New extended version added to standard equations

[zunzun.com]

The site's "standard" extended versions of equations, used as the default selection when function finding, previously contained two categories: the unmodified equation form, and for equations without an explicit offset parameter, an added offset. For example if the equation was "y = a * log(x)", both that and "y = a * log(x) + offset" were included when function finding.

Some years ago I had occasion to fit sine wave data of the form "y = sine_wave + straight_line". At that time I did not have the new Nyquist frequency limited versions of trigonometric equations available, and attempts at that time to fit such "sine + line" data resulted in useless extremely high-frequency sine waves.

With the new Nyquist frequency-limited versions of trigonometric equations now on the site, I remembered this problem and thought that perhaps "sine + line" data could now be properly fit with the new frequency limiting. As it turned out, it worked perfectly.

For this reason I have made some matching changes to the pyeq3 library and the web site code as follows:

1) A new "standard" extended version of equations, currently applied only to the Nyquist-limited versions of trigonometric equations, that adds a straight line to the equation. For example, the three-parameter equation "y = amplitude * sin(pi * (x - center) / width)" will now additionally have a five-parameter version of "y = [sine_function] + [straight line].

2) Because these new equation versions have two additional parameters for the added straight line, I have increased the site's default function finder smoothness control to 5.

3) The web site code for the function finder required some minor technical changes to incorporate the new feature.

It is now trivially easy to apply the new "equation plus straight line" extended version to other equations, though I have not yet done so.

James

[zunzun.com]

I have added the new "plus line" extended version flag to all equations with two or less parameters if they did not have an offset. This had the effect of adding 99 new, relatively simple equations, and they were all computationally easy to fit such that the site performance impact is minimal when function finding. To install the new pyeq3 code, use the command:

python3 -m pip install -U pyeq3

from a command prompt.

James

[zunzun.com]

This new change is working well, so I have removed the default function finder selection for the Polyfunctional family of equations. This can still be selected, but is not longer on by default.

James

On Sunday, December 29, 2019 at 8:50:37 PM UTC-6, zunzun.com wrote:

I have added the new "plus line" extended version flag to all equations with two or less parameters if they did not have an offset...

[zunzun.com]

I have added a new "plus flat plane" extended version to all 3D surface equations with three or less parameters that did not have an offset. This resulted in 94 new, simple surface equations with low additional computation overhead. There are matching changes to both the site code and the pyeq3 fitting library.

James