Open albertomercurio opened 3 years ago
Yes, I don't think it can generate generic linear algebra calls.
Did you try using StaticArrays?
Did you try using StaticArrays?
I'm using very large matrices (usually 1500x1500), this is the reason i use sparse matrices. However, also with a 100x100 matrix it tooks a lot of time to convert L
to a Static Array
SMatrix{N, N}(Matrix(L))
That makes no sense to solve with EnsembleGPUArray. Read the DiffEqGPU documentation on the two forms of GPU problems. You're using the form for 100 ODEs or less, not the one for 1000 ODEs or more.
https://github.com/SciML/DiffEqGPU.jl#within-method-gpu-parallelism-with-direct-cuarray-usage
That's more applicable here.
Do you mean that I need to convert L
and L_t
into CuArray and than evolve each ODE serially with EnsembleSerial()
? If it is the case, can i use EnsembleThreads()
to parallelize that CUDA ODE again?
That would evolve the ODE in parallel on the GPU. You want to use EnsembleSerial unless you have multiple GPUs which you would want to use at the same time.
Ok perfect. Thank you for your help.
However I have the following question. I'm yet able to perform this ODE directly on the GPU, using the differential function
L = CUDA.CUSPARSE.CuSparseMatrixCSR( L )
L_t = CUDA.CUSPARSE.CuSparseMatrixCSR( L_t )
function f(rho, p, t)
A, w_l = p
rho_tmp = similar(rho0_vec)
return L * rho + CUDA.CUSPARSE.mv!('N', A * sin(w_l * t), L_t, rho, 0.0, rho_tmp, '0')
end
where this time L
and L_t
are CuSparse matrices, and they don't take up a lot of memory as the dense matrix form.
This method is a little bit faster than the CPU sparse one, but of course slower if I parallelize the CPU method in the Ensemble Simulation.
Whit this CUDA sparse method the GPU is loaded only up to the 10%, and so the memory. If I could be able to parallelize all the ODEs in the ensemble I think it would get a lot faster than the EnsembleThreads()
method.
Why there is no way to implement this method for an EnsembleGPUArray()
simulation?
To GPU it like this, you'd want to expand it out to its scalar form with something like ModelingToolkit, in order to then do the GPU codegen. EnsembleGPUArray is all about kernel code generation, so it's not using CUDA kernels like those from CUSPARSE since it's really made to generate nonlinear kernels.
Hello,
I'm trying to solve and ODE with my GPU. I tested the example code present in the DiffEqGPU.js repository, and it worked fine.
I have the following function to implement in the ODE Problem
or equivalently
where
A
andw_l
are two numbers, whileL
andL_t
are two global matrices. Following the documentation, I used the following code to run a Parallel Ensemble:where
METHOD!!
can be one of the methods, e.g.EnsembleSerial()
,EnsembleThreads()
,EnsembleCPUArray()
orEnsembleGPUArray()
.The problem is divided in two cases:
L
andL_t
are sparse matrices. In this case all the methods work, except forEnsembleGPUArray()
. In this case the error isStacktrace: [1] check_ir(job::GPUCompiler.CompilerJob{GPUCompiler.PTXCompilerTarget, CUDA.CUDACompilerParams, GPUCompiler.FunctionSpec{typeof(Cassette.overdub), Tuple{Cassette.Context{nametype(CUDACtx), KernelAbstractions.CompilerMetadata{KernelAbstractions.NDIteration.DynamicSize, KernelAbstractions.NDIteration.DynamicCheck, Nothing, CartesianIndices{1, Tuple{Base.OneTo{Int64}}}, KernelAbstractions.NDIteration.NDRange{1, KernelAbstractions.NDIteration.DynamicSize, KernelAbstractions.NDIteration.DynamicSize, CartesianIndices{1, Tuple{Base.OneTo{Int64}}}, CartesianIndices{1, Tuple{Base.OneTo{Int64}}}}}, Nothing, KernelAbstractions.var"##PassType#257", Nothing, Cassette.DisableHooks}, typeof(DiffEqGPU.gpu_gpu_kernel_oop), typeof(drho_dt), CuDeviceMatrix{ComplexF64, 1}, CuDeviceMatrix{ComplexF64, 1}, CuDeviceMatrix{Float64, 1}, Float64}}}, args::LLVM.Module) @ GPUCompiler ~/.julia/packages/GPUCompiler/wHjqZ/src/validation.jl:111 [2] macro expansion @ ~/.julia/packages/GPUCompiler/wHjqZ/src/driver.jl:319 [inlined] [3] macro expansion @ ~/.julia/packages/TimerOutputs/ZQ0rt/src/TimerOutput.jl:236 [inlined] [4] macro expansion @ ~/.julia/packages/GPUCompiler/wHjqZ/src/driver.jl:317 [inlined] [5] emit_asm(job::GPUCompiler.CompilerJob, ir::LLVM.Module; strip::Bool, validate::Bool, format::LLVM.API.LLVMCodeGenFileType) @ GPUCompiler ~/.julia/packages/GPUCompiler/wHjqZ/src/utils.jl:62 [6] cufunction_compile(job::GPUCompiler.CompilerJob) @ CUDA ~/.julia/packages/CUDA/02Kjq/src/compiler/execution.jl:317 [7] cached_compilation(cache::Dict{UInt64, Any}, job::GPUCompiler.CompilerJob, compiler::typeof(CUDA.cufunction_compile), linker::typeof(CUDA.cufunction_link)) @ GPUCompiler ~/.julia/packages/GPUCompiler/wHjqZ/src/cache.jl:89 [8] cufunction(f::typeof(Cassette.overdub), tt::Type{Tuple{Cassette.Context{nametype(CUDACtx), KernelAbstractions.CompilerMetadata{KernelAbstractions.NDIteration.DynamicSize, KernelAbstractions.NDIteration.DynamicCheck, Nothing, CartesianIndices{1, Tuple{Base.OneTo{Int64}}}, KernelAbstractions.NDIteration.NDRange{1, KernelAbstractions.NDIteration.DynamicSize, KernelAbstractions.NDIteration.DynamicSize, CartesianIndices{1, Tuple{Base.OneTo{Int64}}}, CartesianIndices{1, Tuple{Base.OneTo{Int64}}}}}, Nothing, KernelAbstractions.var"##PassType#257", Nothing, Cassette.DisableHooks}, typeof(DiffEqGPU.gpu_gpu_kernel_oop), typeof(drho_dt), CuDeviceMatrix{ComplexF64, 1}, CuDeviceMatrix{ComplexF64, 1}, CuDeviceMatrix{Float64, 1}, Float64}}; name::String, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}) @ CUDA ~/.julia/packages/CUDA/02Kjq/src/compiler/execution.jl:288 [9] macro expansion @ ~/.julia/packages/CUDA/02Kjq/src/compiler/execution.jl:102 [inlined] [10] (::KernelAbstractions.Kernel{CUDAKernels.CUDADevice, KernelAbstractions.NDIteration.DynamicSize, KernelAbstractions.NDIteration.DynamicSize, typeof(DiffEqGPU.gpu_gpu_kernel_oop)})(::Function, ::Vararg{Any, N} where N; ndrange::Int64, dependencies::CUDAKernels.CudaEvent, workgroupsize::Int64, progress::Function) @ CUDAKernels ~/.julia/packages/CUDAKernels/8wtKq/src/CUDAKernels.jl:194 [11] SciML/DifferentialEquations.jl#55 @ ~/.julia/packages/DiffEqGPU/gGgMY/src/DiffEqGPU.jl:414 [inlined] [12] ODEFunction @ ~/.julia/packages/SciMLBase/oTP8b/src/scimlfunctions.jl:334 [inlined] [13] initialize!(integrator::OrdinaryDiffEq.ODEIntegrator{Tsit5, true, CuArray{ComplexF64, 2}, Nothing, Float64, CuArray{Float64, 2}, Float64, Float64, Float64, Float64, Vector{CuArray{ComplexF64, 2}}, ODESolution{ComplexF64, 3, Vector{CuArray{ComplexF64, 2}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{CuArray{ComplexF64, 2}}}, ODEProblem{CuArray{ComplexF64, 2}, Tuple{Float64, Float64}, true, CuArray{Float64, 2}, ODEFunction{true, DiffEqGPU.var"#55#59"{typeof(drho_dt), typeof(DiffEqGPU.gpu_kernel_oop)}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Tsit5, OrdinaryDiffEq.InterpolationData{ODEFunction{true, DiffEqGPU.var"#55#59"{typeof(drho_dt), typeof(DiffEqGPU.gpu_kernel_oop)}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{CuArray{ComplexF64, 2}}, Vector{Float64}, Vector{Vector{CuArray{ComplexF64, 2}}}, OrdinaryDiffEq.Tsit5Cache{CuArray{ComplexF64, 2}, CuArray{ComplexF64, 2}, CuArray{ComplexF64, 2}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}}, DiffEqBase.DEStats}, ODEFunction{true, DiffEqGPU.var"#55#59"{typeof(drho_dt), typeof(DiffEqGPU.gpu_kernel_oop)}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, OrdinaryDiffEq.Tsit5Cache{CuArray{ComplexF64, 2}, CuArray{ComplexF64, 2}, CuArray{ComplexF64, 2}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqGPU.diffeqgpunorm), typeof(opnorm), Nothing, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), DiffEqGPU.var"#12#18", DataStructures.BinaryMinHeap{Float64}, DataStructures.BinaryMinHeap{Float64}, Nothing, Nothing, Int64, Tuple{}, Tuple{}, Tuple{}}, CuArray{ComplexF64, 2}, ComplexF64, Nothing, OrdinaryDiffEq.DefaultInit}, cache::OrdinaryDiffEq.Tsit5Cache{CuArray{ComplexF64, 2}, CuArray{ComplexF64, 2}, CuArray{ComplexF64, 2}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}) @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/a5qvy/src/perform_step/low_order_rk_perform_step.jl:623 [14] init(prob::ODEProblem{CuArray{ComplexF64, 2}, Tuple{Float64, Float64}, true, CuArray{Float64, 2}, ODEFunction{true, DiffEqGPU.var"#55#59"{typeof(drho_dt), typeof(DiffEqGPU.gpu_kernel_oop)}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, alg::Tsit5, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{Val{true}}; saveat::Tuple{}, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Float64, dtmin::Nothing, dtmax::Float64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{Int64}, abstol::Nothing, reltol::Nothing, qmin::Rational{Int64}, qmax::Int64, qsteady_min::Int64, qsteady_max::Int64, beta1::Nothing, beta2::Nothing, qoldinit::Rational{Int64}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqGPU.diffeqgpunorm), internalopnorm::typeof(opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::DiffEqGPU.var"#12#18", verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias_u0::Bool, alias_du0::Bool, initializealg::OrdinaryDiffEq.DefaultInit, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}) @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/a5qvy/src/solve.jl:456 [15] #__solve#466 @ ~/.julia/packages/OrdinaryDiffEq/a5qvy/src/solve.jl:4 [inlined] [16] #solve_call#58 @ ~/.julia/packages/DiffEqBase/oe7VF/src/solve.jl:61 [inlined] [17] solve_up(prob::ODEProblem{CuArray{ComplexF64, 2}, Tuple{Float64, Float64}, true, CuArray{Float64, 2}, ODEFunction{true, DiffEqGPU.var"#55#59"{typeof(drho_dt), typeof(DiffEqGPU.gpu_kernel_oop)}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, sensealg::Nothing, u0::CuArray{ComplexF64, 2}, p::CuArray{Float64, 2}, args::Tsit5; kwargs::Base.Iterators.Pairs{Symbol, Any, NTuple{4, Symbol}, NamedTuple{(:unstable_check, :callback, :merge_callbacks, :internalnorm), Tuple{DiffEqGPU.var"#12#18", Nothing, Bool, typeof(DiffEqGPU.diffeqgpunorm)}}}) @ DiffEqBase ~/.julia/packages/DiffEqBase/oe7VF/src/solve.jl:82 [18] #solve#59 @ ~/.julia/packages/DiffEqBase/oe7VF/src/solve.jl:70 [inlined] [19] batch_solve_up(ensembleprob::EnsembleProblem{ODEProblem{Vector{ComplexF64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, typeof(drho_dt), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, typeof(prob_func), typeof(SciMLBase.DEFAULT_OUTPUT_FUNC), typeof(SciMLBase.DEFAULT_REDUCTION), Nothing}, probs::Vector{ODEProblem{Vector{ComplexF64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, typeof(drho_dt), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}}, alg::Tsit5, ensemblealg::EnsembleGPUArray, I::UnitRange{Int64}, u0::Matrix{ComplexF64}, p::Matrix{Float64}; kwargs::Base.Iterators.Pairs{Symbol, DiffEqGPU.var"#12#18", Tuple{Symbol}, NamedTuple{(:unstable_check,), Tuple{DiffEqGPU.var"#12#18"}}}) @ DiffEqGPU ~/.julia/packages/DiffEqGPU/gGgMY/src/DiffEqGPU.jl:319 [20] batch_solve(ensembleprob::EnsembleProblem{ODEProblem{Vector{ComplexF64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, typeof(drho_dt), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, typeof(prob_func), typeof(SciMLBase.DEFAULT_OUTPUT_FUNC), typeof(SciMLBase.DEFAULT_REDUCTION), Nothing}, alg::Tsit5, ensemblealg::EnsembleGPUArray, I::UnitRange{Int64}; kwargs::Base.Iterators.Pairs{Symbol, DiffEqGPU.var"#12#18", Tuple{Symbol}, NamedTuple{(:unstable_check,), Tuple{DiffEqGPU.var"#12#18"}}}) @ DiffEqGPU ~/.julia/packages/DiffEqGPU/gGgMY/src/DiffEqGPU.jl:284 [21] macro expansion @ ./timing.jl:287 [inlined] [22] solve(ensembleprob::EnsembleProblem{ODEProblem{Vector{ComplexF64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, typeof(drho_dt), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, typeof(prob_func), typeof(SciMLBase.DEFAULT_OUTPUT_FUNC), typeof(SciMLBase.DEFAULT_REDUCTION), Nothing}, alg::Tsit5, ensemblealg::EnsembleGPUArray; trajectories::Int64, batch_size::Int64, unstable_check::Function, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}) @ DiffEqGPU ~/.julia/packages/DiffEqGPU/gGgMY/src/DiffEqGPU.jl:201 [23] #solve#61 @ ~/.julia/packages/DiffEqBase/oe7VF/src/solve.jl:96 [inlined] [24] top-level scope @ ./timing.jl:210 [inlined] [25] top-level scope @ ./In[9]:0 [26] eval @ ./boot.jl:360 [inlined] [27] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String) @ Base ./loading.jl:1094
TaskFailedException
Stacktrace: [1] wait @ ./task.jl:322 [inlined] [2] wait @ ~/.julia/packages/KernelAbstractions/Yy47c/src/cpu.jl:65 [inlined] [3] wait @ ~/.julia/packages/KernelAbstractions/Yy47c/src/cpu.jl:64 [inlined] [4] (::DiffEqGPU.var"#55#59"{typeof(drho_dt), typeof(DiffEqGPU.gpu_kernel_oop)})(du::Matrix{ComplexF64}, u::Matrix{ComplexF64}, p::Matrix{Float64}, t::Float64) @ DiffEqGPU ~/.julia/packages/DiffEqGPU/gGgMY/src/DiffEqGPU.jl:414 [5] ODEFunction @ ~/.julia/packages/SciMLBase/oTP8b/src/scimlfunctions.jl:334 [inlined] [6] initialize!(integrator::OrdinaryDiffEq.ODEIntegrator{Tsit5, true, Matrix{ComplexF64}, Nothing, Float64, Matrix{Float64}, Float64, Float64, Float64, Float64, Vector{Matrix{ComplexF64}}, ODESolution{ComplexF64, 3, Vector{Matrix{ComplexF64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Matrix{ComplexF64}}}, ODEProblem{Matrix{ComplexF64}, Tuple{Float64, Float64}, true, Matrix{Float64}, ODEFunction{true, DiffEqGPU.var"#55#59"{typeof(drho_dt), typeof(DiffEqGPU.gpu_kernel_oop)}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Tsit5, OrdinaryDiffEq.InterpolationData{ODEFunction{true, DiffEqGPU.var"#55#59"{typeof(drho_dt), typeof(DiffEqGPU.gpu_kernel_oop)}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Vector{Matrix{ComplexF64}}, Vector{Float64}, Vector{Vector{Matrix{ComplexF64}}}, OrdinaryDiffEq.Tsit5Cache{Matrix{ComplexF64}, Matrix{ComplexF64}, Matrix{ComplexF64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}}, DiffEqBase.DEStats}, ODEFunction{true, DiffEqGPU.var"#55#59"{typeof(drho_dt), typeof(DiffEqGPU.gpu_kernel_oop)}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, OrdinaryDiffEq.Tsit5Cache{Matrix{ComplexF64}, Matrix{ComplexF64}, Matrix{ComplexF64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqGPU.diffeqgpunorm), typeof(opnorm), Nothing, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), DiffEqGPU.var"#12#18", DataStructures.BinaryMinHeap{Float64}, DataStructures.BinaryMinHeap{Float64}, Nothing, Nothing, Int64, Tuple{}, Tuple{}, Tuple{}}, Matrix{ComplexF64}, ComplexF64, Nothing, OrdinaryDiffEq.DefaultInit}, cache::OrdinaryDiffEq.Tsit5Cache{Matrix{ComplexF64}, Matrix{ComplexF64}, Matrix{ComplexF64}, OrdinaryDiffEq.Tsit5ConstantCache{Float64, Float64}}) @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/a5qvy/src/perform_step/low_order_rk_perform_step.jl:623 [7] init(prob::ODEProblem{Matrix{ComplexF64}, Tuple{Float64, Float64}, true, Matrix{Float64}, ODEFunction{true, DiffEqGPU.var"#55#59"{typeof(drho_dt), typeof(DiffEqGPU.gpu_kernel_oop)}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, alg::Tsit5, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{Val{true}}; saveat::Tuple{}, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Float64, dtmin::Nothing, dtmax::Float64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{Int64}, abstol::Nothing, reltol::Nothing, qmin::Rational{Int64}, qmax::Int64, qsteady_min::Int64, qsteady_max::Int64, beta1::Nothing, beta2::Nothing, qoldinit::Rational{Int64}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqGPU.diffeqgpunorm), internalopnorm::typeof(opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::DiffEqGPU.var"#12#18", verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias_u0::Bool, alias_du0::Bool, initializealg::OrdinaryDiffEq.DefaultInit, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}) @ OrdinaryDiffEq ~/.julia/packages/OrdinaryDiffEq/a5qvy/src/solve.jl:456 [8] #__solve#466 @ ~/.julia/packages/OrdinaryDiffEq/a5qvy/src/solve.jl:4 [inlined] [9] #solve_call#58 @ ~/.julia/packages/DiffEqBase/oe7VF/src/solve.jl:61 [inlined] [10] solve_up(prob::ODEProblem{Matrix{ComplexF64}, Tuple{Float64, Float64}, true, Matrix{Float64}, ODEFunction{true, DiffEqGPU.var"#55#59"{typeof(drho_dt), typeof(DiffEqGPU.gpu_kernel_oop)}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, sensealg::Nothing, u0::Matrix{ComplexF64}, p::Matrix{Float64}, args::Tsit5; kwargs::Base.Iterators.Pairs{Symbol, Any, NTuple{4, Symbol}, NamedTuple{(:unstable_check, :callback, :merge_callbacks, :internalnorm), Tuple{DiffEqGPU.var"#12#18", Nothing, Bool, typeof(DiffEqGPU.diffeqgpunorm)}}}) @ DiffEqBase ~/.julia/packages/DiffEqBase/oe7VF/src/solve.jl:82 [11] #solve#59 @ ~/.julia/packages/DiffEqBase/oe7VF/src/solve.jl:70 [inlined] [12] batch_solve_up(ensembleprob::EnsembleProblem{ODEProblem{Vector{ComplexF64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, typeof(drho_dt), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, typeof(prob_func), typeof(SciMLBase.DEFAULT_OUTPUT_FUNC), typeof(SciMLBase.DEFAULT_REDUCTION), Nothing}, probs::Vector{ODEProblem{Vector{ComplexF64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, typeof(drho_dt), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}}, alg::Tsit5, ensemblealg::EnsembleCPUArray, I::UnitRange{Int64}, u0::Matrix{ComplexF64}, p::Matrix{Float64}; kwargs::Base.Iterators.Pairs{Symbol, DiffEqGPU.var"#12#18", Tuple{Symbol}, NamedTuple{(:unstable_check,), Tuple{DiffEqGPU.var"#12#18"}}}) @ DiffEqGPU ~/.julia/packages/DiffEqGPU/gGgMY/src/DiffEqGPU.jl:319 [13] batch_solve(ensembleprob::EnsembleProblem{ODEProblem{Vector{ComplexF64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, typeof(drho_dt), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, typeof(prob_func), typeof(SciMLBase.DEFAULT_OUTPUT_FUNC), typeof(SciMLBase.DEFAULT_REDUCTION), Nothing}, alg::Tsit5, ensemblealg::EnsembleCPUArray, I::UnitRange{Int64}; kwargs::Base.Iterators.Pairs{Symbol, DiffEqGPU.var"#12#18", Tuple{Symbol}, NamedTuple{(:unstable_check,), Tuple{DiffEqGPU.var"#12#18"}}}) @ DiffEqGPU ~/.julia/packages/DiffEqGPU/gGgMY/src/DiffEqGPU.jl:284 [14] macro expansion @ ./timing.jl:287 [inlined] [15] solve(ensembleprob::EnsembleProblem{ODEProblem{Vector{ComplexF64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, typeof(drho_dt), UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing}, Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, typeof(prob_func), typeof(SciMLBase.DEFAULT_OUTPUT_FUNC), typeof(SciMLBase.DEFAULT_REDUCTION), Nothing}, alg::Tsit5, ensemblealg::EnsembleCPUArray; trajectories::Int64, batch_size::Int64, unstable_check::Function, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}) @ DiffEqGPU ~/.julia/packages/DiffEqGPU/gGgMY/src/DiffEqGPU.jl:201 [16] #solve#61 @ ~/.julia/packages/DiffEqBase/oe7VF/src/solve.jl:96 [inlined] [17] top-level scope @ ./timing.jl:210 [inlined] [18] top-level scope @ ./In[11]:0 [19] eval @ ./boot.jl:360 [inlined] [20] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String) @ Base ./loading.jl:1094