• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lp_25fv47
  • Description: Netlib LP problem 25fv47: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 49 KB. Use SJget(339) or SJget('LPnetlib/lp_25fv47') in MATLAB.
  • download in Matrix Market format, file size: 49 KB.
  • download in Rutherford/Boeing format, file size: 42 KB.


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


    dmperm of LPnetlib/lp_25fv47

    scc of LPnetlib/lp_25fv47

    Matrix properties (click for a legend)  
    number of rows821
    number of columns1,876
    structural full rank?no
    structural rank820
    numerical rank 820
    dimension of the numerical null space1,056
    numerical rank / min(size(A))0.99878
    Euclidean norm of A 436.92
    calculated singular value # 8200.132
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 8210
    gap in the singular values at the numerical rank:
    singular value # 820 / singular value # 821
    calculated condition numberInf
    # of blocks from dmperm29
    # strongly connected comp.3
    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 821-by-1
    cfull 1876-by-1
    lofull 1876-by-1
    hifull 1876-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 nine sparse matrices in the Harwell/Boeing   
    sparse matrix collection: BP_0, BP_200, BP_400, BP_600, BP_800, BP_1000,      
    BP_1200, BP_1400, and BP_1600.  Those nine matrices are square, nonsingular   
    basis matrices that occured during the solution of 25FV47 (also called BP     
    or BP1).                                                                      
    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             
    25FV47      822   1571    11127      70477        5.5018458883E+03            
    From John Reid.  Problem 25FV47 is sometimes called BP or BP1.                
    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)                              
    25FV47                            5.5018467791E+03                            

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU190,271 150,729
    nnz(R) for QR, upper bound nnz(U) for LU39,534 31,848

    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.