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Julia interface to the Elemental linear algebra library.
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JuliaParallel/Elemental.jl
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A package for dense and sparse distributed linear algebra and optimization. The underlying functionality is provided by the C++ libraryElemental written originally byJack Poulson and now maintained by LLNL.
The package is installed withPkg.add("Elemental"). For Julia versions 1.3 and later, Elemental uses the binaries provided by BinaryBuilder, which are linked against the MPI (mpich) provided through BinaryBuilder.
Each of these examples should be run in a separate Julia session.
This example runs on a single processor, and initializes MPI under the hood. However, explicit use of MPI.jl is not required in this case, compared to the other examples below.
julia>using LinearAlgebra, Elementaljulia> A= Elemental.Matrix(Float64)0x0 Elemental.Matrix{Float64}julia> Elemental.gaussian!(A,100,80);julia> U, s, V=svd(A);julia>convert(Matrix{Float64}, s)[1:10]10-element Array{Float64,1}:19.898918.270217.366517.047516.451316.319716.098915.835315.594715.5079
In this example,@mpi_do has to be used to send the parallel instructions to all processors.
julia>using MPI, MPIClusterManagers, Distributedjulia> man=MPIManager(np=4);julia>addprocs(man);julia>@everywhereusing LinearAlgebra, Elementaljulia>@mpi_do man A= Elemental.DistMatrix(Float64);julia>@mpi_do man Elemental.gaussian!(A,1000,800);julia>@mpi_do man U, s, V=svd(A);julia>@mpi_do manprintln(s[1]) From worker5:59.639990420817696 From worker4:59.639990420817696 From worker2:59.639990420817696 From worker3:59.639990420817696
This example is slightly different from the ones above in that it only calculates the singular values. However,it uses the DistributedArrays.jl package, and has a single thread of control. Note, we do not need to use@mpi_doexplicitly in this case.
julia>using MPI, MPIClusterManagers, Distributedjulia> man=MPIManager(np=4);julia>addprocs(man);julia>using DistributedArrays, Elementaljulia> A=drandn(1000,800);julia> Elemental.svdvals(A)[1:5]5-element SubArray{Float64,1,DistributedArrays.DArray{Float64,2,Array{Float64,2}},Tuple{UnitRange{Int64}},0}:59.464959.198459.030958.717858.389
The iterative SVD algorithm is implemented in pure Julia, but the factorized matrix as well as the Lanczos vectors are stored as distributed matrices in Elemental. Notice, thatTSVD.jl doesn't depend on Elemental and is only usingElemental.jl through generic function calls.
julia>using MPI, MPIClusterManagers, Distributedjulia> man=MPIManager(np=4);julia>addprocs(man);julia>@mpi_do manusing Elemental, TSVD, Randomjulia>@mpi_do man A= Elemental.DistMatrix(Float64);julia>@mpi_do man Elemental.gaussian!(A,5000,2000);julia>@mpi_do man Random.seed!(123)# to avoid different initial vectors on the workersjulia>@mpi_do man r=tsvd(A,5);julia>@mpi_do manprintln(r[2][1:5]) From worker3: [1069.6059089732858,115.44260091060129,115.08319164529792,114.87007788947226,114.48092348847719] From worker5: [1069.6059089732858,115.44260091060129,115.08319164529792,114.87007788947226,114.48092348847719] From worker2: [1069.6059089732858,115.44260091060129,115.08319164529792,114.87007788947226,114.48092348847719] From worker4: [1069.6059089732858,115.44260091060129,115.08319164529792,114.87007788947226,114.48092348847719]
@mpi_do man A= Elemental.DistMatrix(Float32)@mpi_do man B= Elemental.DistMatrix(Float32)@mpi_do mancopyto!(A, Float32[21;12])@mpi_do mancopyto!(B, Float32[4,5])
Run distributed ridge regression ½|A*X-B|₂² + λ|X|₂²
@mpi_do man X= Elemental.ridge(A, B,0f0)
Run distributed lasso regression ½|A*X-B|₂² + λ|X|₁ (only supported in recent versions of Elemental)
@mpi_do man X= Elemental.bpdn(A, B,0.1f0)
Right now, the best way to see if a specific function is available, is to look through the source code. We are looking for help to prepare Documenter.jl based documentation for this package, and also to add more functionality from the Elemental library.
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Julia interface to the Elemental linear algebra library.