• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lp_standgub
  • Description: Netlib LP problem standgub: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 10 KB. Use SJget(283) or SJget('LPnetlib/lp_standgub') in MATLAB.
  • download in Matrix Market format, file size: 14 KB.
  • download in Rutherford/Boeing format, file size: 10 KB.

    LPnetlib/lp_standgub

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

    LPnetlib/lp_standgub

    dmperm of LPnetlib/lp_standgub

    scc of LPnetlib/lp_standgub

    Matrix properties (click for a legend)  
    number of rows361
    number of columns1,383
    structural full rank?no
    structural rank360
    numerical rank 360
    dimension of the numerical null space1,023
    numerical rank / min(size(A))0.99723
    Euclidean norm of A 671.32
    calculated singular value # 3600.29855
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.5723e-010
    calculated singular value # 3616.666e-018
    gap in the singular values at the numerical rank:
    singular value # 360 / singular value # 361
    4.4787e+016
    calculated condition number1.0071e+020
    condest-2
    nonzeros3,338
    # of blocks from dmperm2
    # strongly connected comp.4
    explicit zero entries1
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorR. Fourer
    editorR. Fourer
    date1989
    kindlinear programming problem
    2D/3D problem?no
    SJid283
    UFid693

    Additional fieldssize and type
    bfull 361-by-1
    cfull 1383-by-1
    lofull 1383-by-1
    hifull 1383-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         
    STANDGUB    362   1184     3147      27836  B     (see NOTES)             
                                                                              
            BOUND-TYPE TABLE                                                  
    STANDGUB   UP    FX                                                       
                                                                              
    Supplied by Bob Fourer.                                                   
                                                                              
    STANDGUB includes GUB markers; with these lines removed (lines in         
    the expanded MPS file that contain primes, i.e., that mention the rows    
    'EGROUP' and 'ENDX'), STANDGUB becomes the same as problem STANDATA;      
    MINOS does not understand the GUB markers, so we cannot report an         
    optimal value from MINOS for STANDGUB.  STANDMPS amounts to STANDGUB      
    with the GUB constraints as explicit constraints.                         
                                                                              
    Source: consulting.                                                       
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU40,450 40,187
    nnz(R) for QR, upper bound nnz(U) for LU3,386 3,544

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 1 explicit zero entries.

    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.