Matrix: Luong/photogrammetry
Description: Photogrammetry problem, B. Luong, FOGALE nanotech, France
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| (bipartite graph drawing) |
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| 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 = span is 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.