HBSMC
Harwell Boeing
Sparse Matrix Collection

HBSMC is a dataset directory which is the Harwell Boeing Sparse Matrix Collection, a representative collection of large sparse matrices gathered from a large variety of application areas.

The matrices in HBSMC can be used to test, verify, and compare algorithms for solving sparse systems of linear equations. There are also some least squares problems and eigenvalue calculations.

The original collection contained just 36 matrices, and those are directly accessible here. For the more recent and much larger collection, you need to refer to the web site.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

DLAP, a FORTRAN90 library which carries out the iterative solution of sparse linear systems, by Anne Greenbaum and Mark Seager.

HB_IO, a C++ library which reads and writes sparse linear systems stored in the Harwell Boeing (HB) format for sparse matrices.

HB_READ, a FORTRAN90 library which reads files in the Harwell Boeing (HB) sparse matrix format; This is a simplified interface intended to handle only the most common format, complex unsymmetric assembled (CUA) or real unsymmetric assembled (RUA).

HB_TO_MM, a MATLAB program which converts a sparse matrix from Harwell Boeing (HB) to Matrix Market (MM) format.

HB_TO_MSM, a MATLAB program which converts a sparse matrix stored in a Harwell Boeing (HB) format to MATLAB sparse matrix format;

HB_TO_ST, a FORTRAN77 program which converts a sparse matrix from Harwell Boeing (HB) format to Sparse Triplet (ST) format.

SUPERLU, a C program which applies a fast direct solution method to sparse linear systems, and can read a matrix that is stored in the Harwell Boeing sparse matrix format.

Reference:

1. Iain Duff, Roger Grimes, John Lewis,
   User's Guide for the Harwell-Boeing Sparse Matrix Collection,
   October 1992.
2. Iain Duff, Roger Grimes, John Lewis,
   Sparse Matrix Test Problems,
   ACM Transactions on Mathematical Software,
   Volume 15, pages 1-14, March 1989.
3. http://math.nist.gov/MatrixMarket/data/Harwell-Boeing/ the Matrix Market web site.

Code	Pattern	Max Order	Max Nonzeroes	Note
abb313_pra.txt	pattern rectangular assembled	313x176	1557	Sudan survey
add20_rua.txt	real unsymmetric assembled	2395x2395	17319	Steve Hamm 20 bit adder
arc130_rua.txt	real unsymmetric assembled	85x85	304	Laser problem
ash85_psa.txt	pattern symmetric assembled	85x85	304	Holland survey
ash219_pra.txt	pattern rectangular assembled	219x85	438	Survey of Holland
ash292_psa.txt	pattern symmetric assembled	292x292	1250	UK survey
ash331_pra.txt	pattern rectangular assembled	331x104	662	Scotland survey
ash608_pra.txt	pattern rectangular assembled	608x188	1216	England survey
ash958_pra.txt	pattern rectangular assembled	958x292	1916	UK survey
bp_0000_rua.txt	real unsymmetric assembled	822x822	3276	Simplex method basis
bp_0200_rua.txt	real unsymmetric assembled	822x822	3802	Simplex method basis
bp_0400_rua.txt	real unsymmetric assembled	822x822	4028	Simplex method basis
bp_0600_rua.txt	real unsymmetric assembled	822x822	4172	Simplex method basis
bp_0800.txt	real unsymmetric assembled	822x822	4534	Simplex method basis
bp_1000.txt	real unsymmetric assembled	822x822	4661	Simplex method basis
bp_1200.txt	real unsymmetric assembled	822x822	4726	Simplex method basis
bp_1400.txt	real unsymmetric assembled	822x822	4790	Simplex method basis
bp_1600.txt	real unsymmetric assembled	822x822	4841	Simplex method basis
cannes24_psa.txt	pattern symmetric assembled	24x24	92	Lucien Marro symmetric pattern
cg05_cua.txt	complex unsymmetric assembled	25x25	105	Complex test matrix for SUPERLU
cg10_cua.txt	complex unsymmetric assembled	100x100	460	Complex test matrix for SUPERLU
cg20_cua.txt	complex unsymmetric assembled	400x400	1920	Complex test matrix for SUPERLU
cmat_cua.txt	complex unsymmetric assembled	1280x1280	22778	Complex test matrix for SuperLU
curtis54_pua.txt	pattern unsymmetric assembled	54x54	291	Stiff biochemical ODE's
dwg961a_cua.txt	complex unsymmetric assembled	961x961	3405	Dispersive waveguide structures
eris1176_psa.txt	pattern symmetric assembled	1176x1176	9864	Electrical network
fs_541_1_rua.txt	real unsymmetric assembled	541x541	4285	Stage 1 of stiff atmospheric ODE
fs_541_2_rua.txt	real unsymmetric assembled	541x541	4285	Stage 2 of stiff atmospheric ODE
fs_541_3_rua.txt	real unsymmetric assembled	541x541	4285	Stage 3 of stiff atmospheric ODE
fs_541_4_rua.txt	real unsymmetric assembled	541x541	4285	Stage 4 of stiff atmospheric ODE
g05_rua.txt	real unsymmetric assembled	25x25	105	Real test matrix for SUPERLU
g10_rua.txt	real unsymmetric assembled	100x100	460	Real test matrix for SUPERLU
g20_rua.txt	real unsymmetric assembled	400x400	1920	Real test matrix for SUPERLU
gent113_pua.txt	pattern unsymmetric assembled	113x113	655	Statistical application
ibm32_pua.txt	pattern unsymmetric assembled	147x147	1298	IBM conference ad
illc1033.txt	real rectangular assembled	1033x320	4732	Unsymmetric least squares problem
jagmesh1_psa.txt	pattern symmetric assembled	936x936	3600	George: small hole square
jagmesh2_psa.txt	pattern symmetric assembled	1009x1009	3937	George: graded L
jagmesh3_psa.txt	pattern symmetric assembled	1089x1089	4225	George: plain square
jagmesh4_psa.txt	pattern symmetric assembled	1440x1440	5472	George: large hole square
jagmesh5_psa.txt	pattern symmetric assembled	1180x1180	4465	George: plus-shaped region
jagmesh6_psa.txt	pattern symmetric assembled	1377x1377	5185	George: H-shaped domain
jagmesh7_psa.txt	pattern symmetric assembled	1138x1138	4294	George: 3 hole problem
jagmesh8_psa.txt	pattern symmetric assembled	1141x1141	4303	George: 6 hole problem
jagmesh9_psa.txt	pattern symmetric assembled	1349x1349	5225	George: pinched hole problem
lund_a_rsa.txt	real symmetric assembled	147x147	1298	stiffness and mass
lund_b_rsa.txt	real symmetric assembled	147x147	1294	stiffness and mass
mahindas_rua.txt	real unsymmetric assembled	1258x1258	7682	Unsymmetric matrix
mhd1280b_cua.txt	complex unsymmetric assembled	1280x1280	22778	Alfven sprectra in magnetohydrodynamics
shl_000_rua.txt	real unsymmetric assembled	663x663	1687	Simplex method basis
shl_200_rua.txt	real unsymmetric assembled	663x663	1726	Simplex method basis
shl_400_rua.txt	real unsymmetric assembled	663x663	1712	Simplex method basis
str_000_rua.txt	real unsymmetric assembled	363x363	2454	Simplex method basis
str_200_rua.txt	real unsymmetric assembled	363x363	3068	Simplex method basis
str_400_rua.txt	real unsymmetric assembled	363x363	3157	Simplex method basis
str_600_rua.txt	real unsymmetric assembled	363x363	3279	Simplex method basis
utm300_rua.txt	real unsymmetric assembled	300x300	3155	UTM
will57_pua.txt	pattern unsymmetric assembled	57x57	281	Jacobian of a switch circuit
will199_pua.txt	pattern unsymmetric assembled	199x199	701	Stress analysis
young1c_csa.txt	complex unsymmetric assembled	841x841	4089	David Young aero research matrix

The following table lists the contents of the current version of the collection.

Code	Discipline	Matrices	Max Order	Max Nonzeroes
ACOUST	Acoustic scattering	4	841	4089
AIRTFC	Air traffic control	1	2873	15032
ASTROPH	Astrophysics	2	765	24382
BCSPWR	Power network matrices	14	5300	13571
BCSSTRUC1	Dynamic analysis in structural engineering	26	2003	42943
BCSSTRUC2	Static analysis in structural engineering	5	11948	80519
BCSSTRUC3	Structures, eigenproblems	22	15439	133840
BCSSTRUC4	Dynamic analysis in structural engineering	5	4410	111717
BCSSTRUC5	Structures, linear equations	36	44609	1029655
BCSSTRUC6	Structural engineering	2	3345	13047
CANNES	Finite elements in aircraft design	18	838	5424
CEGB	Finite elements in structural engineering	4	3306	9378
CHEMINP	Chemical engineering plant models	5	425	1339
CHEMWEST	Chemical engineering	16	2021	7353
CIRPHYS	Circuit physics	1	991	6027
COUNTERX	Counter examples, small matrices	3	11	76
DWT	Everstine test set, ship structures	30	2680	23853
ECONAUS	Australian economic models	11	2529	90158
ECONIEA	Economic models	9	497x507	53403
FACSIMILE	Chemical kinetics problems	10	760	5976
GEMAT	Optimal power flow problems	3	4929	47369
GRENOBLE	Simulation of Computer Systems	7	1107	5664
JAGMESH	Finite element model problem	9	1440	5472
LANPRO	Linear equations in structural engineering	7	960	8402
LAPLACE	Model PDE problems	3	900	4322
LAPU	Unassembled Laplace finite element matrices	1	25	64
LNS	Fluid flow modeling	7	3937	25407
LOCKHEED	Unassembled structural engineering matrices	4	3491	13507
LSHAPE	Graded L-shape patterns	21	3466	13681
LSQ	Least squares surveying problems	4	1850	10608
MANTEUFFEL	Unassembled finite element matrices	10	5976	15680
NNCENG	Flow in networks	1	434	4710
NUCL	Nuclear reactor core modelling	3	1374	8606
OILGEN	Oil reservoir modelling	19	5005	20033
PLATZ	Oceanography	4	1919	17159
PORES	Reservoir modeling	3	1224	9613
PSADMIT	Power system networks	4	1138	2596
PSMIGR	Demography	3	3140	543162
SAYLOR	Oil reservoir modeling	3	3564	22316
SHERMAN	Oil reservoir modeling	5	5005	20033
SMTAPE	Original Harwell test set	36	822	4841
STEAM	Oil recovery	3	600	13760
WATT	Petroleum Engineering	2	1865	11550

HB Sparse Matrix Storage

The Harwell Boeing Sparse Matrix Collection uses a special kind of sparse matrix storage for most of the matrices in the collection.

The standard sparse matrix format is column oriented. That is, the matrix is represented by a sequence of columns. Each column is held as a sparse vector, represented by a list of row indices of the entries in an integer array and a list of the corresponding values in a separate real array. A single integer array and a single real array are used to store the row indices and the values, respectively, for all the columns.

Data for each column are stored in consecutive locations. The columns are stored in order, and there is no space between columns. A separate integer array holds the location of the first entry of each column, and the first free location. For symmetric and Hermitian matrices, only the entries of the lower triangle are stored, including the diagonal. For antisymmetric matrices, only the strict lower triangle is stored.

Here is a simple example of a 5 by 5 matrix:

        1.0 -3.0  0.0 -1.0  0.0
        0.0  0.0 -2.0  0.0  3.0
        2.0  0.0  0.0  0.0  0.0
        0.0  4.0  0.0 -4.0  0.0
        5.0  0.0 -5.0  0.0  6.0
      

The Harwell Boeing format essentially thinks of this matrix as a collection of 5 column vectors:

        1.0 -3.0 -2.0 -1.0  3.0
        2.0  4.0 -5.0 -4.0  6.0
        5.0
      

This matrix would be stored in the arrays

• COLPTR (the location of the first entry of each column),
• ROWIND (the row index of each entry) and
• VALUES (the numerical value of each entry)

        Subscripts:   1    2    3    4    5    6    7    8    9   10   11

        COLPTR        1    4    6    8   10   12
        ROWIND        1    3    5    1    4    2    5    1    4    2    5
        VALUES      1.0  2.0  5.0 -3.0  4.0 -2.0 -5.0 -1.0 -4.0  3.0  6.0
      

HB Finite Element Matrix Storage

The Harwell Boeing finite element storage format is used for those matrices derived from finite element problems.

Matrices arising in finite element applications are usually assembled from numerous small elemental matrices. The collection includes a few sparse matrices in original unassembled form. The storage of the individual unassembled matrices is based on the general sparse format, which stores a matrix as a list of matrix columns. The elemental representation stores the matrix as a list of elemental matrices. Each elemental matrix is represented by a list of the row/column indices (variables) associated with the element and by a small dense matrix giving the numerical values by columns, or in the symmetric case, only the lower triangular part. The lists of indices are held contiguously, just as for the lists of row indices in the standard format. The dense matrices are held contiguously in a separate array, with each matrix held by columns. Although there is not a one to one correspondence between the arrays of integer and numerical values, the representation does not hold the pointers to the beginning of the real values for each element. These pointers can be created from the index start pointers (ELTPTR) after noting that an element with NU variables has NU*NU real values, or (NU*(NU+1))/2 in the symmetric case.

The unassembled finite element storage scheme can be illustrated with a small, 5 by 5 symmetric example matrix:

        5.0  0.0  0.0  1.0  2.0
        0.0  4.0  3.0  0.0  6.0
        0.0  3.0  7.0  8.0  1.0
        1.0  0.0  8.0  9.0  0.0
        2.0  6.0  1.0  0.0 10.0
      

            1   4         1   5        2   3   5        3   4
        1 (2.0 1.0)   1 (3.0 2.0)  2 (4.0 3.0 6.0)  3 (2.0 8.0)
        4 (1.0 7.0)   5 (2.0 8.0)  3 (3.0 5.0 1.0)  4 (8.0 2.0)
                                   5 (6.0 1.0 2.0)
      

• ELTPTR = location in VARIND of first entry for a given element;
• VARIND = variable index = row index;
• VALUES = numerical values,

 
        Subscripts:  1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
        ELTPTR:      1       3       5           8      10
        VARIND:      1   4   1   5   2   3   5   3   4
        VALUES:      2.  1.  7.  3.  2.  8.  4.  3.  6.  5.  1.  2.  2.  8.  2.
      

You can go up one level to the DATASETS directory.