| Matrix properties | |
| number of rows | 292,008 |
| number of columns | 292,008 |
| nonzeros | 12,935,272 |
| structural full rank? | yes |
| structural rank | 292,008 |
| # of blocks from dmperm | 1 |
| # strongly connected comp. | 1 |
| entries not in dmperm blocks | 0 |
| explicit zero entries | 1,387,472 |
| nonzero pattern symmetry | symmetric |
| numeric value symmetry | symmetric |
| type | complex |
| structure | Hermitian |
| Cholesky candidate? | yes |
| positive definite? | unknown |
| author | C. Sinclair |
| editor | T. Davis |
| date | 2007 |
| kind | materials problem |
| 2D/3D problem? | yes |
| Additional fields | size and type |
| b | sparse 292008-by-1 |
| shift | sparse 292008-by-292008 |
Notes:
The A matrix is produced using 3-D spectral-element elastic wave modelling in
the frequency domain.The medium is homogeneous and isotropic with elastic
coefficients: c11 = 6.30, c44 = 1.00. The B matrix contains only one non-zero
entry, representing a real y-directed source, placed approximately in the
centre. The model size in elements is 10x10x10. Each element is 1m x1m x 1m.
Each element is a 4x4x4 Gauss-Lobbato-Legendre mesh, so the height, width and
depth of the system is 31 nodes. There are 3 unknown complex components at
each node - the x, y and z displacements. The A matrix therefore has
dimension 89373 x 89373. ((10 x 4) - (10 - 1))^3 * 3 = 89373. The solution
will consist of x-z planes. Note that A is complex and b is sparse and real
(b has a single nonzero).
The A matrix was provided with a nonzero imaginary part, but was otherwise
complex Hermitian. To save space in the Matrix Market and Rutherford/Boeing
formats, the A matrix here has had this imaginary diagonal removed. The
shift can be found in the aux.shift auxiliary matrix. To reproduce the
original A matrix, use A = Problem.A + Problem.aux.shift ;
| Ordering statistics: | AMD | METIS |
| nnz(chol(P*(A+A'+s*I)*P')) | 2,070,437,023 | 385,959,851 |
| Cholesky flop count | 4.2e+13 | 1.6e+12 |
| nnz(L+U), no partial pivoting | 4.140582e+09 | 771,627,694 |
| nnz(V) for QR, upper bound nnz(L) for LU | 3.742234e+09 | - |
| nnz(R) for QR, upper bound nnz(U) for LU | 7.912859e+09 | - |
Note that all matrix statistics (except nonzero pattern symmetry) exclude the 1387472 explicit zero entries.
Maintained by Tim Davis, last updated 04-May-2008.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.