• SJSU Singular Matrix Database
• Matrix group: Gset

• Matrix: Gset/G61
• Description: Random matrix, 0.035% uniformly distributed. G60=pattern of G61
• download as a MATLAB mat-file, file size: 151 KB. Use SJget(421) or SJget('Gset/G61') 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 7,000 number of columns 7,000 structural full rank? no structural rank 6,953 numerical rank 6,953 dimension of the numerical null space 47 numerical rank / min(size(A)) 0.99329 Euclidean norm of A 4.9038 calculated singular value # 6953 7.6367e-005 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 6.2172e-012 calculated singular value # 6954 5.4205e-015 gap in the singular values at the numerical rank: singular value # 6953 / singular value # 6954 1.4089e+010 calculated condition number 1.5551e+018 condest Inf nonzeros 34,296 # of blocks from dmperm 545 # strongly connected comp. 45 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type integer structure symmetric Cholesky candidate? yes positive definite? no

 author C. Helmberg editor Y. Ye date 1996 kind undirected weighted random graph 2D/3D problem? no SJid 421 UFid 526

 Ordering statistics: AMD METIS nnz(chol(P*(A+A'+s*I)*P')) 2,088,758 2,557,557 Cholesky flop count 2.7e+009 3.4e+009 nnz(L+U), no partial pivoting 4,170,516 5,108,114 nnz(V) for QR, upper bound nnz(L) for LU 7,498,106 7,061,779 nnz(R) for QR, upper bound nnz(U) for LU 8,979,541 10,364,189

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.