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MatrixDepot

An Extensible Test Matrix Collection for Julia

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An extensible test matrix collection for Julia.

NOTE: If you use Windows, you need to install MinGW/MSYS or Cygwin in order to use the UF sparse matrix collection interface.

Install

To install the release version, type

julia> Pkg.add("MatrixDepot")

Basic Usage

To see all the matrices in the collection, type

julia> using MatrixDepot
julia> matrixdepot()

Matrices:
   1) baart            2) binomial         3) blur             4) cauchy        
   5) chebspec         6) chow             7) circul           8) clement       
   9) companion       10) deriv2          11) dingdong        12) fiedler       
  13) forsythe        14) foxgood         15) frank           16) golub         
  17) gravity         18) grcar           19) hadamard        20) hankel        
  21) heat            22) hilb            23) invhilb         24) invol         
  25) kahan           26) kms             27) lehmer          28) lotkin        
  29) magic           30) minij           31) moler           32) neumann       
  33) oscillate       34) parter          35) pascal          36) pei           
  37) phillips        38) poisson         39) prolate         40) randcorr      
  41) rando           42) randsvd         43) rohess          44) rosser        
  45) sampling        46) shaw            47) spikes          48) toeplitz      
  49) tridiag         50) triw            51) ursell          52) vand          
  53) wathen          54) wilkinson       55) wing          
Groups:
  all           data          eigen         ill-cond    
  inverse       pos-def       random        regprob     
  sparse        symmetric 

We can generate a 4-by-4 Hilbert matrix by typing

julia> matrixdepot("hilb", 4)
4x4 Array{Float64,2}:
 1.0       0.5       0.333333  0.25    
 0.5       0.333333  0.25      0.2     
 0.333333  0.25      0.2       0.166667
 0.25      0.2       0.166667  0.142857

We can type the matrix name to get help.

julia> matrixdepot("hilb")
     Hilbert matrix
    ≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

  The Hilbert matrix has (i,j) element 1/(i+j-1). It is notorious for being
  ill conditioned. It is symmetric positive definite and totally positive.

  Input options:

    •  [type,] dim: the dimension of the matrix;

    •  [type,] row_dim, col_dim: the row and column dimensions.

  Groups: ["inverse", "ill-cond", "symmetric", "pos-def"]

  References: 

  M. D. Choi, Tricks or treats with the Hilbert matrix, Amer. Math. Monthly,
  90 (1983), pp. 301-312.

  N. J. Higham, Accuracy and Stability of Numerical Algorithms, second
  edition, Society for Industrial and Applied Mathematics, Philadelphia, PA,
  USA, 2002; sec. 28.1.

We can also specify the data type

julia> matrixdepot("hilb", Float16, 5, 3)
5x3 Array{Float16,2}:
 1.0      0.5      0.33325
 0.5      0.33325  0.25   
 0.33325  0.25     0.19995
 0.25     0.19995  0.16663
 0.19995  0.16663  0.14282

julia> matrixdepot("hilb", Rational, 4)
4x4 Array{Rational{T<:Integer},2}:
 1//1  1//2  1//3  1//4
 1//2  1//3  1//4  1//5
 1//3  1//4  1//5  1//6
 1//4  1//5  1//6  1//7

Matrices can be accessed by number, range or a mixture of numbers and ranges.

julia> matrixdepot(5)
"chow"

julia> matrixdepot(5:10)
6-element Array{AbstractString,1}:
 "chow"    
 "circul"  
 "clement" 
 "deriv2"  
 "dingdong"
 "fiedler"

julia> matrixdepot(1:4, 6, 10:15)
11-element Array{AbstractString,1}:
 "baart"   
 "binomial"
 "cauchy"  
 "chebspec"
 "circul"  
 "fiedler" 
 "forsythe"
 "foxgood" 
 "frank"   
 "gravity" 
 "grcar" 

We can type a group name to see all the matrices in that group.

julia> matrixdepot("symmetric")
21-element Array{ASCIIString,1}:
 "cauchy"   
 "circul"   
 "clement"  
 "dingdong" 
 "fiedler"  
 "hankel"   
 "hilb"     
 "invhilb"  
 "kms"      
 "lehmer"   
 ⋮          
 "oscillate"
 "pascal"   
 "pei"      
 "poisson"  
 "prolate"  
 "randcorr" 
 "tridiag"  
 "wathen"   
 "wilkinson"

Extend Matrix Depot

We can add more matrices to Matrix Depot by downloading them from UF sparse matrix collection and Matrix Market. See here for more details. In addition, we can add new matrix generators and define new groups of matrices.

Interface to the UF Sparse Matrix Collection

Use matrixdepot(NAME, :get), where NAME is collection_name + '/' + matrix_name, to download a test matrix from the University of Florida Sparse Matrix Collection: http://www.cise.ufl.edu/research/sparse/matrices/list_by_id.html. For example:

julia> matrixdepot("HB/1138_bus", :get)

Use matrixdepot(collection_name/*, :get ) to download a group of all the matrices in collection_name from UF sparse matrix collection. For example:

julia> matrixdepot("MathWorks/*", :get)

When download is complete, we can check matrix information using

julia> matrixdepot("HB/1138_bus")
%%MatrixMarket matrix coordinate real symmetric
%----------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/HB/1138_bus
% name: HB/1138_bus
% [S ADMITTANCE MATRIX 1138 BUS POWER SYSTEM, D.J.TYLAVSKY, JULY 1985.]
% id: 1
% date: 1985
% author: D. Tylavsky
% ed: I. Duff, R. Grimes, J. Lewis
% fields: title A name id date author ed kind
% kind: power network problem
%---------------------------------------------------------------------

and generate it with the Symbol :r or :read.

julia> matrixdepot("HB/1138_bus", :r)
1138x1138 Symmetric{Float64,SparseMatrixCSC{Float64,Int64}}:
 1474.78      0.0       0.0     …   0.0       0.0         0.0    0.0  
    0.0       9.13665   0.0         0.0       0.0         0.0    0.0  
    0.0       0.0      69.6147      0.0       0.0         0.0    0.0  
    0.0       0.0       0.0         0.0       0.0         0.0    0.0  
   -9.01713   0.0       0.0         0.0       0.0         0.0    0.0  
    0.0       0.0       0.0     …   0.0       0.0         0.0    0.0  
    0.0       0.0       0.0         0.0       0.0         0.0    0.0  
    0.0       0.0       0.0         0.0       0.0         0.0    0.0  
    0.0       0.0       0.0         0.0       0.0         0.0    0.0  
    0.0      -3.40599   0.0         0.0       0.0         0.0    0.0  
    ⋮                           ⋱             ⋮                       
    0.0       0.0       0.0         0.0       0.0         0.0    0.0  
    0.0       0.0       0.0     …   0.0     -24.3902      0.0    0.0  
    0.0       0.0       0.0         0.0       0.0         0.0    0.0  
    0.0       0.0       0.0         0.0       0.0         0.0    0.0  
    0.0       0.0       0.0         0.0       0.0         0.0    0.0  
    0.0       0.0       0.0        26.5639    0.0         0.0    0.0  
    0.0       0.0       0.0     …   0.0      46.1767      0.0    0.0  
    0.0       0.0       0.0         0.0       0.0     10000.0    0.0  
    0.0       0.0       0.0         0.0       0.0         0.0  117.647

Note matrixdepot() displays all the matrices in the collection, including the newly downloaded matrices.

julia> matrixdepot()

Matrices:
   1) baart            2) binomial         3) blur             4) cauchy        
   5) chebspec         6) chow             7) circul           8) clement       
   9) companion       10) deriv2          11) dingdong        12) fiedler       
  13) forsythe        14) foxgood         15) frank           16) golub         
  17) gravity         18) grcar           19) hadamard        20) hankel        
  21) heat            22) hilb            23) invhilb         24) invol         
  25) kahan           26) kms             27) lehmer          28) lotkin        
  29) magic           30) minij           31) moler           32) neumann       
  33) oscillate       34) parter          35) pascal          36) pei           
  37) phillips        38) poisson         39) prolate         40) randcorr      
  41) rando           42) randsvd         43) rohess          44) rosser        
  45) sampling        46) shaw            47) spikes          48) toeplitz      
  49) tridiag         50) triw            51) ursell          52) vand          
  53) wathen          54) wilkinson       55) wing            56) HB/1138_bus   

Groups:
  all           data          eigen         ill-cond    
  inverse       pos-def       random        regprob     
  sparse        symmetric  

The NIST Matrix Market interface is similar. See documentation for more details.

References

  • Weijian Zhang and Nicholas J. Higham, "Matrix Depot: An Extensible Test Matrix Collection for Julia", PeerJ Comput. Sci., 2:e58 (2016), [pdf]

  • Nicholas J. Higham, "Algorithm 694, A Collection of Test Matrices in MATLAB", ACM Trans. Math. Software, vol. 17. (1991), pp 289-305 [pdf] [doi]

  • T.A. Davis and Y. Hu, "The University of Florida Sparse Matrix Collection", ACM Transaction on Mathematical Software, vol. 38, Issue 1, (2011), pp 1:1-1:25 [pdf]

  • R.F. Boisvert, R. Pozo, K. A. Remington, R. F. Barrett, & J. Dongarra, " Matrix Market: a web resource for test matrix collections", Quality of Numerical Software (1996) (pp. 125-137). [pdf]

  • Per Christian Hansen, "Test Matrices for Regularization Methods", SIAM Journal on Scientific Computing, vol. 16, 2, (1995) pp.506-512. [pdf] [doi]

First Commit

11/25/2014

Last Touched

4 days ago

Commits

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