{"id":7043,"date":"2023-11-21T12:28:39","date_gmt":"2023-11-21T03:28:39","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=7043"},"modified":"2023-11-21T17:34:57","modified_gmt":"2023-11-21T08:34:57","slug":"%e4%b8%8b%e3%81%94%e3%81%97%e3%82%89%e3%81%88%ef%bc%88ver-2%ef%bc%89%e3%81%97%e3%81%9f%e4%b8%87%e6%9c%89%e5%bc%95%e5%8a%9b%e3%81%ae2%e4%bd%93%e5%95%8f%e9%a1%8c%e3%81%ae%e9%81%8b%e5%8b%95%e6%96%b9-2","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/7043\/","title":{"rendered":"\u4e0b\u3053\u3099\u3057\u3089\u3048\uff08ver.2\uff09\u3057\u305f\u4e07\u6709\u5f15\u529b\u306e2\u4f53\u554f\u984c\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092 Python \u3066\u3099\u6570\u5024\u7684\u306b\u89e3\u304f"},"content":{"rendered":"
\n
<\/div>\n
\n
\n

\u300c\u4e07\u6709\u5f15\u529b\u306e2\u4f53\u554f\u984c\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u524d\u306e\u4e0b\u3054\u3057\u3089\u3048 ver. 2<\/a>\u300d\u3067\u4e0b\u3054\u3057\u3089\u3048\u3057\u305f\u5f0f\u3092 Python \u3067\u6570\u5024\u7684\u306b\u89e3\u304f\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

<\/p>\n

\n
<\/div>\n
\n
\n

\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u904b\u52d5\u65b9\u7a0b\u5f0f<\/h3>\n

\u300c\u4e07\u6709\u5f15\u529b\u306e2\u4f53\u554f\u984c\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u524d\u306e\u4e0b\u3054\u3057\u3089\u3048 ver. 2<\/a>\u300d\u306b\u307e\u3068\u3081\u305f\u3088\u3046\u306b\uff0c\u8ecc\u9053\u9577\u534a\u5f84 $a$ \u3068\u5468\u671f $P$ \u3067\u7121\u6b21\u5143\u5316\u3057\u305f\u5909\u6570\u306b\u5bfe\u3059\u308b\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u306e\u3067\u3042\u3063\u305f\u3002<\/p>\n

\\begin{eqnarray}
\n\\frac{d^2 X}{dT^2} = – 4\\pi^2\\frac{X}{\\left(X^2 + Y^2\\right)^{\\frac{3}{2}}} \\\\
\n\\frac{d^2 Y}{dT^2} = – 4\\pi^2\\frac{Y}{\\left(X^2 + Y^2\\right)^{\\frac{3}{2}}}
\n\\end{eqnarray}<\/p>\n

\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u521d\u671f\u6761\u4ef6<\/h3>\n

\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u5909\u6570\u306b\u5bfe\u3059\u308b\u521d\u671f\u6761\u4ef6\u306f $T = 0$ \u3067<\/p>\n

\\begin{eqnarray}
\nX(0) &=& 1-e \\\\
\nY(0) &=& 0\\\\
\nV_x(0) &=& 0 \\\\
\nV_y(0) &=& 2\\pi\\sqrt{\\frac{1+e}{1-e}}
\n\\end{eqnarray}<\/p>\n

\u3053\u306e\u521d\u671f\u6761\u4ef6\u3067\u6570\u5024\u8a08\u7b97\u3059\u308b\u3068\uff0c\uff08\u898f\u683c\u5316\u3055\u308c\u305f\uff09\u9577\u534a\u5f84 $1$\uff0c\u96e2\u5fc3\u7387 $e$ \u306e\u6955\u5186\u306e\u8ecc\u9053\u304c\u5f97\u3089\u308c\u308b\u30cf\u30ba\u3002<\/p>\n

\u3058\u3083\u3042\uff0c\u305d\u3053\u307e\u3067\u308f\u304b\u3063\u3066\u3044\u308b\u306e\u306a\u3089\uff0c\u306a\u305c\u308f\u3056\u308f\u3056\u6570\u5024\u8a08\u7b97\u3059\u308b\u306e\u304b<\/strong><\/span>\u3068\u3044\u3046\u3068\uff0c\u305d\u308c\u306f\u6955\u5186\u8ecc\u9053\u306e\u89e3\u304c\u6642\u9593 $t$ \u306e\u967d\u95a2\u6570\u3068\u3057\u3066\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u308f\u3051\u3067\u306f\u306a\u3044\u304b\u3089<\/strong><\/span>\u3002\u6642\u523b $t$ \u306e\u3068\u304d\uff0c\u3069\u3053\u306b\u3044\u308b\u304b\u304c\u89e3\u6790\u7684\u306b\u308f\u304b\u3063\u3066\u3044\u306a\u3044\u306e\u3067\uff0c\u305d\u308c\u3092\u77e5\u308a\u305f\u3044\u304b\u3089\u6570\u5024\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
<\/div>\n
\n
\n

\u30e9\u30a4\u30d6\u30e9\u30ea\u306e import<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
In\u00a0[1]:<\/div>\n
\n
\n
\n
import<\/span> numpy<\/span> as<\/span> np<\/span>\r\nimport<\/span> matplotlib.pyplot<\/span> as<\/span> plt<\/span>\r\n\r\n# \u4ee5\u4e0b\u306f\u30b0\u30e9\u30d5\u3092 SVG \u3067 Notebook \u306b\u30a4\u30f3\u30e9\u30a4\u30f3\u8868\u793a\u3055\u305b\u308b\u8a2d\u5b9a<\/span>\r\n%<\/span>config<\/span> InlineBackend.figure_formats = ['svg']\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
Runge-Kutta \u7528\u306b\u9023\u7acb1\u968e\u5fae\u5206\u65b9\u7a0b\u5f0f\u7cfb\u306b<\/h3>\n
\\begin{eqnarray}
\n\\frac{dX}{dT} &=& F_1(V_x) = V_x \\\\
\n\\frac{dY}{dT} &=& F_2(V_y) = V_y \\\\
\n\\frac{dV_x}{dT} &=& F_3(X, Y)
\n= -4\\pi^2 \\frac{X}{\\left(X^2 + Y^2\\right)^{\\frac{3}{2}}} \\\\
\n\\frac{dV_y}{dT} &=& F_4(X, Y)
\n= -4\\pi^2 \\frac{Y}{\\left(X^2 + Y^2\\right)^{\\frac{3}{2}}}
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
In\u00a0[2]:<\/div>\n
\n
\n
\n
from<\/span> scipy.integrate<\/span> import<\/span> solve_ivp<\/span>\r\n\r\n# scipy.integrate.solve_ivp() \u306f<\/span>\r\n# dy\/dt = Fun(t, y) \u306e\u5f62\u3092\u89e3\u304f\u3002\u5909\u6570\u540d\u306f\u6c7a\u3081\u6253\u3061\u3002<\/span>\r\n\r\ndef<\/span> Fun<\/span>(<\/span>t<\/span>,<\/span> y<\/span>):<\/span>\r\n# solve.ivp() \u306b\u6e21\u3059\u95a2\u6570\u306e\u5f15\u6570\u306e\u9806\u756a\u306b\u6ce8\u610f\u3002t \u304c\u5148<\/span>\r\n    X<\/span> =<\/span> y<\/span>[<\/span>0<\/span>]<\/span>\r\n    Y<\/span> =<\/span> y<\/span>[<\/span>1<\/span>]<\/span>\r\n    Vx<\/span> =<\/span> y<\/span>[<\/span>2<\/span>]<\/span>\r\n    Vy<\/span> =<\/span> y<\/span>[<\/span>3<\/span>]<\/span>\r\n    F1<\/span> =<\/span> Vx<\/span>\r\n    F2<\/span> =<\/span> Vy<\/span>\r\n    F3<\/span> =<\/span> -<\/span>4<\/span>*<\/span>np<\/span>.<\/span>pi<\/span>**<\/span>2<\/span> *<\/span> X<\/span>\/<\/span>(<\/span>X<\/span>**<\/span>2<\/span> +<\/span> Y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>(<\/span>3<\/span>\/<\/span>2<\/span>)<\/span>\r\n    F4<\/span> =<\/span> -<\/span>4<\/span>*<\/span>np<\/span>.<\/span>pi<\/span>**<\/span>2<\/span> *<\/span> Y<\/span>\/<\/span>(<\/span>X<\/span>**<\/span>2<\/span> +<\/span> Y<\/span>**<\/span>2<\/span>)<\/span>**<\/span>(<\/span>3<\/span>\/<\/span>2<\/span>)<\/span>\r\n    return<\/span> [<\/span>F1<\/span>,<\/span> F2<\/span>,<\/span> F3<\/span>,<\/span> F4<\/span>]<\/span>\r\n\r\n# \u96e2\u5fc3\u7387 e = 0.6<\/span>\r\ne<\/span> =<\/span> 0.6<\/span>\r\n\r\nt0<\/span> =<\/span> 0<\/span>\r\ntend<\/span> =<\/span> 1<\/span>\r\nt_span<\/span> =<\/span> [<\/span>t0<\/span>,<\/span> tend<\/span>]<\/span>\r\n# \u521d\u671f\u6761\u4ef6 X0, Y0, Vx0, Vy0<\/span>\r\nX0<\/span> =<\/span> 1<\/span>-<\/span>e<\/span>\r\nY0<\/span> =<\/span> 0<\/span>\r\nVx0<\/span> =<\/span> 0<\/span>\r\nVy0<\/span> =<\/span> 2<\/span>*<\/span>np<\/span>.<\/span>pi<\/span>*<\/span>np<\/span>.<\/span>sqrt<\/span>((<\/span>1<\/span>+<\/span>e<\/span>)<\/span>\/<\/span>(<\/span>1<\/span>-<\/span>e<\/span>))<\/span>\r\ny_ini<\/span> =<\/span> [<\/span>X0<\/span>,<\/span> Y0<\/span>,<\/span> Vx0<\/span>,<\/span> Vy0<\/span>]<\/span>\r\n\r\nNdiv<\/span> =<\/span> 36<\/span>\r\nt_list<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>t0<\/span>,<\/span> tend<\/span>,<\/span> Ndiv<\/span>+<\/span>1<\/span>)<\/span>\r\n\r\nsol<\/span> =<\/span> solve_ivp<\/span>(<\/span>Fun<\/span>,<\/span> t_span<\/span>,<\/span> y_ini<\/span>,<\/span> \r\n                t_eval<\/span> =<\/span> t_list<\/span>,<\/span> \r\n                rtol<\/span> =<\/span> 1.e-12<\/span>,<\/span> \r\n                atol<\/span> =<\/span> 1.e-14<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
\u3061\u3087\u3046\u30691\u5468\u671f $T=t\/P = 1$ \u307e\u3067\u3044\u304f\u3068\uff0c$T=0$ \u306e\u6642\u306e\u521d\u671f\u5024\u306b\u306a\u3063\u3066\u3044\u308b\u306f\u305a\u3060\u304b\u3089\uff0c\u6570\u5024\u8aa4\u5dee\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/p>\n
\u6570\u5024\u89e3 sol<\/code> \u304b\u3089 X<\/code> \u3059\u306a\u308f\u3061 y[0]<\/code> \u3092\u53d6\u308a\u51fa\u3059\u306b\u306f\uff0csol.y[0]<\/code>\u3002\u6700\u5f8c\u306e\u9805\u306f sol.y[0][-1]<\/code>\u3002\u6700\u521d\u306e\u9805\uff08\u521d\u671f\u6761\u4ef6\uff09sol.y[0][0]<\/code> \u3068\u306e\u5dee\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
In\u00a0[3]:<\/div>\n
\n
\n
\n
X<\/span> =<\/span> sol<\/span>.<\/span>y<\/span>[<\/span>0<\/span>]<\/span>\r\nY<\/span> =<\/span> sol<\/span>.<\/span>y<\/span>[<\/span>1<\/span>]<\/span>\r\n\r\n# X \u306e\u8aa4\u5dee<\/span>\r\nprint<\/span>(<\/span>X<\/span>[<\/span>-<\/span>1<\/span>]<\/span>-<\/span>X<\/span>[<\/span>0<\/span>])<\/span>\r\n# Y \u306e\u8aa4\u5dee<\/span>\r\nprint<\/span>(<\/span>Y<\/span>[<\/span>-<\/span>1<\/span>]<\/span>-<\/span>Y<\/span>[<\/span>0<\/span>])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n
<\/div>\n
\n
3.717026686445024e-13\r\n-2.693325467165164e-11\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
\u4e00\u5b9a\u6642\u9593\u9593\u9694\u3054\u3068\u306e\u4f4d\u7f6e\u3092\u30b0\u30e9\u30d5\u306b<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
In\u00a0[4]:<\/div>\n
\n
\n
\n
# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba\u306e\u8a2d\u5b9a<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>[<\/span>6<\/span>,<\/span>6<\/span>])<\/span>\r\n\r\n# \u7e26\u6a2a\u306e\u30a2\u30b9\u30da\u30af\u30c8\u6bd4\u3092\u7b49\u3057\u304f\u3057\u3066<\/span>\r\nplt<\/span>.<\/span>axes<\/span>()<\/span>.<\/span>set_aspect<\/span>(<\/span>'equal'<\/span>)<\/span>\r\n\r\n# \u8ef8\u306e\u8a2d\u5b9a<\/span>\r\nplt<\/span>.<\/span>axis<\/span>([<\/span>-<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> -<\/span>1.5<\/span>,<\/span> 1.5<\/span>])<\/span>\r\n\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>sol<\/span>.<\/span>y<\/span>[<\/span>0<\/span>],<\/span> sol<\/span>.<\/span>y<\/span>[<\/span>1<\/span>],<\/span> s<\/span>=<\/span>20<\/span>,<\/span> c<\/span>=<\/span>'blue'<\/span>)<\/span>\r\n\r\n# x\u8ef8 y\u8ef8<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>3<\/span>,<\/span> 3<\/span>),<\/span> linewidth<\/span>=<\/span>0.6<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>3<\/span>,<\/span> 3<\/span>),<\/span> linewidth<\/span>=<\/span>0.6<\/span>);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n
<\/div>\n

\n\"\"<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u305f\u5834\u5408\u306e\u89e3\u3068\u306e\u6bd4\u8f03<\/h3>\n
\u300c\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u3066\u30b1\u30d7\u30e9\u30fc\u306e\u7b2c2\u6cd5\u5247\u3092\u8996\u899a\u7684\u306b\u78ba\u8a8d\u3059\u308b<\/a>\u300d\u306b\u307e\u3068\u3081\u3066\u3044\u308b\u3088\u3046\u306b\uff0c<\/p>\n
\\begin{eqnarray}
\nx &=& r \\cos\\varphi = a(\\cos u \u2013 e)\\\\
\ny &=& r \\sin\\varphi = a \\sqrt{1-e^2} \\sin u\\\\
\n\\frac{2\\pi}{P} t &=& u \u2013 e \\sin u
\n\\end{eqnarray}<\/p>\n
\u3060\u304b\u3089\uff0c\u7121\u6b21\u5143\u5316\u3057\u305f\u5909\u6570\u3067\u306f<\/p>\n
\\begin{eqnarray}
\nX_u(u) &=& \\frac{x}{a} = \\cos u \u2013 e\\\\
\nY_u(u) &=& \\frac{y}{a} = \\sqrt{1-e^2} \\sin u\\\\
\n2\\pi T &=& u \u2013 e \\sin u, \\quad T = \\frac{t}{P}
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3<\/h4>\n
$$g(u) \\equiv u – e \\sin u$$<\/p>\n
\u3068\u3057\u3066 $T_i = \\frac{i}{N_{\\rm div}}$ \u306e\u3068\u304d\u306b\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f $g(u_i) = 2\\pi T_i $ \u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u3066 $u_i$ \u3092\u6c42\u3081\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
In\u00a0[5]:<\/div>\n
\n
\n
\n
from<\/span> scipy.optimize<\/span> import<\/span> root_scalar<\/span>\r\n\r\n# root_scalar \u3092\u4f7f\u3046\u3068\u304d\u306f\uff0c\u5909\u6570\u540d\u306f x \u6c7a\u3081\u6253\u3061<\/span>\r\ndef<\/span> g<\/span>(<\/span>x<\/span>):<\/span>\r\n    global<\/span> e<\/span>,<\/span> T<\/span>\r\n    return<\/span> x<\/span> -<\/span> e<\/span>*<\/span>np<\/span>.<\/span>sin<\/span>(<\/span>x<\/span>)<\/span> -<\/span> 2<\/span>*<\/span>np<\/span>.<\/span>pi<\/span>*<\/span>T<\/span>\r\n\r\nTlist<\/span> =<\/span> np<\/span>.<\/span>linspace<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>,<\/span> Ndiv<\/span>+<\/span>1<\/span>)<\/span>\r\n\r\nui<\/span> =<\/span> []<\/span>\r\n\r\nfor<\/span> T<\/span> in<\/span> Tlist<\/span>:<\/span>\r\n    ans<\/span> =<\/span> root_scalar<\/span>(<\/span>g<\/span>,<\/span> bracket<\/span> =<\/span> [<\/span>0<\/span>,<\/span> 2<\/span>*<\/span>np<\/span>.<\/span>pi<\/span>],<\/span> xtol<\/span> =<\/span> 1.e-14<\/span>)<\/span>\r\n    ui<\/span>.<\/span>append<\/span>(<\/span>ans<\/span>.<\/span>root<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
\u4e00\u5b9a\u6642\u9593\u9593\u9694\u3054\u3068\u306e\u4f4d\u7f6e<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
In\u00a0[6]:<\/div>\n
\n
\n
\n
def<\/span> Xu<\/span>(<\/span>u<\/span>):<\/span>\r\n    global<\/span> e<\/span>\r\n    return<\/span> np<\/span>.<\/span>cos<\/span>(<\/span>u<\/span>)<\/span> -<\/span> e<\/span>\r\n\r\ndef<\/span> Yu<\/span>(<\/span>u<\/span>):<\/span>\r\n    global<\/span> e<\/span>\r\n    return<\/span> np<\/span>.<\/span>sqrt<\/span>(<\/span>1<\/span>-<\/span>e<\/span>**<\/span>2<\/span>)<\/span> *<\/span> np<\/span>.<\/span>sin<\/span>(<\/span>u<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
2\u3064\u306e\u89e3\u306e\u6bd4\u8f03<\/h4>\n
\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u305f\u89e3\u3067\u3042\u308b X<\/code>, Y<\/code> \u3068\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u305f\u89e3\u3067\u3042\u308b Xu(ui)<\/code>, Yu(ui)<\/code> \u306f\uff0c\u5f53\u7136\u306a\u304c\u3089\u6570\u5024\u8aa4\u5dee\u306e\u7bc4\u56f2\u5185\u3067\u4e00\u81f4\u3057\u3066\u3044\u308b\u306f\u305a\u3067\u3042\u308b\u3002<\/p>\n
2\u3064\u306e\u30ea\u30b9\u30c8\u306e\u5f15\u304d\u7b97\u3092\u3057\u3066\u5dee\u3092\u8abf\u3079\u308b\u300237\u7d44\u5168\u3066\u8868\u793a\u3059\u308b\u3068\u5197\u9577\u306a\u306e\u3067\uff0c\u4ee3\u8868\u3057\u30663\u7d44\u307b\u3069\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
In\u00a0[7]:<\/div>\n
\n
\n
\n
# 2\u3064\u306e\u6570\u5024\u89e3 X, Xu(ui) \u306e\u5dee<\/span>\r\nprint<\/span>((<\/span>X<\/span> -<\/span> Xu<\/span>(<\/span>ui<\/span>))[<\/span>10<\/span>])<\/span>\r\nprint<\/span>((<\/span>X<\/span> -<\/span> Xu<\/span>(<\/span>ui<\/span>))[<\/span>20<\/span>])<\/span>\r\nprint<\/span>((<\/span>X<\/span> -<\/span> Xu<\/span>(<\/span>ui<\/span>))[<\/span>30<\/span>])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n
<\/div>\n
\n
-1.0742517986273015e-12\r\n-3.3602010063304988e-12\r\n-1.111388758801013e-11\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
\u5ff5\u306e\u305f\u3081\u306b2\u3064\u306e\u6570\u5024\u89e3\u3092\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068\uff0c\u5f53\u7136\u306a\u304c\u3089\u91cd\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
In\u00a0[8]:<\/div>\n
\n
\n
\n
# \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba\u306e\u8a2d\u5b9a<\/span>\r\nfig<\/span> =<\/span> plt<\/span>.<\/span>figure<\/span>(<\/span>figsize<\/span>=<\/span>[<\/span>6<\/span>,<\/span>6<\/span>])<\/span>\r\n\r\n# \u7e26\u6a2a\u306e\u30a2\u30b9\u30da\u30af\u30c8\u6bd4\u3092\u7b49\u3057\u304f\u3057\u3066<\/span>\r\nplt<\/span>.<\/span>axes<\/span>()<\/span>.<\/span>set_aspect<\/span>(<\/span>'equal'<\/span>)<\/span>\r\n\r\n# \u8ef8\u306e\u8a2d\u5b9a<\/span>\r\nplt<\/span>.<\/span>axis<\/span>([<\/span>-<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> -<\/span>1.5<\/span>,<\/span> 1.5<\/span>])<\/span>\r\n\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>X<\/span>,<\/span> Y<\/span>,<\/span> s<\/span>=<\/span>20<\/span>,<\/span> c<\/span>=<\/span>'blue'<\/span>,<\/span>label<\/span> =<\/span> \"\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\"<\/span>)<\/span>\r\nplt<\/span>.<\/span>scatter<\/span>(<\/span>Xu<\/span>(<\/span>ui<\/span>),<\/span> Yu<\/span>(<\/span>ui<\/span>),<\/span> c<\/span>=<\/span>\"red\"<\/span>,<\/span> s<\/span>=<\/span>2<\/span>,<\/span> label<\/span> =<\/span> \"\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\"<\/span>)<\/span>\r\n\r\n# x\u8ef8 y\u8ef8<\/span>\r\nplt<\/span>.<\/span>axhline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>3<\/span>,<\/span> 3<\/span>),<\/span> linewidth<\/span>=<\/span>0.6<\/span>)<\/span>\r\nplt<\/span>.<\/span>axvline<\/span>(<\/span>0<\/span>,<\/span> color<\/span>=<\/span>'black'<\/span>,<\/span> dashes<\/span>=<\/span>(<\/span>3<\/span>,<\/span> 3<\/span>),<\/span> linewidth<\/span>=<\/span>0.6<\/span>)<\/span>\r\nplt<\/span>.<\/span>legend<\/span>();<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n
<\/div>\n
\"\"<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
\u300c\u4e07\u6709\u5f15\u529b\u306e2\u4f53\u554f\u984c\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u524d\u306e\u4e0b\u3054\u3057\u3089\u3048 ver. 2\u300d\u3067\u4e0b\u3054\u3057\u3089\u3048\u3057\u305f\u5f0f\u3092 Python \u3067\u6570\u5024\u7684\u306b\u89e3\u304f\u3002<\/p>
\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[13,11,22],"tags":[],"class_list":["post-7043","post","type-post","status-publish","format-standard","hentry","category-matplotlib","category-python","category-22","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7043","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=7043"}],"version-history":[{"count":4,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7043\/revisions"}],"predecessor-version":[{"id":7050,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7043\/revisions\/7050"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=7043"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=7043"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=7043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}