Mantissa

Mantissa (Mathematical Algorithms for Numerical Tasks In Space System Applications) is a handy tool packed with algorithms that help with dynamics simulation and 3D geometry computations. If you’re diving into this software, you're in for a treat!

Features of Mantissa

This library comes loaded with a variety of cool features, including:

• A small set of linear algebra classes


• Least squares estimators (we've got one based on Gauss-Newton and another on Levenberg-Marquardt that works even for over-determined systems)


• Some curve fitting classes


• Integrators for ordinary differential equations (ODEs), whether you prefer fixed steps or adaptive step size control.


• Vectors and rotations in 3D space


• Algebra-related classes like rational and double polynomials


• A bunch of orthogonal polynomials including Chebyshev, Hermite, Laguerre, and Legendre.


• Random number generators including Robert M. Ziff's four tap shift register and Makoto Matsumoto’s Mersenne twister.


• Basic statistical analysis classes to find min, max, mean, and standard deviation.


• Optimization algorithms using methods like the Nelder-Mead simplex method.

The Power of ODE Integration

Mantissa is designed to be a versatile library but shines when it comes to integrating Ordinary Differential Equations. This feature is super efficient and provides a full ODE integration framework that's easy to use yet powerful.

Dense Output & Event Handling

All integrators give you dense output. What does that mean? It means not only do you get the state vector at set times, but also an easy way to get the state in between those times!

The integrators can handle multiple switching functions too! This allows them to react to discrete events based on user-defined conditions. When these events happen, the steps can shorten as needed so they occur right at step boundaries—even if you're using a fixed-step integrator.

User Control During Integration

You have options here! You can stop integration when events trigger (known as G-stop), change the state vector, or just keep going. This is super helpful for dealing with tricky spots in your differential equations while still getting accurate results.

The end result of your integration can be stored directly into an array provided by you. If you want more details throughout the process though, you can hook up an object implementing the StepHandler interface. This lets you grab intermediate results during integration!

Simplifying Complex Models

If you're storing data for later use—like in files or databases—Mantissa makes it easy since its objects are serializable. Plus, some integrators come with fixed steps set from the start while others adjust their steps dynamically based on how accurate you want your results to be.

If you'd like full control over your integration process or if the automatic guesses aren't working out for you, feel free to set your own initial step size!