• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
  • Click here for a description of the LPnetlib group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups


  • Matrix: LPnetlib/lp_scorpion
  • Description: Netlib LP problem scorpion: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 9 KB. Use SJget(274) or SJget('LPnetlib/lp_scorpion') in MATLAB.
  • download in Matrix Market format, file size: 8 KB.
  • download in Rutherford/Boeing format, file size: 7 KB.

    LPnetlib/lp_scorpion

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

    LPnetlib/lp_scorpion

    dmperm of LPnetlib/lp_scorpion

    Matrix properties (click for a legend)  
    number of rows388
    number of columns466
    structural full rank?yes
    structural rank388
    numerical rank 358
    dimension of the numerical null space108
    numerical rank / min(size(A))0.92268
    Euclidean norm of A 3.7914
    calculated singular value # 3580.051301
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.0695e-013
    calculated singular value # 3592.0149e-015
    gap in the singular values at the numerical rank:
    singular value # 358 / singular value # 359
    2.5461e+013
    calculated condition number1.305e+016
    condest-2
    nonzeros1,534
    # of blocks from dmperm110
    # strongly connected comp.1
    entries not in dmperm blocks523
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorJ. Ho, E. Loute
    editorR. Fourer
    date1981
    kindlinear programming problem
    2D/3D problem?no
    SJid274
    UFid673

    Additional fieldssize and type
    bfull 388-by-1
    cfull 466-by-1
    lofull 466-by-1
    hifull 466-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 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         
    SCORPION    389    358     1708      12186        1.8781248227E+03        
                                                                              
    Supplied by Bob Fourer.                                                   
    When included in Netlib: Extra free rows omitted.                         
                                                                              
    Source: J.K. Ho and E. Loute, "A Set of Staircase Linear Programming      
    Test Problems", Math. Prog. 20 (1981), pp. 245-250.                       
                                                                              
    

    Ordering statistics:AMD METIS DMPERM+
    nnz(V) for QR, upper bound nnz(L) for LU6,563 2,553 896
    nnz(R) for QR, upper bound nnz(U) for LU3,332 2,666 1,319

    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.