Best-Fitting the Continuous Parameters of Linear/Non-Linear Algorithmic Models of Arbitrarily Large Datasets with Extreme Accuracy

“Tweaks” refer to the small changes of parameter values which are used to compute the numerical partial derivatives of an algorithmic model as the model converges on a best-fit of a given dataset. I called these analytics “Pseudoinverse System Analysis” (1983 – @ Honeywell MavD, Minneapolis,MN) and used them professionally for 35+ years; in applied mathematics these algorithms are an approach to “linear & non-linear parameter identification”. “Parameters” are the  coefficients of equations.

The full environment can be accessed on the FTP side of my/this website at:  Introductory files and an image are posted there, including “”, which contains the full environment. “Tweak-Engine-Directory.txt” provides a content summary.  The source code was written in Fortran 95 using Absoft’s Pro Fortran 9.0 (32 bit) compiler.

The Tweak-Engine source code is Public Domain = Free, and so are all of the algorithms realized therein. To access the full environment on a computer running Windows – download the .zip file to a dedicated subdirectory and unzip it. Then rename “Tweak.exf” to “Tweak.exe”  & you’ll be ready to go.

The /Images subdirectory has 17 screen selfies viewing five different solution trajectories.

October 16th, 2018: Two subdirectories are added. Both color-code and line-number the four source code .f95 files; one subdirectory uses Microsoft’s .prn file format and the other uses standard .tif format. The link to the .tif files is  The 43 lines of Fortran source code L:585 -thru- L: 627 are the core analytics of accumulating [BtB] and [BtZ] for math models with arbitrarily many variables, arbitrarily many outputs, of arbitrarily large datasets. The inverse of [BtB] is multiplied by [BtZ]  to determine the direction in which to adjust the parameters for a better fit.  The 46 lines of Fortran source code are the homogeneous analytics of Seven Degrees-of-Freedom (7-DoF – X, Y, Z, Roll, Pitch, Yaw, & Scale) scaled rigid body motion. The 7-DoF equations are validated by the precise placement of oriented text in the .3dv output graphic.

The technical challenge is to deploy this & other scientific knowhow in service of the common good. E.g.:   &  Appendix “P”, pages 49-50.

April 10th, 2019: At first glance Tweak-Engine may seem to be part of  ‘artificial intelligence’. Not so. AI algorithms thrash on data in hopes of finding an approximate model in poorly explicable ways. Tweak-Engine can evaluate multi-variable  models with many more orders of magnitude of accuracy than  human intelligence  typically achieves; an exception is that STEM theoreticians do arrive at exact answers to  particular problems, often as a result of extreme personal mental dedication & perseverance. Since human intellect generates the equations which Tweak-Engine exercises – the tool stands ready as an extremely powerful theoretician’s sidekick within the science of  mind-machine interfaces.

I envision the day when “PSA” / “Tweak” is another key on scientific pocket calculators, like “sine” & “cosine”… or a voice command within your Oculus 7-DoF spatial environment, as the case may be.







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