{"id":5276,"date":"2026-04-28T14:10:00","date_gmt":"2026-04-28T05:10:00","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=5276"},"modified":"2026-04-28T14:10:00","modified_gmt":"2026-04-28T05:10:00","slug":"xlpack-py-mpl-ex3","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/manual2\/xlpack-py-mpl-ex3\/","title":{"rendered":"XLPack for Python \u304a\u3088\u3073 XLPack for Matplotlib \u306e\u4f7f\u7528\u4f8b (3) \u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3 (\u30a2\u30ec\u30f3\u30b9\u30c8\u30fc\u30d5\u8ecc\u9053)"},"content":{"rendered":"\n\u8cea\u91cf\u304c \\(\\mu\\) \u3068 \\(\\mu’ (= 1 – \\mu)\\) \u306e2\u3064\u306e\u5929\u4f53\u304c\u5e73\u9762\u5185\u56de\u8ee2\u904b\u52d5\u3092\u3057\u3066\u304a\u308a, \u305d\u306e2\u3064\u306b\u6bd4\u3079\u3066\u8cea\u91cf\u304c\u7121\u8996\u3067\u304d\u308b\u7b2c3\u306e\u7269\u4f53\u304c\u540c\u4e00\u5e73\u9762\u5185\u3092\u904b\u52d5\u3059\u308b\u3082\u306e\u3068\u3057\u307e\u3059. \u305d\u306e\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059 (\u53c2\u8003\u6587\u732e: E. Hairer, \u4ed6\u300c\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5 I\u300d(2007) \u30b7\u30e5\u30d7\u30ea\u30f3\u30ac\u30fc\u30fb\u30b8\u30e3\u30d1\u30f3).
\n\\[
\n\\begin{align}
\n& y_1” = y_1 + 2y_2′ – \\mu'(y_1 + \\mu)\/D_1 – \\mu(y_1 – \\mu’)\/D_2 \\\\
\n& y_2” = y_2 – 2y_1′ – \\mu’y_2\/D_1 – \\mu y_2\/D_2 \\\\
\n& \u305f\u3060\u3057, \\\\
\n& D_1 = ((y_1 + \\mu)^2 + y_2^2)^{3\/2} \\\\
\n& D_2 = ((y_1 – \\mu’)^2 + y_2^2)^{3\/2} \\\\
\n& \\mu = 0.012277471, \\mu’ = 1 – \\mu \\\\
\n\\end{align}
\n\\]\n\u6b21\u306e\u521d\u671f\u5024\u3092\u7528\u3044\u308b\u3068, \\(t = 17.0652165601579625588917206249\\) \u3067\u5468\u671f\u89e3\u3068\u306a\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059.
\n\\[
\n\\begin{align}
\n& y_1(0) = 0.994, y_1′(0) = 0 \\\\
\n& y_2(0) = 0, y_2′(0) = -2.00158510637908252240537862224 \\\\
\n\\end{align}
\n\\]\n\u3053\u308c\u306f\u30a2\u30ec\u30f3\u30b9\u30c8\u30fc\u30d5\u8ecc\u9053\u3068\u3088\u3070\u308c\u3066\u3044\u307e\u3059.<\/p>\n

\u3053\u3053\u3067\u306f, 1\u5468\u671f\u5206\u306e\u6570\u5024\u89e3\u3092\u6c42\u3081\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u3067\u8868\u793a\u3059\u308b\u3053\u3068\u306b\u3057\u307e\u3059.<\/p>\n

1. \u5168\u4f53\u306e\u69cb\u6210<\/h2>\n

\u30e1\u30a4\u30f3\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a\u3067\u3059.<\/p>\n

\n
Const Tend = 17.065216560158\r\n\r\nSub Main()\r\n    Dim Xt() As Double, Yt() As Double\r\n    Dim Dt As Double, Nt As Long, Info As Long\r\n    Dt = 0.1\r\n    Nt = Int(Tend \/ Dt) + 1\r\n    ReDim Xt(Nt), Yt(Nt)\r\n    Call ODE(Tend, Dt, Nt, Xt(), Yt(), Info)\r\n    Call Animate(Nt, Xt(), Yt(), Dt)\r\nEnd Sub<\/code><\/pre>\n<\/div>\n
\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3 ODE() \u306f\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u6c42\u3081\u307e\u3059. \u5f97\u3089\u308c\u305f\u89e3\u306f\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3 Animate() \u306b\u3088\u308a\u8868\u793a\u3055\u308c\u307e\u3059. Animate() \u3067\u306f XLPack for Python \u307e\u305f\u306f XLPack for Matplotlib \u3092\u4f7f\u7528\u3057\u3066\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u3067\u8868\u793a\u3092\u884c\u3044\u307e\u3059.<\/p>\n
\u5b9f\u884c\u7d50\u679c\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059.<\/p>\n
2. \u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3<\/h2>\n
\u3053\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u306f 2 \u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306a\u306e\u3067, 1 \u968e\u306e\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u5f62\u306b\u5909\u6570\u5909\u63db\u3057\u3066 4 \u5143\u306e\u65b9\u7a0b\u5f0f\u3068\u3057\u3066\u89e3\u304d\u307e\u3059.<\/p>\n
\n
Const Xinit = 0.994\r\n\r\nSub F(N As Long, T As Double, Y() As Double, Yp() As Double)\r\n    Const Mu = 0.012277471, Mup = 1 - Mu\r\n    Dim D1 As Double, D2 As Double\r\n    Yp(0) = Y(2)\r\n    Yp(1) = Y(3)\r\n    D1 = ((Y(0) + Mu) ^ 2 + Y(1) ^ 2) ^ (3# \/ 2#)\r\n    D2 = ((Y(0) - Mup) ^ 2 + Y(1) ^ 2) ^ (3# \/ 2#)\r\n    Yp(2) = Y(0) + 2 * Y(3) - Mup * (Y(0) + Mu) \/ D1 - Mu * (Y(0) - Mup) \/ D2\r\n    Yp(3) = Y(1) - 2 * Y(2) - Mup * Y(1) \/ D1 - Mu * Y(1) \/ D2\r\nEnd Sub\r\n\r\nSub ODE(Tend As Double, Dt As Double, Nt As Long, Xt() As Double, Yt() As Double, Info As Long)\r\n    Const N = 4, Mode = 3, Tol = 0.0000000001 '1.0e-10\r\n    Dim Y(N - 1) As Double, T As Double, Tout As Double\r\n    Dim RTol(0) As Double, ATol(0) As Double, I As Integer\r\n    RTol(0) = Tol\r\n    ATol(0) = Tol\r\n    T = 0\r\n    Y(0) = Xinit: Y(1) = 0: Y(2) = 0: Y(3) = -2.00158510637908\r\n    Info = 0\r\n    Xt(0) = Y(0)\r\n    Yt(0) = Y(1)\r\n    For I = 0 To Nt - 1\r\n        Tout = (I + 1) * Dt\r\n        If Tout > Tend Then Tout = Tend\r\n        Call Derkfa(N, AddressOf F, T, Y(), Tout, Tend, RTol(), ATol(), Mode, Info)\r\n        If Info < 0 Or Info > 10 Then Exit Sub\r\n        Xt(I + 1) = Y(0)\r\n        Yt(I + 1) = Y(1)\r\n    Next\r\nEnd Sub<\/code><\/pre>\n<\/div>\n
\u5f97\u3089\u308c\u305f\u89e3\u306f, Xt(), Yt() \u306b\u4fdd\u5b58\u3057\u307e\u3059.<\/p>\n
3. \u89e3\u306e\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u8868\u793a<\/h2>\n
\u5f97\u3089\u308c\u305f\u89e3\u3092 \u8868\u793a\u3059\u308b Python \u306e\u30b3\u30fc\u30c9\u3092 XLPack for Python \u3092\u4f7f\u3063\u3066\u76f4\u63a5\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059.<\/p>\n
\u914d\u5217\u30c7\u30fc\u30bf\u306f\u305d\u306e\u307e\u307e\u6e21\u3059\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u306e\u3067, \u3044\u3063\u305f\u3093\u30ef\u30fc\u30af\u30b7\u30fc\u30c8\u306b\u66f8\u304d\u51fa\u3057\u3066\u304b\u3089 Python \u5074\u3067 xlc_get() \u3092\u4f7f\u3063\u3066\u8aad\u307f\u8fbc\u3093\u3067\u3044\u307e\u3059.<\/p>\n
\n
Sub Animate(Nt As Long, Xt() As Double, Yt() As Double, Dt As Double)\r\n    Const Col = 2, Row = 6\r\n    Dim I As Long\r\n    For I = 0 To Nt\r\n        Cells(Row + I, Col) = Xt(I)\r\n        Cells(Row + I, Col + 1) = Yt(I)\r\n    Next\r\n    '-- Python codes\r\n    PY \"import matplotlib.pyplot as plt\"\r\n    PY \"import matplotlib.animation as animation\"\r\n    PY \"from XLPackPy import *\"\r\n    PY \"fig = plt.figure()\"\r\n    PY \"ax = fig.gca()\"\r\n    PY \"ax.grid()\"\r\n    PY \"ax.plot(0, 0, '-o', color = 'orange')\"\r\n    PY \"ax.plot(1, 0, '-o', color = 'yellow')\"\r\n    PY \"ax.set_xlim(-1.5, 1.5)\"\r\n    PY \"ax.set_ylim(-1.5, 1.5)\"\r\n    PY \"xt = xlc_get(5, 1,\" + Str(5 + Nt) + \")\"\r\n    PY \"yt = xlc_get(5, 2,\" + Str(5 + Nt) + \")\"\r\n    PY \"xtrace = []; ytrace = []; artist = []\"\r\n    PY \"for i in range(len(xt)):\" + vbNewLine + _\r\n        \"  a_x = [xt[i]]; a_y = [yt[i]]\" + vbNewLine + _\r\n        \"  a, = ax.plot(a_x, a_y, 'o-', color = 'b')\" + vbNewLine + _\r\n        \"  xtrace.append(xt[i]); ytrace.append(yt[i])\" + vbNewLine + _\r\n        \"  trace, = ax.plot(xtrace, ytrace, ':c', lw=1)\" + vbNewLine + _\r\n        \"  artist.append((a, trace))\"\r\n    PY \"ani = animation.ArtistAnimation(fig, artist, interval = 100, blit = True, repeat = False)\"\r\n    PY \"plt.show()\"\r\nEnd Sub<\/code><\/pre>\n<\/div>\n
XLPack for Matplotlib \u3092\u4f7f\u3046\u3068\u540c\u3058\u51e6\u7406\u3092\u5168\u3066 VBA \u3067\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059. \u5185\u90e8\u7684\u306b\u306f Python \u3092\u547c\u3073\u51fa\u3057\u3066\u51e6\u7406\u3057\u307e\u3059.<\/p>\n
\n
Dim Plt As New PyPlot\r\nDim Animation As New Animation\r\n\r\nSub Animate(Nt As Long, Xt() As Double, Yt() As Double, Dt As Double)\r\n    Dim Ex(0) As Double, Ey(0) As Double, Mx(0) As Double, My(0) As Double\r\n    Dim X(0) As Double, Y(0) As Double, I As Long\r\n    Dim Fig As Figure, Ax As Axs, Artist() As PyObject\r\n    Dim Emarker As PyObject, Mmarker As PyObject\r\n    Dim Anim As ArtistAnimation\r\n    Ex(0) = 0: Ey(0) = 0\r\n    Mx(0) = Xinit: My(0) = 0\r\n    ReDim Artist(Nt, 1)\r\n    Set Fig = Plt.Figure()\r\n    Set Ax = Fig.Gca()\r\n    Call Ax.Grid\r\n    Call Ax.Set_xlim(-1.5, 1.5)\r\n    Call Ax.Set_ylim(-1.5, 1.5)\r\n    Set Emarker = Ax.Plot(1, Ex(), Ey(), \"\", \"color=orange,marker=o\")\r\n    Set Mmarker = Ax.Plot(1, Mx(), My(), \"\", \"color=yellow,marker=o\")\r\n    For I = 0 To Nt\r\n        X(0) = Xt(I): Y(0) = Yt(I)\r\n        Set Artist(I, 0) = Ax.Plot(1, X(), Y(), \"\", \"color=b,marker=o\")\r\n        Set Artist(I, 1) = Ax.Plot(I + 1, Xt(), Yt(), \":c\", \"lw=1\")\r\n    Next\r\n    Dim Ani As PyObject\r\n    Set Anim = Animation.ArtistAnimation(Fig, Nt + 1, 2, Artist(), \"interval =\" + Str(Dt * 1000) + \", repeat = False\")\r\n    Call Plt.Show\r\nEnd Sub<\/code><\/pre>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
\u8cea\u91cf\u304c \\(\\mu\\) \u3068 \\(\\mu’ (= 1 – \\mu)\\) \u306e2\u3064\u306e\u5929\u4f53\u304c\u5e73\u9762\u5185\u56de\u8ee2\u904b\u52d5\u3092\u3057\u3066\u304a\u308a, \u305d\u306e2\u3064\u306b\u6bd4\u3079\u3066\u8cea\u91cf\u304c\u7121\u8996\u3067\u304d\u308b\u7b2c3\u306e\u7269\u4f53\u304c\u540c\u4e00\u5e73\u9762\u5185\u3092\u904b\u52d5\u3059\u308b\u3082\u306e\u3068\u3057\u307e\u3059. \u305d\u306e […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[49],"tags":[],"class_list":["post-5276","post","type-post","status-publish","format-standard","hentry","category-manual2"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/5276","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/comments?post=5276"}],"version-history":[{"count":13,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/5276\/revisions"}],"predecessor-version":[{"id":5326,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/5276\/revisions\/5326"}],"wp:attachment":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/media?parent=5276"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/categories?post=5276"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/tags?post=5276"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}