Mathematica：使用 NIntegrate 和 '（微分）对数据进行误差拟合函数

Question

我一直在尝试将函数拟合到数据集。 IT 使用没有积分（如 NIntegrate）和微分（'）的函数。我正在尝试使用积分和微分让它发挥作用：

deltaData = {{1.00, 0}, {0.96, 0.3416}, {0.92, 0.4749}, {0.88, 0.5715}, {0.84, 0.648}, {0.80, 0.711}, {0.76, 0.764}, {0.72, 0.8089}, {0.66, 0.864}, {0.62, 0.8939}, {0.58, 0.919}, {0.54, 0.9399}, {0.50, 0.9569}, {0.46, 0.9704}, {0.42, 0.9809}, {0.38, 0.9885}, {0.34, 0.9938}, {0.30, 0.9971}, {0.26, 0.9989}, {0.22, 0.9997}, {0.16, 1}, {0.14, 1}};

deltaFit = 
  NonlinearModelFit[
   deltaData, (1 + a*T + c*T^2 + e*T^3 + g*T^4 + i*T^5 + k*T^6)/(1 + 
      b*T + d*T^2 + f*T^3 + h*T^4 + j*T^5 + l*T^6), {a, b, c, d, e, f,
     g, h, i, j, k, l}, T];

Plot[deltaFit[T], {T, 0, 1}]

data = {{0.203, 0.031}, {0.203, 0.030}, {0.246, 0.055}, {0.267, 0.072}, {0.300, 0.105}, {0.300, 0.105}, {0.330, 0.147}, {0.373, 0.214}, {0.397, 0.255}, {0.415, 0.293}, {0.445, 0.351}, {0.477, 0.430}, {0.493, 0.463}, {0.520, 0.538}, {0.541, 0.590}, {0.582, 0.717}, {0.589, 0.733}, {0.625, 0.847}, {0.645, 0.911}, {0.685, 1.029}, {0.688, 1.043}, {0.730, 1.181}, {0.751, 1.247}, {0.782, 1.338}, {0.793, 1.375}, {0.830, 1.472}, {0.856, 1.531}, {0.878, 1.585}};
AlphaBCS = 1.746;

delta[T_, p_, alpha_] := p*deltaFit[T] + (1 - p)*deltaFit[T]/alpha;
fx[T_, x_, p_, alpha_] := (Exp[AlphaBCS/T*(x^2 + delta[T, p, alpha]^2)^(1/2)] + 1)^(-1);
Ses[T_, p_, alpha_] := -6*AlphaBCS/Pi^2* NIntegrate[fx[T, x, p, alpha]*Log[fx[T, x, p, alpha]] + (1 - fx[T, x, p, alpha])*Log[1 - fx[T, x, p, alpha]], {x, 0,100}];
Ces[T_, p_, alpha_] := T*Ses'[T, p, alpha];

cesFit = NonlinearModelFit[data, Ces[T, p, alpha], {{p, 0.5}, {alpha, 1.764}}, T];

我不知道为什么会收到错误，因为代码在我执行的第一次配合中工作。这是错误消息：

The function value ... a bunch of numbers ... Ses' ... more numbers ... is not a list of real numbers with dimensions {28} at {p,alpha} = {0.5`,1.764`}.

有人知道我做错了什么吗？有什么东西可以代替配合或集成来完成这项工作吗？

Answer 1

@Bill：谢谢您指出这一点！这是我更正后的代码：

dSes[T_, p_, alpha_] = D[Ses[T, p, alpha], T];
Ces[T_, p_, alpha_] := T*dSes[T, p, alpha];

现在差异化起作用了。但是当我运行 fit 时，出现以下错误： 一长串数字、括号，Compile'$... 不是维度为 {28}、{p,alpha} = {0.5,1.764} 的实数列表。