Matrix Storage Schemes for BLAS Routines

Developer Reference for Intel® oneAPI Math Kernel Library for C

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Date 3/22/2024

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Matrix Storage Schemes for BLAS Routines

Matrix arguments of BLAS and CBLAS routines can use the following storage schemes:

Full storage: a matrix A is stored in a two-dimensional array a, with the matrix element A_ij stored in the array element a[i + j*lda] for column-major layout and a[j + i*lda] for row-major layout, where lda is the leading dimension for the array.
Packed storage scheme allows you to store symmetric, Hermitian, or triangular matrices more compactly. For column-major layout, the upper or lower triangle of the matrix is packed by columns in a one dimensional array. For row-major layout, the upper or lower triangle of the matrix is packed by rows in a one dimensional array.
Band storage: a band matrix is stored compactly in a two-dimensional array. For column-major layout, columns of the matrix are stored in the corresponding columns of the array, and diagonals of the matrix are stored in a specific row of the array. For row-major layout, rows of the matrix are stored in the corresponding rows of the array, and diagonals of the matrix are stored in a specific column of the array.

For more information on matrix storage schemes, see Matrix Arguments in the Appendix “Routine and Function Arguments”.

Row-Major and Column-Major Layout

The BLAS routines follow the Fortran convention of storing two-dimensional arrays using column-major layout. When calling BLAS routines from C, remember that they require arrays to be in column-major format, not the row-major format that is the convention for C. Unless otherwise specified, the psuedo-code examples for the BLAS routines illustrate matrices stored using column-major layout.

The CBLAS interface allows you to specify either column-major or row-major layout for BLAS Level 2 and Level 3 routines, by setting the layout parameter to CblasColMajor or CblasRowMajor.

Parent topic: BLAS Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

Matrix Storage Schemes for BLAS Routines

Row-Major and Column-Major Layout