• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
  • Click here for a description of the LPnetlib group.
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  • Matrix: LPnetlib/lp_tuff
  • Description: Netlib LP problem tuff: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 20 KB. Use SJget(299) or SJget('LPnetlib/lp_tuff') in MATLAB.
  • download in Matrix Market format, file size: 20 KB.
  • download in Rutherford/Boeing format, file size: 14 KB.

    LPnetlib/lp_tuff

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

    LPnetlib/lp_tuff

    dmperm of LPnetlib/lp_tuff

    scc of LPnetlib/lp_tuff

    Matrix properties (click for a legend)  
    number of rows333
    number of columns628
    structural full rank?no
    structural rank302
    numerical rank 302
    dimension of the numerical null space326
    numerical rank / min(size(A))0.90691
    Euclidean norm of A 10003
    calculated singular value # 3020.0092575
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.1423e-009
    calculated singular value # 3034.2204e-013
    gap in the singular values at the numerical rank:
    singular value # 302 / singular value # 303
    2.1935e+010
    calculated condition number4.4642e+020
    condest-2
    nonzeros4,561
    # 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
    SJid299
    UFid699

    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:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU28,027 21,594
    nnz(R) for QR, upper bound nnz(U) for LU8,469 8,825

    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.