Intel® oneAPI Math Kernel Library Developer Reference - C
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 Aij 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”.
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.