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# What is rocALUTION?

rocALUTION is a sparse linear algebra library with focus on exploring fine-grained parallelism on top of the AMD ROCm runtime and toolchains, targeting modern processors and accelerators including multi and many-core CPU and GPU platforms. The main goal of this package is to provide a portable library for iterative sparse methods on state of the art hardware. rocALUTION can be seen as the middleware between different parallel backends and application-specific packages. Based on C++ and HIP, it provides a portable, generic and flexible design that allows seamless integration with other scientific software packages.

The major features and characteristics of the rocALUTION library are:

- Various backends

    - Host - fallback backend, designed for CPUs

    - GPU/HIP - accelerator backend, designed for HIP capable AMD GPUs

    - OpenMP - designed for multi-core CPUs

    - MPI - designed for multi-node and multi-GPU configurations

- Easy to use

    The syntax and structure of the library provide easy learning curves. With the help of examples, anyone can try out the library. No knowledge in HIP, OpenMP, or MPI programming is required.

- No special hardware requirements

    There are no hardware requirements to install and run rocALUTION. All you need is a GPU device and HIP.

- Variety of iterative solvers

    - Fixed-Point iteration - Jacobi, Gauss-Seidel, Symmetric-Gauss Seidel, SOR and SSOR

    - Krylov subspace methods - CR, CG, BiCGStab, BiCGStab(l), GMRES, IDR, QMRCGSTAB, Flexible CG/GMRES

    - Mixed-precision defect-correction scheme

    - Chebyshev iteration

    - Multiple MultiGrid schemes, geometric and algebraic

- Various preconditioners

    - Matrix splitting - Jacobi, (Multi-colored) Gauss-Seidel, Symmetric Gauss-Seidel, SOR, SSOR

    - Factorization - ILU(0), ILU(p) (based on levels), ILU(p,q) (power(q)-pattern method), Multi-Elimination ILU (nested/recursive), ILUT (based on threshold) and IC(0)

    - Approximate Inverse - Chebyshev matrix-valued polynomial, SPAI, FSAI and TNS

    - Diagonal-based preconditioner for Saddle-point problems

    - Block-type of sub-preconditioners/solvers

    - Additive Schwarz and Restricted Additive Schwarz

    - Variable type preconditioners

- Generic and robust design

    rocALUTION is based on a generic and robust design allowing expansion in the direction of new solvers and preconditioners and support for various hardware types. Furthermore, the design of the library allows the use of all solvers as preconditioners in other solvers. For example you can easily define a CG solver with a Multi-Elimination preconditioner, where the last-block is preconditioned with another Chebyshev iteration method which is preconditioned with a multi-colored Symmetric Gauss-Seidel scheme.

- Portable code and results

    All code based on rocALUTION is portable and independent of HIP or OpenMP. The code will compile and run everywhere. All solvers and preconditioners are based on a single source code, which delivers portable results across all supported backends (variations are possible due to different rounding modes on the hardware). The only difference which you can see for a hardware change is the performance variation.

- Support for several sparse matrix formats

    Compressed Sparse Row (CSR), Modified Compressed Sparse Row (MCSR), Dense (DENSE), Coordinate (COO), ELL, Diagonal (DIA), Hybrid format of ELL and COO (HYB).

The code is open-source under MIT license, see License and hosted on the GitHub rocALUTION page.