I am fitting a function with different number of floating parameters using lsqnonlin in matlab.
The first fitting produces better fitting, resnorm of 2.5. matlab displays:
Norm of First-order
Iteration Func-count f(x) step optimality
0 24 17492.8 9.07e+05
1 48 143.52 0.106514 2.14e+04
2 72 28.1836 0.322225 9.21e+03
3 96 8.22318 0.190289 471
4 120 4.64683 0.106685 469
5 144 4.21385 0.110651 50.6
6 168 3.84595 0.132576 6.57
7 192 3.80318 0.0785982 0.574
8 216 3.80298 0.00714585 0.0696
9 240 3.80298 8.99227e-05 0.0165
The 2nd fitting's resnorm is 3.6. matlab displays:
Norm of First-order
Iteration Func-count f(x) step optimality
0 38 17492.8 9.07e+05
1 76 158.945 0.112853 3.12e+04
2 114 31.4081 0.296493 9.11e+03
3 152 8.51237 0.171055 627
4 190 4.73721 0.485675 1.01e+03
5 228 4.25786 0.268581 121
6 266 3.82232 0.424431 12.9
7 304 3.67385 0.483489 13
8 342 3.65582 0.290754 21
9 380 3.64699 0.331376 25.9
10 418 3.64327 0.237147 16
11 456 3.64078 0.236815 13.3
12 494 3.63925 0.203176 9.54
13 532 3.63819 0.186138 7.32
14 570 3.63747 0.165213 5.52
15 608 3.63697 0.148463 4.2
16 646 3.63663 0.132661 3.17
17 684 3.6364 0.118115 2.35
18 722 3.63624 0.102959 1.73
19 760 3.63616 0.0842739 1.2
20 798 3.63612 0.0589477 0.731
21 836 3.63611 0.0309845 0.391
22 874 3.6361 0.0119255 0.192
Both these fittings: "lsqnonlin stopped because the final change in the sum of squares relative to its initial value is less than the default value of the function tolerance."
How do I interpret the displays for fitting result, without looking at resnorm?
From what I can see, the 1st fittings "norm of step" is much less. The final result of f(x) and first-order optimality are similar.
What does each column mean? How do I interpret them?
Iteration - The iteration number.
Func Count - Number of function evaluations.
f(x) - The value of the function at x.
Norm of step - Size of the current step.
First-Order Optimality - First-order optimality is a measure of how close a point x is to optimal.
What you want to look at is the fact that the first order optimality -> 0 (and your residuals -> 0 too), as this will indicate your algorithm is converging or has converged on an optimal solution. The first fitting you must have provided a better guess or used a better algorithm, because it converged in only 9 iterations, whereas your second fitting converged in 22.