Special matrix types for optimizations

[mcopik]

We should use specific matrix types to enable possible optimizations. We have two problems here: how to create those types and how to implement expressions without assuming that user knows the exact type in each expression?

For example:

? result = f(A, B);

? here can be a general or a specific matrix type, depending on types of A and B, how f preserves those types and whether linear algebra toolkit implements it properly.

Types:

• triangular

• symmetric/Hermitian

• tridiagonal(banded)

• Eigen

• Blaze

• Armadillo

• MTL4

[mcopik]

Blaze:

• we have specific types for triangular, symmetric and hermitian matrices, there is no type for band matrix
• we have standard way how to determine result type of each operation at compile time

[mcopik]

Eigen: there are views which require that original matrix still exists.
https://forum.kde.org/viewtopic.php?f=74&t=137795&sid=c63c1a676a3483739825ea908cb152ed

Possible solutions:

1. wrapper storing matrix + view
2. generator singleton storing all allocated matrices and keeping them valid

Views exist for symmetric, triangular. There is an implementation of band matrix but it is practically useless.

Unfortunately I got no clear answer regarding Eigen capabilities and auto x = (...).eval(); It looks safe though.

[mcopik]

Armadillo: there is a support for creating symmetric/triangular matrices:
http://arma.sourceforge.net/docs.html#symmat
http://arma.sourceforge.net/docs.html#trimat
and diagonal:
http://arma.sourceforge.net/docs.html#diagmat

No mailing list/forum, I wrote an email.

[mcopik]

MTL4: virtually nothing.