• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lpi_cplex2
  • Description: Netlib LP problem cplex2: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 6 KB. Use SJget(275) or SJget('LPnetlib/lpi_cplex2') in MATLAB.
  • download in Matrix Market format, file size: 5 KB.
  • download in Rutherford/Boeing format, file size: 4 KB.

    LPnetlib/lpi_cplex2

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

    LPnetlib/lpi_cplex2

    Matrix properties (click for a legend)  
    number of rows224
    number of columns378
    structural full rank?yes
    structural rank224
    numerical rank 223
    dimension of the numerical null space155
    numerical rank / min(size(A))0.99554
    Euclidean norm of A 15.555
    calculated singular value # 2230.03364
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    6.7146e-013
    calculated singular value # 2244.1489e-016
    gap in the singular values at the numerical rank:
    singular value # 223 / singular value # 224
    8.1083e+013
    calculated condition number3.7492e+016
    condest-2
    nonzeros1,215
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorE. Klotz
    editorJ. Chinneck
    date1993
    kindlinear programming problem
    2D/3D problem?no
    SJid275
    UFid711

    Additional fieldssize and type
    bfull 224-by-1
    cfull 378-by-1
    lofull 378-by-1
    hifull 378-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                                                         
    -------------------                                                         
                                                                                
    CPLEX1, CPLEX2:  medium and large problems respectively.  CPLEX1            
    referred to as CPLEX problem in Chinneck [1993], and is remarkably          
    non-volatile, showing a single small IIS regardless of the IIS algorithm    
    applied.  CPLEX2 is an almost-feasible problem. Contributor:  Ed Klotz,     
    CPLEX Optimization Inc.                                                     
                                                                                
    Name       Rows   Cols   Nonzeros Bounds      Notes                         
    cplex2      225    221     1059   B                                         
                                                                                
    REFERENCES                                                                  
    ----------                                                                  
                                                                                
    J.W.  Chinneck (1993).  "Finding the Most Useful Subset of Constraints      
    for Analysis in an Infeasible Linear Program", technical report             
    SCE-93-07, Systems and Computer Engineering, Carleton University,           
    Ottawa, Canada.                                                             
                                                                                
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU5,305 5,551
    nnz(R) for QR, upper bound nnz(U) for LU2,167 2,353

    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.