• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lpi_ex72a
  • Description: Netlib LP problem ex72a: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 5 KB. Use SJget(271) or SJget('LPnetlib/lpi_ex72a') in MATLAB.
  • download in Matrix Market format, file size: 3 KB.
  • download in Rutherford/Boeing format, file size: 3 KB.

    LPnetlib/lpi_ex72a

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

    LPnetlib/lpi_ex72a

    Matrix properties (click for a legend)  
    number of rows197
    number of columns215
    structural full rank?yes
    structural rank197
    numerical rank 192
    dimension of the numerical null space23
    numerical rank / min(size(A))0.97462
    Euclidean norm of A 2.9288
    calculated singular value # 1920.052594
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    9.5479e-014
    calculated singular value # 1939.5623e-016
    gap in the singular values at the numerical rank:
    singular value # 192 / singular value # 193
    5.5001e+013
    calculated condition number6.1712e+015
    condest-2
    nonzeros467
    # 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
    SJid271
    UFid712

    Additional fieldssize and type
    bfull 197-by-1
    cfull 215-by-1
    lofull 215-by-1
    hifull 215-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                         
    ex72a       198    215      682   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 LU707 736
    nnz(R) for QR, upper bound nnz(U) for LU801 858

    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.