Hmatrix.jl

Hmatrix.jl is a hierarchical matrix library in Julia. Current implementations include construction, matrix vector multiplication, LU factorization and solve. It is written to achieve linear complexity for both storage and computation.

Installing

]add https://github.com/kailaix/Hmatrix.jl
]build Hmatrix

Testing

]test Hmatrix

Getting Started

Hparams.verbose = true
X = LinRange(0,10,2000)|>collect
Hparams.Geom = X  # create a geometric cluster 
Hparams.Kernel = (x,y)->1/(1+(x-y)^2) # define the kernel
Hparams.MaxBlock = 500 # maximum number of leaves in a block
Hparams.MinBlock = 64 # minimum number of leaves in a block
Hparams.MaxRank = 5 # maximum rank for compression
c, H = NewHmat() # create a new H matrix
A = FullMat(Hparams.Kernel, c.X, c.X) # computing the full matrix

H can be used just like a normal matrix

y = rand(2000)
H*y
H\y
lu(H)

Authors

• Kailai Xu - Kailai Xu

Research Work

Xu, Kailai, and Eric Darve. "Efficient Numerical Method for Models Driven by L\'evy Process via Hierarchical Matrices." arXiv preprint arXiv:1812.08324 (2018).

License

This project is licensed under the MIT License - see the LICENSE.md file for details