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Sparse Storage Formats

Compressed Sparse Row (CSR)

There are a variety of matrix storage formats available for representing the sparse matrix. One of the most popular is the CSR format that is represented by three arrays: row_ptr, col_ind and val, and the index parameter.

CSR Matrix Elements	Description
num_rows	Number of rows in the sparse matrix.
num_cols	Number of columns in the sparse matrix.
index	Parameter that is used to specify whether the matrix has zero or one-based indexing.
val	An array that contains the non-zero elements of the sparse matrix stored row by row.
col_ind	An integer array of column indices for non-zero elements stored in the val array, such that col_ind[i] is the column number (using zero- or one-based indexing) of the element of the sparse matrix stored in val[i].
row_ptr	An integer array of size equal to num_rows + 1. Element j of this integer array gives the position of the element in the val array that is first non-zero element in a row j of A. Note that this position is equal to row_ptr[j] - index. The last element of the row_ptr array (row_ptr[num_rows]) stores the sum of, number of nonzero elements and index*(number of nonzero elements + index*).

Examples of CSR format

A sparse matrix can be represented in a CSR format in the following ways:

Case 1:

Assuming zero-based indexing and a real square matrix.

num_rows	3
num_cols	3
index	0
row_ptr	0	2	4	5
col_ind	0	2	1	2	0
val	1.0	2.0	-1.0	4.0	3.0

Case 2:

Assuming one-based indexing and real rectangular matrix with an empty row.

num_rows	4
num_cols	5
index	1
row_ptr	1	3	6	6	8
col_ind	1	3	2	3	5	1	4
val	1.0	2.0	-1.0	4.0	1.0	3.0	1.0

Supported Types LAPACK Routines