• 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/tomo_4900
  • Description: TOMO 4900x4900: Create a 2D tomography test problem.
  • download as a MATLAB mat-file, file size: 4 MB. Use SJget(268) or SJget('Regtools/tomo_4900') in MATLAB.
  • download in Matrix Market format, file size: 5 MB.
  • download in Rutherford/Boeing format, file size: 5 MB.


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


    Matrix properties (click for a legend)  
    number of rows4,900
    number of columns4,900
    structural full rank?yes
    structural rank4,900
    numerical rank 4,897
    dimension of the numerical null space3
    numerical rank / min(size(A))0.99939
    Euclidean norm of A 77.135
    calculated singular value # 48970.00013581
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 48986.4091e-016
    gap in the singular values at the numerical rank:
    singular value # 4897 / singular value # 4898
    calculated condition number5.1232e+017
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetry 2%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    editorPer Christian Hansen
    kindill-posed problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 4900-by-1
    xfull 4900-by-1


        Constructed by the call [A,b,x]= tomo(70)                            
      where tomo is from Regularization Tools. The description of            
      tomo from http://www2.imm.dtu.dk/~pch/Regutools/ is:                   
                    [A,b,x] = tomo(N,f);                                     
      This function creates a simple two-dimensional tomography test problem.
      A 2D domain [0,N] x [0,N] is divided into N^2 cells of unit size, and a
      total of round(f*N^2) rays in random directions penetrate this domain. 
      The default value is f = 1.                                            
      Each cell is assigned a value (stored in the vector x), and for each   
      ray the corresponding element in the right-hand side b is the line     
      integral along the ray, i.e.                                           
         sum_{cells in ray}  x_{cell j} * length_{cell j}                    
      where length_{cell j} is the length of the ray in the j-th cell.       
      The matrix A is sparse, and each row (corresponding to a ray) holds    
      the value length_{cell j} in the j-th position.  Hence:                
         b = A*x .                                                           
      Once a solution x_reg has been computed, it can be visualized by means 
      of imagesc(reshape(x_reg,N,N)).                                        
      The exact solution, reshape(x,N,N), is identical to the exact image in 
      the function blur.                                                     
      Note that the code for tomo uses random numbers and repeated calls to  
      tomo will produce different matrices.                                  

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))10,405,178 10,048,489
    Cholesky flop count3.1e+010 2.9e+010
    nnz(L+U), no partial pivoting20,805,456 20,092,078
    nnz(V) for QR, upper bound nnz(L) for LU11,242,706 7,780,797
    nnz(R) for QR, upper bound nnz(U) for LU11,950,713 11,997,846

    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.