1. A survey of Exascale Linear Algebra Libraries for Data Assimilation
Giuliano Laccetti, Marco Lapegna
University of Naples Federico II
ABSTRACT: Over 70% of real world applications are based on Linear Algebra operations on vectors and matrices residing in core modules and performing time consuming computations. For a such reason several Linear Algebra Libraries are developed since the ’70s and still new and large projects are targeting this scientific area on new HPC systems. The advantages were manifold: the availability of high quality Linear Algebra librarieson exascale systems and software environments allow computational scientists to focus the attention on their own application, without taking into account issues related to the underlying computing environments. On the other hand, since the above mentioned applications mainly spent their time doing linear algebra operations, application developers could obtain maximal performance and accuracy by using this standard library. Additionally, the widespread use of Linear Algebra libraries made it easy to exchange/port high-level libraries, again offering optimal performance. Data Assimilation problems is a typical case in this sense: it is based on several Linear Algebra kernels such as Lanczos iterative algorithms, preconditioning, covariance computation and related factorizations, so that they can take advantage from the availability of recent and ongoing projects like MAGMA, NLAFET and high level computing environments like PETSc. The high modularity of these software tools make possibile the solution of Data Assimilation problems on very different platforms as well as hybrid architectures.
Data Assimilation Problems
Newton solvers for Non Linear Problems
(Jacobian/Adjoint Free Newton Krylov solvers)
Lanczos iterative algorithms
Preconditioning
(spectral / Ritz pairs)
covariance
computation
ScaLAPACK
PBLAS
CUDA /
Xeon PHI
BLACS/
MPI
Pthreads / OpenMP
LAPACK
BLAS
for specific platform
(Intel MKL, AMD ACML)
parallel
distributed
shared
sequential
low level
tools
CUDA
NOT YET DEFINED
ScaLAPACK
PETSc
NLAFET
MAGMA
new linear algebra software targeted on new heterogeneous/hybrid "Multicore+GPU" architectures.
Supported platforms
Intel and AMD multicore CPUs
NVIDIA GPU and Intel Xeon Phi accelerators
Driver routines
main linear algebra factorization
Least Squares problems
Eigenvalues and Singular Value Decomposition
Interfaces for LAPACK and BLAS
classical linear algebra software, still a reference point for distributed memory architectures.
Based on
BLAS/ PBLAS/LAPACK for the computation
BLACS/MPI for the communications
Driver routines
main linear algebra factorization
Least Squares problems
Eigenvalues and Singular Value Decomposition
MAGMA can be integrated to target GPU and multicore devices (to be verify)
high level, well known environment for data structures and routine for parallel solution of applications based on PDE
Based on
BLAS and LAPACK for the computation
MPI for the communications
Driver routines
main linear algebra factorization
Newton based nonlinear systems
preconditioners
sparse and dense matrices, several data structure formats
ongoing UE-funded project for linear algebra software on exascale HPC heterogeneous systems
Based on
To be defined
Driver routines
dense linear system and eigenvalues
direct solution of sparselinear systems
communication optimal algorithms for iterative methods