• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lpi_box1
  • Description: Netlib LP problem box1: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 4 KB. Use SJget(272) or SJget('LPnetlib/lpi_box1') in MATLAB.
  • download in Matrix Market format, file size: 4 KB.
  • download in Rutherford/Boeing format, file size: 3 KB.

    LPnetlib/lpi_box1

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

    LPnetlib/lpi_box1

    Matrix properties (click for a legend)  
    number of rows231
    number of columns261
    structural full rank?yes
    structural rank231
    numerical rank 214
    dimension of the numerical null space47
    numerical rank / min(size(A))0.92641
    Euclidean norm of A 6.013
    calculated singular value # 2140.13184
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.3181e-013
    calculated singular value # 2151.3318e-015
    gap in the singular values at the numerical rank:
    singular value # 214 / singular value # 215
    9.899e+013
    calculated condition number3.4229e+016
    condest-2
    nonzeros651
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typeinteger
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorZ. You
    editorJ. Chinneck
    date1992
    kindlinear programming problem
    2D/3D problem?no
    SJid272
    UFid707

    Additional fieldssize and type
    bfull 231-by-1
    cfull 261-by-1
    lofull 261-by-1
    hifull 261-by-1
    z0full 1-by-1

    Notes:

    An infeasible Netlib LP problem, in lp/infeas.  For more information        
    send email to netlib@ornl.gov with the message:                             
                                                                                
    	send index from lp                                                         
    	send readme from lp/infeas                                                 
                                                                                
    The lp/infeas directory contains infeasible linear programming test problems
    collected by John W. Chinneck, Carleton Univ, Ontario Canada.  The following
    are relevant excerpts from lp/infeas/readme (by John W. Chinneck):          
                                                                                
    In the following, IIS stands for Irreducible Infeasible Subsystem, a set    
    of constraints which is itself infeasible, but becomes feasible when any    
    one member is removed.  Isolating an IIS from within the larger set of      
    constraints defining the model is one analysis approach.                    
                                                                                
    PROBLEM DESCRIPTION                                                         
    -------------------                                                         
                                                                                
    BOX1, EX72A, EX73A:  medium problems derived from research on using the     
    infeasibility version of viability analysis [Chinneck 1992] to analyze      
    petri net models.  All three problems are volatile, showing IISs of         
    widely differing size depending on the algorithm applied.  Contributor:     
    Zhengping You, Carleton University.                                         
                                                                                
    Name       Rows   Cols   Nonzeros Bounds      Notes                         
    box1        232    261      912   B            all cols are LO bounded      
                                                                                
    REFERENCES                                                                  
    ----------                                                                  
                                                                                
    J.W.  Chinneck (1992).  "Viability Analysis:  A Formulation Aid for All     
    Classes of Network Models", Naval Research Logistics, Vol.  39, pp.         
    531-543.                                                                    
                                                                                
    Added to Netlib on Sept. 19, 1993                                           
                                                                                
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU854 634
    nnz(R) for QR, upper bound nnz(U) for LU1,164 1,163

    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.