parallel programming application to matrix algebra in the spectral method for control systems analysis, synthesis and identification

The article describes the matrix algebra libraries based on the modern technologies of parallel programming for the Spectrum software, which can use a spectral method (in the spectral form of mathematical description) to analyse, synthesise and identify deterministic and stochastic dynamical systems. The developed matrix algebra libraries use the following technologies for the GPUs: OmniThreadLibrary, OpenMP, Intel Threading Building Blocks, Intel Cilk Plus for CPUs nVidia CUDA, OpenCL, and Microsoft Accelerated Massive Parallelism.

The developed libraries support matrices with real elements (single and double precision). The matrix dimensions are limited by 32-bit or 64-bit memory model and computer configuration. These libraries are general-purpose and can be used not only for the Spectrum software. They can also find application in the other projects where there is a need to perform operations with large matrices.

The article provides a comparative analysis of the libraries developed for various matrix operations (addition, subtraction, scalar multiplication, multiplication, powers of matrices, tensor multiplication, transpose, inverse matrix, finding a solution of the system of linear equations) through the numerical experiments using different CPU and GPU. The article contains sample programs and performance test results for matrix multiplication, which requires most of all computational resources in regard to the other operations.