• SJSU Singular Matrix Database
  • Matrix group: Regtools
  • Click here for a description of the Regtools group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups


  • Matrix: Regtools/heat_100
  • Description: HEAT 100x100 Test problem: inverse heat equation.
  • download as a MATLAB mat-file, file size: 9 KB. Use SJget(241) or SJget('Regtools/heat_100') in MATLAB.
  • download in Matrix Market format, file size: 25 KB.
  • download in Rutherford/Boeing format, file size: 6 KB.

    Regtools/heat_100

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

    Regtools/heat_100

    dmperm of Regtools/heat_100

    Matrix properties (click for a legend)  
    number of rows100
    number of columns100
    structural full rank?yes
    structural rank100
    numerical rank 97
    dimension of the numerical null space3
    numerical rank / min(size(A))0.97
    Euclidean norm of A 0.35606
    calculated singular value # 974.1059e-007
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    5.5511e-015
    calculated singular value # 983.497e-021
    gap in the singular values at the numerical rank:
    singular value # 97 / singular value # 98
    1.1741e+014
    calculated condition number4.0368e+037
    condest7.0113e+082
    nonzeros5,050
    # of blocks from dmperm100
    # strongly connected comp.100
    entries not in dmperm blocks4,950
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorCarasso, Elden
    editorPer Christian Hansen
    date1982
    kindill-posed problem
    2D/3D problem?no
    SJid241
    UFid-

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

    Notes:

        Constructed by the call [A,b,x]= heat(100)                           
                                                                             
      where heat is from Regularization Tools. The description of            
      heat from http://www2.imm.dtu.dk/~pch/Regutools/ is:                   
                                                                             
                  [A,b,x] = heat(n,kappa)                                    
                                                                             
      A first kind Volterra integral equation with [0,1] as                  
      integration interval.  The kernel is K(s,t) = k(s-t) with              
         k(t) = t^(-3/2)/(2*kappa*sqrt(pi))*exp(-1/(4*kappa^2*t)) .          
      Here, kappa controls the ill-conditioning of the matrix:               
         kappa = 5 gives a well-conditioned problem                          
         kappa = 1 gives an ill-conditioned problem.                         
      The default is kappa = 1.                                              
                                                                             
      An exact soltuion is constructed, and then the right-hand side         
      b is produced as b = A*x.                                              
    

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))5,050 5,050 100
    Cholesky flop count3.4e+005 3.4e+005 1.0e+002
    nnz(L+U), no partial pivoting10,000 10,000 5,050
    nnz(V) for QR, upper bound nnz(L) for LU4,951 5,050 100
    nnz(R) for QR, upper bound nnz(U) for LU5,050 5,050 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.