• SJSU Singular Matrix Database
  • Matrix group: Marini
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  • Matrix: Marini/eurqsa
  • Description: Economic time series reconciliation; Di Fonzo (Univ Padua) & Marini (ISTAT)
  • download as a MATLAB mat-file, file size: 295 KB. Use SJget(688) or SJget('Marini/eurqsa') in MATLAB.
  • download in Matrix Market format, file size: 148 KB.
  • download in Rutherford/Boeing format, file size: 140 KB.


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


    dmperm of Marini/eurqsa

    scc of Marini/eurqsa

    Matrix properties (click for a legend)  
    number of rows7,245
    number of columns7,245
    structural full rank?yes
    structural rank7,245
    numerical rank 7,035
    dimension of the numerical null space210
    numerical rank / min(size(A))0.97101
    Euclidean norm of A 3.4758e+006
    calculated singular value # 70350.036893
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 70361.6118e-010
    gap in the singular values at the numerical rank:
    singular value # 7035 / singular value # 7036
    calculated condition number2.2634e+021
    # of blocks from dmperm3
    # strongly connected comp.3
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?unknown

    authorT. Di Fonzo, M. Marini
    editorT. Davis
    kindeconomic problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 7245-by-1


    Economic statistics are often published in the form of time series, as a   
    collection of observations sampled at equally-spaced time periods (months, 
    quarters). Economic concepts behind such statistics are often linked by a  
    system of linear relationships, deriving from the economic theory. However,
    these restrictions are rarely met by the original time series for various  
    reasons.  Then, data sets of real-world variables generally show           
    discrepancies with respect to prior restrictions on their values.  The     
    adjustment of a set of data in order to satisfy a number of accounting     
    restrictions -and thus to remove any discrepancy -is generally known as    
    the reconciliation problem.                                                
    The matrix comes from a real application composed of 183 quarterly time    
    series observed over 28 quarters, which form the system of European        
    national accounts by institutional sectors (EURQSA). Then, the number of   
    observations to be reconciled is n = 28 x 183 = 5124. The variables are    
    connected by a system of 30 linear relationships. Moreover, each quarterly 
    time series must be in line with the same variables observed yearly (due   
    to different compilation practices quarterly and annual estimates might    
    differ). The total number of constraints of the system is k = 2121. On     
    the whole, matrix A has dimension 7245, with block (1,1) of dimension 5124.

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))153,155 171,926 -
    Cholesky flop count1.3e+007 1.8e+007 -
    nnz(L+U), no partial pivoting299,065 336,607 -
    nnz(V) for QR, upper bound nnz(L) for LU1,174,854 1,001,859 1,174,843
    nnz(R) for QR, upper bound nnz(U) for LU2,203,468 2,058,825 2,204,263

    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.