HSL

"HSL (formerly the Harwell Subroutine Library) is a collection of state-of-the-art packages for large-scale scientific computation written and developed by the Numerical Analysis Group at the STFC Rutherford Appleton Laboratory and other experts. HSL offers users a high standard of reliability and has an international reputation as a source of robust and efficient numerical software. Among its best known packages are those for the solution of sparse linear systems of equations and sparse eigenvalue problems. MATLAB interfaces are offered for selected packages.

The Library was started in 1963 and was originally used at the Harwell Laboratory on IBM mainframes running under OS and MVS. Over the years, the Library has evolved and has been extensively used on a wide range of computers, from supercomputers to modern PCs. Recent additions include optimised support for multicore processors.

The available routines are:

• 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 ALGERBA
  • 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_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

  • 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

  • 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

• 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

     

     

    http://www.hsl.rl.ac.uk/