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

我应该如何编写目标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，其中优化程序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
4

1 回答 1

2

你是对的，你的目标函数没有意义。你可以做一个最小二乘拟合。那么目标函数应该定义为：

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：

在此处输入图像描述

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
于 2018-09-29T20:28:34.727 回答