Parallel Matricization for n-D Array Operations

Success of today's computing depends on finding and operating into data flood with very high number of dimensions. Traditional computing technique for multidimensional data is about half century old and shows worst performance when data dimension is very high. Thus efficient representation and operation on it is cramming needs for data scientist. Two dimensional/row-column representation is facile for imagination and visualization. This paper describes an implementation scheme for higher dimensional array with row-column abstraction on parallel environment like GPU. The representation is just fitting odd dimensions along row-direction and even dimensions along column direction which form groups of 2-D block. Each 2-D block of size blockIdx.xxthreadIdx.x is independent of each other. Performance of proposed representation is measured with matrix-matrix addition and multiplication operation. Experimental results show better performance over other representation scheme like Extended Karnaugh Map Representation (EKMR). The scheme can be used for implementing very higher dimensional array in both general purpose and scientific computing on GPU.