• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lp_modszk1
  • Description: Netlib LP problem modszk1: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 23 KB. Use SJget(298) or SJget('LPnetlib/lp_modszk1') in MATLAB.
  • download in Matrix Market format, file size: 18 KB.
  • download in Rutherford/Boeing format, file size: 18 KB.

    LPnetlib/lp_modszk1

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

    LPnetlib/lp_modszk1

    dmperm of LPnetlib/lp_modszk1

    scc of LPnetlib/lp_modszk1

    Matrix properties (click for a legend)  
    number of rows687
    number of columns1,620
    structural full rank?no
    structural rank686
    numerical rank 686
    dimension of the numerical null space934
    numerical rank / min(size(A))0.99854
    Euclidean norm of A 4.8756
    calculated singular value # 6860.12112
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.4388e-012
    calculated singular value # 6871.8003e-021
    gap in the singular values at the numerical rank:
    singular value # 686 / singular value # 687
    6.7277e+019
    calculated condition number2.7082e+021
    condest-2
    nonzeros3,168
    # of blocks from dmperm3
    # strongly connected comp.3
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorI. Maros
    editorD. Gay
    date1994
    kindlinear programming problem
    2D/3D problem?no
    SJid298
    UFid644

    Additional fieldssize and type
    bfull 687-by-1
    cfull 1620-by-1
    lofull 1620-by-1
    hifull 1620-by-1
    z0full 1-by-1

    Notes:

    A Netlib LP problem, in lp/data.  For more information                    
    send email to netlib@ornl.gov with the message:                           
                                                                              
    	 send index from lp                                                      
    	 send readme from lp/data                                                
                                                                              
    The following are relevant excerpts from lp/data/readme (by David M. Gay):
                                                                              
    The column and nonzero counts in the PROBLEM SUMMARY TABLE below exclude  
    slack and surplus columns and the right-hand side vector, but include     
    the cost row.  We have omitted other free rows and all but the first      
    right-hand side vector, as noted below.  The byte count is for the        
    MPS compressed file; it includes a newline character at the end of each   
    line.  These files start with a blank initial line intended to prevent    
    mail programs from discarding any of the data.  The BR column indicates   
    whether a problem has bounds or ranges:  B stands for "has bounds", R     
    for "has ranges".  The BOUND-TYPE TABLE below shows the bound types       
    present in those problems that have bounds.                               
                                                                              
    The optimal value is from MINOS version 5.3 (of Sept. 1988)               
    running on a VAX with default options.                                    
                                                                              
                           PROBLEM SUMMARY TABLE                              
                                                                              
    Name       Rows   Cols   Nonzeros    Bytes  BR      Optimal Value         
    MODSZK1     688   1620     4158      40908  B     3.2061972906E+02        
                                                                              
            BOUND-TYPE TABLE                                                  
    MODSZK1             FR                                                    
                                                                              
    From Istvan Maros.                                                        
    Concerning the problems he submitted, Istvan Maros says that              
    MODSZK1 is a "real-life problem" that                                     
    is "very degenerate" and on which a dual simplex algorithm "may require   
    up to 10 times" fewer iterations than a primal simplex algorithm.  It     
    "is a multi-sector economic planning model (a kind of an input/output     
    model in economy)" and "is an old problem of mine and it is not easy to   
    recall more."                                                             
                                                                              
    Added to Netlib on  17 Jan. 1994                                          
                                                                              
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU71,390 59,384
    nnz(R) for QR, upper bound nnz(U) for LU12,434 13,987

    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.