Implement Sparse Left-Looking LU factorization #1289
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solve_upper_triangular to CsrMatrix
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Add `solve_upper_triangular` to `CsrMatrix` This allows a sparse matrix to be used for efficient solving with a dense LU decomposition. Add CscBuilder For partial construction of Csc matrices Start working on actual LU factorization Complete basic version of sparse LU factorization Reformat to compile in old version Add LU tests Add upper triangular solve Complete tests of Sparse LU factorization
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This allows a sparse matrix to be used for efficient solving with a dense LU decomposition.
It generally follows lectures from Tim Davis
https://www.youtube.com/watch?v=wiL_jIuENkk&ab_channel=TimDavis
(Lectures 1-3), and implements a basic left looking sparse LU factorization.
I primarily focus on CSC matrices, since they are what is focused on in the lecture, identical to what is done in Matlab.
I believe for most use cases this should be efficient and correct, and thus it serves as a useful to building even more customized solvers down the line.
Summary of changes:
Sparsity Pattern Builder: Allowing for building up sparsity patterns, rather than constructing them all in one go. This seemed to be a drawback of the previous design, and I've added a builder to construct Sparsity Patterns. This was necessary when computing the sparsity of the decomposed LU matrix.
Sparse lower triangular solving. For most users, the result will probably want
LUx = b, withba dense vector. While constructing the LU matrix though, it calls a sparseLy = s, withssparse. This allows for building up a sparse LU pattern iteratively. The LU matrix is packed into a single sparse matrix, with the diagonal belonging to U, andLhas implicit 1s along the diagonal.Dense lower/upper triangular solving. This is what the end user will interact with. I've added it to take slices, but I should probably convert it to DMatrices. Slices feel more natural to me though, since it decouples the requirement of the input being a matrix, as it's just solving a vector anyway.
r? @sebcrozet @Andlon
Not sure if y'all have time to review.
Motivation:
Currently I'm trying to reimplement a paper that uses libigl within Rust, but there's a significant amount of library functionality that is missing. Specifically, quadratic programming doesn't exist, so this is a step to making it available.
Closes #1197