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NumericalShadow.jl

Numerical tools for estimating numerical shadows and q-shadows, with random-state and random-unitary generators for CPU and CUDA backends.

Installation

using Pkg
Pkg.add("NumericalShadow")

For local development:

using Pkg
Pkg.develop(path=".")

Quick Start (CPU)

using NumericalShadow
using KernelAbstractions

A = ComplexF64[1 0; 0 -1]
samples = 10_000

sampler(backend, d, n) = random_pure(backend, ComplexF64, d, n)
h = shadow(CPU(), A, samples, sampler, 2_000)

Quick Start (CUDA, Optional)

using NumericalShadow
using KernelAbstractions
using CUDA

if CUDA.functional()
    backend = CUDABackend()
    U = random_unitary(backend, ComplexF64, 8, 1024)
    @show size(U)  # (8, 8, 1024)
end

Benchmarks

Run the dedicated CUDA QR benchmark:

julia --project=benchmarks benchmarks/benchmark_cuda_batched_qr.jl

Run the broader benchmark suite:

julia --project=benchmarks benchmarks/runbenchmarks.jl

Example Plots (Shadow.pdf Problems 2/3/4)

Generate sample datasets:

julia --project=. examples/problem2_k_shadow.jl
julia --project=. examples/problem3_c_shadow.jl
julia --project=. examples/problem4_C_shadow.jl

These examples now write HDF5 files (.h5) to examples/results/.

Render PNG plots (Julia + CairoMakie):

julia --project=examples -e 'using Pkg; Pkg.instantiate()'
julia --project=examples examples/plot_problem_shadows.jl

Testing

julia --project=. -e 'using Pkg; Pkg.test()'

Enable slower statistical tests:

NUMERICALSHADOW_RUN_SLOW_TESTS=true julia --project=. -e 'using Pkg; Pkg.test()'

Public API

  • move_to_backend
  • shadow, qshadow, product_qshadow
  • random_pure, random_overlap, random_unitary, random_max_ent