Matrix: LPnetlib/lp_etamacro

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

LPnetlib/lp_etamacro graph
(bipartite graph drawing)

scc of LPnetlib/lp_etamacro

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  • download as a MATLAB mat-file, file size: 10 KB. Use UFget(621) or UFget('LPnetlib/lp_etamacro') in MATLAB.
  • download in Matrix Market format, file size: 13 KB.
  • download in Rutherford/Boeing format, file size: 10 KB.

    Matrix properties
    number of rows400
    number of columns816
    structural full rank?yes
    structural rank400
    # of blocks from dmperm1
    # strongly connected comp.2
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

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

    Additional fieldssize and type
    bfull 400-by-1
    cfull 816-by-1
    lofull 816-by-1
    hifull 816-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                                                    
    	 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 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             
    ETAMACRO    401    688     2489      21915  B    -7.5571521774E+02            
            BOUND-TYPE TABLE                                                      
    ETAMACRO   UP LO FX                                                           
    From Michael Saunders, Systems Optimization Laboratory at Stanford University.
    When included in Netlib: Cost coefficients negated.                           
    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)                              
    ETAMACRO    -7.5571523337E+02    -7.5571522100E+02                            
    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   
    ---- --------  ----  ----  -----  -----------------  ----  ----  ----  ----   
     12. ETAMACRO   401   689   2489  7.5571521E+02 MAX   904  15.0   927  17.6   
    * 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:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD49,135
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD15,611

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

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;

    LPnetlib/lp_etamacro 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.