Matrix: LPnetlib/lp_tuff

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

LPnetlib/lp_tuff graph
(bipartite graph drawing)


LPnetlib/lp_tuff dmperm of LPnetlib/lp_tuff
scc of LPnetlib/lp_tuff

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  • Matrix group: LPnetlib
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  • download as a MATLAB mat-file, file size: 17 KB. Use UFget(699) or UFget('LPnetlib/lp_tuff') in MATLAB.
  • download in Matrix Market format, file size: 20 KB.
  • download in Rutherford/Boeing format, file size: 14 KB.

    Matrix properties
    number of rows333
    number of columns628
    nonzeros4,561
    structural full rank?no
    structural rank302
    # of blocks from dmperm12
    # strongly connected comp.41
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorJ. Tomlin
    editorD. Gay
    date1989
    kindlinear programming problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 333-by-1
    cfull 628-by-1
    lofull 628-by-1
    hifull 628-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         
    TUFF        334    587     4523      29439  B     2.9214776509E-01        
                                                                              
            BOUND-TYPE TABLE                                                  
    TUFF       UP LO FX FR                                                    
                                                                              
    Empty RHS section.                                                        
                                                                              
    From John Tomlin.                                                         
    On the problems supplied by John Tomlin, MINOS 5.3 reports that about     
    10% to 57% of its steps are degenerate:                                   
         Name     Steps  Degen  Percent                                       
         TUFF       745    345   46.31                                        
                                                                              
    Added to Netlib on  27 June 1989.                                         
    

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD28,027
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD8,469

    SVD-based statistics:
    norm(A)10002.9
    min(svd(A))3.15187e-17
    cond(A)3.17363e+20
    rank(A)302
    sprank(A)-rank(A)0
    null space dimension31
    full numerical rank?no
    singular value gap8.01808e+10

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

    LPnetlib/lp_tuff 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.