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

Matrix properties (click for a legend) | |

number of rows | 7,245 |

number of columns | 7,245 |

structural full rank? | yes |

structural rank | 7,245 |

numerical rank | 7,035 |

dimension of the numerical null space | 210 |

numerical rank / min(size(A)) | 0.97101 |

Euclidean norm of A | 3.4758e+006 |

calculated singular value # 7035 | 0.036893 |

numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = | 3.3737e-006 |

calculated singular value # 7036 | 1.6118e-010 |

gap in the singular values at the numerical rank: singular value # 7035 / singular value # 7036 | 2.289e+008 |

calculated condition number | 2.2634e+021 |

condest | Inf |

nonzeros | 46,142 |

# of blocks from dmperm | 3 |

# strongly connected comp. | 3 |

entries not in dmperm blocks | 0 |

explicit zero entries | 0 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | yes |

positive definite? | unknown |

author | T. Di Fonzo, M. Marini |

editor | T. Davis |

date | 2008 |

kind | economic problem |

2D/3D problem? | no |

SJid | 688 |

UFid | 1,891 |

Additional fields | size and type |

b | full 7245-by-1 |

Notes:

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 count | 1.3e+007 | 1.8e+007 | - |

nnz(L+U), no partial pivoting | 299,065 | 336,607 | - |

nnz(V) for QR, upper bound nnz(L) for LU | 1,174,854 | 1,001,859 | 1,174,843 |

nnz(R) for QR, upper bound nnz(U) for LU | 2,203,468 | 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.