• 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_shell
  • Description: Netlib LP problem shell: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 17 KB. Use SJget(300) or SJget('LPnetlib/lp_shell') in MATLAB.
  • download in Matrix Market format, file size: 17 KB.
  • download in Rutherford/Boeing format, file size: 15 KB.


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


    Matrix properties (click for a legend)  
    number of rows536
    number of columns1,777
    structural full rank?yes
    structural rank536
    numerical rank 535
    dimension of the numerical null space1,242
    numerical rank / min(size(A))0.99813
    Euclidean norm of A 16
    calculated singular value # 5350.38107
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 5361.6128e-014
    gap in the singular values at the numerical rank:
    singular value # 535 / singular value # 536
    calculated condition number9.9207e+014
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorJ. Reid
    editorD. Gay
    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


    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    
    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:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU56,680 51,183
    nnz(R) for QR, upper bound nnz(U) for LU4,266 4,546

    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.