• SJSU Singular Matrix Database
• Matrix group: Gset

• Matrix: Gset/G55
• Description: Random matrix, 0.05% uniformly distributed. G55=pattern of G56
• download as a MATLAB mat-file, file size: 101 KB. Use SJget(9) or SJget('Gset/G55') in MATLAB.

Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

 Matrix properties (click for a legend) number of rows 5,000 number of columns 5,000 structural full rank? no structural rank 4,966 numerical rank 4,966 dimension of the numerical null space 34 numerical rank / min(size(A)) 0.9932 Euclidean norm of A 6.2311 calculated singular value # 4966 7.6838e-005 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 4.4409e-012 calculated singular value # 4967 4.3488e-015 gap in the singular values at the numerical rank: singular value # 4966 / singular value # 4967 1.7669e+010 calculated condition number 4.5272e+018 condest Inf nonzeros 24,996 # of blocks from dmperm 411 # strongly connected comp. 32 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type binary structure symmetric Cholesky candidate? yes positive definite? unknown

 author C. Helmberg editor Y. Ye date 1996 kind duplicate undirected random graph 2D/3D problem? no SJid 9 UFid 519

Notes:

```This matrix is the nonzero pattern of Gset/G56
```

 Ordering statistics: AMD METIS nnz(chol(P*(A+A'+s*I)*P')) 1,091,404 1,317,912 Cholesky flop count 1.0e+009 1.3e+009 nnz(L+U), no partial pivoting 2,177,808 2,630,824 nnz(V) for QR, upper bound nnz(L) for LU 3,896,150 3,680,788 nnz(R) for QR, upper bound nnz(U) for LU 4,732,160 5,432,189

Maintained by Leslie Foster, last updated 24-Apr-2009.

Entries 5 through 14 in the table of matrix properties and the singular
value plot were created using SJsingular code. The other plots
and statistics are produced using utilities from the SuiteSparse package.
Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.