Compressed storage of special matrices for C + + array applications

Matrix:

A matrix is a mathematical model that is often used in numerical programming, which consists of a number of m rows and N columns (M=n is called a phalanx). In programs written in advanced languages, a two-dimensional array is usually used to represent the matrix, which enables each element in the matrix to find a corresponding storage location in a two-dimensional array. However, some high-order matrices with the following characteristics are often found in the calculation of numerical analysis, that is, the matrix has many values of the same or 0-valued elements, in order to save storage space, they need to "compress storage", that is, do not save or save the same value of the same or 0-valued elements.

Operation: The matrix can be added, subtract, multiply and so on.

Storage compression Target:

Save storage space

How to compress:

0 Yuan does not store

Multiple values are the same

To compress stored objects:

Sparse matrices

Special matrices

Special matrices:

A matrix with a certain regularity in the distribution of the same or 0 elements is called a special matrix example: symmetric matrices, upper (lower) triangular matrices are special matrices

Special matrix compression Storage (with symmetric matrices as an example)

Symmetric matrices are n-order matrices satisfying the following conditions: aij= aji 1<= i,j<= N

k= 0 1 2 3 4 5 6 N (n+1)/2-1