• 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_200
  • Description: HEAT 200x200 Test problem: inverse heat equation.
  • download as a MATLAB mat-file, file size: 40 KB. Use SJget(242) or SJget('Regtools/heat_200') in MATLAB.
  • download in Matrix Market format, file size: 85 KB.
  • download in Rutherford/Boeing format, file size: 15 KB.

    Regtools/heat_200

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

    Regtools/heat_200

    dmperm of Regtools/heat_200

    Matrix properties (click for a legend)  
    number of rows200
    number of columns200
    structural full rank?yes
    structural rank200
    numerical rank 195
    dimension of the numerical null space5
    numerical rank / min(size(A))0.975
    Euclidean norm of A 0.35555
    calculated singular value # 1953.6249e-008
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    1.1102e-014
    calculated singular value # 1963.449e-021
    gap in the singular values at the numerical rank:
    singular value # 195 / singular value # 196
    1.051e+013
    calculated condition number2.7654e+058
    condest3.5615e+152
    nonzeros20,100
    # of blocks from dmperm200
    # strongly connected comp.200
    entries not in dmperm blocks19,900
    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
    SJid242
    UFid-

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

    Notes:

        Constructed by the call [A,b,x]= heat(200)                           
                                                                             
      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'))20,100 20,100 200
    Cholesky flop count2.7e+006 2.7e+006 2.0e+002
    nnz(L+U), no partial pivoting40,000 40,000 20,100
    nnz(V) for QR, upper bound nnz(L) for LU11,641 20,100 200
    nnz(R) for QR, upper bound nnz(U) for LU20,100 20,100 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.