• SJSU Singular Matrix Database
  • Matrix group: Regtools
  • Click here for a description of the Regtools group.
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  • Matrix: Regtools/i_laplace_500
  • Description: I_LAPLACE 500x500 Test problem: inverse Laplace transformation.
  • download as a MATLAB mat-file, file size: 829 KB. Use SJget(247) or SJget('Regtools/i_laplace_500') in MATLAB.
  • download in Matrix Market format, file size: 1 MB.
  • download in Rutherford/Boeing format, file size: 1 MB.

    Regtools/i_laplace_500

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

    Regtools/i_laplace_500

    dmperm of Regtools/i_laplace_500

    scc of Regtools/i_laplace_500

    Matrix properties (click for a legend)  
    number of rows500
    number of columns500
    structural full rank?no
    structural rank363
    numerical rank 39
    dimension of the numerical null space461
    numerical rank / min(size(A))0.078
    Euclidean norm of A 5.3209
    calculated singular value # 397.505e-013
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    4.4409e-013
    calculated singular value # 402.9763e-013
    gap in the singular values at the numerical rank:
    singular value # 39 / singular value # 40
    2.5216
    calculated condition numberInf
    condestInf
    nonzeros104,149
    # of blocks from dmperm16
    # strongly connected comp.31
    explicit zero entries0
    nonzero pattern symmetry 76%
    numeric value symmetry 0%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorVarah
    editorPer Christian Hansen
    date1983
    kindill-posed problem
    2D/3D problem?no
    SJid247
    UFid-

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

    Notes:

        Constructed by the call [A,b,x]= i_laplace(500)                      
                                                                             
      where i_laplace is from Regularization Tools. The description of       
      i_laplace from http://www2.imm.dtu.dk/~pch/Regutools/ is:              
                                                                             
      [A,b,x,t] = i_laplace(n,example)                                       
                                                                             
      Discretization of the inverse Laplace transformation by means of       
      Gauss-Laguerre quadrature.  The kernel K is given by                   
         K(s,t) = exp(-s*t) ,                                                
      and both integration intervals are [0,inf).                            
                                                                             
      The following examples are implemented, where f denotes                
      the solution, and g denotes the right-hand side:                       
         1: f(t) = exp(-t/2),        g(s) = 1/(s + 0.5)                      
         2: f(t) = 1 - exp(-t/2),    g(s) = 1/s - 1/(s + 0.5)                
         3: f(t) = t^2*exp(-t/2),    g(s) = 2/(s + 0.5)^3                    
         4: f(t) = | 0 , t <= 2,     g(s) = exp(-2*s)/s.                     
                   | 1 , t >  2                                              
                                                                             
      The quadrature points are returned in the vector t.                    
    

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))65,501 65,034
    Cholesky flop count9.7e+006 9.5e+006
    nnz(L+U), no partial pivoting130,502 129,568
    nnz(V) for QR, upper bound nnz(L) for LU58,878 124,815
    nnz(R) for QR, upper bound nnz(U) for LU110,715 110,715

    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.