A singular value of A is guaranteed^{1} to be in the interval pictured by the blue bars around each of the calculated singular values.

Routine svds_err, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.

Routine spnrank, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 14407 to 14412 and associated error bounds.

Matrix properties (click for a legend) | |

number of rows | 120,576 |

number of columns | 23,740 |

structural full rank? | no |

structural rank | 18,660 |

numerical rank | 14,409 |

dimension of the numerical null space | 9,331 |

numerical rank / min(size(A)) | 0.60695 |

Euclidean norm of A | 5.4772 |

calculated singular value # 14409 | 0.91233 |

numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = | 1.0709e-010 |

calculated singular value # 14410 | 9.7861e-016 |

gap in the singular values at the numerical rank: singular value # 14409 / singular value # 14410 | 9.3227e+014 |

calculated condition number | -2 |

condest | -2 |

nonzeros | 146,520 |

# of blocks from dmperm | 2 |

# strongly connected comp. | 75,727 |

explicit zero entries | 360 |

nonzero pattern symmetry | 0% |

numeric value symmetry | 0% |

type | integer |

structure | rectangular |

Cholesky candidate? | no |

positive definite? | no |

author | V. Welker |

editor | J.-G. Dumas |

date | 2008 |

kind | combinatorial problem |

2D/3D problem? | no |

SJid | 699 |

UFid | 2,052 |

Additional fields | size and type |

T | full 147240-by-3 |

Notes:

Simplicial complexes from Homology from Volkmar Welker. From Jean-Guillaume Dumas' Sparse Integer Matrix Collection, http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html http://www.mathematik.uni-marburg.de/~welker/ Filename in JGD collection: Homology/D6-6.sms The original file contains 720 duplicate entries, and is the only file in the JGD collection with duplicates. The original triplets can be found in Problem.aux.T, where the kth triplet is row k of T: row index T(k,1), column index T(k,2), value T(k,3), so that A = spconvert (Problem.aux.T)

Ordering statistics: | AMD |
METIS |

nnz(V) for QR, upper bound nnz(L) for LU | 1,478,161 | 1,501,913 |

nnz(R) for QR, upper bound nnz(U) for LU | 440,884 | 460,417 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 360 explicit zero entries.
*

*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.
*