Andrew provides model data against which Motofit, Parratt32, drydoc, and reflfit were compared. Below is a table of how well the various fitting routines available in yanera works with that same data, and same inital conditions.

On the left is a list of the constrained and unconstrained fitting methods. By "constrained", I mean whether one can set maximum and minimum limits for a parameter. In all cases, a parameter can be held fixed. We record the number of iterations, the execution time (in minutes:seconds), and the final chi-squared of fit for each method.

In the cases tested, fitting is much slower. Levenberg-Marquardt algorithms work well to achieve resonable chi-squared in about 8 minutes of compute time. It should be noted that they converge very rapidly at first, but slow down after the first few iterations. This is a consequence of the slow approach of b to 0.

The Neadler-Mead simplex method iterates much faster (since is doesn't take derivatives), but converges much more slowly. The final result by simulated annealing is comparable to the layer model, but takes much longer. So far, only one method has failed show much convergence.

Layer model | Function model | |||||||

Iterations | Time | Chi-Sq | Iterations | Time | Chi-Sq | |||

UNCONSTRAINED | ||||||||

CONJUGATE_FR | 500 | 01:12.93 | 1.353 | |||||

CONJUGATE_PR | 500 | 01:15.70 | 1.141 | |||||

VECTOR_BFGS | 500 | 01:10.88 | 1.255 | |||||

STEEP_DESC | 500 | 00:57.38 | 51.269 | |||||

NMSIMPLEX | 1500 | 00:07.03 | 1.145 | 1500 | 02:49.94 | 72.110 | ||

LMDR | 12 | 00:01.20 | 1.106 | |||||

LMSDR | 16 | 00:01.64 | 1.106 | 13 | 07:03.45 | 1.550 | ||

CONSTRAINED | ||||||||

SIMAN | 1000/50 | 01:38.38 | 2.375 | 1000/50 | 18:47.10 | 2.654 | ||

CLMDR | 20 | 00:01.24 | 1.297 | |||||

CLMSDR | 22 | 00:01.47 | 1.297 | |||||

OOL_SPG | 500 | 00:20.36 | 1.596 | |||||

OOL_GENCAN | 18 | 01:07.04 | 1.106 | > 20:00.00 | ||||

LEVMAR | 8 | 00:00.82 | 1.106 | 13 | 07:43.75 | 1.242 | ||

Starting Chi-Sq | 5378.800 | Starting Chi-Sq | 1978.9 |

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