AMDGPU.jl

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Linear Algebra ​

Standard LinearAlgebra functions work directly on ROCArray, dispatching to AMD's rocBLAS (dense BLAS) and rocSOLVER (LAPACK-style factorizations). You write ordinary Julia linear algebra; the GPU libraries are used automatically.

Supported out of the box on ROCArray:

  • Matrix–matrix and matrix–vector products (*, mul!), including mixed- and low-precision (Float16) matmul.

  • BLAS level-1 operations: dot, norm, axpy!, axpby!, rmul!.

  • Triangular solves and \ (linear systems, LU-based).

  • Factorizations: cholesky, lu, qr, svd.

julia
julia> A = ROCArray(Float32[4 1; 1 3]);

julia> b = ROCArray(Float32[1, 2]);

julia> x = A \ b;                       # solve, LU via rocSOLVER

julia> Array(A * x) ≈ Array(b)
true

julia> C = cholesky(A);                 # Cholesky factorization

julia> Array(C.U' * C.U) ≈ Array(A)
true

Element types follow rocBLAS/rocSOLVER: Float32, Float64, ComplexF32, and ComplexF64 (with Float16 also supported for matmul).

Singular value decomposition ​

svd, svd!, and svdvals run on ROCMatrix via rocSOLVER. The alg keyword selects the backend — JacobiAlgorithm() (the default, usually fastest on AMD GPUs) or QRAlgorithm():

julia
using AMDGPU.rocSOLVER: JacobiAlgorithm, QRAlgorithm

F = svd(A)                              # Jacobi by default; F.U, F.S, F.Vt
s = svdvals(A)                          # singular values only
Ff = svd(A; full = true, alg = QRAlgorithm())

Because svdvals is supported, so is cond. (opnorm(A, 2) is not yet available — it relies on scalar indexing internal to LinearAlgebra.)

Direct library access ​

Lower-level routines are available in the AMDGPU.rocBLAS and AMDGPU.rocSOLVER submodules for cases the generic interface does not cover — for example batched factorizations, or the raw gesvd! (QR) and gesvdj! (Jacobi) SVD kernels.