Hello all,
Gilles suggested that I should write some considerations about
improvement to common maths automatic differentiation here. I've opened
an Issue here: https://issues.apache.org/jira/browse/MATH-1452 (I really
do not like mailing lists). But since I've done my own implementation on
top of Commons Maths, I can share it. The implementation is in Kotlin,
so I won't be able to contribute it to commons math as is, but still we
can discuss how to backport it to java.
Here is the source code of two classes which solve
https://issues.apache.org/jira/browse/MATH-1448 and partially MATH-1452:
https://bitbucket.org/Altavir/dataforge/src/1433da0d2f19ab26d709de8750e002847a4b4887/dataforge-maths/src/main/kotlin/hep/dataforge/maths/expressions/AD.kt?at=ad&fileviewer=file-view-default
The class on the top is a Context for mathematical operations with AD
numbers. Since CM already have Fields, it implements the Field. The idea
is that context stores some critical properties of numbers which are
shared between instances like order of differentiation and parameters
names. In this case the object equality check used instead of instance
equality, so to context with same orders and set of names are still
equal. The AD class below is just a wrapper for DerivativeStructure that
also includes Field context. Binary operations additionally perform
check if argument uses the same context as `this` object.
The actual check occurs here:
https://bitbucket.org/Altavir/dataforge/src/1433da0d2f19ab26d709de8750e002847a4b4887/dataforge-maths/src/main/kotlin/hep/dataforge/maths/expressions/AD.kt?at=ad&fileviewer=file-view-default#AD.kt-78.
In theory, one can perform field transformation, merging parameters sets
from both ADs, but it requires understanding about inner workings of
DerivativeStructure which I lack. Basically what I need is an ability to
create a new DerivativeStructure with parameter number i mapped to
number j.
The proposed solution does not seem to involve any major performance
impact. Name resolution happens only when one calls derivative with
given name and is not really a great performance impact since string
hashes are calculated on string creation. The only place with actual
performance impact is when field transformation happens (if it will be
implemented), but this transformation is supposed to be rare and it
currently not possible at all.
The test code in kotlin looks like this:
https://bitbucket.org/Altavir/dataforge/src/8131099f29ebf27fb170ace037cda61df9790fc2/dataforge-maths/src/test/java/hep/dataforge/maths/expressions/ADTest.kt?at=ad&fileviewer=file-view-default.
It is kotlin though, it would be much more verbatim in java. I plan also
to implement expressions which would allow lazy calculations of AD
structures like (NamedVector)->AD. This one could be more or less easily
done in Java.
With best regards, Alexander Nozik.
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