Matrix: LPnetlib/lp_afiro

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

LPnetlib/lp_afiro graph
(bipartite graph drawing)


LPnetlib/lp_afiro

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  • Matrix group: LPnetlib
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  • download as a MATLAB mat-file, file size: 3 KB. Use UFget(597) or UFget('LPnetlib/lp_afiro') in MATLAB.
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    Matrix properties
    number of rows27
    number of columns51
    nonzeros102
    structural full rank?yes
    structural rank27
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorM. Saunders
    editorD. Gay
    date
    kindlinear programming problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 27-by-1
    cfull 51-by-1
    lofull 51-by-1
    hifull 51-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                                                    
    	 send minos 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             
    AFIRO        28     32       88        794       -4.6475314286E+02            
                                                                                  
    From Michael Saunders, Systems Optimization Laboratory at Stanford University.
                                                                                  
    The following are relevant excerts from lp/data/minos (by Michael Saunders),  
    regarding experience with MINOS 5.0 on the problems he provided:              
                                                                                  
                                                         (unscaled)   (scaled)    
    File   Name    Rows  Cols  Elems  Optimal Objective  Itns  Time  Itns  Time   
    ---- --------  ----  ----  -----  -----------------  ----  ----  ----  ----   
      1. AFIRO       28    32     88 -4.6475314E+02         6   0.5     6   0.5   
                                                                                  
    * Objective  is the first row of type N.  It is minimized except as shown.    
                                                                                  
    * Itns       is the number of iterations required to solve the problem        
                 by the primal simplex method, as implemented in the Fortran      
                 code MINOS 5.0 (May 1985), using default values for all          
                 parameters.  (The initial basis is triangular.)                  
                                                                                  
    * Time       is the processor time required on an IBM 3081K.  The MINOS       
                 source code was compiled with the IBM Fortran 77 compiler        
                 VS FORTRAN, using the options NOSDUMP, NOSYM and OPT(3).         
                                                                                  
    

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD262
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD110

    SVD-based statistics:
    norm(A)6.78113
    min(svd(A))0.605605
    cond(A)11.1973
    rank(A)27
    sprank(A)-rank(A)0
    null space dimension0
    full numerical rank?yes

    singular values (MAT file):click here
    SVD method used:s = svd (full (R)) ; where [~,R,E] = spqr (A') with droptol of zero
    status:ok

    LPnetlib/lp_afiro 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.