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https://issues.apache.org/jira/browse/MATH-1325?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15267993#comment-15267993
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Fran Lattanzio commented on MATH-1325:
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I pushed an initial cut of the multivariate finite differencing code. For now,
this only consists of:
1. Generating coefficients (exactly) via tensor product of univariate coeffs.
2. Taking multivariate numerical partials using a fixed bandwidth. The
bandwidth strategy is, however, pluggable, so we could insert something smarter
in the future.
Also, I made some changes to the Precision class to support rounding to exact
IEEE powers of 2. I wasn't totally happy with where this code ended up, but
Precision already had the necessary bit masks etc. to support this, so it was
certainly the easiest place...
I will try to add more unit tests, improve the JavaDocs, and finish off the
exception handling in the next 4-5 day.
> Improve finite differencing infrastructure
> ------------------------------------------
>
> Key: MATH-1325
> URL: https://issues.apache.org/jira/browse/MATH-1325
> Project: Commons Math
> Issue Type: New Feature
> Reporter: Fran Lattanzio
> Priority: Minor
>
> The existing finite difference framework in commons math is a limiting
> because it accepts only fixed bandwidth parameters. Furthermore, the finite
> difference coefficients/descriptions are not exposed to the user in any
> reasonable fashion (e.g. a user doing a numerical ODE solve probably wants to
> just grab suitable coefficients from somewhere).
> Conceptually, I think the work of finite difference can be broadly divided
> into three tasks:
> 1. Generation of finite difference coefficients. Again, one should be able to
> do this and get the results outside of the context of taking an actual
> derivative. Ideally, we could generate coefficients for any flavor (forward,
> central, backward) and order.
> 2. Selection of the bandwidth. This is, to be honest, the trickiest part of
> computing a numerical derivative. There is some "art" to picking a proper
> bandwidth that will generate an accurate numerical derivative - there are two
> competing sources of error (roundoff, due to the finite representation of
> floating points; and truncation, due to the inherent nature of finite
> differences). Ideally, we want to pick a bandwidth that will minimize the
> *total* error.
> 3. Actually computing the finite difference derivative estimate. This is
> really easy once you have 1. and 2.
> 4. Extend 1-3 to include support for multivariate finite differences.
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