fminsearch 中的错误来解决这个 4 变量问题？

Question

我正在尝试使用 fminsearch 求解下面的等式，但我认为 objective 函数是错误的。

我应该如何编写 objective 函数或修改代码的任何其他部分？这基本上是一个拟合问题，其中优化过程应将方程拟合到给定数据。

% Consider the following data:

Data = ...
  [0.0000    5.8955
   0.1000    3.5639
   0.2000    2.5173
   0.3000    1.9790
   0.4000    1.8990
   0.5000    1.3938
   0.6000    1.1359
   0.7000    1.0096
   0.8000    1.0343
   0.9000    0.8435
   1.0000    0.6856
   1.1000    0.6100
   1.2000    0.5392
   1.3000    0.3946
   1.4000    0.3903
   1.5000    0.5474
   1.6000    0.3459
   1.7000    0.1370
   1.8000    0.2211
   1.9000    0.1704
   2.0000    0.2636];

% Let's plot these data points.
t = Data(:,1);
y = Data(:,2);

plot(t,y,'ro')
title('Data points')
hold on

% fit the function: y =  c(1)*exp(-lam(1)*t) + c(2)*exp(-lam(2)*t)
%
% define the parameters in terms of one variable x:
%  x(1) = c(1)
%  x(2) = lam(1)
%  x(3) = c(2)
%  x(4) = lam(2)
%
% Then define the curve as a function of the parameters x and the data t:

F = @(x,t)(x(1)*exp(-x(2)*t) + x(3)*exp(-x(4)*t));

% We arbitrarily set our initial point x0 as follows: c(1) = 1,
% lam(1) = 1, c(2) = 1, lam(2) = 0:

x0 = [1 1 1 0];

% We run the solver and plot the resulting fit
options = optimset('TolFun',1e-5,'TolX',1e-5,'MaxFunEvals',10,'MaxIter',4000,'Display','iter');
[x,fval,exitflag,output] = fminsearch(F,x0,options)

plot(t,F(x,t))
hold off

Answer 1

你是对的，你的 objective 函数没有意义。你可以做一个 least squares fitting。那么objective函数应该定义为：

F = @(x,t) (x(1)*exp(-x(2)*t) + x(3)*exp(-x(4)*t));
Obj = @(x) (norm(F(x, Data(:,1))-Data(:,2)));

然后

x0 = [1 1 1 0];
options = optimset('TolFun',1e-5, 'TolX', 1e-5, 'MaxFunEvals',1000, 'MaxIter', 4000,'Display','iter');
[x,fval,exitflag,output] = fminsearch(Obj,x0,options);

tp = 0:0.01:2;
plot(Data(:,1), Data(:,2), 'ro');
title('Data points')
hold on
plot(tp,F(x,tp));
hold off

给我：

编辑：

假设你已经知道一个参数并且你想使用函数句柄，你可以这样做

p = ... % Your calculation to get the parameter. In your case x(3) from the previous F
F = @(x, p, t) (x(1)*exp(-x(2)*t) + p*exp(-x(3)*t));
helper = @(x, p) (norm(F(x, p, Data(:,1))-Data(:,2)));
Obj = @(x) (helper(x, p));

x0 = [1 1 0]; % Note that there's now one variable/parameter less
options = optimset('TolFun',1e-5, 'TolX', 1e-5, 'MaxFunEvals',1000, 'MaxIter', 4000,'Display','iter');
[x,fval,exitflag,output] = fminsearch(Obj,x0,options);

tp = 0:0.01:2;
plot(Data(:,1), Data(:,2), 'ro');
title('Data points')
hold on
plot(tp,F(x,p,tp)); % Note that you need to pass p to F
hold off

fminsearch 中的错误来解决这个 4 变量问题？

Error in fminsearch to solve this 4-variable problem?

matlab

fminsearch