Matrix: LPnetlib/lp_fit2d

Description: Netlib LP problem fit2d: minimize c'*x, where Ax=b, lo<=x<=hi

LPnetlib/lp_fit2d graph
(bipartite graph drawing)


  • Home page of the UF Sparse Matrix Collection
  • 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
  • download as a MATLAB mat-file, file size: 132 KB. Use UFget(626) or UFget('LPnetlib/lp_fit2d') in MATLAB.
  • download in Matrix Market format, file size: 328 KB.
  • download in Rutherford/Boeing format, file size: 168 KB.

    Matrix properties
    number of rows25
    number of columns10,524
    structural full rank?yes
    structural rank25
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    bfull 25-by-1
    cfull 10524-by-1
    lofull 10524-by-1
    hifull 10524-by-1
    z0full 1-by-1


    A Netlib LP problem, in lp/data.  For more information                    
    send email to 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         
    FIT2D        26  10500   138018     482330  B    -6.8464293294E+04        
            BOUND-TYPE TABLE                                                  
    FIT2D      UP                                                             
    Supplied by Bob Fourer.                                                   
    When included in Netlib: Cost coefficients negated.                       
    Concerning FIT1D, FIT1P, FIT2D, FIT2P, Bob Fourer says                    
        The pairs FIT1P/FIT1D and FIT2P/FIT2D are primal and                  
        dual versions of the same two problems [except that we                
        have negated the cost coefficients of the dual problems               
        so all are minimization problems].  They originate from               
        a model for fitting linear inequalities to data, by                   
        minimization of a sum of piecewise-linear penalties.                  
        The FIT1 problems are based on 627 data points and 2-3                
        pieces per primal pl penalty term.  The FIT2 problems                 
        are based on 3000 data points (from a different sample                
        altogether) and 4-5 pieces per pl term.                               
    Bob Bixby reports that the CPLEX solver (running on a Sparc station)      
    finds slightly different optimal values for some of the problems.         
    On a MIPS processor, MINOS version 5.3 (with crash and scaling of         
    December 1989) also finds different optimal values for some of the        
    problems.  The following table shows the values that differ from those    
    shown above.  (Whether CPLEX finds different values on the recently       
    added problems remains to be seen.)                                       
    Problem        CPLEX(Sparc)          MINOS(MIPS)                          
    FIT2D                            -6.8464293232E+04                        
    Added to Netlib on  31 Jan. 1990                                          

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD262,500
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD325

    SVD-based statistics:
    null space dimension0
    full numerical rank?yes

    singular values (MAT file):click here
    SVD method used:s = svd (full (R)) ; where [~,R,E] = spqr (A') with droptol of zero

    LPnetlib/lp_fit2d 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.