Matrix: LPnetlib/lp_d6cube

Description: Netlib LP problem d6cube: minimize c'*x, where Ax=b, lo<=x<=hi

LPnetlib/lp_d6cube graph
(bipartite graph drawing)

LPnetlib/lp_d6cube dmperm of LPnetlib/lp_d6cube
scc of LPnetlib/lp_d6cube

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  • download as a MATLAB mat-file, file size: 60 KB. Use UFget(616) or UFget('LPnetlib/lp_d6cube') in MATLAB.
  • download in Matrix Market format, file size: 110 KB.
  • download in Rutherford/Boeing format, file size: 65 KB.

    Matrix properties
    number of rows415
    number of columns6,184
    structural full rank?no
    structural rank404
    # of blocks from dmperm3
    # strongly connected comp.12
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    bfull 415-by-1
    cfull 6184-by-1
    lofull 6184-by-1
    hifull 6184-by-1
    z0full 1-by-1


    A Netlib LP problem, in lp/data.  For more information                    
    send email to 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:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD1,123,643
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD55,246

    SVD-based statistics:
    null space dimension11
    full numerical rank?no
    singular value gap1.71302e+14

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;

    LPnetlib/lp_d6cube svd

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.