SPD test matrices for sTiles development and benchmarking. INLA precision matrices, structural and thermal FEM problems, circuits, and related application areas.
Prepared by Esmail Abdul Fattah
Each matrix is stored in MatrixMarket coordinate format (.mtx) as the
lower triangle of a symmetric matrix. The dimension and number of nonzeros are taken
directly from the file header, and the reported density is computed with respect to the
stored lower triangle. Select a matrix name or its thumbnail to open the corresponding
page, including the full sparsity pattern and download.
| # | Name | Group | Application | Dimension | NNZ (lower △) | Density | Sparsity |
|---|
The benchmark suite comprises 88 sparse symmetric positive definite matrices drawn from two complementary sources. Of these, 62 are obtained from the SuiteSparse Matrix Collection (Davis and Hu, 2011) and span a broad range of application domains, including structural engineering, thermal and thermomechanical analysis, circuit simulation, computational fluid dynamics, model order reduction, and mesh and graph problems.
The remaining 28 matrices are INLA precision matrices arising in Bayesian latent Gaussian models, generated with the integrated nested Laplace approximation (INLA) framework.
Matrices that are not symmetric positive definite in their original form are modified to enforce positive definiteness, so that each admits a Cholesky factorization.
The suite is assembled to cover a wide variety of sparsity structures across distinct application areas, so that the solver is evaluated on a heterogeneous set of problems rather than on a single problem class.
We acknowledge the SuiteSparse Matrix Collection and its maintainers for making these problems publicly available. Reference: T. A. Davis and Y. Hu, “The University of Florida Sparse Matrix Collection,” ACM Transactions on Mathematical Software, vol. 38, no. 1, 2011.