/>\n&#8211; \\frac{\\boldsymbol{p}}{r^3}$$<\/p>\n<p>$\\boldsymbol{p} = (0, 1, 0), \\quad z = 0$ \u3068\u3057\u3066<\/p>\n<p>\\begin{eqnarray}<br \/>\nE_x &amp;=&amp; \\frac{3}{\\left( x^2 + y^2 \\right)^{5\/2}} x y \\\\<br \/>\nE_y &amp;=&amp; \\frac{3}{\\left( x^2 + y^2 \\right)^{5\/2}} y^2 &#8211; \\frac{1}{\\left( x^2 + y^2 \\right)^{3\/2}} \\\\<br \/>\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u96fb\u6c17\u53cc\u6975\u5b50\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\">\u96fb\u6c17\u53cc\u6975\u5b50\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-gnuplot\">\n<pre><span class=\"c\"># \u96fb\u5834 E<\/span>\r\n<span class=\"nf\">Ex<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"mf\">3.<\/span><span class=\"o\">*<\/span> <span class=\"n\">x<\/span><span class=\"o\">*<\/span><span class=\"n\">y<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">5<\/span> \r\n<span class=\"nf\">Ey<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"mf\">3.<\/span><span class=\"o\">*<\/span> <span class=\"n\">y<\/span><span class=\"o\">*<\/span><span class=\"n\">y<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">5<\/span> <span class=\"o\">-<\/span> <span class=\"mf\">1.<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span>\r\n\r\n<span class=\"c\"># \u898f\u683c\u5316\u3055\u308c\u305f hat E<\/span>\r\n<span class=\"nf\">E<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">hEx<\/span>(x,y) <span class=\"o\">=<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">hEy<\/span>(x,y) <span class=\"o\">=<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">reset<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">xtics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">ytics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">border<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">zeroaxis<\/span>\r\n\r\n<span class=\"c\"># special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n<span class=\"c\"># urange, vrange \u3067\u8a2d\u5b9a<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">urange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">vrange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">size<\/span> <span class=\"n\">ratio<\/span> <span class=\"mi\">1<\/span>\r\n\r\n<span class=\"c\"># x \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">samples<\/span> <span class=\"mi\">17<\/span>\r\n<span class=\"c\"># y \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">isosamples<\/span> <span class=\"mi\">17<\/span>\r\n\r\n<span class=\"nv\">scaling<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.18<\/span>\r\n\r\n<span class=\"c\"># \u96fb\u6c17\u53cc\u6975\u5b50 p<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">arrow<\/span> <span class=\"mi\">1<\/span> <span class=\"n\">from<\/span> <span class=\"mi\">0<\/span><span class=\"o\">,<\/span> <span class=\"mi\">-0<\/span><span class=\"mf\">.2<\/span> <span class=\"n\">to<\/span> <span class=\"mi\">0<\/span><span class=\"o\">,<\/span> <span class=\"mf\">0.2<\/span> <span class=\"n\">filled<\/span> <span class=\"n\">lw<\/span> <span class=\"mi\">5<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"red\"<\/span> <span class=\"n\">lt<\/span> <span class=\"mi\">1<\/span>\r\n\r\n<span class=\"k\">set<\/span> <span class=\"nb\">title<\/span> <span class=\"s\">\"\u96fb\u6c17\u53cc\u6975\u5b50\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\"<\/span>\r\n<span class=\"k\">plot<\/span> <span class=\"s\">\"++\"<\/span> <span class=\"nb\">using<\/span> <span class=\"mi\">1<\/span><span class=\"o\">:<\/span><span class=\"mi\">2<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">hEx<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">hEy<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span>\\\r\n     <span class=\"nb\">w<\/span> <span class=\"n\">vec<\/span> <span class=\"nb\">notitle<\/span> <span class=\"n\">lw<\/span> <span class=\"mf\">1.8<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3602 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/vec-fig05.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834-$\\boldsymbol{B}$\">\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834 $\\boldsymbol{B}$<\/h3>\n<p>$$\\boldsymbol{B} = \\frac{\\boldsymbol{I}\\times\\boldsymbol{\\rho}}{\\rho^2}$$$$ \\boldsymbol{I} = (0, 0, I), \\quad \\boldsymbol{\\rho} = (x, y, 0)$$\\begin{eqnarray}<br \/>\nB_x &amp;=&amp; &#8211; \\frac{ I y}{x^2 + y^2} \\\\<br \/>\nB_y &amp;=&amp; \\frac{ I x}{x^2 + y^2}<br \/>\n\\end{eqnarray}<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e9%9d%99%e7%a3%81%e5%a0%b4%ef%bc%9a%e9%9b%bb%e6%b5%81%e5%af%86%e5%ba%a6%e3%81%8b%e3%82%89%e7%9b%b4%e6%8e%a5%e9%9d%99%e7%a3%81%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/#i-2\" target=\"_blank\" rel=\"noopener\">\u76f4\u7dda\u96fb\u6d41\u306b\u3088\u308b\u78c1\u5834<\/a>\u300d<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834\">\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-gnuplot\">\n<pre><span class=\"c\"># \u78c1\u5834 B<\/span>\r\n<span class=\"nf\">Bx<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"o\">-<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"n\">y<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">By<\/span>(x, y) <span class=\"o\">=<\/span>   <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">reset<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">xtics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">ytics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">border<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">zeroaxis<\/span>\r\n\r\n<span class=\"c\"># special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n<span class=\"c\"># urange, vrange \u3067\u8a2d\u5b9a<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">urange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">vrange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">size<\/span> <span class=\"n\">ratio<\/span> <span class=\"mi\">1<\/span>\r\n\r\n<span class=\"c\"># x \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">samples<\/span> <span class=\"mi\">15<\/span>\r\n<span class=\"c\"># y \u8ef8\u65b9\u5411\u306e\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">isosamples<\/span> <span class=\"mi\">15<\/span>\r\n\r\n<span class=\"nv\">scaling<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.25<\/span>\r\n\r\n<span class=\"c\"># \u96fb\u7dda\u306e\u4f4d\u7f6e<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">1<\/span> <span class=\"n\">point<\/span> <span class=\"n\">pt<\/span> <span class=\"mi\">6<\/span> <span class=\"n\">ps<\/span> <span class=\"mf\">1.5<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"blue\"<\/span> <span class=\"n\">at<\/span> <span class=\"mi\">0<\/span><span class=\"o\">,<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">2<\/span> <span class=\"n\">center<\/span> <span class=\"n\">at<\/span> <span class=\"n\">first<\/span> <span class=\"mi\">0<\/span><span class=\"o\">,<\/span><span class=\"mi\">0<\/span> <span class=\"s\">\"+\"<\/span> <span class=\"n\">tc<\/span> <span class=\"s\">\"blue\"<\/span>\r\n\r\n<span class=\"k\">set<\/span> <span class=\"nb\">title<\/span> <span class=\"s\">\"\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834\"<\/span>\r\n<span class=\"k\">plot<\/span> <span class=\"s\">\"++\"<\/span> <span class=\"nb\">using<\/span> <span class=\"mi\">1<\/span><span class=\"o\">:<\/span><span class=\"mi\">2<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">Bx<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">By<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span>\\\r\n     <span class=\"nb\">w<\/span> <span class=\"n\">vec<\/span> <span class=\"nb\">notitle<\/span> <span class=\"n\">lw<\/span> <span class=\"mf\">1.8<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3603 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/vec-fig06.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834\u306e\u5411\u304d\">\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834\u306e\u5411\u304d<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-gnuplot\">\n<pre><span class=\"c\"># \u78c1\u5834 B<\/span>\r\n<span class=\"nf\">Bx<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"o\">-<\/span> <span class=\"n\">y<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">By<\/span>(x, y) <span class=\"o\">=<\/span>   <span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c\"># \u898f\u683c\u5316\u3055\u308c\u305f hat B<\/span>\r\n<span class=\"nf\">B<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">Bx<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">By<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">hBx<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Bx<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">B<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\r\n<span class=\"nf\">hBy<\/span>(x, y) <span class=\"o\">=<\/span> <span class=\"n\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">By<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">B<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">reset<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">xtics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">ytics<\/span>\r\n<span class=\"k\">unset<\/span> <span class=\"nb\">border<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">zeroaxis<\/span>\r\n<span class=\"c\"># \u8868\u793a\u7bc4\u56f2\u306e\u8a2d\u5b9a<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">size<\/span> <span class=\"n\">ratio<\/span> <span class=\"mi\">1<\/span>\r\n\r\n<span class=\"c\"># special filename \"++\" \u306e\u3068\u304d\u306f<\/span>\r\n<span class=\"c\"># urange, vrange \u3067\u8a2d\u5b9a<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">urange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">vrange<\/span> <span class=\"p\">[<\/span><span class=\"mi\">-3<\/span><span class=\"o\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">]<\/span>\r\n\r\n<span class=\"k\">set<\/span> <span class=\"nb\">samples<\/span> <span class=\"mi\">17<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">isosamples<\/span> <span class=\"mi\">17<\/span>\r\n\r\n<span class=\"nv\">scaling<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.25<\/span>\r\n\r\n<span class=\"c\"># \u96fb\u7dda\u306e\u4f4d\u7f6e<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">1<\/span> <span class=\"n\">point<\/span> <span class=\"n\">pt<\/span> <span class=\"mi\">6<\/span> <span class=\"n\">ps<\/span> <span class=\"mf\">1.5<\/span> <span class=\"n\">lc<\/span> <span class=\"s\">\"blue\"<\/span> <span class=\"n\">at<\/span> <span class=\"mi\">0<\/span><span class=\"o\">,<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"k\">set<\/span> <span class=\"nb\">label<\/span> <span class=\"mi\">2<\/span> <span class=\"n\">center<\/span> <span class=\"n\">at<\/span> <span class=\"n\">first<\/span> <span class=\"mi\">0<\/span><span class=\"o\">,<\/span><span class=\"mi\">0<\/span> <span class=\"s\">\"+\"<\/span> <span class=\"n\">tc<\/span> <span class=\"s\">\"blue\"<\/span>\r\n\r\n<span class=\"k\">set<\/span> <span class=\"nb\">title<\/span> <span class=\"s\">\"\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834\u306e\u5411\u304d\"<\/span>\r\n<span class=\"k\">plot<\/span> <span class=\"s\">\"++\"<\/span> <span class=\"nb\">using<\/span> <span class=\"mi\">1<\/span><span class=\"o\">:<\/span><span class=\"mi\">2<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">hBx<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span><span class=\"o\">:<\/span><span class=\"p\">(<\/span><span class=\"nf\">hBy<\/span><span class=\"p\">(<\/span><span class=\"err\">$<\/span><span class=\"mi\">1<\/span><span class=\"o\">,<\/span><span class=\"err\">$<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span> \\\r\n     <span class=\"nb\">w<\/span> <span class=\"n\">vec<\/span> <span class=\"nb\">notitle<\/span> <span class=\"n\">lw<\/span> <span class=\"mf\">1.8<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3604 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/vec-fig07.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u96fb\u78c1\u6c17\u5b66\u306e\u6388\u696d\u306e\u6e96\u5099\u3002<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a\u300c\u9759\u96fb\u5834\uff1a\u96fb\u8377\u5bc6\u5ea6\u304b\u3089\u76f4\u63a5\u9759\u96fb\u5834\u3092\u6c42\u3081\u308b\u300d<\/li>\n<\/ul>\n<p>gnuplot \u3067\u306f\uff0cspecial file-name &#8220;++&#8221; \u3092\u4f7f\u3046\u3068\uff0c\u30c7\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb\u3092\u4f5c\u3089\u305a\u306b\u30d9\u30af\u30c8\u30eb\u5834\u3092\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3061\u3087\u3063\u3068\u51fa\u6765\u4e0a\u304c\u308a\u304c\u3057\u3087\u307c\u3044\u304c\uff0c\u7c21\u5358\u306b\u30d9\u30af\u30c8\u30eb\u5834\u3092\u8868\u793a\u3067\u304d\u308b\u306e\u3067\u4f7f\u3063\u3066\u307f\u308b\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3595\/\">\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":[15,19],"tags":[],"class_list":["post-3595","post","type-post","status-publish","format-standard","hentry","category-gnuplot","category-19","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/3595","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=3595"}],"version-history":[{"count":14,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/3595\/revisions"}],"predecessor-version":[{"id":3899,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/3595\/revisions\/3899"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=3595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=3595"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=3595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}