**Matrix: Luong/photogrammetry**

Description: Photogrammetry problem, B. Luong, FOGALE nanotech, France

(bipartite graph drawing) |

Matrix properties | |

number of rows | 1,388 |

number of columns | 390 |

nonzeros | 11,816 |

structural full rank? | yes |

structural rank | 390 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 1 |

explicit zero entries | 0 |

nonzero pattern symmetry | 0% |

numeric value symmetry | 0% |

type | real |

structure | rectangular |

Cholesky candidate? | no |

positive definite? | no |

author | B. Luong |

editor | T. Davis |

date | 2008 |

kind | computer graphics/vision problem |

2D/3D problem? | yes |

Additional fields | size and type |

b | full 1388-by-1 |

Notes:

Photogrammetry problem from Bruno Luong, FOGALE nanotech, France. The problem of interest is: [U S V]=svd(full(A),0); s=diag(S); The spectrum has two parts: - the singular values s(1) to s(end-7) are 1.7486e-004 to 3.4655e-007 (ratio 504.57). - the singular values s(end-6) to s(end) is smaller than 2.9614e-012 (ratio > 5.9e7). So in this problem, the following are considered: K = spanis the kernel of A, and L = span= orthogonal(K) is isomorph to Im(A).

Ordering statistics: | result |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 212,121 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 33,931 |

SVD-based statistics: | |

norm(A) | 0.000174861 |

min(svd(A)) | 4.01803e-13 |

cond(A) | 4.35191e+08 |

rank(A) | 390 |

sprank(A)-rank(A) | 0 |

null space dimension | 0 |

full numerical rank? | yes |

singular values (MAT file): | click here |

SVD method used: | s = svd (full (A)) ; |

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.
*