Calculating (A - B(D^-1)B^T )^-1 with CUDA

Question

What might be the most efficient way of calculating the following expression using CUDA C ?

(A - B(D^-1)B^T )^-1

where D is a very large symmetric matrix and A is a small symmetric matrix, which makes B and B^T medium sized rectangular non-symmetric matrices. Of course (^-1) and (^T) are the inverse and transpose operations, respectively.

Answer 1

If you are available to "low" level programming, then matrix inversion could be performed by CULA or MAGMA libraries.

CULA Dense contains single (real or complex) precision of System Solve, Linear Least Squares Solve, and Constrained Linear Least Squares Solve. CULA Sparse is a collection of iterative solvers for sparse matrices. Magma contains dgetrf and dgetri to calculate inverses of square double precision matrices.

For matrix multiplications, including transpositions, you could use cuBLAS routines.

If you prefer "higher" level programming, then ArrayFire enables you to perform matrix multiplications, inversions, transposes, solution of linear systems, and elementwise operations with a more naturale mathematical syntax. Also, Matlab has a GPU Computing Support for NVIDIA CUDA-Enabled GPUs.