Matrix: JGD_G5/IG5-11

Description: Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery.

 (bipartite graph drawing)

• Matrix group: JGD_G5
• download as a MATLAB mat-file, file size: 41 KB. Use UFget(1970) or UFget('JGD_G5/IG5-11') in MATLAB.

 Matrix properties number of rows 1,227 number of columns 1,692 nonzeros 22,110 structural full rank? no structural rank 902 # of blocks from dmperm 10 # strongly connected comp. 791 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

Notes:

```Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery.
Univ. Paris Sud.

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.

IG5-6: 30 x 77 : rang = 30  (Iteratif: 0.01 s, Gauss: 0.01 s)
IG5-7: 62 x 150 : rang = 62  (Iteratif: 0.02 s, Gauss: 0.01 s)
IG5-8: 156 x 292 : rang = 154  (Iteratif: 0.08 s, Gauss: 0.01 s)
IG5-9: 342 x 540 : rang = 308  (Iteratif: 0.46 s, Gauss: 0.02 s)
IG5-10: 652 x 976 : rang = 527  (Iteratif: 2.1 s, Gauss: 0.07 s)
IG5-11: 1227 x 1692 : rang = 902  (Iteratif: 7.5 s, Gauss: 0.22 s)
IG5-12: 2296 x 2875 : rang = 1578  (Iteratif: 26 s, Gauss: 0.93 s)
IG5-13: 3994 x 4731 : rang = 2532  (Iteratif: 80 s, Gauss: 3.35 s)
IG5-14: 6727 x 7621 : rang = 3906  (Iteratif: 244 s, Gauss: 10.06 s)
IG5-15: 11358 x 11987 : rang = 6146  (Iteratif: s, Gauss: 29.74 s)
IG5-16: 18485 x 18829 : rang = 9519  (Iteratif: s, Gauss: 621.97 s)
IG5-17: 27944 x 30131 : rang = 14060  (Iteratif: s, Gauss: 1973.8 s)

Filename in JGD collection: G5/IG5-11.txt2
```

 Ordering statistics: result nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD 210,506 nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD 596,832

 SVD-based statistics: norm(A) 74.1239 min(svd(A)) 5.67406e-17 cond(A) 1.30636e+18 rank(A) 902 sprank(A)-rank(A) 0 null space dimension 325 full numerical rank? no singular value gap 7.44747e+12

 singular values (MAT file): click here SVD method used: s = svd (full (A)) ; status: ok