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From Luc Maisonobe <Luc.Maison...@free.fr>
Subject [math] contributing Levenberg-Marquardt, Gauss-Newton, ODE, Brendt solver and more
Date Sun, 21 May 2006 19:45:12 GMT
Hello,

I am the creator of the Mantissa library 
(http://www.spaceroots.org/software/mantissa/index.html), a Java library 
providing some mathematical algorithms.

Mantissa provides several algorithms that could be useful for 
Commons-Math. I think the objectives of the two libraries are quite 
similar, but I don't know (yet) the point were you consider "commons 
problems" addressed by Commons-Math end and where problems are 
considered too specific to be provided here.

I would be very glad to donate parts of Mantissa code to Commons-Math if 
you wish so. Mantissa is released under a revised-BSD type license, but 
I am quite happy with Apache license too and ready to change.

I don't think everything in Mantissa is useful for Commons-Math. IMHO, 
the most interesting parts are :

  - the estimation package
    Gauss-Newton estimator (based on LU decomposition),
    Levenberg-Marquardt estimator (based on QR decomposition)
  - the fitting package (curve fitting, using the estimation package)
  - the Ordinary Differential Equations package
    this is clearly THE best package in Mantissa, with several
    state of the art integrators with fixed steps, variable stepsize
    (including Dormand-Prince 8 (5,3) and Gragg-Bulirsch-Stoer),
    all of them supporting continuous output and multiple switching
    functions (can be used for G-stop, but not limited to that), well
   tested and used
  - the roots package
   provides a Brent algorithm when the derivatives are not available


Some package that may be interesting are :

 - the geometry package
   mainly for the 3D rotations implementations using quaternions
   internally and axes/angles, Cardan angles, Euler angles, matrices,
   single or double vectors pairs and quaternions in the interface
 - the functions package
   providing notions like computable or sampled functions
 - the quadrature package
   (Riemann, trapezoid, enhanced Simpson, Gauss-Legendre up
    to 5 points, easily extended)
 - the utilities package
   for the array mapping paradigm

Some package that are probably not interesting are :

 - the algebra package
   orthogonal polynomials, inefficient and awkward implementation
 - the raw linear algebra package
   basic implementation developped for speed ... not sure the goal was
   achieved and using only straightforward algorithms, not state of the art
 - the random number generators
   supports correlated vectors generation


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