• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lp_d6cube
  • Description: Netlib LP problem d6cube: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 63 KB. Use SJget(426) or SJget('LPnetlib/lp_d6cube') in MATLAB.
  • download in Matrix Market format, file size: 112 KB.
  • download in Rutherford/Boeing format, file size: 65 KB.

    LPnetlib/lp_d6cube

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

    LPnetlib/lp_d6cube

    dmperm of LPnetlib/lp_d6cube

    scc of LPnetlib/lp_d6cube

    Matrix properties (click for a legend)  
    number of rows415
    number of columns6,184
    structural full rank?no
    structural rank404
    numerical rank 404
    dimension of the numerical null space5,780
    numerical rank / min(size(A))0.97349
    Euclidean norm of A 703.41
    calculated singular value # 4040.62595
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    7.0304e-010
    calculated singular value # 4052.6545e-015
    gap in the singular values at the numerical rank:
    singular value # 404 / singular value # 405
    2.358e+014
    calculated condition number7.6084e+093
    condest-2
    nonzeros37,704
    # of blocks from dmperm3
    # strongly connected comp.12
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typeinteger
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorR. Hughes
    editorD. Gay
    date1993
    kindlinear programming problem
    2D/3D problem?no
    SJid426
    UFid616

    Additional fieldssize and type
    bfull 415-by-1
    cfull 6184-by-1
    lofull 6184-by-1
    hifull 6184-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         
    D6CUBE      416   6184    43888     167633  B     3.1549166667E+02        
                                                                              
            BOUND-TYPE TABLE                                                  
    D6CUBE        LO                                                          
                                                                              
    Supplied by Robert Hughes.                                                
                                                                              
    Of D6CUBE, Robert Hughes says, "Mike Anderson and I are working on the    
    problem of finding the minimum cardinality of triangulations of the       
    6-dimensional cube.  The optimal objective value of the problem I sent    
    you provides a lower bound for the cardinalities of all triangulations    
    which contain a certain simplex of volume 8/6! and which contains the     
    centroid of the 6-cube in its interior.  The linear programming           
    problem is not easily described."                                         
                                                                              
    Added to Netlib on 26 March 1993                                          
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU1,123,643 1,192,343
    nnz(R) for QR, upper bound nnz(U) for LU55,246 56,704

    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.