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CUDSS

https://github.com/exanauts/cudss.jl

Science Score: 44.0%

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Repository

Basic Info
  • Host: GitHub
  • Owner: exanauts
  • License: mit
  • Language: Julia
  • Default Branch: main
  • Size: 79.5 MB
Statistics
  • Stars: 38
  • Watchers: 7
  • Forks: 2
  • Open Issues: 12
  • Releases: 23
Created over 2 years ago · Last pushed 7 months ago
Metadata Files
Readme License Citation

README.md

CUDSS.jl: Julia interface for NVIDIA cuDSS

docs-dev

Overview

CUDSS.jl is a Julia interface to the NVIDIA cuDSS library. NVIDIA cuDSS provides three factorizations (LDU, LDLᵀ, LLᵀ) for solving sparse linear systems on GPUs.

Why CUDSS.jl?

Unlike other CUDA libraries that are commonly bundled together, cuDSS is currently in preview. For this reason, it is not included in CUDA.jl. To maintain consistency with the naming conventions used for other CUDA libraries (such as CUBLAS, CUSOLVER, CUSPARSE, etc.), we have named this interface CUDSS.jl.

Installation

CUDSS.jl can be installed and tested through the Julia package manager:

julia julia> ] pkg> add CUDSS pkg> test CUDSS

Content

CUDSS.jl provides a structured approach for leveraging NVIDIA cuDSS functionalities. It introduces the types CudssSolver and CudssBatchSolver along with three core routines: cudss, cudss_set, and cudss_get. Additionally, specialized methods for the CuSparseMatrixCSR type have been incorporated for cholesky, ldlt, lu and \. To further enhance performance, in-place variants including cholesky!, ldlt!, lu! and ldiv! have been implemented. These variants optimize performance by reusing the symbolic factorization as well as storage. This ensures efficient solving of sparse linear systems on GPUs.

Examples

Example 1: Sparse unsymmetric linear system with one right-hand side

```julia using CUDA, CUDA.CUSPARSE using CUDSS using SparseArrays, LinearAlgebra

T = Float64 n = 100 Acpu = sprand(T, n, n, 0.05) + I xcpu = zeros(T, n) b_cpu = rand(T, n)

Agpu = CuSparseMatrixCSR(Acpu) xgpu = CuVector(xcpu) bgpu = CuVector(bcpu)

solver = CudssSolver(A_gpu, "G", 'F')

cudss("analysis", solver, xgpu, bgpu) cudss("factorization", solver, xgpu, bgpu) cudss("solve", solver, xgpu, bgpu)

rgpu = bgpu - Agpu * xgpu norm(r_gpu)

In-place LU

dgpu = rand(T, n) |> CuVector Agpu = Agpu + Diagonal(dgpu) cudssset(solver, Agpu)

ccpu = rand(T, n) cgpu = CuVector(c_cpu)

cudss("refactorization", solver, xgpu, cgpu) cudss("solve", solver, xgpu, cgpu)

rgpu = cgpu - Agpu * xgpu norm(r_gpu) ```

Example 2: Sparse symmetric linear system with multiple right-hand sides

```julia using CUDA, CUDA.CUSPARSE using CUDSS using SparseArrays, LinearAlgebra

T = Float64 R = real(T) n = 100 p = 5 Acpu = sprand(T, n, n, 0.05) + I Acpu = Acpu + Acpu' Xcpu = zeros(T, n, p) Bcpu = rand(T, n, p)

Agpu = CuSparseMatrixCSR(Acpu |> tril) Xgpu = CuMatrix(Xcpu) Bgpu = CuMatrix(Bcpu)

structure = T <: Real ? "S" : "H" solver = CudssSolver(A_gpu, structure, 'L')

cudss("analysis", solver, Xgpu, Bgpu) cudss("factorization", solver, Xgpu, Bgpu) cudss("solve", solver, Xgpu, Bgpu)

Rgpu = Bgpu - CuSparseMatrixCSR(Acpu) * Xgpu norm(R_gpu)

In-place LDLᵀ

dgpu = rand(R, n) |> CuVector Agpu = Agpu + Diagonal(dgpu) cudssset(solver, Agpu)

Ccpu = rand(T, n, p) Cgpu = CuMatrix(C_cpu)

cudss("refactorization", solver, Xgpu, Cgpu) cudss("solve", solver, Xgpu, Cgpu)

Rgpu = Cgpu - ( CuSparseMatrixCSR(Acpu) + Diagonal(dgpu) ) * Xgpu norm(Rgpu) ```

Example 3: Sparse hermitian positive definite linear system with multiple right-hand sides

```julia using CUDA, CUDA.CUSPARSE using CUDSS using SparseArrays, LinearAlgebra

T = ComplexF64 R = real(T) n = 100 p = 5 Acpu = sprand(T, n, n, 0.01) Acpu = Acpu * Acpu' + I Xcpu = zeros(T, n, p) Bcpu = rand(T, n, p)

Agpu = CuSparseMatrixCSR(Acpu |> triu) Xgpu = CuMatrix(Xcpu) Bgpu = CuMatrix(Bcpu)

structure = T <: Real ? "SPD" : "HPD" solver = CudssSolver(A_gpu, structure, 'U')

cudss("analysis", solver, Xgpu, Bgpu) cudss("factorization", solver, Xgpu, Bgpu) cudss("solve", solver, Xgpu, Bgpu)

Rgpu = Bgpu - CuSparseMatrixCSR(Acpu) * Xgpu norm(R_gpu)

In-place LLᴴ

dgpu = rand(R, n) |> CuVector Agpu = Agpu + Diagonal(dgpu) cudssset(solver, Agpu)

Ccpu = rand(T, n, p) Cgpu = CuMatrix(C_cpu)

cudss("refactorization", solver, Xgpu, Cgpu) cudss("solve", solver, Xgpu, Cgpu)

Rgpu = Cgpu - ( CuSparseMatrixCSR(Acpu) + Diagonal(dgpu) ) * Xgpu norm(Rgpu) ```

Owner

  • Name: Exanauts
  • Login: exanauts
  • Kind: organization

An eclectic collection of ECP ExaSGD project codes

Citation (CITATION.cff) 

cff-version: 1.2.0
title: >-
  CUDSS.jl: Julia interface for NVIDIA cuDSS
message: >-
  If you use this software, please cite it using the
  metadata from this file.
type: software
authors:
  - given-names: Alexis
    family-names: Montoison
    email: alexis.montoison@polymtl.ca
    affiliation: >-
      Argonne National Laboratory, GERAD and Polytechnique Montréal
    orcid: 'https://orcid.org/0000-0002-3403-5450'
keywords:
  - Julia
  - cuDSS
  - direct methods
  - sparse linear systems
  - GPU computing
license: MIT
repository-code: >-
  https://github.com/exanauts/CUDSS.jl

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  • Total versions: 23
juliahub.com: CUDSS
  • Versions: 23
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Dependent repos count: 10.0%
Dependent packages count: 40.4%
Average: 41.9%
Forks count: 52.7%
Stargazers count: 64.6%
Last synced: 6 months ago

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