[Octave-bug-tracker] [bug #49076] Should perform matrix chain multiplication optimization

[anonymous]

Follow-up Comment #3, bug #49076 (project octave):

Comment:

This problem shows up frequently in CS textbooks as a pedagogic example on
dynamic programming but nobody can show real-life code where the following all
apply:

* Should be three or many more matrices that are not square OR equally and
oppositely rectangular. This eliminates most problems in optimization (BFGS)
and linear algebra (SVD) which use either x'BB'x or x'Ax both better solved by
symmetric decomposition.

* Should be large matrices for the effect to be significant. This removes the
common case of chain multiplication: transformation matrices for computer
graphics and 3D manipulation. They never exceed 4x4 and many of them are
hardware-optimized as well.

* Should be dynamically changing sizes, otherwise static offline analysis of
the matrix chain is just fine.

* The user should be likely enough to encounter instances of matrix chain
multiplication but not be aware of the associativity relation or the benefit
of offline static analysis. This is the biggest stopper.

Recommendation: There really are no such real-life problems that make it worth
implementing such a just-in-time performance analysis for numerical software.
Much better to leave it as a pedagogic example.

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