Sparse BLAS Functionality

Developer Reference for Intel® oneAPI Math Kernel Library for C

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Date 4/28/2026

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Sparse BLAS Functionality

Sparse BLAS Level 1

In the following table for functionality, \(sm\) = \(\text{sparse matrix}\), \(dm\) = \(\text{dense matrix}\), \(sv\) = \(\text{sparse vector}\), \(dv\) = \(\text{dense vector}\), \(sc\) = \(\text{scalar}\).

In the following table for operations, \(\text{dense vectors}\) = \(x\), \(y\), \(\text{sparse vectors}\) = \(w\), \(v\), \(\text{dense matrices}\) = \(X\), \(Y\), \(\text{sparse matrices}\) = \(A\), \(B\), \(C\), and \(\text{scalars}\) = \(\alpha\), \(\beta\), \(d\).

Functionality	Operations	CPU	OpenMP Offload Intel GPU
Sparse Vector - Dense Vector addition (AXPY)	`\(y \leftarrow \alpha \cdot w + y\)`	Yes	No
Sparse Vector - Sparse Vector Dot product (SPDOT) (sv.sv -> sc)	`\(d \leftarrow dot(w,v)\)`	N/A	N/A
	with `\(dot(w,v) = \sum_{i}(w_{i} \cdot v_{i})\)`	No	No
	with `\(dot(w,v) = \sum_{i}(conj(w_{i}) \cdot v_{i})\)`	No	No
Sparse Vector - Dense Vector Dot product (SPDOT) (sv.dv -> sc)	`\(d \leftarrow dot(w,x)\)`	N/A	N/A
	with `\(dot(w,v) = \sum_{i}(w_{i} \cdot v_{i})\)`	Yes	No
	with `\(dot(w,v) = \sum(conj(w_{i}) \cdot v_{i} )\)`	Yes	No
Dense Vector - Sparse Vector Conversion (sv <-> dv)	—	N/A	N/A
	`\(x = scatter(w)\)`	Yes	No
	`\(w = gather(x,windx)\)`	Yes	No

Sparse BLAS Level 2

Functionality	Operations	CPU	OpenMP Offload Intel GPU
General Matrix-Vector multiplication (GEMV) (sm*dv->dv)	`\(y \leftarrow \beta\cdot y + \alpha \cdot op(A)\cdot x\)`	N/A	N/A
	with `\(op(A) = A\)`	Yes	No
	with `\(op(A) = A^{T}\)`	Yes	No
	with `\(op(A) = A^{H}\)`	Yes	No
Symmetric Matrix-Vector multiplication (SYMV) (sm*dv->dv)	`\(y \leftarrow \beta\cdot y + \alpha \cdot op(A)\cdot x\)`	N/A	N/A
	with `\(op(A) = A\)`	Yes	No
	with `\(op(A) = A^{T}\)`	Yes	No
	with `\(op(A) = A^{H}\)`	Yes	No
Triangular Matrix-Vector multiplication (TRMV) (sm*dv->dv)	`\(y \leftarrow \beta\cdot y + \alpha \cdot op(A)\cdot x\)`	N/A	N/A
	with `\(op(A) = A\)`	Yes	No
	with `\(op(A) = A^{T}\)`	Yes	No
	with `\(op(A) = A^{H}\)`	Yes	No
General Matrix-Vector mult with dot product (GEMVDOT) (sm*dv -> dv, dv.dv->sc)	`\(y \leftarrow \beta\cdot y + \alpha\cdot op(A)\cdot x\)`, `\(d = dot(x,y)\)`	N/A	N/A
	with `\(op(A) = A\)`	Yes	No
	with `\(op(A) = A^{T}\)`	Yes	No
	with `\(op(A) = A^{H}\)`	Yes	No
Triangular Solve (TRSV) (inv(sm)*dv -> dv)	solve for `\(y\)`: `\(op(A)\cdot y = \alpha\cdot x\)`	N/A	N/A
	with `\(op(A) = A\)`	Yes	No
	with `\(op(A) = A^{T}\)`	Yes	No
	with `\(op(A) = A^{H}\)`	Yes	No

Sparse BLAS Level 3

Functionality	Operations	CPU	OpenMP Offload Intel GPU
General Sparse Matrix - Dense Matrix Multiplication (GEMM) (sm*dm->dm)	`\(Y \leftarrow \alpha\cdot op(A)\cdot op(X) + \beta\cdot Y\)`	N/A	N/A
	with `\(op(A) = A\)`, `\(op(X) = X\)`	Yes	No
	with `\(op(A) = A^{T}\)` , `\(op(X) = X\)`	Yes	No
	with `\(op(A) = A^{H}\)` , `\(op(X) = X\)`	Yes	No
	with `\(op(A) = A\)`, `\(op(X) = X^{T}\)`	No	No
	with `\(op(A) = A^{T}\)` , `\(op(X) = X^{T}\)`	No	No
	with `\(op(A) = A^{H}\)`, `\(op(X) = X^{T}\)`	No	No
	with `\(op(A) = A\)`, `\(op(X) = X^{H}\)`	No	No
	with `\(op(A) = A^{T}\)` , `\(op(X) = X^{H}\)`	No	No
	with `\(op(A) = A^{H}\)` , `\(op(X) = X^{H}\)`	No	No
General Dense Matrix - Sparse Matrix Multiplication (GEMM) (dm*sm->dm)	`\(Y \leftarrow \alpha\cdot op(X)\cdot op(A) + \beta\cdot Y\)`	N/A	N/A
	with `\(op(A) = A\)`, `\(op(X) = X\)`	No	No
	with `\(op(A) = A^{T}\)` , `\(op(X) = X\)`	No	No
	with `\(op(A) = A^{H}\)` , `\(op(X) = X\)`	No	No
	with `\(op(A) = A\)`, `\(op(X) = X^{T}\)`	No	No
	with `\(op(A) = A^{T}\)` , `\(op(X) = X^{T}\)`	No	No
	with `\(op(A) = A^{H}\)`, `\(op(X) = X^{T}\)`	No	No
	with `\(op(A) = A\)`, `\(op(X) = X^{H}\)`	No	No
	with `\(op(A) = A^{T}\)`, `\(op(X) = X^{H}\)`	No	No
	with `\(op(A) = A^{H}\)`, `\(op(X) = X^{H}\)`	No	No
General Sparse Matrix - Sparse Matrix Multiplication (GEMM) (sm*sm->sm)	`\(C \leftarrow \alpha\cdot op(A)\cdot op(B) + \beta\cdot C\)`	N/A	N/A
	with `\(op(A)=A\)`, `\(op(B)=B\)`	Yes	No
	with `\(op(A)=A^{T}\)`, `\(op(B)=B\)`	Yes	No
	with `\(op(A)=A^{H}\)`, `\(op(B)=B\)`	Yes	No
	with `\(op(A)=A\)`, `\(op(B)=B^{T}\)`	Yes	No
	with `\(op(A)=A^{T}\)`, `\(op(B)=B^{T}\)`	Yes	No
	with `\(op(A)=A^{H}\)`, `\(op(B)=B^{T}\)`	Yes	No
	with `\(op(A)=A\)`, `\(op(B)=B^{H}\)`	Yes	No
	with `\(op(A)=A^{T}\)`, `\(op(B)=B^{H}\)`	Yes	No
	with `\(op(A)=A^{H}\)`, `\(op(B)=B^{H}\)`	Yes	No
General Sparse Matrix - Sparse Matrix Multiplication (GEMM) (sm*sm->dm)	`\(Y \leftarrow \alpha\cdot op(A)\cdot op(B) + \beta\cdot Y\)`	N/A	N/A
	with `\(op(A)=A\)`, `\(op(B)=B\)`	Yes	No
	with `\(op(A)=A^{T}\)`, `\(op(B)=B\)`	Yes	No
	with `\(op(A)=A^{H}\)`, `\(op(B)=B\)`	Yes	No
	with `\(op(A)=A\)`, `\(op(B)=B^{T}\)`	No	No
	with `\(op(A)=A^{T}\)`, `\(op(B)=B^{T}\)`	No	No
	with `\(op(A)=A^{H}\)`, `\(op(B)=B^{T}\)`	No	No
	with `\(op(A)=A\)`, `\(op(B)=B^{H}\)`	No	No
	with `\(op(A)=A^{T}\)`, `\(op(B)=B^{H}\)`	No	No
	with `\(op(A)=A^{H}\)`, `\(op(B)=B^{H}\)`	No	No
Symmetric Rank-K update (SYRK) (sm*sm->sm)	`\(C \leftarrow op(A)\cdot op(A)^{H}\)`	N/A	N/A
	with `\(op(A)=A\)`	Yes	No
	with `\(op(A)=A^{T}\)`	Yes	No
	with `\(op(A)=A^{H}\)`	Yes	No
Symmetric Rank-K update (SYRK) (sm*sm->dm)	`\(Y \leftarrow op(A)\cdot op(A)^H\)`	N/A	N/A
	with `\(op(A)=A\)`	Yes	No
	with `\(op(A)=A^{T}\)`	Yes	No
	with `\(op(A)=A^{H}\)`	Yes	No
Symmetric Triple Product (SYPR) (op(sm)smsm -> sm)	`\(C \leftarrow op(A)\cdot B\cdot op(A)^{H}\)`	N/A	N/A
	with `\(op(A)=A\)`	Yes	No
	with `\(op(A)=A^{T}\)`	Yes	No
	with `\(op(A)=A^{H}\)`	Yes	No
Triangular Solve (TRSM) (inv(sm)*dm -> dm)	solve for `\(Y\)`: `\(op(A)\cdot Y = \alpha\cdot X\)`	N/A	N/A
	with `\(op(A)=A\)`	Yes	No
	with `\(op(A)=A^{T}\)`	Yes	No
	with `\(op(A)=A^{H}\)`	Yes	No

Other Sparse BLAS Operations

Functionality	Operations	CPU	OpenMP Offload Intel GPU
Symmetric Gauss-Seidel Preconditioner (SYMGS) (update `\(A\cdot x=b\)`, `\(A=L+D+U\)`)	`\(x^{0} \leftarrow \alpha\cdot x\)`; `\((L+D)\cdot x^{1}=b-U\cdot x^{0}\)`; `\((U+D)\cdot x=b-L\cdot x^{1}\)`	Yes	No
Symmetric Gauss-Seidel Preconditioner with Matrix-Vector product (SYMGS_MV) (update `\(A\cdot x=b\)`, `\(A=L+D+U\)`)	`\(x^{0} \leftarrow \alpha\cdot x\)`; `\((L+D)\cdot x^{1}=b-U\cdot x^{0}\)`; `\((U+D)\cdot x=b-L\cdot x^{1}\)`; `\(y=A\cdot x\)`	Yes	No
LU Smoother (LU_SMOOTHER) (update `\(A\cdot x=b\)`, where `\(A=L+D+U\)` and `\(E\approx \text{inv}(D)\)` )	`\(r=b-A\cdot x\)`; `\((L+D)\cdot E\cdot(U+D)\cdot dx=r\)`; `\(y=x+dr\)`	Yes	No
Sparse Matrix Add (ADD) (sm+sm->sm)	`\(C \leftarrow \alpha\cdot op(A) + B\)`	N/A	N/A
	with `\(op(A) = A\)`	Yes	No
	with `\(op(A) = A^{T}\)`	Yes	No
	with `\(op(A) = A^{H}\)`	Yes	No

Sparse BLAS Helper Functions

Functionality	Operations	CPU	OpenMP Offload Intel GPU
Sort Indices of Matrix (ORDER)	N/A	Yes	No
Transpose of Sparse Matrix (TRANSPOSE)	`\(A \leftarrow op(A)\)` with op=trans or conjtrans	N/A	N/A
	transpose CSR/CSC matrix	Yes	No
	transpose BSR matrix	Yes	No
Sparse Matrix Format Converter (CONVERT)	N/A	Yes	No
Dense to Sparse Matrix Format Converter (CONVERT)	N/A	Yes	No
Copy Matrix Handle (COPY)	N/A	Yes	No
Create CSR Matrix Handle	N/A	Yes	No
Create CSC Matrix Handle	N/A	Yes	No
Create COO Matrix Handle	N/A	Yes	No
Create BSR Matrix Handle	N/A	Yes	No
Export CSR Matrix	Allows access to internal data in the CSR Matrix handle	Yes	No
Export CSC Matrix	Allows access to internal data in the CSC Matrix handle	Yes	No
Export COO Matrix	Allows access to internal data in the COO Matrix handle	Yes	No
Export BSR Matrix	Allows access to internal data in the BSR Matrix handle	Yes	No
Set Value in Matrix	N/A	Yes	No

Sparse BLAS Optimizization Stages

Functionality	Operations	CPU	OpenMP Offload Intel GPU
add MEMORY hint and optimize	Chooses to allow larger memory requiring optimizations or not.	Yes	No
Add GEMV hint and optimize	N/A	Yes	No
Add SYMV hint and optimize	N/A	Yes	No
Add TRMV hint and optimize	N/A	Yes	No
add TRSV hint and optimize	N/A	Yes	No
add GEMM hint and optimize	N/A	Yes	No
add TRSM hint and optimize	N/A	Yes	No
add DOTMV hint and optimize	N/A	Yes	No
add SYMGS hint and optimize	N/A	Yes	No
add SYMGS_MV hint and optimize	N/A	Yes	No
add LU_SMOOTHER hint and optimize	N/A	Yes	No

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Developer Reference for Intel® oneAPI Math Kernel Library for C

Sparse BLAS Functionality

Sparse BLAS Level 1

Sparse BLAS Level 2

Sparse BLAS Level 3

Other Sparse BLAS Operations

Sparse BLAS Helper Functions

Sparse BLAS Optimizization Stages