• SJSU Singular Matrix Database
  • Matrix group: Regtools
  • Click here for a description of the Regtools group.
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  • Matrix: Regtools/i_laplace_1000
  • Description: I_LAPLACE 1000x1000 Test problem: inverse Laplace transformation.
  • download as a MATLAB mat-file, file size: 2 MB. Use SJget(248) or SJget('Regtools/i_laplace_1000') in MATLAB.
  • download in Matrix Market format, file size: 4 MB.
  • download in Rutherford/Boeing format, file size: 3 MB.

    Regtools/i_laplace_1000

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

    Regtools/i_laplace_1000

    dmperm of Regtools/i_laplace_1000

    scc of Regtools/i_laplace_1000

    Matrix properties (click for a legend)  
    number of rows1,000
    number of columns1,000
    structural full rank?no
    structural rank581
    numerical rank 43
    dimension of the numerical null space957
    numerical rank / min(size(A))0.043
    Euclidean norm of A 7.5262
    calculated singular value # 431.2196e-012
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    8.8818e-013
    calculated singular value # 445.3894e-013
    gap in the singular values at the numerical rank:
    singular value # 43 / singular value # 44
    2.2629
    calculated condition numberInf
    condestInf
    nonzeros301,876
    # of blocks from dmperm22
    # strongly connected comp.276
    explicit zero entries0
    nonzero pattern symmetry 67%
    numeric value symmetry 0%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorVarah
    editorPer Christian Hansen
    date1983
    kindill-posed problem
    2D/3D problem?no
    SJid248
    UFid-

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

    Notes:

        Constructed by the call [A,b,x]= i_laplace(1000)                     
                                                                             
      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'))201,905 201,889
    Cholesky flop count4.5e+007 4.5e+007
    nnz(L+U), no partial pivoting402,810 402,778
    nnz(V) for QR, upper bound nnz(L) for LU213,086 170,188
    nnz(R) for QR, upper bound nnz(U) for LU263,450 263,450

    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.