Package: cholespy
What is this repo?This is a minimalistic, self-contained sparse Cholesky solver, supporting
solving both on the CPU and on the GPU, easily integrable in your tensor
pipeline.When we were working on our "Large Steps in Inverse Rendering of Geometry" paper[1], we found it quite challenging to hook up an existing sparse
linear solver to our pipeline, and we managed to do so by adding dependencies on
large projects (i.e.cusparseandscikit-sparse), only to use a small part
of its functionality. Therefore, we decided to implement our own library, that
serves one purpose: efficiently solving sparse linear systems on the GPU or CPU,
using a Cholesky factorization.Under the hood, it relies on CHOLMOD for sparse matrix factorization. For the
solving phase, it uses CHOLMOD for the CPU version, and uses the result of an
analysis step runoncewhen building the solver for fast solving on the GPU[2].It achieves comparable performance as other frameworks, with the dependencies
nicely shipped along.Benchmark run on a Linux Ryzen 3990X workstation with a TITAN RTX.The Python bindings are generated withnanobind, which makes it easily
interoperable with most tensor frameworks (Numpy, PyTorch, JAX...)InstallingWith PyPI (recommended)pipinstallcholespyFrom sourcegitclone--recursivehttps://github.com/rgl-epfl/cholespy
pipinstall./cholespyDocumentationThere is only one class in the module, with two variants:CholeskySolverF, CholeskySolverD. The only difference is thatCholeskySolverFsolves the
system in single precision whileCholeskySolverDuses double precision. This
is mostly useful for solving on the GPU, as the CPU version relies on CHOLMOD,
which only supports double precision anyway.The most common tensor frameworks (PyTorch, NumPy, TensorFlow...) are supported
out of the box. You can pass them directly to the module without any need for
manual conversion.Since both variants have the same signature, we only detailCholeskySolverFbelow:cholespy.CholeskySolverF(n_rows, ii, jj, x, type)Parameters:n_rows- The number of rows in the (sparse) matrix.ii- The first array of indices in the sparse matrix representation. IftypeisCOO, then this is the array of row indices. If it isCSC(resp.CSR), then it is the array of column (resp. row) indices, such that row
(resp. column) indices for column (resp. row)kare stored injj[ii[k]:ii[k+1]]and the corresponding entries are inx[ii[k]:ii[k+1]].jj- The second array of indices in the sparse matrix representation. IftypeisCOO, then this is the array of column indices. If it isCSC(resp.CSR), then it is the array of row (resp. column) indices.x- The array of nonzero entries.type- The matrix representation type, of typeMatrixType. Available types
areMatrixType.COO,MatrixType.CSCandMatrixType.CSR.cholespy.CholeskySolverF.solve(b, x)Parametersb- Right-hand side of the equation to solve. Can be a vector or a matrix.
If it is a matrix, it must be of shape(n_rows, n_rhs). It must be on the
same device as the tensors passed to the solver constructor. If using CUDA
arrays, then the maximum supported value forn_rhsis128.x- Placeholder for the solution. It must be on the same device and have the
same shape asb.xandbmusthave the same dtype as the solver used, i.e.float32forCholeskySolverForfloat64forCholeskySolverD. Sincexis modified in
place, implicit type conversion is not supported.Example usagefromcholespyimportCholeskySolverF,MatrixTypeimporttorch# Identity matrixn_rows=20rows=torch.arange(n_rows,device='cuda')cols=torch.arange(n_rows,device='cuda')data=torch.ones(n_rows,device='cuda')solver=CholeskySolverF(n_rows,rows,cols,data,MatrixType.COO)b=torch.ones(n_rows,device='cuda')x=torch.zeros_like(b)solver.solve(b,x)# b = [1, ..., 1]References[1] Nicolet, B., Jacobson, A., & Jakob, W. (2021). Large steps in inverse rendering of geometry. ACM Transactions on Graphics (TOG), 40(6), 1-13.[2] Naumov, M. (2011). Parallel solution of sparse triangular linear systems in the preconditioned iterative methods on the GPU. NVIDIA Corp., Westford, MA, USA, Tech. Rep. NVR-2011, 1.