Matrix: LPnetlib/lp_shell

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

LPnetlib/lp_shell graph
(bipartite graph drawing)


LPnetlib/lp_shell

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  • Matrix group: LPnetlib
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  • download as a MATLAB mat-file, file size: 13 KB. Use UFget(683) or UFget('LPnetlib/lp_shell') in MATLAB.
  • download in Matrix Market format, file size: 17 KB.
  • download in Rutherford/Boeing format, file size: 15 KB.

    Matrix properties
    number of rows536
    number of columns1,777
    nonzeros3,558
    structural full rank?yes
    structural rank536
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typeinteger
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorJ. Reid
    editorD. Gay
    date1978
    kindlinear programming problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 536-by-1
    cfull 1777-by-1
    lofull 1777-by-1
    hifull 1777-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                                                    
                                                                                  
    ------------------------------------------------------------------------------
    This LP problem is the source of three sparse matrices in the Harwell/Boeing  
    sparse matrix collection: SHL_0, SHL_200, and SHL_400.  Those three matrices  
    are square, nonsingular basis matrices that occured during the solution of    
    SHELL.                                                                        
    ------------------------------------------------------------------------------
                                                                                  
    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             
    SHELL       537   1775     4900      38049  B     1.2088253460E+09            
                                                                                  
            BOUND-TYPE TABLE                                                      
    SHELL      UP LO FX                                                           
                                                                                  
    From John Reid.                                                               
                                                                                  
    

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD56,680
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD4,266

    SVD-based statistics:
    norm(A)16.0004
    min(svd(A))1.57846e-14
    cond(A)1.01367e+15
    rank(A)535
    sprank(A)-rank(A)1
    null space dimension1
    full numerical rank?no
    singular value gap2.41422e+13

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

    LPnetlib/lp_shell 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.