Matrix: Luong/photogrammetry

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

 (bipartite graph drawing)

• Matrix group: Luong
• download as a MATLAB mat-file, file size: 84 KB. Use UFget(1895) or UFget('Luong/photogrammetry') in MATLAB.

 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