• SJSU Singular Matrix Database
  • Matrix group: Regtools
  • Click here for a description of the Regtools group.
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  • Matrix: Regtools/i_laplace_200
  • Description: I_LAPLACE 200x200 Test problem: inverse Laplace transformation.
  • download as a MATLAB mat-file, file size: 193 KB. Use SJget(246) or SJget('Regtools/i_laplace_200') in MATLAB.
  • download in Matrix Market format, file size: 307 KB.
  • download in Rutherford/Boeing format, file size: 291 KB.

    Regtools/i_laplace_200

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

    Regtools/i_laplace_200

    dmperm of Regtools/i_laplace_200

    Matrix properties (click for a legend)  
    number of rows200
    number of columns200
    structural full rank?no
    structural rank193
    numerical rank 34
    dimension of the numerical null space166
    numerical rank / min(size(A))0.17
    Euclidean norm of A 3.3631
    calculated singular value # 342.6128e-013
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    8.8818e-014
    calculated singular value # 358.3556e-014
    gap in the singular values at the numerical rank:
    singular value # 34 / singular value # 35
    3.127
    calculated condition number4.876e+032
    condest1.5185e+306
    nonzeros24,055
    # of blocks from dmperm11
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 85%
    numeric value symmetry 0%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorVarah
    editorPer Christian Hansen
    date1983
    kindill-posed problem
    2D/3D problem?no
    SJid246
    UFid-

    Additional fieldssize and type
    bfull 200-by-1
    xfull 200-by-1

    Notes:

        Constructed by the call [A,b,x]= i_laplace(200)                      
                                                                             
      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'))14,758 17,890
    Cholesky flop count1.3e+006 2.1e+006
    nnz(L+U), no partial pivoting29,316 35,580
    nnz(V) for QR, upper bound nnz(L) for LU13,500 20,100
    nnz(R) for QR, upper bound nnz(U) for LU20,100 20,100

    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.