Module smath - v2.2.0

Getting Started

Small math? Simple math? Or supplemental math? Canonically, "SMath" is pronounced "smath" and stands for "small math (library.)" Similar to JavaScript's builtin Math object, SMath exports one global object with several math-related helper functions. There is no need to instantiate the class, just call functions directly. See the examples below to get started using SMath!

Executables

SMath is also packaged with an executabe that can be run directly through npx in the terminal - even outside of a NodeJS project! In fact, open your terminal now, and type the following to show a list of valid npx smath commands!

npx smath help
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Commands are all structured like this.

npx smath [cmd] [args]
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This example command returns the value 0.4.

npx smath normalize 4 0 10
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Most SMath functions are available through npx, except for calculus functions which require a functional argument.

Data Fitting

SMath also exports the DataFit object which contains only 1 function, fit() which is used for curve fitting. All other exports are purely for defining types used within fit(). fit() uses a genetic-style algorithm to fit a curve.

How it works

It generates many sets of parameters to test, and keeps ones with smaller error than the previous iteration. Parameter sets with larger errors are discarded. Each subsequent iteration uses the sets of parameters with the least error and "mutates" them randomly.

Because of these random mutations, running the same code multiple times may yield slightly different results. See best practices for mitigation tactics.

Complexity

The folling factors affect computation time and resources:

• Number of iterations
• Number of independent/unknown function parameters
• Number of data points

Each one alone has a linear effect on performance, but combined has an incremental effect.

time = iterations * ( parameters + dataset )

The dimensionality, or number of free x variables per data point, should not have an impact on computation time.

Best Practices

For production software that relies on a best curve fit for data, it's best to avoid critical operations using fit() for a few reasons.

1. fit() uses an algorithm that generates random mutations in a set of parameters, which could yield slightly different results, even if run on the same dataset.
2. If the number of iterations is very high (in the millions or higher), it could have a significant effect on software performance.
3. Due to a limitation in JavaScript/TypeScript, the input function parameters cannot be optional or have default values. If they do have default values, assign them inside the function body.

To circumvent some of these issues, the following is recommended.

1. Use datafit during the testing phase of application development, and use the best-fit parameters as constants in the final application.
2. If that is not possible, datafit may be helpful for determining an initial guess of curve fit constants, which can be input to fit() during production. The number of iterations could be reduced if the initial guess is reasonably close to the desired result.
3. Using datafit primarily for data visualization or rough estimation.
4. For operations that need datafit, a suggestion would be to run multiple iterations of fit() itself, and using each output as the subsequent call's input. This will converge to a result more effectively but could take longer.

And here are some general good practices.

1. Avoid overfitting your data. That means, you should never have more function unknowns than the number of data points. fit() allows this for the rare chance that it is needed. Typically, having more, accurate data, is better for curve fitting.
2. Reject outliers. fit() does not do this. Any outliers existing in the dataset will be treated like normal data points and could negatively impact the best fit.

There are also some great arguments and use cases for this function, namely...

1. Data analysis and visualization.
2. Quickly iterating on different model functions for determining which best fits the data.
3. Curve fitting for multivariate or nonlinear models.
4. The ease of use of it all! It's just one function call with as little as 2 inputs!