Matrix: LPnetlib/lp_pilot4

Description: Netlib LP problem pilot4: minimize c'*x, where Ax=b, lo<=x<=hi

LPnetlib/lp_pilot4 graph
(bipartite graph drawing)


LPnetlib/lp_pilot4 dmperm of LPnetlib/lp_pilot4

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  • Matrix group: LPnetlib
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  • download as a MATLAB mat-file, file size: 36 KB. Use UFget(655) or UFget('LPnetlib/lp_pilot4') in MATLAB.
  • download in Matrix Market format, file size: 29 KB.
  • download in Rutherford/Boeing format, file size: 23 KB.

    Matrix properties
    number of rows410
    number of columns1,123
    nonzeros5,264
    structural full rank?yes
    structural rank410
    # of blocks from dmperm9
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorStanford
    editorR. Fourer
    date
    kindlinear programming problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 410-by-1
    cfull 1123-by-1
    lofull 1123-by-1
    hifull 1123-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         
    PILOT4      411   1000     5145      40936  B    -2.5811392641E+03        
                                                                              
            BOUND-TYPE TABLE                                                  
    PILOT4     UP    FX FR PL                                                 
                                                                              
    Supplied by Bob Fourer.                                                   
    When included in Netlib: Cost coefficients unchanged (PILOT4 appeared     
    to be a minimization problem already).                                    
                                                                              
    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)                          
    PILOT4      -2.5811392589E+03    -2.5811392624E+03                        
                                                                              
    Source for PILOT.JA, PILOT.WE, PILOT4, PILOTNOV: Systems Optimization     
    Laboratory, Stanford University.                                          
    

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD88,693
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD14,742

    SVD-based statistics:
    norm(A)59355.4
    min(svd(A))0.14054
    cond(A)422339
    rank(A)410
    sprank(A)-rank(A)0
    null space dimension0
    full numerical rank?yes

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

    LPnetlib/lp_pilot4 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.