The Compression Storage Research for Uniform Block Diagonal Matrix

摘要

Matrix is a mathematical object. We are not interested in data itself in the data structure, but how to store the elements in the matrix, so that various operations can be performed effectively. We often use a two-dimensional array to store the elements in the matrix sequentially. If adopt this method of storage, when there is large number of zero elements and have regular distribution a particular element will consume large amounts of storage unit. For high order matrix, the storage method is not only waste storage unit, but also takes a lot of time for invalid computation, it is obviously not desirable. In order to save the storage space, we need to compress storage for such matrix. The main purpose of the compressed storage is to make more of the same nonzero elements share the same storage unit according to the distribution of matrix element, while the zero elements don't allocate storage space. In this paper, we studied the single vector compressed storage and the multi vectors compressed storage of the uniform block diagonal matrix, and obtained the corresponding storage address mapping function, so as to help the scientific research worker.