• SJSU Singular Matrix Database
• Matrix group: Rothberg
• Click here for a description of the Rothberg group.
• Click here for a list of all matrices
• Click here for a list of all matrix groups

• Matrix: Rothberg/struct3
• Description: Finite element matrix, from Ed Rothberg, Silicon Graphics, Inc.
• download as a MATLAB mat-file, file size: 753 KB. Use SJget(510) or SJget('Rothberg/struct3') in MATLAB.
• download in Matrix Market format, file size: 1 MB.
• download in Rutherford/Boeing format, file size: 643 KB.

A singular value of A is guaranteed1 to be in the interval pictured by the blue bars around each of the calculated singular values.

Routine svds_err, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.
Routine spnrank, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 41591 to 41596 and associated error bounds.  Matrix properties (click for a legend) number of rows 53,570 number of columns 53,570 structural full rank? yes structural rank 53,570 numerical rank 41,593 dimension of the numerical null space 11,977 numerical rank / min(size(A)) 0.77642 Euclidean norm of A 26.147 calculated singular value # 41593 3.6237e-006 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 1.9032e-010 calculated singular value # 41594 4.4303e-013 gap in the singular values at the numerical rank: singular value # 41593 / singular value # 41594 8.1792e+006 calculated condition number -2 condest Inf nonzeros 1,173,694 # of blocks from dmperm 2 # strongly connected comp. 2 entries not in dmperm blocks 0 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type binary structure symmetric Cholesky candidate? yes positive definite? no

 author E. Rothberg editor T. Davis date 1997 kind structural problem 2D/3D problem? yes SJid 510 UFid 807

 Ordering statistics: AMD METIS DMPERM+ nnz(chol(P*(A+A'+s*I)*P')) 4,945,868 4,600,416 4,488,562 Cholesky flop count 1.0e+009 7.9e+008 7.0e+008 nnz(L+U), no partial pivoting 9,838,166 9,147,262 8,923,554 nnz(V) for QR, upper bound nnz(L) for LU 9,586,863 6,964,487 6,806,585 nnz(R) for QR, upper bound nnz(U) for LU 18,314,276 13,182,923 12,885,627

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.