Data Storage

Full-Storage Format for Vectors

All elements in a vector are stored.

Sparse Matrix Storage Format

The compressed sparse row (CSR) format is specified by the following arrays: value, column, and pointerB, For the conjugate gradient (CG) method, only the upper or lower triangular part of a matrix is stored.

as described in Table 1.

**Table 1** Storage arrays of sparse matrix A in CSR format
Array	Description
value	Non-zero elements in matrix A, stored in row-major order The array length is equal to the number of non-zero elements in matrix A.
column	Number of the column in matrix A that contains the i-th value in the value array The array length is equal to the number of non-zero elements in matrix A.
pointerB	For zero-based indexing, pointerB(j) indicates the index of the element in the value array that is the first non-zero element in the jth row of matrix A. Array length = Number of rows of matrix A + 1

Matrix A $\text{[math]}$ can be represented in CSR format as in Table 2.

When the CG method is used, only the upper triangular matrix needs to be stored. See Table 3.

**Table 2** Matrix A in CSR format
Matrix	Indexing Method	CSR Format
$\text{[math]}$	Zero-based indexing	value = [2, -3, 7, -3, 1, -6, 1, -4, 5, 7, -6, 5] column = [0, 1, 3, 0, 2, 3, 1, 2, 3, 0, 1, 2] pointerB = [0, 3, 6, 9, 12]

**Table 3** Upper triangular part of symmetric matrix A in CSR format
Matrix	Indexing Method	CSR Format
$\text{[math]}$	Zero-based indexing	value = [2, -3, 7, 1, -6, -4, 5] column = [0, 1, 3, 2, 3, 2, 3] pointerB = [0, 3, 5, 7, 7]

Parent topic: Data Types and Data Storage