• 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_500
  • Description: HEAT 500x500 Test problem: inverse heat equation.
  • download as a MATLAB mat-file, file size: 487 KB. Use SJget(243) or SJget('Regtools/heat_500') in MATLAB.
  • download in Matrix Market format, file size: 504 KB.
  • download in Rutherford/Boeing format, file size: 169 KB.

    Regtools/heat_500

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

    Regtools/heat_500

    dmperm of Regtools/heat_500

    Matrix properties (click for a legend)  
    number of rows500
    number of columns500
    structural full rank?yes
    structural rank500
    numerical rank 492
    dimension of the numerical null space8
    numerical rank / min(size(A))0.984
    Euclidean norm of A 0.35525
    calculated singular value # 4923.3503e-013
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    2.7756e-014
    calculated singular value # 4933.7152e-023
    gap in the singular values at the numerical rank:
    singular value # 492 / singular value # 493
    9.0181e+009
    calculated condition number1.8493e+124
    condest5.4564e+270
    nonzeros125,250
    # of blocks from dmperm500
    # strongly connected comp.500
    entries not in dmperm blocks124,750
    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
    SJid243
    UFid-

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

    Notes:

        Constructed by the call [A,b,x]= heat(500)                           
                                                                             
      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'))125,250 125,250 500
    Cholesky flop count4.2e+007 4.2e+007 5.0e+002
    nnz(L+U), no partial pivoting250,000 250,000 125,250
    nnz(V) for QR, upper bound nnz(L) for LU63,257 125,250 500
    nnz(R) for QR, upper bound nnz(U) for LU125,250 125,250 125,250

    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.