• 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/shaw_500
  • Description: SHAW 500x500 Test problem: one-dimensional image restoration model.
  • download as a MATLAB mat-file, file size: 2 MB. Use SJget(255) or SJget('Regtools/shaw_500') in MATLAB.
  • download in Matrix Market format, file size: 1 MB.
  • download in Rutherford/Boeing format, file size: 1 MB.

    Regtools/shaw_500

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

    Regtools/shaw_500

    Matrix properties (click for a legend)  
    number of rows500
    number of columns500
    structural full rank?yes
    structural rank500
    numerical rank 20
    dimension of the numerical null space480
    numerical rank / min(size(A))0.04
    Euclidean norm of A 2.9933
    calculated singular value # 206.9264e-013
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.2204e-013
    calculated singular value # 212.9771e-015
    gap in the singular values at the numerical rank:
    singular value # 20 / singular value # 21
    232.66
    calculated condition number1.971e+020
    condest2.5405e+021
    nonzeros250,000
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typereal
    structuresymmetric
    Cholesky candidate?yes
    positive definite?no

    authorShaw
    editorPer Christian Hansen
    date1972
    kindill-posed problem
    2D/3D problem?no
    SJid255
    UFid-

    Additional fieldssize and type
    bfull 500-by-1
    xfull 500-by-1

    Notes:

        Constructed by the call [A,b,x]= shaw(500)                      
                                                                        
      where shaw is from Regularization Tools. The description of       
      shaw from http://www2.imm.dtu.dk/~pch/Regutools/ is:              
                                                                        
                         [A,b,x] = shaw(n)                              
                                                                        
      Discretization of a first kind Fredholm integral equation with    
      [-pi/2,pi/2] as both integration intervals.  The kernel K and     
      the solution f, which are given by                                
         K(s,t) = (cos(s) + cos(t))*(sin(u)/u)^2                        
         u = pi*(sin(s) + sin(t))                                       
         f(t) = a1*exp(-c1*(t - t1)^2) + a2*exp(-c2*(t - t2)^2) ,       
      are discretized by simple quadrature to produce A and x.          
      Then the discrete right-hand b side is produced as b = A*x.       
                                                                        
      The order n must be even.                                         
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))125,250 125,250
    Cholesky flop count4.2e+007 4.2e+007
    nnz(L+U), no partial pivoting250,000 250,000
    nnz(V) for QR, upper bound nnz(L) for LU125,250 125,250
    nnz(R) for QR, upper bound nnz(U) for LU125,250 125,250

    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.