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

• Matrix: TKK/tube1
• Description: Tube problem from R. Kouhia
• download as a MATLAB mat-file, file size: 255 KB. Use SJget(697) or SJget('TKK/tube1') in MATLAB.
• download in Matrix Market format, file size: 854 KB.
• download in Rutherford/Boeing format, file size: 327 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 3581 to 3586 and associated error bounds. Matrix properties (click for a legend) number of rows 21,498 number of columns 21,498 structural full rank? yes structural rank 21,498 numerical rank 3,583 dimension of the numerical null space 17,915 numerical rank / min(size(A)) 0.16667 Euclidean norm of A 43.257 calculated singular value # 3583 0.0027604 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 1.5275e-010 calculated singular value # 3584 1.337e-012 gap in the singular values at the numerical rank: singular value # 3583 / singular value # 3584 2.0646e+009 calculated condition number -2 condest Inf nonzeros 897,056 # of blocks from dmperm 1 # strongly connected comp. 1 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? unknown

 author R. Kouhia editor T. Davis date 2008 kind structural problem 2D/3D problem? yes SJid 697 UFid 1,914

Notes:

```Matrix problems from Reijo Kouhia, Structural Mechanics, Helsinki
University of Technology.   http://users.tkk.fi/~kouhia/sparse.html
```

 Ordering statistics: AMD METIS nnz(chol(P*(A+A'+s*I)*P')) 2,258,376 2,375,329 Cholesky flop count 4.7e+008 4.5e+008 nnz(L+U), no partial pivoting 4,495,254 4,729,160 nnz(V) for QR, upper bound nnz(L) for LU 6,666,632 3,487,803 nnz(R) for QR, upper bound nnz(U) for LU 12,131,864 6,675,094

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.