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From Al Chou <hotfusion...@yahoo.com>
Subject Re: [math] proposed ordering for task list, scope of initial release
Date Sat, 07 Jun 2003 19:15:01 GMT
--- Phil Steitz <steitzp@yahoo.com> wrote:
[deletia]
> OK, long-winded disclaimer aside, here is how I see the task list ordered:
> 
> * The RealMatrixImpl class is missing some key method implementations. The
> critical thing is solution of linear systems. We need to implement a
> numerically sound solution algorithm. This will enable inverse() and also
> support general linear regression. -- I think that Brent is working on this. 
>  
> 
> * Improve numerical accuracy of Univariate and BivariateRegression
> statistical
> computations. Encapsulate basic double[] |-> double mean, variance, min, max
> computations using improved formulas and add these to MathUtils. (probably
> should add float[], int[], long[] versions as well.) Then refactor all
> univariate implementations that use stored values (including UnivariateImpl
> with finite window) to use the improved versions. -- Mark?  I am chasing down
> the TAS reference to document the source of the _NR_ formula, which I will
> add
> to the docs if someone else does the implementation.

I was starting to code the updating (storage-less) variance formula, based on
the Stanford article you cited, as a patch.  I believe the storage-using
corrected two-pass algorithm is pretty trivial to code once we feel we're on
solid ground with the reference to cite.


> * Define full package structure and develop user's guide following the
> package
> structure.  I have started work on the user's guide, but found this
> impossible
> without the package structure defined.  I will post a separate message
> summarizing what has been proposed up to now and making a recommendation.
> 
> * t-test statistic needs to be added and we should probably add the
> capability
> of actually performing t- and chi-square tests at fixed significance levels
> (.1, .05, .01, .001). -- This is virtually done, just need to define a nice,
> convenient interface for doing one- and two-tailed tests.  Thanks to Brent,
> we
> can actually support user-supplied significance levels (next item)
> 
> * numerical approximation of the t- and chi-square distributions to enable
> user-supplied significance levels.  See above.  Someone just needs to put a
> fork in this. Tim? Brent?
> 
> * *new* add support for F distribution and F test, so that we can report
> signinficance level of correlation coefficient in bivariate regression /
> signinficance of model.  I will do this if no one else wants to.
> 
> * Framework and implementation strategie(s) for finding roots or real-valued
> functions of one (real) variable.  Here again -- largely done.  I would
> prefer
> to wait until J gets back and let him submit his framework and R. Brent's
> algorithm.  Then "our" Brent's implementation and usage can be integrated
> (actually not much to do, from the looks of the current code) and I will add
> my "bean equations" stuff (in progress).

I may have time to submit my Ridders' method implementation using J.'s
framework before he returns 2 days hence.  Should I bother to try, or should I
wait until he submits his code as a patch via Bugzilla?


> * Extend distribution framework to support discrete distributions and
> implement
> binomial and hypergeometric distributions.  I will do this if no one else
> wants
> to.  If someone else does it, you should make sure to use the log binomials
> in
> computations.
> 
> * Exponential growth and decay (set up for financial applications) I think
> this
> is just going to be a matter of finding the right formulas to add to
> MathUtils.
>  I don't want to get carried away with financial computations, but some
> simple,
> commonly used formulas would be a nice addition to the package. We should
> also
> be thinking about other things to add to MathUtils -- religiously adhering to
> th guiding principles, of course.  Al's sign() is an excellent example of the
> kind of thing that we should be adding, IMHO.

Thanks for the compliment!  I think I finally understand what you mean with the
exponential stuff:  compount interest calculation, for the most part, with
continuous compounding requiring the exponential.


> * Polynomial Interpolation -- let Al tell us what to do here.  Even better,
> let Al do it (he he).   

I actually did some research last night (I told myself I was going to bed
early, hah) on rational function interpolation, trying to find a primary source
for the algorithm rather than again rely on a secondary source in the form of
NR.  I guess I'll continue along this path, as I really want a clean room
implementation of it for my own use.  I'd feel better using rational functions
rather than polynomials for their generally larger radius of convergence.



Al

=====
Albert Davidson Chou

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