Matrix: LPnetlib/lp_pilot87

Description: Netlib LP problem pilot87: minimize c'*x, where Ax=b, lo<=x<=hi

LPnetlib/lp_pilot87 graph
(bipartite graph drawing)

LPnetlib/lp_pilot87 dmperm of LPnetlib/lp_pilot87
scc of LPnetlib/lp_pilot87

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  • Matrix group: LPnetlib
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  • download as a MATLAB mat-file, file size: 392 KB. Use UFget(656) or UFget('LPnetlib/lp_pilot87') in MATLAB.
  • download in Matrix Market format, file size: 376 KB.
  • download in Rutherford/Boeing format, file size: 271 KB.

    Matrix properties
    number of rows2,030
    number of columns6,680
    structural full rank?yes
    structural rank2,030
    # of blocks from dmperm2
    # strongly connected comp.2
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorJ. Stone
    editorI. Lustig
    kindlinear programming problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 2030-by-1
    cfull 6680-by-1
    lofull 6680-by-1
    hifull 6680-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          
    PILOT87    2031   4883    73804     514192  B     3.0171072827E+02         
    Supplied by Irv Lustig, which he obtained from John Stone.                 
    When included in Netlib: Extra free rows omitted.                          
    Bob Bixby reports that the CPLEX solver (running on a Sparc station)       
    finds slightly different optimal values for some of the problems.          
    On a MIPS processor, MINOS version 5.3 (with crash and scaling of          
    December 1989) also finds different optimal values for some of the         
    problems.  The following table shows the values that differ from those     
    shown above.  (Whether CPLEX finds different values on the recently        
    added problems remains to be seen.)                                        
    Problem        CPLEX(Sparc)          MINOS(MIPS)                           
    PILOT87                           3.0171074161E+02                         
    Added to Netlib on  15 June 1990.                                          
    Modified, in Netlib, on  21 Oct. 1991 (minor cleanups): removed lower bound
    of 49.5 on U[OG]ST0[12], which are subsequently fixed at 99 (UOST[12]) or  

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD3,438,865
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD422,518

    SVD-based statistics:
    null space dimension0
    full numerical rank?yes

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

    LPnetlib/lp_pilot87 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.