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# S-curves fitting in RCE - PowerPoint Presentation

## S-curves fitting in RCE - PPT Presentation

Nick Sinev Maximilian Swiatlowski The most of the code fitintc was written by MSwiatlowski I have optimized its speed by minimizing number of multiplications in the innermost loop of the fitter code using only 32 bits integers there replacing divisions and multiplications whene ID: 284491

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Slide1

S-curves fitting in RCE

Nick Sinev, Maximilian

SwiatlowskiSlide2

The most of the code (

fitint.c

) was written by M.Swiatlowski. I have optimized its speed by minimizing number of multiplications in the innermost loop of the fitter code, using only 32 bits integers there, replacing divisions and multiplications whenever possible by bit shifts.I have checked fitter performance by comparing output to the input parameters of s-curve generator, which I wrote.

What is newSlide3

Row unfitted estimations

I have generated 3000 s-curves with mu0=4000 and sigma=130.

First thing before fitting – estimation of parameters (“guessing”).

Here are results of such guessSlide4

Fitting results

Here we can see fitting results for the same curvesSlide5

Fitter speed

I have generated s-curves for different sigma and for different number of tests in each point (100 and 400). Fitting time depends on both.Slide6

Fitter speed – depend on number of points

We can expect, that major factor in the fitting time is a number of points to fit. Left curve shows such number

vs

sigma for curves with different number of test per point, and right plot shows data from previous page, but all on one plot.Slide7

Fit errors

As expected, fit errors depend on number of tests in s-curve measurement. We got errors in mu0 and sigma of about 7 e for s-curves with 100 tests in each point, and if we try s-curves with 400 points, we get errors of about 3.5 e (as seen above).Slide8

To get maximum precision using all integer arithmetic we want to use as large numbers as possible. But we need to be careful about possible overflows. For results, shown earlier I have used multiplier 100000 for logarithms of error function values. This gives maximum number in the accumulated sum inside fitter of about 300 millions for sigma=200 and number of tests 400. This is not quit comfortable, taking into account that largest signed 32 bit integer is only about 2 billions.

So, I tested fitter with multiplier of only 8192 for logarithms, and found, that fitter accuracy does not change noticeably in that case, but maximum accumulated number does not exceed 30 millions for sigma 300 and number of tests 400, which gives us larger possible ranges for input parameters.

Limits

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