• 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/parallax_1000
  • Description: PARALLAX 26x1000 Stellar parallax problem with 28 fixed, real observations.
  • download as a MATLAB mat-file, file size: 172 KB. Use SJget(252) or SJget('Regtools/parallax_1000') in MATLAB.
  • download in Matrix Market format, file size: 240 KB.
  • download in Rutherford/Boeing format, file size: 196 KB.


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


    Matrix properties (click for a legend)  
    number of rows26
    number of columns1,000
    structural full rank?yes
    structural rank26
    numerical rank 24
    dimension of the numerical null space976
    numerical rank / min(size(A))0.92308
    Euclidean norm of A 0.93258
    calculated singular value # 243.8521e-013
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 253.336e-014
    gap in the singular values at the numerical rank:
    singular value # 24 / singular value # 25
    calculated condition number4.6294e+014
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetry 0%
    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 26-by-1


        Constructed by the call [A,b]= parallax(1000)                       
      where parallax is from Regularization Tools. The description of       
      parallax from http://www2.imm.dtu.dk/~pch/Regutools/ is:              
                     [A,b] = parallax(n)                                    
      Stellar parallax problem with 28 fixed, real observations.            
      The underlying problem is a Fredholm integral equation of the         
      first kind with kernel                                                
         K(s,t) = (1/sigma*sqrt(2*pi))*exp(-0.5*((s-t)/sigma)^2) ,          
      and it is discretized by means of a Galerkin method with n            
      orthonormal basis functions.  The right-hand side consists of         
      a measured distribution function of stellar parallaxes, and its       
      length is fixed, m = 26.  The exact solution, which represents        
      the true distribution of stellar parallaxes, in not known.            

    Ordering statistics:AMD METIS
    nnz(V) for QR, upper bound nnz(L) for LU25,675 25,675
    nnz(R) for QR, upper bound nnz(U) for LU351 351

    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.