cuNumeric.jl

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Linear Algebra ​

cuNumeric.jl provides matrix multiplication, batched solves, SVD, QR, and related helpers for NDArray.

solve, svd, and qr accept Float32, Float64, ComplexF32, and ComplexF64. Integer and Bool inputs require @allowpromotion or allowpromotion and produce Float64 outputs.

Matrix multiply ​

For two 2D arrays, * performs matrix multiplication; use .* for an elementwise product.

julia
using LinearAlgebra
using cuNumeric

A = cuNumeric.rand(Float32, 128, 128)
B = cuNumeric.rand(Float32, 128, 128)

C = A * B                 # allocates a new result
mul!(similar(C), A, B)    # in-place GEMM into an existing array
LinearAlgebra.mul! Method
julia
LinearAlgebra.mul!(out::NDArray, arr1::NDArray, arr2::NDArray)

Compute the matrix multiplication of arr1 and arr2, storing the result in out.

This function performs the operation in-place, modifying out.

Examples

julia
a = cuNumeric.ones(2, 3)
b = cuNumeric.ones(3, 2)
out = cuNumeric.zeros(2, 2)
LinearAlgebra.mul!(out, a, b)
source

Solve (batched) ​

cuNumeric.solve(A, b) solves linear systems and returns an array with the same shape as b. A has shape (..., m, m) and b has shape (..., m) or (..., m, n).

julia
A = cuNumeric.rand(Float32, 64, 64)
b = cuNumeric.rand(Float32, 64)
x = cuNumeric.solve(A, b)

B = cuNumeric.rand(Float32, 64, 4)
X = cuNumeric.solve(A, B)

As = cuNumeric.rand(Float32, 8, 32, 32)
Bs = cuNumeric.rand(Float32, 8, 32, 2)
Xs = cuNumeric.solve(As, Bs)

Singular value decomposition ​

cuNumeric.svd(A, full_matrices=true) returns (U, S, Vh) for a 2D m × n array. With k = min(m, n), the output shapes are:

  • Full: U is m × m, S has length k, and Vh is n × n.

  • Thin: U is m × k, S has length k, and Vh is k × n.

julia
A = cuNumeric.rand(Float32, 128, 64)
U, S, Vh = cuNumeric.svd(A, false)

S is real-valued for both real and complex inputs.

QR decomposition ​

cuNumeric.qr(A) returns the economy-size factors (Q, R) for a 2D m × n array. With k = min(m, n), Q is m × k and R is k × n.

julia
A = cuNumeric.rand(Float32, 128, 64)
Q, R = cuNumeric.qr(A)

SVD and QR currently accept only 2D arrays; batched decompositions are not supported.

Helpers ​

These helpers live on NDArray and are also listed in the Public API:

  • cuNumeric.transpose

  • cuNumeric.eye

  • cuNumeric.diag (2D to 1D)

  • cuNumeric.trace

Not available yet ​

There is no public cholesky, eig, lu, matrix inv, or ldiv! yet. Elementwise inv / ^-1 are unary operations, not matrix inverse.