Initial Release

[avik-pal]

• Basic Operations
  • Broadcasting
    • Type Stability?
  • Reduction Operations
  • Unary Operations
• Linear Algebra
  • QR
  • LU
  • Cholesky
  • Direct Ldiv
  • Batched Matrix Multiplication
• CUDA
  • QR
    • Batched Solve?
    • Square
    • Long Rectangle
  • LU
    • Batched Solve?
  • Cholesky
  • Direct Ldiv
    • Square
    • Long Rectangle
    • Wide Rectangle
  • Batched Matrix Multiply
• Tests
• Aqua
• Compatibility with LinearSolve.jl
  • Krylov GMRES gives incomplete results
• Basic Usage example with NonlinearSolve.jl

[avik-pal]

For LinearSolve.jl, LU and QR should just work, with a fallback for \ looping over each batch. To make this efficient for GPU arrays, we need to use the batched solvers directly -- surprisingly CUBLAS and CUSOLVER have APIs for direct batched linear solves but don't provide APIs to use the batched QR and such to do the linear solve efficiently.

Currently I make the assumption that the batchsize of A and b must match. But it is easy to generalize. @ChrisRackauckas the case that you mentioned where there is 1 A and N bs, it is easy to generalize and use trsm vs trsv on our end itself. So all users need to do is:

LinearProblem(BatchedArray(rand(4, 4, 1)), BatchedArray(4, 16))  # Single `A` but 16 - `b`s

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[avik-pal]

SimpleNonlinearSolve.jl example usage

using BatchedArrays, SimpleNonlinearSolve

u0 = BatchedArray(rand(3, 5))

prob1 = NonlinearProblem((u, p) -> u .^ 2 .- p, u0, 2.0)

solve(prob1, SimpleBroyden())

solve(prob1, SimpleDFSane())

solve(prob1, SimpleLimitedMemoryBroyden(; threshold = 2))

solve(prob1, SimpleNewtonRaphson())

solve(prob1, SimpleKlement())

solve(prob1, SimpleHalley())

I am leaving out TR for now since there is a potential correctness issue that needs some careful investigation. As a summary of this, branching is almost impossible to handle nicely if there are conditional computations inside the branch.

Fun part: Methods using Jacobian will be much faster using BatchedArrays since we can automatically color and propagate all the batch duals together. So the current SimpleNewtonRaphson with BatchedArrays is faster than the pre 1.0 BatchedSimpleNewtonRaphson