Sparse direct solvers are a fundamental tool in computational analysis, providing a very general method for obtaining high-quality results to almost any problem. For the case of symmetric, positive-definite matrices, CHOLMOD is a high performance library for sparse Cholesky factorization. CHOLMOD is part of the SuiteSparse linear algebra package authored by Prof. Tim Davis of Texas A&M University. SuiteSparse and CHOLMOD have long been used throughout industry and academia – most particularly as linear system solvers invoked by the Matlab 'backslash' operator (as in x = A\b).
CHOLMOD has supported GPU acceleration since 2012 with version 4.0.0 . In SuiteSparse-4.3.1 performance has been further improved, providing speedups of 3x or greater vs. the CPU for the sparse factorization operation.
The figure below shows the performance achieved in the sparse factorization operation when solving the twelve largest matrices available from the Florida Sparse Matrix Collection. Maximum speedup vs. CPU is 3.5x. Average speedup is 2.4x. Larger matrices, with larger fill ratios tend to show better speedups. Testing of the 100 largest symmetric positive-definite matrices from the Florida collection show beneficial GPU acceleration for any factorization which takes longer than 0.28 seconds.
Testing was performed using:
CHOLMOD, along with the rest of SuiteSparse, is available from www.suitesparse.com.