25MAR2017 SolveSys  Equation Library and Nonlinear Systems Solver

02052017, 10:51 PM
(This post was last modified: 03262017 03:27 AM by Han.)
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25MAR2017 SolveSys  Equation Library and Nonlinear Systems Solver
25MARCH2017 (Ver. 1.000)
CHANGELOG
Download link at bottom of post; same link but zip file has been updated. NOTE: I am putting any further development (i.e. no new features) until summer; until then, any new update will only address bugs in the current version. Sorry, but I need to direct my focus on other things. Of course, I will still keep up with requests and relevant posts to this thread. ABOUT THE APP This app is intended to replicate and combine programs from the HP48 series of calculators for organizing equations and launching an equation solver. While there are a few usercreated programs/apps that help manage equations, most of them have the formulas builtin (hardcoded into the source code of the program/app). This app attempts to allow users to build their own equations library. The user can then also launch a numerical solver. Using the builtin Solve app may be adequate for some users, but it lacks the ability to handle more general systems. The current Solve app is quite deficient in that in requires the number of equations in a system be the same as the number of variables. Therefore, overdetermined or underdetermined systems cannot be solved numerically. Usually underdetermine systems have an infinite number of results, and a numerical solver should ideally try to return a solution that is as close to the initial guess as possible. For overdetermined systems, a solution usually does not exist. Most numerical solvers would return a "leastsquares" solution. This app implements the NewtonRaphson algorithm for solving a system of equations. In order to handle illconditioned, overdetermined, underdetermined, rankdeficient (etc.) Jacobian matrices, the SVD is used to determine the pseudoinverse of the Jacobian (the pseudoinverse coincides with the regular inverse of a matrix for nonsingular matrices). Users have reported that the app can handle complex values just fine. Minimal testing seems to confirm this. INSTALLATION AND USAGE (Please refer to the reference manual included in the zip file) REFERENCE MANUAL The reference manual will likely see another update in which all the images are updated to nicer, crisp images created by \( \LaTeX\ \) and pstricks. For now, though, I will leave them there so that there is at least some frame of reference, and for old time's sake. The equations will also likely get a face lift as the variables are updated to follow typical mathematical conventions (e.g. subscripts). While the HP Prime currently does not support subscripted variables, the correspondence between the calculator's variables and those in the reference manual should be obvious (e.g. \( v_0 \) vs. \( \tt{v0} \) ). If you notice any typos, please let me know. OTHER NOTES: There are two versions: a merged version (SVD merged into the source code for Equation Library) and the separated version. Does it make a difference which version I use? Yes, if you plan to work with under/over determined systems or systems whose Jacobian is either singular or near singular, it can make a major difference. PRIOR CHANGES: (08MAR2017 v0.900)
TODO
The current firmware seems to exhibit issues with CAS programs. If you should find the app not working suddenly, type restart; at the command line (NOTE: this will delete all CAS results) and "recompile" the app and/or the SVD program (simply open and close their files in the program editor). Turn the calculator off and then on to save the memory state. DOWNLOADS Version 1.000 (same file name, just redownload to get the update) Equation Library Prime.zip (Size: 540.99 KB / Downloads: 1056) Graph 3D  QPI  SolveSys 

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