Routines and Supported Operations
This section describes operations supported by the Sparse BLAS Level 2 and Level 3 routines. The following notations are used here:
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- Ais a sparse matrix;
- BandCare dense matrices;
- Dis a diagonal scaling matrix;
- xandyare dense vectors;
- alphaandbetaare scalars;
op(
is one of the
possible operations:
A
)- op(;A) =A
- op(- transpose ofA) =ATA;
- op(- conjugated transpose ofA) =AHA.
inv(op(
denotes the
inverse of
A
))op(
.
A
)The Sparse BLAS Level 2 and Level 3 routines support the following operations:
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- 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
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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 Sparse BLAS Level 2 and Level 3 routines do not support in-place operations.
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Complete list of all routines is given in the
“Sparse BLAS
Level 2 and Level 3 Routines”
.