heat Provide a solver for triangular systems

Feature functionality Provide a solver for the linear equation $Ax = b$, where $b \in \mathbb{K}^{m \times n}$, $A \in \mathbb{K}^{m \times m}$ are two-dimensional DNDarrays such that $A$ is either upper- or lower-triangular.

Intended scope:

different combinations of split for $A$ and $b$
of course, scalability of the routine is desired

Additional context

Often required in combination with Cholesky decompositon #886
also required in context of linear regression (implementing a "QR + triangular solve"-based linear regressor for massive data could be a cool second part of a corresponding student project or PR)

Feb 08 '23 12:02 mrfh92

Hi, mrfh92, I wanted to work on this problem, can you please tell me whether this feature has to be added to /core/linalg/solver.py or with the cholesky matrix in /core/linalg/basics.py.

Feb 13 '23 15:02 Gaurav17Joshi

I would suggest to put triangular_solve into .../solver.py and to create a new file /core/linalg/cholesky.py for cholesky. If you have questions, feel free to concact me.

Feb 13 '23 17:02 mrfh92

Hi, I have created a new function triangular_solver in .../solver.py. It takes in A and B as inputs and returns the solution x for Ax = B, also, this function raises error flag if the user does not input a triangular matrix or the matrix is not full rank.