{"id":5254,"date":"2026-04-28T14:11:49","date_gmt":"2026-04-28T05:11:49","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=5254"},"modified":"2026-04-28T14:11:49","modified_gmt":"2026-04-28T05:11:49","slug":"xlpack-py-mpl-ex1","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/manual2\/xlpack-py-mpl-ex1\/","title":{"rendered":"XLPack for Python \u304a\u3088\u3073 XLPack for Matplotlib \u306e\u4f7f\u7528\u4f8b (1) 3D \u8868\u793a (\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f)"},"content":{"rendered":"\n\\(x = 0 \\sim 1, y = 0 \\sim 1\\) \u306e\u6b63\u65b9\u5f62\u9818\u57df\u306b\u304a\u3044\u3066, \u6b21\u306e\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3082\u306e\u3068\u3057\u307e\u3059.
\n\\[
\n-d^2u\/dx^2 – d^2u\/dy^2 = 0
\n\\]\n\u305f\u3060\u3057, \u5883\u754c\u6761\u4ef6\u306f
\n\\[
\nu(x, 0) = 0, u(0, y) = 0, u(x, 1) = x, u(1, y) = y \\space (\u30c7\u30a3\u30ea\u30af\u30ec\u6761\u4ef6)
\n\\]\n\u3068\u3057\u307e\u3059.<\/p>\n

\u3053\u306e\u3088\u3046\u306a\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u306f, \u4f8b\u3048\u3070\u71b1\u5e73\u8861\u72b6\u614b\u306b\u3042\u308b\u677f\u306e\u6e29\u5ea6\u5206\u5e03\u306e\u8a18\u8ff0\u306a\u3069\u306b\u9069\u7528\u3055\u308c\u307e\u3059.<\/p>\n

\u3053\u306e\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u3068\u3057\u3066\u306f\u5dee\u5206\u6cd5\u304c\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059. 5 \u70b9\u5dee\u5206\u8fd1\u4f3c\u306b\u3088\u308a\u6570\u5024\u89e3\u3092\u6c42\u3081\u308b\u4f8b\u306f\u4ee5\u4e0b\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044.<\/p>\n

16. \u758e\u884c\u5217\u306e\u7dda\u5f62\u8a08\u7b97<\/a><\/p>\n

\u3053\u3053\u3067\u306f\u6709\u9650\u8981\u7d20\u6cd5\u3092\u7528\u3044\u3066\u89e3\u3092\u6c42\u3081 3D \u8868\u793a\u3059\u308b\u4f8b\u3092\u8aac\u660e\u3057\u307e\u3059.<\/p>\n

\\(x, y\\) \u65b9\u5411\u306b\u6b63\u65b9\u5f62\u9818\u57df\u3092\u305d\u308c\u305e\u308c \\(Nx, Ny\\) \u7b49\u5206\u3057\u3066\u9577\u65b9\u5f62\u683c\u5b50\u306b\u5206\u5272\u3057\u307e\u3059. \u3055\u3089\u306b\u305d\u308c\u305e\u308c\u3092\uff12\u5206\u5272\u3057\u3066\u4e09\u89d2\u8981\u7d20\u3068\u3057\u305f\u5358\u7d14\u30e1\u30c3\u30b7\u30e5\u3092\u751f\u6210\u3059\u308b\u3053\u3068\u306b\u3057\u307e\u3059.
\n\"\"<\/p>\n

\u3053\u308c\u3092\u7528\u3044\u3066\u6709\u9650\u8981\u7d20\u6cd5\u306b\u3088\u308a\u89e3\u3092\u6c42\u3081\u307e\u3059. \u306a\u304a, \u4e0a\u56f3\u306f 7 \u7b49\u5206 (\u683c\u5b50\u70b9\u6570 8 x 8)\u306e\u4f8b\u3092\u793a\u3057\u307e\u3059\u304c, \u5b9f\u969b\u306e\u8a08\u7b97\u3067\u306f 19 \u7b49\u5206 (\u683c\u5b50\u70b9\u6570 20 x 20) (Nx = 19, Ny = 19) \u3068\u3057\u307e\u3057\u305f.<\/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
Sub Main()\r\n    Const Nx = 19, Ny = 19\r\n    Const Nb2 = 0, LdKnc = 4, LdKs = 3\r\n    Const N = (Nx + 1) * (Ny + 1), Ne = 2 * Nx * Ny, Nb = 2 * (Nx + Ny)\r\n    Dim X(N - 1) As Double, Y(N - 1) As Double\r\n    Dim P(N - 1) As Double, Q(N - 1) As Double, F(N - 1) As Double\r\n    Dim Knc(LdKnc - 1, Ne - 1) As Long, Ks(LdKs - 1, Nb - 1) As Long\r\n    Dim Lb(Nb - 1) As Long, Ib(Nb - 1) As Long, Bv(Nb - 1) As Double\r\n    Dim Ks2() As Long, Alpha() As Double, Beta() As Double\r\n    Dim Val(20 * N) As Double, Ptr(N) As Long, Ind(20 * N) As Long\r\n    Dim B(N - 1) As Double, U(N - 1) As Double\r\n    Dim Ux As Double, Err As Double\r\n    Dim Info As Long\r\n    Dim I As Long, J As Long\r\n    '-- Set mesh data\r\n    Call SetData(Nx, Ny, N, Ne, Nb, X(), Y(), Knc(), Ks(), Lb(), P(), Q(), F(), Ib(), Bv())\r\n    '-- Assemble FEM matrix\r\n    Call Fem2p(N, Ne, X(), Y(), Knc(), P(), Q(), F(), Nb, Ib(), Bv(), Nb2, Ks2(), Alpha(), Beta(), Val(), Ptr(), Ind(), B(), Info)\r\n    '-- Solve equation by CG method\r\n    Dim Iter As Long, Res As Double\r\n    Call Cg1(N, Val(), Ptr(), Ind(), B(), U(), Info, Iter, Res)\r\n    Debug.Print \"Info =\" + Str(Info) + \", Iter =\" + Str(Iter) + \", Res =\" + Str(Res)\r\n    If Info <> 0 Then Exit Sub\r\n    '-- Plot solution\r\n    Call Plot(Nx, Ny, U())\r\nEnd Sub<\/code><\/pre>\n<\/div>\n
XLPack \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3 Fem2p() \u306f\u6709\u9650\u8981\u7d20\u884c\u5217\u306e\u7d44\u307f\u7acb\u3066\u3092\u884c\u3044\u307e\u3059. \u758e\u884c\u5217 (CSR) \u5f62\u5f0f\u306e\u4fc2\u6570\u884c\u5217\u3068\u53f3\u8fba\u30d9\u30af\u30c8\u30eb\u304b\u3089\u306a\u308b\u65b9\u7a0b\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059. \u4fc2\u6570\u884c\u5217\u306f\u5bfe\u79f0\u884c\u5217\u306a\u306e\u3067, \u65b9\u7a0b\u5f0f\u306f XLPack \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3 Cg1() \u3092\u4f7f\u3063\u3066\u5171\u5f79\u52fe\u914d\u6cd5\u306b\u3088\u308a\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059.<\/p>\n
\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3 SetData() \u306f Fem2p() \u306e\u5165\u529b\u3068\u306a\u308b\u683c\u5b50\u70b9, \u6709\u9650\u8981\u7d20, \u304a\u3088\u3073, \u5883\u754c\u6761\u4ef6\u306e\u30c7\u30fc\u30bf\u3092\u8a2d\u5b9a\u3057\u307e\u3059.<\/p>\n
\u5f97\u3089\u308c\u305f\u89e3\u306f\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3 Plot() \u306b\u3088\u308a\u8868\u793a\u3055\u308c\u307e\u3059. Plot() \u3067\u306f XLPack for Python \u307e\u305f\u306f XLPack for Matplotlib \u3092\u4f7f\u7528\u3057\u3066 3D \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
\"\"<\/p>\n
2. \u5165\u529b\u30c7\u30fc\u30bf\u306e\u8a2d\u5b9a<\/h2>\n
\u4e09\u89d2\u8981\u7d20\u306b\u3088\u308b\u5358\u7d14\u30e1\u30c3\u30b7\u30e5\u306f XLPack \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3 Mesh23() \u3092\u4f7f\u3063\u3066\u751f\u6210\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059.<\/p>\n
\u6b21\u306b, \u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570 p(x, y) = 1, q(x, y) = 0, f(x, y) = 0 \u3092\u8a2d\u5b9a\u3057\u307e\u3059. \u307e\u305f, \u30c7\u30a3\u30ea\u30af\u30ec\u5883\u754c\u6761\u4ef6\u3092\u8a2d\u5b9a\u3057\u307e\u3059.<\/p>\n
\u3053\u308c\u3089\u3092\u884c\u3046\u306e\u304c\u6b21\u306e\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3\u3067\u3059.<\/p>\n
\n
Sub SetData(Nx As Long, Ny As Long, N As Long, Ne As Long, Nb As Long, X() As Double, Y() As Double, Knc() As Long, Ks() As Long, Lb() As Long, P() As Double, Q() As Double, F() As Double, Ib() As Long, Bv() As Double)\r\n    Dim Id() As Long\r\n    Dim I As Long, J As Long, K As Long\r\n    '-- Generates simple rectangular mesh for 2D triangular element\r\n    Call Mesh23(Nx, Ny, X(), Y(), Knc(), Ks(), Lb())\r\n    '-- Set p(x, y) = 1, q(x, y) = 0 and f(x, y) = 0\r\n    For I = 0 To N - 1\r\n        P(I) = 1\r\n        Q(I) = 0\r\n        F(I) = 0\r\n    Next\r\n    '-- Set boundary condition 1\r\n    ReDim Id(N - 1)\r\n    For I = 0 To Nb - 1\r\n        For J = 1 To 2\r\n            Id(Ks(J, I) - 1) = Lb(I)\r\n        Next\r\n    Next\r\n    K = 0\r\n    For I = 0 To N - 1\r\n        If Id(I) = 1 Or Id(I) = 4 Then\r\n            Bv(K) = 0\r\n        ElseIf Id(I) = 2 Then\r\n            Bv(K) = Y(I)\r\n        ElseIf Id(I) = 3 Then\r\n            Bv(K) = X(I)\r\n        Else\r\n            GoTo Continue\r\n        End If\r\n        Ib(K) = I + 1\r\n        K = K + 1\r\nContinue:\r\n    Next\r\nEnd Sub<\/code><\/pre>\n<\/div>\n
3. \u89e3\u306e 3D \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
\n
Sub Plot(Nx As Long, Ny As Long, U() As Double)\r\n    Dim I As Long\r\n    For I = 0 To (Nx + 1) * (Ny + 1) - 1\r\n        Cells(6 + I, 2) = U(I)\r\n    Next\r\n    '-- Python codes\r\n    PY \"import matplotlib.pyplot as plt\"\r\n    PY \"from matplotlib import cm\"\r\n    PY \"import numpy as np\"\r\n    PY \"from XLPackPy import *\"\r\n    PY \"nx =\" + Str(Nx) + \"+ 1\"\r\n    PY \"ny =\" + Str(Ny) + \"+ 1\"\r\n    PY \"U = xlc_get(5, 1, 4 + nx*ny)\"\r\n    PY \"X = np.empty((ny, nx))\"\r\n    PY \"Y = np.empty((ny, nx))\"\r\n    PY \"Z = np.empty((ny, nx))\"\r\n    PY _\r\n      \"for i in range(ny):\" + vbNewLine + _\r\n      \"  for j in range(nx):\" + vbNewLine + _\r\n      \"    X[i][j] = (1.0\/(nx - 1))*j\" + vbNewLine + _\r\n      \"    Y[i][j] = (1.0\/(ny - 1))*i\" + vbNewLine + _\r\n      \"    Z[i][j] = U[nx*i + j]\"\r\n    PY \"fig = plt.figure()\"\r\n    PY \"ax3 = fig.add_subplot(projection='3d')\"\r\n    PY \"surf = ax3.plot_surface(X, Y, Z, cmap=cm.coolwarm)\"\r\n    PY \"fig.colorbar(surf, shrink=0.5, aspect=5)\"\r\n    PY \"plt.show()\"\r\nEnd Sub<\/code><\/pre>\n<\/div>\n
XLPack for Matplotlib \u3092\u4f7f\u3046\u3068\u5168\u3066 VBA \u3067\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059. Fig.Add_subplot_3d() \u306f Python \u306e fig.add_subplot(projection=’3d’) \u306b\u76f8\u5f53\u3057\u307e\u3059. \u305d\u306e\u4ed6\u306f Python \u306e\u30b3\u30fc\u30c9\u3068\u307b\u307c\u540c\u3058\u306b\u306a\u308a\u307e\u3059.<\/p>\n
\n
Dim Plt As New Pyplot\r\n\r\nSub Plot(Nx As Long, Ny As Long, U() As Double)\r\n    Dim X() As Double, Y() As Double, Z() As Double\r\n    ReDim X(Ny, Nx), Y(Ny, Nx), Z(Ny, Nx)\r\n    Dim I As Long, J As Long\r\n    Dim Fig As Figure, Ax3 As Axs3d, Surf As PyObject\r\n    '-- Prepare data\r\n    For I = 0 To Ny\r\n        For J = 0 To Nx\r\n            X(I, J) = (1# \/ Nx) * I\r\n            Y(I, J) = (1# \/ Ny) * J\r\n            Z(I, J) = U((Nx + 1) * I + J)\r\n        Next\r\n    Next\r\n    '-- Plot by Matplotlib\r\n    Set Fig = Plt.Figure()\r\n    Set Ax3 = Fig.Add_subplot_3d()\r\n    Set Surf = Ax3.Plot_surface(Ny + 1, Nx + 1, X(), Y(), Z(), \"coolwarm\")\r\n    Call Fig.Colorbar(Surf, KwArgs:=\"shrink=0.5, aspect=5\")\r\n    Call Plt.Show\r\nEnd Sub<\/code><\/pre>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
\\(x = 0 \\sim 1, y = 0 \\sim 1\\) \u306e\u6b63\u65b9\u5f62\u9818\u57df\u306b\u304a\u3044\u3066, \u6b21\u306e\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3082\u306e\u3068\u3057\u307e\u3059. \\[ -d^2u\/dx^2 – d^2u\/dy^2 = 0 \\] \u305f\u3060\u3057, \u5883\u754c\u6761\u4ef6 […]<\/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-5254","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\/5254","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=5254"}],"version-history":[{"count":9,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/5254\/revisions"}],"predecessor-version":[{"id":5324,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/5254\/revisions\/5324"}],"wp:attachment":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/media?parent=5254"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/categories?post=5254"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/tags?post=5254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}