Contents

# Routines and Supported Operations

This section describes operations supported by the
Intel® oneAPI Math Kernel Library
Sparse BLAS Level 2 and Level 3 routines. The following notations are used here:
• A
is a sparse matrix;
• B
and
C
are dense matrices;
• D
is a diagonal scaling matrix;
• x
and
y
are dense vectors;
• alpha
and
beta
are scalars;
op(
A
)
is one of the possible operations:
• op(
A
) =
A
;
• op(
A
) =
A
T
- transpose of
A
;
• op(
A
) =
A
H
- conjugated transpose of
A
.
inv(op(
A
))
denotes the inverse of
op(
A
)
.
The
Intel® oneAPI Math Kernel Library
Sparse BLAS Level 2 and Level 3 routines support the following operations:
• computing the vector product between a sparse matrix and a dense vector:
`y := alpha*op(A)*x + beta*y`
• solving a single triangular system:
`y := alpha*inv(op(A))*x`
• computing a product between sparse matrix and dense matrix:
`C := alpha*op(A)*B + beta*C`
• solving a sparse triangular system with multiple right-hand sides:
`C := alpha*inv(op(A))*B`
Intel® oneAPI Math Kernel Library
provides an additional set of the Sparse BLAS Level 2 routines with
simplified interfaces
. Each of these routines operates on a matrix of the fixed type. The following operations are supported:
• computing the vector product between a sparse matrix and a dense vector (for general and symmetric matrices):
`y := op(A)*x`
• solving a single triangular system (for triangular matrices):
`y := inv(op(A))*x`
Matrix type is indicated by the field <
mtype
> in the routine name (see section Naming Conventions in Sparse BLAS Level 2 and Level 3).
The routines with simplified interfaces support only four sparse matrix storage formats, specifically:
• CSR format in the 3-array variation accepted in the direct sparse solvers and in the CXML;
• diagonal format accepted in the CXML;
• coordinate format;
• BSR format in the 3-array variation.
Note that routines with both typical (conventional) and simplified interfaces use the same computational kernels that work with certain internal data structures.
The
Intel® oneAPI Math Kernel Library
Sparse BLAS Level 2 and Level 3 routines do not support in-place operations.
Complete list of all routines is given in the
“Sparse BLAS Level 2 and Level 3 Routines”
.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.