Sparse BLAS CSC Matrix Storage Format

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

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Sparse BLAS CSC Matrix Storage Format

The Intel® oneAPI Math Kernel Library (oneMKL) Sparse BLAS compressed sparse column (CSC) format is specified by four arrays:

values
columns
pointerB
pointerE

In addition, each sparse matrix has an associated variable, indexing , which specifies whether the matrix indices are 0-based ( indexing=0 ) or 1-based ( indexing=1 ). The following table describes the arrays in terms of the values, row, and column positions of the non-zero elements in a sparse matrix A :

values

A real or complex array that contains the non-zero elements of A . Values of the non-zero elements of A are mapped into the values array using the column-major layout.

rows

Element i of the integer array rows is the number of the row in A that contains the i -th value in the values array.

pointerB

Element j of this integer array gives the index of the element in the values and rows arrays that is the first non-zero element in column j of A . Note that the 1-based position of this element in the arrays is equal to pointerB[j]-indexing+1 .

pointerE

An integer array that contains column indices, such that pointerE[j]-1 is the index of the element in the values and rows arrays that is the last non-zero element in column j of A . Note that the 1-based position of this element in the arrays is equal to pointerE[j]-indexing .

The length of the values and columns arrays is equal to the number of non-zero elements in A . The length of the pointerB and pointerE arrays is equal to the number of columns in A .

The CSC format is similar to the CSR format, but the indices are compressed along the columns instead of the rows. Storing a matrix in CSC format and storing the transpose of that same matrix in CSR format will result in identical arrays.

NOTE:

Note that the Intel® oneAPI Math Kernel Library (oneMKL) Sparse BLAS routines support the CSC format both with one-based indexing and zero-based indexing.

For example, consider matrix B :

It can be represented in the CSC format as:

Storage Arrays for a Matrix in CSC Format

one-based indexing
`values`	=	(1	-2	-4	-1	5	8	4	2	-3	6	7	4	-5)
`rows`	=	(1	2	4	1	2	5	3	4	1	3	4	3
`pointerB`	=	(1	4	7	9
`pointerE`	=	(4	7	9	12
zero-based indexing
`values`	=	(1	-2	-4	-1	5	8	4	2	-3	6	7	4	-5)
`rows`	=	(0	1	3	0	1	4	2	3	0	2	3	2
`pointerB`	=	(0	3	6	8
`pointerE`	=	(3	6	8	11

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Sparse BLAS CSC Matrix Storage Format