Interfacing the HSL

[dpo]

Below is the full list of HSL packages from https://www.hsl.rl.ac.uk/catalogue.

This issue is used to track the progress on HSL interfaces and to assign a priority to each.
Next to each package, please indicate:

• a link to the pull request where the interface is implemented;
• a priority level: 🥇 = high, 🥈 = medium, 🥉 = low.

As a guideline:

• functionality that is already available in pure Julia should have low priority;
• functionality that is already available via an interface to another low-level library should have low or medium priority.

Tick the box when an interface is complete and the pull request has been merged.

We will proceed in stages.

• Stage 1:

  • Packages with a C interface 🏆

• Stage 2:

  • MA Section
  • MC Section

• Next stages: TBD

---

EIGENVALUES AND EIGENVECTORS

EA: Eigenvalues and eigenvectors of real symmetric matrices

• EA16 Compute selected eigenpairs using rational Lanczos method
• HSL_EA19 Sparse symmetric or Hermitian: leftmost eigenpairs
• HSL_EA20 s-root of a sparse self-adjoint positive-definite pencil
• EA22 Sparse symmetric: simultaneous iteration
• EA25 Sparse symmetric: Lanczos for the spectrum

EB: Eigenvalues and eigenvectors of general matrices

• EB13 Sparse unsymmetric: Arnoldi’s method
• EB22 Sparse unsymmetric: subspace iteration

EP: Parallel eigenvalues and eigenvectors of real symmetric matrices

• EP25 Sparse symmetric: Lanczos for the spectrum

MATHEMATICAL FUNCTIONS

FA: Random numbers

• FA14 Uniform distribution
• HSL_FA14 Uniform distribution

FD: Simple Functions

• FD15 Real-valued machine constants

SORTING

KB: Sorting numbers

• KB05 Sort numbers into ascending order using Quicksort
• KB06 Sort numbers into descending order using Quicksort
• KB07 Sort numbers into ascending order with indexing using Quicksort
• KB08 Sort numbers into descending order with indexing using Quicksort
• HSL_KB22 Sorting reals using the Heapsort method

LINEAR PROGRAMMING

LA: Linear prgramming, i.e. minimization of a linear function subject to linear constraints

• LA04 Sparse linear programming: steepest-edge simplex method
• LA15 Sparse mathematical programming bases: factorize and update

LINEAR ALGEBRA

MA: Solution of linear systems

• MA38 Sparse unsymmetric system: unsymmetric multifrontal method
• MA41 Sparse unsymmetric system: unsymmetric multifrontal method
• MA42 Sparse unsymmetric system: out-of-core frontal method
• HSL_MA42_ELEMENT Unsymmetric finite-element system: out-of-core frontal method (real and complex)
• HSL_MA42 Sparse unsymmetric system: out-of-core frontal method
• MA43 Sparse unsymmetric system: row-by-row frontal method
• MA44 Over-determined linear system: least-squares solution
• MA46 Sparse unsymmetric finite-element system: multifrontal
• MA48 Sparse unsymmetric system: driver for conventional direct method
• HSL_MA48 Sparse unsymmetric system: driver for conventional direct method 🏆 🥈
• MA49 Sparse over-determined system: least squares by QR
• MA50 Sparse unsymmetric system: conventional direct method
• MA51 Auxiliary for MA48 and MA50: identify ignored rows or columns in the rectangular or rank-deficient case, compute determinant
• MA52 Sparse unsymmetric finite-element system: out-of-core multiple front method
• HSL_MA54 Definite symmetric full matrix: partial or complete factorization and solution
• HSL_MA55 Band symmetric positive-definite system
• MA57 Sparse symmetric system: multifrontal method
• HSL_MA57 Sparse symmetric system: multifrontal method 🏆 🥉
• MA60 Iterative refinement and error estimation
• MA61 Sparse symmetric positive-definite system: incomplete factorization
• MA62 Sparse symmetric finite-element system: out-of-core frontal method
• HSL_MA64 Indefinite symmetric full matrix: partial or complete factorization and solution
• MA65 Unsymmetric banded system of linear equations
• MA67 Sparse symmetric system, zeros on diagonal: blocked conventional
• MA69 Unsymmetric system whose leading subsystem is easy to solve
• HSL_MA69 Unsymmetric system whose leading subsystem is easy to solve
• MA72 Sparse symmetric finite-element system: out-of-core multiple front method
• HSL_MA74 Unsymmetric full matrix: partial or complete factorization and solution
• MA75 Sparse over-determined system: weighted least squares
• HSL_MA77 Sparse symmetric system: multifrontal out of core 🏆 🥇
• HSL_MA78 Sparse unsymmetric finite-element system: multifrontal out of core
• HSL_MA79 Sparse symmetric system: mixed precision
• HSL_MA85 Sparse diagonally-weighted linear least squares solver
• HSL_MA86 Sparse solver for real and complex indefinite matrices using OpenMP 🏆 🥇
• HSL_MA87 Sparse Cholesky solver for real/complex matrices using OpenMP 🏆 🥇
• HSL_MA97 Bit-compatible parallel sparse symmetric/Hermitian solver using OpenMP 🏆 🥉

MC: Computations with real matrices and vectors

• MC13 Permute a sparse matrix to block triangular form
• MC21 Permute a sparse matrix to put entries on the diagonal
• MC22 Permute a sparse matrix given row and column permutations
• MC25 Permute a sparse matrix to block triangular form
• MC26 Sparse rectangular matrix: compute normal matrix
• MC29 Sparse unsymmetric matrix: calculate scaling factors
• MC30 Sparse symmetric matrix: calculate scaling factors
• MC33 Sparse unsymmetric matrix: permute to bordered block triangular form
• MC34 Sparse symmetric structure: expand from lower triangle
• HSL_MC34 Sparse symmetric structure: expand from lower triangle
• MC37 Sparse symmetric matrix: represent as a sum of element matrices
• MC38 Sparse rectangular matrix held by columns: transpose
• MC44 Unassembled finite-element matrix: generate the element or supervariable connectivity graph
• MC46 Sparse rectangular matrix held by rows: transpose
• MC47 Sparse symmetric pattern: approximate minimum-degree ordering allowing dense rows
• MC53 Generate an ordering for finite-element matrices within a subdomain
• MC54 Write a sparse matrix in Rutherford-Boeing format
• MC55 Write a supplementary file in Rutherford-Boeing format
• MC56 Read a file or a supplementary file held in Rutherford-Boeing format
• HSL_MC56 Read a file containing a sparse matrix held in format
• MC57 Assemble a set of finite-element matrices
• MC58 Estimate rank and find independent rows/columns of a sparse unsymmetric or rectangular matrix
• MC59 Sort a sparse matrix to an ordering by columns
• MC60 Sparse symmetric pattern: reduce the profile and wavefront
• MC61 Straightforward interface to MC60
• MC62 Generate a row ordering for a row-by-row frontal solver
• MC63 Generate an element assembly ordering for a frontal solver
• MC64 Permute and scale a sparse unsymmetric matrix to put large entries on the diagonal
• HSL_MC64 Permute and scale a sparse unsymmetric or rectangular matrix to put large entries on the diagonal 🏆 🥇
• HSL_MC65 Construct and manipulate matrices in compressed sparse row format
• HSL_MC66 Permute an unsymmetric sparse matrix to singly bordered blocked diagonal form
• MC67 Refine a profile-reducing permutation of a symmetric matrix
• HSL_MC68 Symmetric sparse matrix: compute elimination orderings 🏆 🥉
• HSL_MC69 Matrix format converter 🏆 🥉
• MC71 Unsymmetric matrix: estimate 1-norm
• MC72 Full unsymmetric matrix: calculate scaling factors
• HSL_MC73 Sparse symmetric matrix: compute Fiedler vector and permute to reduce the profile and wavefront
• MC75 Sparse unsymmetric matrix: estimate condition number
• MC77 Sparse unsymmetric matrix: calculate scaling factors
• HSL_MC78 Analysis phase in Cholesky algorithm 🏆 🥉
• HSL_MC79 Sparse matrix: maximum matching and Dulmage-Mendelsohn decomposition 🏆 🥉
• HSL_MC80 Sparse symmetric matrix: matching-based ordering and scaling
• HSL_MC81 Randomized methods for low-rank matrix approximation

ME: Solution of complex linear systems and other calculations for complex matrices

• ME22 Permute a sparse matrix given row and column permutations
• ME38 Sparse unsymmetric system: unsymmetric multifrontal method
• ME42 Sparse unsymmetric system: out-of-core frontal method
• ME43 Sparse unsymmetric system: row-by-row frontal method
• ME48 Sparse unsymmetric system: driver for conventional direct method
• ME50 Sparse unsymmetric system: conventional direct method
• ME57 Sparse Hermitian or complex symmetric: multifrontal method
• HSL_ME57 Sparse solver for complex symmetric or Hermitian linear systems
• ME62 Sparse Hermitian or complex symmetric finite-element system: out-of-core frontal method

See also
HSL_MA86 (Parallel sparse symmetric indefinite/Hermitian)
HSL_MA87 (Parallel sparse Cholesky)
HSL_MA97 (Bit-compatible parallel sparse symmetric/Hermitian)

MF: Computations with complex matrices and vectors

• MF29 Sparse unsymmetric matrix: calculate scaling factors
• MF30 Sparse symmetric matrix: calculate scaling factors
• MF64 Permute and scale a sparse complex unsymmetric matrix to put large entries on the diagonal
• MF71 Unsymmetric matrix: estimate 1-norm

MI: Iterative methods for sparse matrices

• HSL_MI02 Symmetric possibly-indefinite system: SYMMBK method
• MI11 Unsymmetric system: incomplete LU factorization
• MI12 Unsymmetric system: approximate-inverse preconditioner
• HSL_MI13 Preconditioners for saddle-point systems
• MI15 Unsymmetric system: flexible GMRES
• HSL_MI20 Unsymmetric system: algebraic multigrid preconditioner 🏆 🥈
• MI21 Symmetric positive-definite system: conjugate gradient method
• MI23 Unsymmetric system: CGS (conjugate gradient squared) method
• MI24 Unsymmetric system: GMRES (generalized minimal residual) method
• MI25 Unsymmetric system: BiCG (BiConjugate Gradient) method
• MI26 Unsymmetric system: BiCGStab (BiConjugate Gradient Stabilized) method
• HSL_MI27 Projected preconditioned conjugate gradient method for saddle-point systems
• HSL_MI28 Symmetric system: incomplete Cholesky factorization
• HSL_MI29 MPGMRES: an extension of GMRES which allows multiple preconditioners
• HSL_MI30 Symmetric indefinite saddle-point system: signed incomplete Cholesky factorization
• HSL_MI31 Symmetric positive-definite system: conjugate gradient method, stopping according to the A-norm of the error
• HSL_MI32 Symmetric possibly-indefinite system: MINRES method
• HSL_MI35 Sparse least squares: incomplete factorization preconditioner #134

MP: MPI dependant packages

• HSL_MP01 MPI constants
• HSL_MP42 Unsymmetric finite-element system: multiple-front method, element entry
• HSL_MP43 Sparse unsymmetric system: multiple-front method, equation entry
• HSL_MP48 Sparse unsymmetric system: parallel direct method
• HSL_MP54 Parallel Cholesky solver
• HSL_MP62 Symmetric finite-element system: multiple-front method
• HSL_MP82 Tall-skinny QR factorization

NONLINEAR EQUATIONS

NS: Solution of systems of nonlinear equations in several unknowns

• NS23 Sparse nonlinear over-determined equations: Marquardt method

INPUT/OUTPUT

OF: File management

• HSL_OF01 Fortran virtual memory

POLYNOMIAL AND RATIONAL FUNCTIONS

PA: Zeros of polynomials

• PA16 Complex coefficients: all roots by the method of Madsen and Reid
• PA17 Real coefficients: all roots by the method of Madsen and Reid

TEST PROGRAM GENERATORS

YM: Generate test programs for chapter M of the library

• YM11 Generate a random sparse matrix

FORTRAN SYSTEM FACILITES

ZB: Array allocation

• HSL_ZB01 Reallocate an array

ZD: Derived types

• HSL_ZD11 Derived type for sparse matrix storage schemes

[amontoison]

I added a trophy 🏆 for packages with a C interface.

[dpo]

Thanks. I added a priority next to them.