**Matrix: AG-Monien/biplane-9**

Description: 2D grid

(undirected graph drawing) |

Matrix properties | |

number of rows | 21,701 |

number of columns | 21,701 |

nonzeros | 84,076 |

structural full rank? | no |

structural rank | 21,691 |

# of blocks from dmperm | 277 |

# strongly connected comp. | 1 |

explicit zero entries | 0 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | binary |

structure | symmetric |

Cholesky candidate? | no |

positive definite? | no |

author | R. Diekmann, R. Preis |

editor | R. Diekmann, R. Preis |

date | 1998 |

kind | 2D/3D problem |

2D/3D problem? | yes |

Additional fields | size and type |

coord | full 21701-by-2 |

Notes:

AG-Monien Graph Collection, Ralf Diekmann and Robert Preis http://www2.cs.uni-paderborn.de/fachbereich/AG/monien/RESEARCH/PART/graphs.html A collection of test graphs from various sources. Many of the graphs include XY or XYZ coordinates. This set also includes some graphs from the Harwell-Boeing collection, the NASA matrices, and some random matrices which are not included here in the AG-Monien/ group of the UF Collection. In addition, two graphs already appear in other groups: AG-Monien/big : same as Nasa/barth5, Pothen/barth5 (not included here) AG-Monien/cage_3_11 : same as Pajek/GD98_c (included here) The AG-Monien/GRID subset is not included. It contains square grids that are already well-represented in the UF Collection. Six of the problem sets are included as sequences, each sequence being a single problem instance in the UF Collection: bfly: 10 butterfly graphs 3..12 cage: 45 cage graphs 3..12 cca: 10 cube-connected cycle graphs, no wrap ccc: 10 cube-connected cycle graphs, with wrap debr: 18 De Bruijn graphs se: 13 shuffle-exchange graphs Problem.aux.G{:} are the graphs in these 6 sequences. Problem.aux.Gname{:} are the original names of each graph, and Problemm.aux.Gcoord{:} are the xy or xyz coordinates of each node, if present.

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 342,013 |

Cholesky flop count | 1.5e+07 |

nnz(L+U), no partial pivoting, with AMD | 662,325 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 409,961 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 758,576 |

SVD-based statistics: | |

norm(A) | 3.99612 |

min(svd(A)) | 1.14588e-17 |

cond(A) | 3.48738e+17 |

rank(A) | 21,659 |

sprank(A)-rank(A) | 32 |

null space dimension | 42 |

full numerical rank? | no |

singular value gap | 5.71582e+09 |

singular values (MAT file): | click here |

SVD method used: | s = svd (full (R)) ; where [~,R,E] = spqr (A) with droptol of zero |

status: | ok |

For a description of the statistics displayed above, click here.

*Maintained by Tim Davis, last updated 12-Mar-2014.Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.
*