• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lp_wood1p
  • Description: Netlib LP problem wood1p: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 177 KB. Use SJget(358) or SJget('LPnetlib/lp_wood1p') in MATLAB.
  • download in Matrix Market format, file size: 288 KB.
  • download in Rutherford/Boeing format, file size: 143 KB.

    LPnetlib/lp_wood1p

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

    LPnetlib/lp_wood1p

    Matrix properties (click for a legend)  
    number of rows244
    number of columns2,595
    structural full rank?yes
    structural rank244
    numerical rank 243
    dimension of the numerical null space2,352
    numerical rank / min(size(A))0.9959
    Euclidean norm of A 22731
    calculated singular value # 2431.4051
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    9.4406e-009
    calculated singular value # 2441.7575e-010
    gap in the singular values at the numerical rank:
    singular value # 243 / singular value # 244
    7.995e+009
    calculated condition number1.2934e+014
    condest-2
    nonzeros70,216
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    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
    SJid358
    UFid701

    Additional fieldssize and type
    bfull 244-by-1
    cfull 2595-by-1
    lofull 2595-by-1
    hifull 2595-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 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         
    WOOD1P      245   2594    70216     328905        1.4429024116E+00        
                                                                              
    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                                       
         WOOD1P    1059    471   44.48                                        
                                                                              
    Added to Netlib on  27 June 1989                                          
                                                                              
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU248,714 463,570
    nnz(R) for QR, upper bound nnz(U) for LU19,080 25,051

    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.