Libraries
SLATE
Next-generation software library for dense linear algebra operations designed to replace ScaLAPACK for modern HPC systems.
Dense Linear AlgebraEigenvalue ProblemsHigh-Performance ComputingHermitian/SymmetricQuasi-Hermitian/SymmetricGPU AccelerationDistributed Memory
Key Features
- Full coverage of LAPACK and ScaLAPACK functionality
- Parallel BLAS operations with GPU acceleration
- Dense linear system solvers
- Least squares solvers
- Singular value and eigenvalue solvers
- Support for distributed-memory systems
- Built on MPI and OpenMP standards
- Integration with vendor libraries (MKL, cuBLAS, rocBLAS, etc.)
- Modern C++ design with task-based parallelism
- Optimized for both GPU-accelerated and multi-core systems
Language
C++
License
BSD-3
ChASE
A modern C++ implementation of the Chebyshev Accelerated Subspace Eigenvalue Solver for computing selected eigenpairs of large Hermitian and quasi-Hermitian matrices.
Dense Linear AlgebraEigenvalue ProblemsHigh-Performance ComputingHermitian/SymmetricQuasi-Hermitian/SymmetricGPU AccelerationSubspace IterationDistributed Memory
Key Features
- Optimized for dense Hermitian eigenproblems
- Optimized for dense quasi-Hermitian eigenproblems (Bethe–Salpeter equations)
- Highly efficient parallel implementation
- GPU acceleration support
- Subspace iteration
- Excellent scalability for large matrices
- Distributed memory support
- Multi-GPU support
Language
C++
License
BSD-3
SLEPc
A PETSc-based toolkit for the (partial) solution of various types of eigenvalue problems, focusing on large-scale sparse or matrix-free problems with iterative algorithms.
Sparse Linear AlgebraEigenvalue ProblemsSingular Value ProblemsHigh-Performance ComputingHermitian/SymmetricNon-Hermitian/SymmetricQuasi-Hermitian/SymmetricGPU AccelerationDistributed Memory
Key Features
- Covers both standard and generalized eigenproblems, either Hermitian or non-Hermitian
- Support for structured eigenproblems (Bethe–Salpeter and other)
- Easy selection of available solvers: Krylov-Schur, Jacobi-Davidson, LOBPCG, contour integral, etc.
- Built-in support for shift-and-invert spectral transformation, as well as polynomial filters
- Also (partial) solution of different singular value problems: SVD, GSVD, HSVD
- Polynomial eigenvalue problems (either quadratic or higher degree) with or without (implicit) linearization
- Support for general nonlinear eigenvalue problems involving almost any nonlinear function (including rational, square root, exponential)
- Basic functionality for computing the action of a matrix function on a vector
- Tight integration with PETSc, leveraging all linear system solvers and basic infrastructure
- MPI and GPU parallelism
- Real or complex arithmetic, with single, double, or quad precision
Language
C
License
BSD-2
DLA-Future
DLA-Future
A distributed linear algebra library implemented using C++ std::execution. It provides an asynchronous C++ interface, a synchronous C interface, and a synchronous ScaLAPACK-like C interface.
Dense Linear AlgebraEigenvalue ProblemsHigh-Performance ComputingHermitian/SymmetricGPU AccelerationDistributed Memory
Key Features
- Dense Symmetric/Hermitian eigenproblems
- Dense Symmetric/Hermitian generalized eigenproblems
- Cholesky factorization and inverse of positive definite matrices
- Highly efficient parallel implementation
- Integration with vendor libraries (MKL, cuBLAS, rocBLAS, etc.)
- Modern C++ design with C++ standard task-based parallelism (std::execution)
- Multi-core systems support
- NVIDIA GPU acceleration support
- AMD GPU acceleration support
- Multi-node and multi-GPU support through MPI
- Real or complex arithmetic, with single or double precision
- Installable with Spack
Language
C++
License
BSD-3
DLA-Future-Fortran
DLA-Future-Fortran
Fortran wrappers for DLA Future.
Dense Linear AlgebraEigenvalue ProblemsHigh-Performance ComputingHermitian/SymmetricGPU AccelerationDistributed Memory
Key Features
- Dense Symmetric/Hermitian eigenproblems
- Dense Symmetric/Hermitian generalized eigenproblems
- Cholesky factorization and inverse of positive definite matrices
- Highly efficient parallel implementation
- Integration with vendor libraries (MKL, cuBLAS, rocBLAS, etc.)
- Modern C++ design with C++ standard task-based parallelism (std::execution)
- Multi-core systems support
- NVIDIA GPU acceleration support
- AMD GPU acceleration support
- Multi-node and multi-GPU support through MPI
- Real or complex arithmetic, with single or double precision
- Installable with Spack
Language
Fortran
License
BSD-3
COSMA
COSMA is a parallel, high-performance, GPU-accelerated, communication-optimal matrix-matrix multiplication.
Dense Linear AlgebraHigh-Performance ComputingGPU AccelerationDistributed Memory
Key Features
- Dense matrix-matrix multiplication
- Communication-optimal implementation
- Highly efficient parallel implementation
- Integration with vendor libraries (MKL, cuBLAS, rocBLAS, etc.)
- Multi-core systems support
- NVIDIA GPU acceleration support
- AMD GPU acceleration support
- Multi-node and multi-GPU support through MPI
- Real or complex arithmetic, with single or double precision
- Installable with Spack
Language
C++
License
BSD-3
ELPA
Highly efficient and highly scalable direct eigensolvers for symmetric (hermitian) matrices.
Dense Linear AlgebraEigenvalue ProblemsHigh-Performance ComputingHermitian/SymmetricQuasi-Hermitian/SymmetricGPU AccelerationDistributed Memory
Key Features
- Dense Hermitian standard and generalized eigenproblems
- Dense quasi-Hermitian eigenproblems (skew-symmetric and related Bethe–Salpeter)
- 1- and 2-stage direct eigensolver algorithms. 2-stage solver is especially efficient when only a part of the eigenspectrum is needed
- Distributed dense matrix-matrix multiplication
- Support for NVIDIA, AMD, and Intel GPUs
- Demonstrated pre-exascale runs: full eigenspectrum of 3,200,000*3,200,000 real double matrix on LUMI
Language
Fortran
License
LGPL-3
NTPoly
NTPoly is a massively parallel library for computing the functions of sparse, symmetric matrices based on polynomial expansions.
High-Performance ComputingDistributed MemorySparse Linear AlgebraHermitian/Symmetric
Key Features
- Sparse matrix-matrix multiplication
- Highly efficient parallel implementation
- Multi-core systems support
- Real or complex arithmetic
- General polynomials (standard, chebyshev, hermite)
- Transcendental functions (trigonometric, exponential, logarithm)
- Matrix roots and inverses
- Density matrix purification, sign function, polar decomposition
Language
Fortran, C++, Python
License
MIT
Chameleon
Dense linear algebra subroutines for heterogeneous and distributed architectures
Dense Linear AlgebraHigh-Performance ComputingGPU AccelerationDistributed MemoryHermitian/Symmetric
Key Features
- Dense matrix mutiplication (GEMM, SYMM, TRMM)
- Dense matrix factorization and linear system solve (GETR, POTR, GEQR, GELQ, GELS)
- Integration with vendor libraries (Blis/Flame, OpenBLAS, MKL, cuBLAS, rocBLAS, etc.)
- Multi-core systems support
- NVIDIA GPU acceleration support
- AMD GPU acceleration support
- Multi-node and multi-GPU support through MPI
- Real or complex arithmetic, with single or double precision
- Installable with CMake, GNU Guix, Homebrew, Spack
Language
C
License
CeCILL-C
Library Category Distribution
Overview of library categorizations.
Dense Linear Algebra
7
Libraries
Sparse Linear Algebra
2
Libraries
Eigenvalue Problems
6
Libraries
Singular Value Problems
1
Library
High-Performance Computing
9
Libraries
Hermitian/Symmetric
8
Libraries
Non-Hermitian/Symmetric
1
Library
Quasi-Hermitian/Symmetric
4
Libraries
GPU Acceleration
8
Libraries
Distributed Memory
9
Libraries
Subspace Iteration
1
Library