HSL
These are the beginnings of a set of interfaces to HSL packages for sparse linear algebra.
Certain HSL packages are freely available to all, others are freely available to academics only. Please refer to the website above for licensing information. In all cases, users are responsible for obtaining HSL packages.
Installing
julia> ]
pkg> add HSLAt this point, make sure that there isn't a stray METIS library on your library
path. You especially want to make sure that METIS 5 is not accessible because
the HSL library currently interfaced only supports METIS 4. If you have such
library accessible, it is important to remove it from the library path, at
least temporarily. For example, if you are on OSX and are using Homebrew, you
can hide METIS 5 with brew unlink metis. After the install procedure is
complete, it is fine to link metis again with brew link metis.
Set the environment variable HSL_ARCHIVES_PATH to specify where the source archives tar.gz and zip are stored.
You can use the zip archives as long as unzip is installed on your system.
If archives are stored in different folders, you can also set the environment variable <ALGNAME>_PATH, e.g. HSL_MA57_PATH or MC21_PATH.
The HSL Julia module will take care of compilation.
Once the source archives have been placed in the locations indicated by the environment variables, run
julia> ]
pkg> build HSL
pkg> test HSLNote that a C and Fortran compilers are required. Should it be necessary, you can set the compilers to use by setting the environment variables
HSL_FC: the Fortran 90/95 compiler (default:gfortran)HSL_F77: the Fortran 77 compiler (default: the same asFC)HSL_CC: the C compiler (default:gcc).
Supported Packages
HSL_MA97
Supported versions:
- 2.6.0
- 2.7.0
HSL_MA97: an OpenMP-based direct solver for symmetric linear systems. Example:
using MatrixMarket
using HSL
K = MatrixMarket.mmread("K.mtx") # only the lower triangle
rhs = readdlm("rhs.rhs")
LBL = Ma97(K)
ma97_factorize!(LBL)
x = ma97_solve(LBL, rhs) # or x = LBL \ rhsRectangular Systems
There is a convenience interface to solve rectangular systems that complements the sparse QR factorization in Julia.
When A is m-by-n with m < n and has full row rank,
(x, y) = ma97_solve(A, b)solves for the minimum-norm solution, i.e., x such that Ax = b and x + Aᵀ y = 0. The call
(x, y) = ma97_min_norm(A, b)is also defined, and is equivalent to the above.
When m > n and has full column rank,
(r, x) = ma97_solve(A, b)solves for the least-squares solution, i.e., x such that r = b - Ax satisfies Aᵀ r = 0. The call
(r, x) = ma97_least_squares(A, b)is also defined, and is equivalent to the above.
HSL_MA57
HSL_MA57 version 5.2.0: a sparse, multifrontal solver for symmetric linear systems. Example:
using MatrixMarket
using HSL
K = MatrixMarket.mmread("examples/K_0.mtx") # only the lower triangle
rhs = readdlm("examples/rhs_0.rhs")
rhss = hcat(rhs, rhs)
## factorize and solve
LDL = Ma57(K)
ma57_factorize!(LDL)
LDL.info.rank
x = ma57_solve(LDL, rhs) # or x = LBL \ rhs
norm(K*x - rhs)
xx = ma57_solve(LDL, rhss) # or x = LBL \ rhssRectangular Systems
There is a convenience interface to solve rectangular systems that complements the sparse QR factorization in Julia.
When A is m-by-n with m < n and has full row rank,
(x, y) = ma57_solve(A, b)solves for the minimum-norm solution, i.e., x such that Ax = b and x + Aᵀ y = 0. The call
(x, y) = ma57_min_norm(A, b)is also defined, and is equivalent to the above.
When m > n and has full column rank,
(r, x) = ma57_solve(A, b)solves for the least-squares solution, i.e., x such that r = b - Ax satisfies Aᵀ r = 0. The call
(r, x) = ma57_least_squares(A, b)is also defined, and is equivalent to the above. Example:
using MatrixMarket
using HSL
K = MatrixMarket.mmread("examples/K_0.mtx") # only the lower triangle
rhs = readdlm("examples/rhs_0.rhs")
## solve min norm
K_mn = K[1:200,:]
x_mn, y_mn = ma57_min_norm(K_mn, rhs[1:200]) # == ma57_solve(K_mn, rhs[1:200])
## solve least squares
K_ls = K[:,1:200]
r_ls, x_ls = ma57_least_squares(K_ls, rhs) # == ma57_solve(K_ls, rhs)