Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 7/13/2023
Public

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Vector Arguments

Compressed sparse vectors. Let a be a vector stored in an array, and assume that the only non-zero elements of a are the following:

a(k1), a(k2), a(k3) . . . a(knz), 

where nz is the total number of non-zero elements in a.

In Sparse BLAS, this vector can be represented in compressed form by two arrays, x (values) and indx (indices). Each array has nz elements:

x(1)=a(k1), x(2)=a(k2), . . . x(nz)= a(knz), 
indx(1)=k1, indx(2)=k2, . . . indx(nz)= knz. 

Thus, a sparse vector is fully determined by the triple (nz, x, indx). If you pass a negative or zero value of nz to Sparse BLAS, the subroutines do not modify any arrays or variables.

Full-storage vectors. Sparse BLAS routines can also use a vector argument fully stored in a single array (a full-storage vector). If y is a full-storage vector, its elements must be stored contiguously: the first element in y(1), the second in y(2), and so on. This corresponds to an increment incy = 1 in BLAS Level 1. No increment value for full-storage vectors is passed as an argument to Sparse BLAS routines or functions.