Routines and Supported Operations

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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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 withsimplified 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).

NOTE:

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”.

Parent topic: Sparse BLAS Level 2 and Level 3 Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

Routines and Supported Operations