Create a triangular solver

UCL-ARC / householder

A native Rust library for advanced Linear Algebra routines

https://docs.rs/householder/latest/householder/

Apache License 2.0

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Create a triangular solver #13

Open tbetcke opened 2 years ago

tbetcke commented 2 years ago

Triangular solves are a core task of many more advanced matrix algorithms. We want to implement.

A simple serial triangular solve.
A multithreaded triangular solve using a threadpool.

The multithreaded version also requires serial triangular solves. So it is natural that both needs to be done. A precondition for this issue is a decision on the parallelization framework in #11 .

strasdat commented 2 years ago

Once we have a triangular solver, I might be motivated to implement a dense LDL (https://en.wikipedia.org/wiki/Cholesky_decomposition#LDL_decomposition) decomposition, to solve linear systems Ax=b, with A being positive semi-definite.

tbetcke commented 2 years ago

Sounds good. My goal for Householder is that eventually we have modern task based algorithms for all decompositions. For LDL^T see for example (https://hal.inria.fr/hal-00809663/document). However,

we still want single core algorithms as well (lots of applications where you want to do small decompositions within a thread and not have your linear algebra spread out of all threads)
Also for parallel algorithms we usually need to single core versions as components.