1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
|
// Check for the maximum iteration
function y=yth(t, x)
y = x(1)*exp(-x(2)*t)
endfunction
// we have the m measures (ti, yi):
m = 10;
tm = [0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5]';
ym = [0.79, 0.59, 0.47, 0.36, 0.29, 0.23, 0.17, 0.15, 0.12, 0.08]';
// measure weights (here all equal to 1...)
wm = ones(m,1);
// and we want to find the parameters x such that the model fits the given
// data in the least square sense:
//
// minimize f(x) = sum_i wm(i)^2 ( yth(tm(i),x) - ym(i) )^2
// initial parameters guess
x0 = [1.5; 0.8];
// in the first examples, we define the function fun and dfun
// in scilab language
function y=myfun(x, tm, ym, wm)
y = wm.*( yth(tm, x) - ym )
endfunction
options = list("MaxIter",10)
//Error
//Maximum Number of Iterations Exceeded. Output may not be optimal.
// gradient =
//
// 512.91855 - 4714.171
// lambda =
//
// lower: [0,0]
// upper: [0,0]
// output =
//
// Iterations: 10
// Cpu_Time: 0.12
// Objective_Evaluation: 11
// Dual_Infeasibility: 4714.171
// Message: "Maximum Number of Iterations Exceeded. Output may not be optimal"
// exitflag =
//
// 1
// residual =
//
// 4.8006782
// 5.767661
// 6.7598659
// 7.8617282
// 9.0596638
// 10.40234
// 11.920987
// 13.599744
// 15.516066
// 17.701171
// resnorm =
//
// 1235.2439
// xopt =
//
// 4.9162235
// - 0.5142398
[xopt,resnorm,residual,exitflag,output,lambda,gradient] = lsqnonlin(myfun,x0,[],[],options)
|
