• 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_cycle
  • Description: Netlib LP problem cycle: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 110 KB. Use SJget(360) or SJget('LPnetlib/lp_cycle') in MATLAB.
  • download in Matrix Market format, file size: 106 KB.
  • download in Rutherford/Boeing format, file size: 83 KB.


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


    dmperm of LPnetlib/lp_cycle

    scc of LPnetlib/lp_cycle

    Matrix properties (click for a legend)  
    number of rows1,903
    number of columns3,371
    structural full rank?no
    structural rank1,875
    numerical rank 1,875
    dimension of the numerical null space1,496
    numerical rank / min(size(A))0.98529
    Euclidean norm of A 2018.6
    calculated singular value # 18750.00013791
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 18765.3761e-014
    gap in the singular values at the numerical rank:
    singular value # 1875 / singular value # 1876
    calculated condition number1.5806e+020
    # of blocks from dmperm98
    # strongly connected comp.29
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    bfull 1903-by-1
    cfull 3371-by-1
    lofull 3371-by-1
    hifull 3371-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                                                
    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         
    CYCLE      1904   2857    21322     166648  B    -5.2263930249E+00        
            BOUND-TYPE TABLE                                                  
    CYCLE      UP       FR                                                    
    Empty RHS section.                                                        
    From John Tomlin.                                                         
    On the problems supplied by John Tomlin, MINOS 5.3 reports that about     
    10% to 57% of its steps are degenerate:                                   
         Name     Steps  Degen  Percent                                       
         CYCLE     3156   1485   47.05                                        
    Added to Netlib on 27 June 1989                                           

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU395,322 189,805
    nnz(R) for QR, upper bound nnz(U) for LU92,074 64,618

    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.