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zunzuncode/pyeq2

1ab7124
Corrected new equation calculation

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A large collection of equations for Python 2 curve fitting and surface fitting that can output source code in several computing languages, and run a genetic algorithm for initial parameter estimation. Comes with cluster, parallel, IPython, GUI, NodeJS, and web-based graphical examples. Includes orthogonal distance and relative error regressions. You will need to install python and scipy to run this software. see http://commonproblems.readthedocs.io/en/latest/ On Debian or Ubuntu Linux, you can use this command to get both: sudo apt-get install python-scipy On other operating systems, try the Canopy Express Free version: https://store.enthought.com/ This repository is for Python 2, if you are using Python 3 please use https://bitbucket.org/zunzuncode/pyeq3 instead. See the Examples directory to get started. If your copy of pyeq2 does not include the Examples directory, you can find the examples at https://bitbucket.org/zunzuncode/pyeq2 Prior to the invention of electronic calculation, only manual methods were available, of course - meaning that creating mathematical models from experimental data was done by hand. Even Napier's invention of logarithms did not help much in reducing the tediousness of this task. Linear regression techniques worked, but how to then compare models? And so the F-statistic was created for the purpose of model selection, since graphing models and their confidence intervals was practically out of the question. Forward and backward regression techniques used linear methods, requiring less calculation than nonlinear methods, but limited the possible mathematical models to linear combinations of functions. With the advent of computerized calculations, nonlinear methods which were impractical in the past could be automated and made practical. However, the nonlinear fitting methods all required starting points for their solvers - meaning in practice you had to have a good idea of the final equation parameters to begin with! If however a genetic or monte carlo algorithm searched error space for initial parameters prior to running the nonlinear solvers, this problem could be strongly mitigated. This meant that instead of hit-or-miss forward and backward regression, large numbers of known linear *and* nonlinear equations could be fitted to an experimental data set, and then ranked by a fit statistic such as AIC or SSQ errors. Note that for an initial guesstimate of parameter values, not all data need be used. A reduced size data set with min, max, and (hopefully) evenly spaced additional data points in between are used. The total number of data points required is the number of equation parameters plus a few extra points. Reducing the data set size used by the code's genetic algorithm greatly reduces total processing time. I tested many different methods before choosing the one in the code, a genetic algorithm named "Differential Evolution". I hope you find this code useful, and to that end I have sprinkled explanatory comments throughout the code. If you have any questions or comments, please e-mail me directly at zunzun@zunzun.com. James R. Phillips 2548 Vera Cruz Drive Birmingham, AL 35235 USA email: zunzun@zunzun.com