On 10/20/06, Alexandar Hansen <[EMAIL PROTECTED]> wrote:
Maybe I'm missing something, but to me 1e-21 is the same as 1e-27 in computer language. Let's assume a small amount of error in measurements of 1%. With that amount of random error, I couldn't possibly expect much less than 1e-3 or 1e-4 as an overall chi2. Is there significance to having this high of precision when our measurements could never reach it?
Very much so. The function tolerance between iterations is set to 1e-25. In model-free analysis this is the chi-squared function difference between two iterations of the optimisation algorithm (not to be confused with the iterations of the Method of Multipliers constraint algorithm, the iterations of the step length selection algorithm for the line search optimisation algorithms, the iterations over the runs of the 'full_analysis.py' script, or the iterations over the global models of the 'full_analysis.py' script (there are many other iterations as well, but I should probably stop now)). The reason for this is because the sum of many small steps can be quite large. As I showed on my poster at ICMRBS (and will hopefully soon be published), the model-free space is quite convoluted. In the two timescale models, it is common to have a long convoluted shallow tunnel through the model-free space close the the local/global minimum. If a function tolerance of 1e-5 is used, then the optimisation algorithms are unable to slide down the tunnel to reach the minimum. The result is that ts is overestimated by an order of magnitude and the S2f and S2s parameters have their values swapped!!! Although the change in chi-squared is small for each step, the overall change from the top to the bottom of the tunnel is large. This is why high precision optimisation after a very rough grid search is essential for correct model-free results. This relates to the fact that the changes in the optimised function value are not correlated to changes in the parameter values. Rather the change in parameter values is related to the complex curvature of the space which itself is directly correlated with the experimental errors. In order to reach the local minimum, if a part of the space which needs to be traversed is shallow and curved (a shallow valley, a narrow hole through the space, a broad yet long and twisted plane or valley, etc.) then you will need a small enough function tolerance to continue past these geometric features. In the model-free space, 1e-25 is optimal. Edward P.S. As for 1e-21 being the same as 1e-27, this is only the case if you are talking about differences between values many orders of magnitude greater that this. For absolute floating point values, the value of the exponent part of the floating point doesn't influence the precision of the rest of the number. _______________________________________________ relax (http://nmr-relax.com) This is the relax-devel mailing list [email protected] To unsubscribe from this list, get a password reminder, or change your subscription options, visit the list information page at https://mail.gna.org/listinfo/relax-devel
