• SJSU Singular Matrix Database
• Matrix group: Nasa

• Matrix: Nasa/barth4
• Description: BARTH4: Nasa matrix, but with a diagonal added to the original matrix
• download as a MATLAB mat-file, file size: 87 KB. Use SJget(333) or SJget('Nasa/barth4') 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 6,019 number of columns 6,019 structural full rank? yes structural rank 6,019 numerical rank 6,018 dimension of the numerical null space 1 numerical rank / min(size(A)) 0.99983 Euclidean norm of A 4.3897 calculated singular value # 6018 3.8524e-006 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 5.3459e-012 calculated singular value # 6019 6.7673e-017 gap in the singular values at the numerical rank: singular value # 6018 / singular value # 6019 5.6926e+010 calculated condition number 6.4866e+016 condest 6.1703e+021 nonzeros 23,492 # of blocks from dmperm 33 # strongly connected comp. 33 entries not in dmperm blocks 426 explicit zero entries 0 nonzero pattern symmetry 0% numeric value symmetry 0% type binary structure unsymmetric Cholesky candidate? no positive definite? no

 author NASA editor G. Kumfert, A. Pothen date 1995 kind duplicate structural problem 2D/3D problem? yes SJid 333 UFid 755

Notes:

```Let A=Nasa/barth4, then Pothen/barth4 = spones(A+A') with xyz coord.
```

 Ordering statistics: AMD METIS DMPERM+ nnz(chol(P*(A+A'+s*I)*P')) 113,825 118,925 110,109 Cholesky flop count 3.6e+006 3.8e+006 3.5e+006 nnz(L+U), no partial pivoting 221,631 231,831 214,625 nnz(V) for QR, upper bound nnz(L) for LU 65,968 74,798 65,717 nnz(R) for QR, upper bound nnz(U) for LU 135,773 142,792 126,763

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.