• SJSU Singular Matrix Database
  • Matrix group: Meszaros
  • Click here for a description of the Meszaros group.
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  • Matrix: Meszaros/iprob
  • Description: Problematic linear programming problem, Meszaros test set
  • download as a MATLAB mat-file, file size: 42 KB. Use SJget(133) or SJget('Meszaros/iprob') in MATLAB.
  • download in Matrix Market format, file size: 42 KB.
  • download in Rutherford/Boeing format, file size: 42 KB.

    Meszaros/iprob

    Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

    Meszaros/iprob

    Matrix properties (click for a legend)  
    number of rows3,001
    number of columns3,001
    structural full rank?yes
    structural rank3,001
    numerical rank 3,000
    dimension of the numerical null space1
    numerical rank / min(size(A))0.99967
    Euclidean norm of A 1.3226e+005
    calculated singular value # 30001
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    8.7341e-008
    calculated singular value # 30013.921e-017
    gap in the singular values at the numerical rank:
    singular value # 3000 / singular value # 3001
    2.5503e+016
    calculated condition number3.373e+021
    condest8.918e+022
    nonzeros9,000
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetry 50%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    author
    editorC. Meszaros
    date2004
    kindlinear programming problem
    2D/3D problem?no
    SJid133
    UFid1,790

    Additional fieldssize and type
    bfull 3001-by-1
    cfull 3001-by-1
    lofull 3001-by-1
    hifull 3001-by-1
    z0full 1-by-1

    Notes:

    http://www.sztaki.hu/~meszaros/public_ftp/lptestset      
    Converted to standard form via Resende and Veiga's mpsrd:
    minimize c'*x, subject to A*x=b and lo <= x <= hi        
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))6,001 6,001
    Cholesky flop count1.2e+004 1.2e+004
    nnz(L+U), no partial pivoting9,001 9,001
    nnz(V) for QR, upper bound nnz(L) for LU6,001 4,504,500
    nnz(R) for QR, upper bound nnz(U) for LU4,504,501 4,504,501

    Maintained by Leslie Foster, last updated 24-Apr-2009.

    Entries 5 through 14 in the table of matrix properties and the singular
    value plot were created using SJsingular code. The other plots
    and statistics are produced using utilities from the SuiteSparse package.
    Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.