• SJSU Singular Matrix Database
  • Matrix group: Regtools
  • Click here for a description of the Regtools group.
  • Click here for a list of all matrices
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  • Matrix: Regtools/wing_1000
  • Description: WING 1000x1000 Test problem with a discontinuous solution.
  • download as a MATLAB mat-file, file size: 7 MB. Use SJget(264) or SJget('Regtools/wing_1000') in MATLAB.
  • download in Matrix Market format, file size: 10 MB.
  • download in Rutherford/Boeing format, file size: 9 MB.

    Regtools/wing_1000

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

    Regtools/wing_1000

    Matrix properties (click for a legend)  
    number of rows1,000
    number of columns1,000
    structural full rank?yes
    structural rank1,000
    numerical rank 8
    dimension of the numerical null space992
    numerical rank / min(size(A))0.008
    Euclidean norm of A 0.44698
    calculated singular value # 84.4084e-013
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    5.5511e-014
    calculated singular value # 93.4528e-015
    gap in the singular values at the numerical rank:
    singular value # 8 / singular value # 9
    127.68
    calculated condition number1.1567e+022
    condest5.2683e+022
    nonzeros1,000,000
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetry 0%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorWing and Zahrt
    editorPer Christian Hansen
    date1991
    kindill-posed problem
    2D/3D problem?no
    SJid264
    UFid-

    Additional fieldssize and type
    bfull 1000-by-1
    xfull 1000-by-1

    Notes:

        Constructed by the call [A,b,x]= wing(1000)                     
                                                                        
      where wing is from Regularization Tools. The description of       
      wing from http://www2.imm.dtu.dk/~pch/Regutools/ is:              
                                                                        
                  [A,b,x] = wing(n,t1,t2)                               
                                                                        
      Discretization of a first kind Fredholm integral eqaution with    
      kernel K and right-hand side g given by                           
         K(s,t) = t*exp(-s*t^2)                       0 < s,t < 1       
         g(s)   = (exp(-s*t1^2) - exp(-s*t2^2)/(2*s)  0 < s   < 1       
      and with the solution f given by                                  
         f(t) = | 1  for  t1 < t < t2                                   
                | 0  elsewhere.                                         
                                                                        
      Here, t1 and t2 are constants satisfying t1 < t2.  If they are    
      not speficied, the values t1 = 1/3 and t2 = 2/3 are used.         
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))500,500 500,500
    Cholesky flop count3.3e+008 3.3e+008
    nnz(L+U), no partial pivoting1,000,000 1,000,000
    nnz(V) for QR, upper bound nnz(L) for LU500,500 500,500
    nnz(R) for QR, upper bound nnz(U) for LU500,500 500,500

    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.