• SJSU Singular Matrix Database
  • Matrix group: LPnetlib
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  • Matrix: LPnetlib/lp_brandy
  • Description: Netlib LP problem brandy: minimize c'*x, where Ax=b, lo<=x<=hi
  • download as a MATLAB mat-file, file size: 12 KB. Use SJget(282) or SJget('LPnetlib/lp_brandy') in MATLAB.
  • download in Matrix Market format, file size: 11 KB.
  • download in Rutherford/Boeing format, file size: 9 KB.

    LPnetlib/lp_brandy

    Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

    LPnetlib/lp_brandy

    dmperm of LPnetlib/lp_brandy

    scc of LPnetlib/lp_brandy

    Matrix properties (click for a legend)  
    number of rows220
    number of columns303
    structural full rank?no
    structural rank193
    numerical rank 193
    dimension of the numerical null space110
    numerical rank / min(size(A))0.87727
    Euclidean norm of A 455.78
    calculated singular value # 1930.071209
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.7224e-011
    calculated singular value # 1946.2275e-014
    gap in the singular values at the numerical rank:
    singular value # 193 / singular value # 194
    1.1435e+012
    calculated condition numberInf
    condest-2
    nonzeros2,202
    # of blocks from dmperm58
    # strongly connected comp.40
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structurerectangular
    Cholesky candidate?no
    positive definite?no

    authorM. Saunders
    editorD. Gay
    date
    kindlinear programming problem
    2D/3D problem?no
    SJid282
    UFid607

    Additional fieldssize and type
    bfull 220-by-1
    cfull 303-by-1
    lofull 303-by-1
    hifull 303-by-1
    z0full 1-by-1

    Notes:

    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                                                    
    	 send minos 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 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             
    BRANDY      221    249     2150      14028        1.5185098965E+03            
                                                                                  
    From Michael Saunders, Systems Optimization Laboratory at Stanford University.
    When included in Netlib: Extra right-hand side vectors omitted.               
                                                                                  
    The following are relevant excerts from lp/data/minos (by Michael Saunders),  
    regarding experience with MINOS 5.0 on the problems he provided:              
                                                                                  
                                                         (unscaled)   (scaled)    
    File   Name    Rows  Cols  Elems  Optimal Objective  Itns  Time  Itns  Time   
    ---- --------  ----  ----  -----  -----------------  ----  ----  ----  ----   
      7. BRANDY     221   249   2150  1.5185099E+03       292   4.9   377   5.9   
                                                                                  
    * Objective  is the first row of type N.  It is minimized except as shown.    
                                                                                  
    * Itns       is the number of iterations required to solve the problem        
                 by the primal simplex method, as implemented in the Fortran      
                 code MINOS 5.0 (May 1985), using default values for all          
                 parameters.  (The initial basis is triangular.)                  
                                                                                  
    * Time       is the processor time required on an IBM 3081K.  The MINOS       
                 source code was compiled with the IBM Fortran 77 compiler        
                 VS FORTRAN, using the options NOSDUMP, NOSYM and OPT(3).         
                                                                                  
    

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU8,293 8,371
    nnz(R) for QR, upper bound nnz(U) for LU3,612 3,718

    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.