• SJSU Singular Matrix Database
  • Matrix group: Regtools
  • Click here for a description of the Regtools group.
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  • Matrix: Regtools/i_laplace_100
  • Description: I_LAPLACE 100x100 Test problem: inverse Laplace transformation.
  • download as a MATLAB mat-file, file size: 63 KB. Use SJget(245) or SJget('Regtools/i_laplace_100') in MATLAB.
  • download in Matrix Market format, file size: 99 KB.
  • download in Rutherford/Boeing format, file size: 94 KB.

    Regtools/i_laplace_100

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

    Regtools/i_laplace_100

    Matrix properties (click for a legend)  
    number of rows100
    number of columns100
    structural full rank?yes
    structural rank100
    numerical rank 28
    dimension of the numerical null space72
    numerical rank / min(size(A))0.28
    Euclidean norm of A 2.3749
    calculated singular value # 289.0882e-014
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    4.4409e-014
    calculated singular value # 291.2597e-014
    gap in the singular values at the numerical rank:
    singular value # 28 / singular value # 29
    7.2149
    calculated condition number5.5101e+032
    condest9.9509e+049
    nonzeros7,590
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetry 91%
    numeric value symmetry 0%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorVarah
    editorPer Christian Hansen
    date1983
    kindill-posed problem
    2D/3D problem?no
    SJid245
    UFid-

    Additional fieldssize and type
    bfull 100-by-1
    xfull 100-by-1

    Notes:

        Constructed by the call [A,b,x]= i_laplace(100)                      
                                                                             
      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'))5,004 5,050
    Cholesky flop count3.3e+005 3.4e+005
    nnz(L+U), no partial pivoting9,908 10,000
    nnz(V) for QR, upper bound nnz(L) for LU5,050 5,050
    nnz(R) for QR, upper bound nnz(U) for LU5,050 5,050

    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.