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

Matrix properties (click for a legend) | |

number of rows | 3,159 |

number of columns | 15,905 |

structural full rank? | yes |

structural rank | 3,159 |

numerical rank | 3,133 |

dimension of the numerical null space | 12,772 |

numerical rank / min(size(A)) | 0.99177 |

Euclidean norm of A | 6088.5 |

calculated singular value # 3133 | 0.32776 |

numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = | 1.4466e-008 |

calculated singular value # 3134 | 1.1457e-013 |

gap in the singular values at the numerical rank: singular value # 3133 / singular value # 3134 | 2.8607e+012 |

calculated condition number | 1.0253e+017 |

condest | -2 |

nonzeros | 2,872,265 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 2 |

entries not in dmperm blocks | 0 |

explicit zero entries | 0 |

nonzero pattern symmetry | 0% |

numeric value symmetry | 0% |

type | integer |

structure | rectangular |

Cholesky candidate? | no |

positive definite? | no |

author | N. Thiery |

editor | J.-G. Dumas |

date | 2008 |

kind | combinatorial problem |

2D/3D problem? | no |

SJid | 676 |

UFid | 2,148 |

Notes:

Brute force disjoint product matrices in tree algebra on n nodes, Nicolas Thiery From Jean-Guillaume Dumas' Sparse Integer Matrix Collection, http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html http://www.lapcs.univ-lyon1.fr/~nthiery/LinearAlgebra Linear algebra for combinatorics Abstract: Computations in algebraic combinatorics often boils down to sparse linear algebra over some exact field. Such computations are usually done in high level computer algebra systems like MuPAD or Maple, which are reasonnably efficient when the ground field requires symbolic computations. However, when the ground field is, say Q or Z/pZ, the use of external specialized libraries becomes necessary. This document, geared toward developpers of such libraries, present a brief overview of my needs, which seems to be fairly typical in the community. Filename in JGD collection: Kocay/Trec14.txt2

Ordering statistics: | AMD |
METIS |

nnz(V) for QR, upper bound nnz(L) for LU | 35,970,189 | 32,996,897 |

nnz(R) for QR, upper bound nnz(U) for LU | 4,741,823 | 4,840,721 |

*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.