\u975e\u7dda\u5f62\u6700\u9069\u5316\u306e\u5834\u5408\u3068\u540c\u3058\u3088\u3046\u306b, \u76ee\u7684\u306e\u89e3\u306b\u3067\u304d\u308b\u3060\u3051\u8fd1\u3044\u521d\u671f\u5024\u3092\u4e0e\u3048\u308b\u3088\u3046\u306b\u3059\u3079\u304d\u3067\u3042\u308b\u3053\u3068\u306f\u5909\u308f\u308a\u307e\u305b\u3093.<\/p>\n
\u4f8b\u984c<\/h5>\n
NIST (\u30a2\u30e1\u30ea\u30ab\u56fd\u7acb\u6a19\u6e96\u6280\u8853\u7814\u7a76\u6240) \u306e\u30db\u30fc\u30e0\u30da\u30fc\u30b8 (https:\/\/www.itl.nist.gov\/div898\/strd\/nls\/data\/misra1a.shtml<\/a>) \u306b\u63b2\u8f09\u3055\u308c\u3066\u3044\u308b\u30c6\u30b9\u30c8\u30c7\u30fc\u30bf\u3092\u4f7f\u7528\u3057\u307e\u3059. <\/p>\n \u6b21\u306e\u3088\u3046\u306a\u30e2\u30c7\u30eb\u95a2\u6570\u3092\u4f7f\u7528\u3057\u307e\u3059. \u30c6\u30b9\u30c8\u30c7\u30fc\u30bf\u306e\u521d\u671f\u5024\u306f 2 \u7a2e\u985e\u6307\u5b9a\u3055\u308c\u3066\u304a\u308a, (500, 0.0001) \u3068 (250, 0.0005) \u3067\u3059. \u793a\u3055\u308c\u3066\u3044\u308b\u89e3\u306f \\(c_1 = 2.3894212918 \\times 10^2, c_2 = 5.5015643181 \\times 10^{-4}\\) \u3067\u3059.<\/p>\n Lmdif1<\/strong> \u3092\u4f7f\u3063\u305f\u30d7\u30ed\u30b0\u30e9\u30e0\u4f8b\u3092\u793a\u3057\u307e\u3059.<\/p>\n \u76ee\u7684\u95a2\u6570\u3092\u5916\u90e8\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3\u3068\u3057\u3066\u7528\u610f\u3057, \u521d\u671f\u5024\u3068\u8981\u6c42\u7cbe\u5ea6\u3092\u6307\u5b9a\u3057\u3066 Lmdif1<\/strong> \u3092\u547c\u3073\u51fa\u3057\u307e\u3059. Lmdif1<\/strong> \u306f, \u521d\u671f\u5024\u3068\u3057\u3066\u4e0e\u3048\u3089\u308c\u305f\u8fd1\u4f3c\u89e3\u3092\u51fa\u767a\u70b9\u306b\u53cd\u5fa9\u8a08\u7b97\u3092\u884c\u3044, \u305d\u306e\u8fd1\u508d\u306e\u6700\u5c0f\u4e8c\u4e57\u89e3\u3092\u6c42\u3081\u307e\u3059.<\/p>\n \u3053\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u5b9f\u884c\u3059\u308b\u3068\u6b21\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3057\u305f. \u306a\u304a, \u5f97\u3089\u308c\u305f\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u4f7f\u3063\u305f\u8a08\u7b97\u5024(\u30aa\u30ec\u30f3\u30b8\u306e\u7dda)\u3068\u30c7\u30fc\u30bf(\u9752\u3044\u70b9)\u3092\u30b0\u30e9\u30d5\u306b\u3057\u307e\u3057\u305f.<\/p>\n \u3053\u306e\u4f8b\u3067\u306f\u3069\u3061\u3089\u306e\u521d\u671f\u5024\u306e\u5834\u5408\u3082\u6b63\u3057\u3044\u89e3\u304c\u6c42\u3081\u3089\u308c\u307e\u3057\u305f.<\/p>\n \u30ea\u30d0\u30fc\u30b9\u30b3\u30df\u30e5\u30cb\u30b1\u30fc\u30b7\u30e7\u30f3\u7248 (RCI) \u306e Lmdif1_r<\/strong> \u3092\u4f7f\u3063\u305f\u30d7\u30ed\u30b0\u30e9\u30e0\u4f8b\u3092\u793a\u3057\u307e\u3059.<\/p>\n RCI \u30b5\u30d6\u30eb\u30fc\u30c1\u30f3\u3067\u306f, \u76ee\u7684\u95a2\u6570\u3092\u5916\u90e8\u95a2\u6570\u3068\u3057\u3066\u4e0e\u3048\u308b\u306e\u3067\u306f\u306a\u304f, IRev = 1 \u307e\u305f\u306f 2 \u306e\u3068\u304d\u306b XX() \u306e\u5024\u3092\u4f7f\u3063\u3066\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3057 YY() \u306b\u5165\u308c\u3066\u518d\u5ea6 Lmdif1_r<\/strong> \u3092\u547c\u3073\u51fa\u3057\u307e\u3059. RCI\u306e\u8a73\u7d30\u306b\u3064\u3044\u3066\u306f \u3053\u3061\u3089<\/a> \u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044. <\/p>\n \u3053\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u5b9f\u884c\u3059\u308b\u3068\u4e0a\u3068\u540c\u3058\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059.<\/p>\n XLPack\u30bd\u30eb\u30d0\u30fc\u30a2\u30c9\u30a4\u30f3\u306e\u300c\u975e\u7dda\u5f62\u6700\u5c0f\u4e8c\u4e57\u6cd5\u300d\u3092\u4f7f\u3063\u3066\u89e3\u304f\u3053\u3068\u3082\u3067\u304d\u307e\u3059. C \u5217\u3067 B8, C8 \u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u5024\u3092\u4f7f\u3063\u3066\u30e2\u30c7\u30eb\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3057\u307e\u3059. \u4f8b\u3048\u3070, \u5f0f =B$8*(1-EXP(-C$8*A11)) \u304cC11\u30bb\u30eb\u306b\u5165\u529b\u3055\u308c\u3066\u3044\u307e\u3059. D \u5217\u3067\u306f\u6b8b\u5dee\u3092\u6c42\u3081\u3066\u3044\u307e\u3059. \u4f8b\u3048\u3070, \u5f0f =B11-C11 \u304cD11\u30bb\u30eb\u306b\u5165\u529b\u3055\u308c\u3066\u3044\u307e\u3059. \u30bd\u30eb\u30d0\u30fc\u306f\u3053\u306e\u6b8b\u5dee\u304b\u3089\u6700\u5c0f\u4e8c\u4e57\u89e3\u3092\u6c42\u3081\u307e\u3059.<\/p>\n
\n\\[
\nf(x) = c_1(1 – exp(-c_2x))
\n\\]\n\u30c7\u30fc\u30bf\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059.
\n\\[
\n\\begin{array}{cccc}
\n\\hline
\ny & x \\\\ \\hline
\n10.07 & 77.6 \\\\
\n14.73 & 114.9 \\\\
\n17.94 & 141.1 \\\\
\n23.93 & 190.8 \\\\
\n29.61 & 239.9 \\\\
\n35.18 & 289.0 \\\\
\n40.02 & 332.8 \\\\
\n44.82 & 378.4 \\\\
\n50.76 & 434.8 \\\\
\n55.05 & 477.3 \\\\
\n61.01 & 536.8 \\\\
\n66.40 & 593.1 \\\\
\n75.47 & 689.1 \\\\
\n81.78 & 760.0 \\\\
\n\\hline
\n\\end{array}
\n\\]\n\u3053\u306e\u30c7\u30fc\u30bf\u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059. <\/p>\n![\"\"](\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2025\/03\/Ex14D_1.png\")
<\/p>\n14.3.1 VBA \u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f7f\u7528\u3057\u305f\u89e3\u304d\u65b9 (1)<\/h4>\n
Const Ndata = 14, Nparam = 2\r\nDim Xdata(Ndata - 1) As Double, Ydata(Ndata - 1) As Double\r\n\r\nSub F(M As Long, N As Long, X() As Double, Fvec() As Double, IFlag As Long)\r\n Dim I As Long\r\n For I = 0 To M - 1\r\n Fvec(I) = Ydata(I) - X(0) * (1 - Exp(-Xdata(I) * X(1)))\r\n Next\r\nEnd Sub\r\n\r\nSub Start()\r\n Dim X(Nparam - 1) As Double, Fvec(Ndata - 1) As Double, Tol As Double\r\n Dim Info As Long, I As Long\r\n '--- Input data\r\n For I = 0 To Ndata - 1\r\n Xdata(I) = Cells(9 + I, 1)\r\n Ydata(I) = Cells(9 + I, 2)\r\n Next\r\n '--- Start calculation\r\n Tol = 0.0000000001 '** 1e-10\r\n For I = 0 To 1\r\n '--- Initial values\r\n X(0) = Cells(6 + I, 1)\r\n X(1) = Cells(6 + I, 2)\r\n '--- Nonlinear least squares\r\n Call Lmdif1(AddressOf F, Ndata, Nparam, X(), Fvec(), Tol, Info)\r\n '--- Output result\r\n Cells(6 + I, 3) = X(0)\r\n Cells(6 + I, 4) = X(1)\r\n Cells(6 + I, 5) = Info\r\n Next\r\nEnd Sub<\/code><\/pre>\n<\/div>\n![\"\"](\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2015\/10\/Ex14_1.png\")
<\/p>\n14.3.2 VBA \u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f7f\u7528\u3057\u305f\u89e3\u304d\u65b9 (2)<\/h4>\n
Sub Start_r()\r\n Const M As Long = 14, N As Long = 2\r\n Dim X(Nparam - 1) As Double, Fvec(Ndata - 1) As Double, Tol As Double\r\n Dim Info As Long, I As Long, J As Long\r\n Dim XX(Nparam - 1) As Double, YY(Ndata - 1) As Double, IRev As Long, IFlag As Long\r\n Dim Xdata(Ndata - 1) As Double, Ydata(Ndata - 1) As Double\r\n '--- Input data\r\n For I = 0 To Ndata - 1\r\n Xdata(I) = Cells(9 + I, 1)\r\n Ydata(I) = Cells(9 + I, 2)\r\n Next\r\n '--- Start calculation\r\n Tol = 0.0000000001 '** 1e-10\r\n For I = 0 To 1\r\n '--- Initial values\r\n X(0) = Cells(6 + I, 1)\r\n X(1) = Cells(6 + I, 2)\r\n '--- Nonlinear least squares\r\n IRev = 0\r\n Do\r\n Call Lmdif1_r(Ndata, Nparam, X(), Fvec(), Tol, Info, XX(), YY(), IRev)\r\n If IRev = 1 Or IRev = 2 Then\r\n For J = 0 To Ndata - 1\r\n YY(J) = Ydata(J) - XX(0) * (1 - Exp(-Xdata(J) * XX(1)))\r\n Next\r\n End If\r\n Loop While IRev <> 0\r\n '--- Output result\r\n Cells(6 + I, 3) = X(0)\r\n Cells(6 + I, 4) = X(1)\r\n Cells(6 + I, 5) = Info\r\n Next\r\nEnd Sub<\/code><\/pre>\n<\/div>\n14.3.3 \u30bd\u30eb\u30d0\u30fc\u3092\u4f7f\u7528\u3057\u305f\u89e3\u304d\u65b9<\/h4>\n
![\"\"](\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2015\/10\/Ex14S_1.png\")
<\/p>\n