feat: more linear algebra coverage

[avik-pal]

once this lands we should be in a decent place to target LinearSolve.jl

• cross
  • emit mlir
  • testing
• svd
  • emit mlir
  • svdvals
  • ldiv
  • testing
• cholesky
  • emit mlir
  • ldiv
  • testing
• qr
  • emit mlir
  • ldiv
  • testing
• factorize
  • emit mlir
  • ldiv
  • testing

[avik-pal]

julia> @code_hlo svd(x_ra; full=true)
module @reactant_svd attributes {mhlo.num_partitions = 1 : i64, mhlo.num_replicas = 1 : i64} {
  func.func @main(%arg0: tensor<8x8xf32> {enzymexla.memory_effects = []}) -> (tensor<8x8xf32>, tensor<8xf32>, tensor<8x8xf32>) attributes {enzymexla.memory_effects = []} {
    %0 = stablehlo.transpose %arg0, dims = [1, 0] : (tensor<8x8xf32>) -> tensor<8x8xf32>
    %1:5 = stablehlo.custom_call @cusolver_gesvd_ffi(%0) {api_version = 4 : i32, compute_uv = true, enzymexla.guaranteed_symmetric = false, full_matrices = true, operand_layouts = [dense<[0, 1]> : tensor<2xindex>], result_layouts = [dense<[0, 1]> : tensor<2xindex>, dense<0> : tensor<1xindex>, dense<[0, 1]> : tensor<2xindex>, dense<[0, 1]> : tensor<2xindex>, dense<> : tensor<0xindex>], transposed = false} : (tensor<8x8xf32>) -> (tensor<8x8xf32>, tensor<8xf32>, tensor<8x8xf32>, tensor<8x8xf32>, tensor<i64>)
    %2 = stablehlo.transpose %1#2, dims = [1, 0] : (tensor<8x8xf32>) -> tensor<8x8xf32>
    %3 = stablehlo.transpose %1#3, dims = [1, 0] : (tensor<8x8xf32>) -> tensor<8x8xf32>
    return %2, %1#1, %3 : tensor<8x8xf32>, tensor<8xf32>, tensor<8x8xf32>
  }
}

julia> @jit svd(x_ra; full=true)
E0000 00:00:1763244269.299329  239787 pjrt_stream_executor_client.cc:2085] Execution of replica 0 failed: INVALID_ARGUMENT: Wrong number of attributes: expected 3 but got 0
ERROR: INVALID_ARGUMENT: Wrong number of attributes: expected 3 but got 0

Stacktrace:
 [1] reactant_err(msg::Cstring)
   @ Reactant.XLA /mnt/software/lux/Reactant.jl/src/xla/Utils.jl:12
 [2] execute
   @ /mnt/software/lux/Reactant.jl/src/xla/IFRT/LoadedExecutable.jl:126 [inlined]
 [3] execute_sharded
   @ /mnt/software/lux/Reactant.jl/src/xla/IFRT/LoadedExecutable.jl:166 [inlined]
 [4] macro expansion
   @ /mnt/software/lux/Reactant.jl/src/Compiler.jl:3308 [inlined]
 [5] (::Reactant.Compiler.Thunk{typeof(svd), Symbol("##svd_reactant#563"), false, Tuple{…}, Reactant.XLA.IFRT.LoadedExecutable, Reactant.XLA.IFRT.Device, Reactant.XLA.IFRT.Client, Tuple{}, Vector{…}})(args::ConcreteIFRTArray{Float32, 2, Nothing})
   @ Reactant.Compiler /mnt/software/lux/Reactant.jl/src/Compiler.jl:3790
 [6] top-level scope
   @ /mnt/software/lux/Reactant.jl/src/Compiler.jl:2597
 [7] top-level scope
   @ none:1
Some type information was truncated. Use `show(err)` to see complete types.