Chameleon

Dense linear algebra

Written in C, Fortran interface, CMake Algorithms: GEMM, POTRF, GETRF, GEQRF, GESVD, ... Matrices forms: general, symmetric, triangular Precisions: s, d, c, z Runtime systems: PaRSEC, StarPU Distributed MPI and CUDA capabilities

Task-based Cholesky (POTRF) algorithm

Fmr

Fast Methods for Randomized numerical linear algebra

Randomized SVD with a fixed rank r

Cppdiodon

Parallel C++ library for Multivariate Data Analysis of large datasets

Written in C++, CMake Algorithms: Principal Component Analysis (PCA), Multidimensional Scaling (MDS), Correspondence Analysis (CoA) Matrices forms: general, symmetric Precisions: s, d Runtime systems: StarPU Distributed MPI and CUDA capabilities Reads matrices as .txt, .csv, .tar.gz/.bz2 and hdf5 files

MDS representation on the two first axis

PaStiX

Sparse linear algebra, supernodal direct solver

• Written in C, Fortran/Python/Julia interfaces, CMake
• Algorithms: POTRF, GETRF, TRSM, ...
• Matrices forms: general, symmetric, triangular
• Storage formats: CSC, CSR, and IJV
• Precisions: s, d, c, z
• Low-Rank compression
• Runtime systems: PaRSEC, StarPU
• Distributed MPI and CUDA capabilities
• Ordering/partitioning: Metis, Scotch

Symbolic factorization

qr_mumps

Sparse linear algebra, multifrontal direct solver

Written in Fortran 2008, C interface, CMake Algorithms: GEMM, POTRF, GETRF, GEQRF, ... Matrices forms: general, symmetric, triangular Precisions: s, d, c, z Runtime system: StarPU Multithreaded, CUDA capabilities Ordering/Partitioning: Colamd, Metis, Scotch

qr_mumps Direct Acyclic Graph

MaPHyS++

Sparse linear algebra, algebraic domain decomposition

• Written in C++, C and Fortran interfaces, CMake
• Use Direct solvers: MUMPS, PaStiX or qr_mumps
• Use Krylov subspace solver: fabulous
• Use Eigen solver: arpack (preconditioning)
• Matrices forms: general, symmetric
• Storage formats: IJV, armadillo, eigen3
• Precisions: s, d, c, z
• Distributed MPI, hybrid MPI/threads

Algebraic domain decomposition

fabulous

Sparse linear algebra, Block Krylov iterative solver

• Written in C++, C and Fortran interfaces, CMake
• This library currently implements multiple variants of Block Krylov iterative solvers:
  • BCG (Block Conjugate Gradient)
  • BF-BCG (Breadown Free BCG)
  • BGCR (Block Generalized Conjugate Residual)
  • BGMRES (Block General Minimum Residual)
  • IB-BGMRES (BGMRES with inexact breakdown)
  • BGMRES-DR (BGMRES with deflated restarting)
  • IB-BGMRES-DR (BGMRES with inexact breakdown and deflated restarting)
  • IB-BGCRO-DR (Block Generalized Conjugate Residual Method with Inner Orthogonalization with inexact breakdown and deflated restarting)

fabulous BGMRES-DR convergence

StarPU

Runtime system for heterogeneous multicore architectures

Written in C, Fortran interface, GNU autotools Supported on GNU/Linux, Mac OS X and Windows Scheduling: eager, work stealing, prio, dmda, ... Data structures vectors, dense matrices, CSR/BCSR/COO sparse matrices, specific, ... Enforces memory coherency over the machine Distributed MPI, CUDA, OpenCL, OpenMP interface Out of core capabilities, supports HDF5 for I/Os

A StarPU overview

Scotch

Graph partitioning and matrix ordering

• Written in C, Fortran interface, Makefile
• Provides algorithms to partition graph structures, as well as mesh structures defined as node-element bipartite graphs and which can also represent hypergraphs
• Can map any weighted source graph onto any weighted target graph
• Computes amalgamated block orderings of sparse matrices, for efficient solving using BLAS routines
• Offers extended support for adaptive graphs and meshes through the handling of disjoint edge arrays
• Running time is linear in the number of edges of the source graph, and logarithmic in the number of vertices of the target graph for mapping computations
• Distributed MPI (PT-Scotch)

Graph partitioning of a car