• 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_sierra
  • Description: Netlib LP problem sierra: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 23 KB. Use SJget(317) or SJget('LPnetlib/lp_sierra') in MATLAB.
  • download in Matrix Market format, file size: 31 KB.
  • download in Rutherford/Boeing format, file size: 22 KB.


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


    Matrix properties (click for a legend)  
    number of rows1,227
    number of columns2,735
    structural full rank?yes
    structural rank1,227
    numerical rank 1,217
    dimension of the numerical null space1,518
    numerical rank / min(size(A))0.99185
    Euclidean norm of A 1e+005
    calculated singular value # 12174.4721e-005
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 12185.9006e-015
    gap in the singular values at the numerical rank:
    singular value # 1217 / singular value # 1218
    calculated condition number3.1967e+019
    # 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

    authorR. Helgason, J. Kennington, P. Wong
    editorR. Fourer
    kindlinear programming problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 1227-by-1
    cfull 2735-by-1
    lofull 2735-by-1
    hifull 2735-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         
    SIERRA     1228   2036     9252      76627  B     1.5394362184E+07        
            BOUND-TYPE TABLE                                                  
    SIERRA     UP                                                             
    Supplied by Bob Fourer.                                                   
    When included in Netlib: Explicit zeros omitted.                          
    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)                          
    SIERRA                            1.5394364186E+07                        
    Source: GFRD-PNC, SIERRA: R. Helgason, J. Kennington, and P. Wong,        
    "An Application of Network Programming for National Forest Planning",     
    Technical Report OR 81006, Dept. of Operations Research, Southern         
    Methodist University.                                                     

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU121,258 127,804
    nnz(R) for QR, upper bound nnz(U) for LU12,744 14,528

    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.