| Matrix properties | |
| number of rows | 680,943 |
| number of columns | 680,943 |
| nonzeros | 30,290,827 |
| structural full rank? | yes |
| structural rank | 680,943 |
| # of blocks from dmperm | 1 |
| # strongly connected comp. | 1 |
| entries not in dmperm blocks | 0 |
| explicit zero entries | 3,359,762 |
| 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 680943-by-1 |
| shift | sparse 680943-by-680943 |
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 represents a real
y-directed source, placed approximately in the centre. The model size in
elements is 20x20x20. 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
61 nodes. There are 3 unknown components at each node - the x, y and z
displacements. The A matrix therefore has dimension 680943 x 680943, where
((20 x 4) - (20 - 1))^3 * 3 = 680943. The problem domain is earth sciences.
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')) | 9.565681e+09 | 1,291,593,889 |
| Cholesky flop count | 4.3e+14 | 9.0e+12 |
| nnz(L+U), no partial pivoting | 1.913068e+10 | 2.582507e+09 |
| nnz(V) for QR, upper bound nnz(L) for LU | 1.648625e+10 | - |
| nnz(R) for QR, upper bound nnz(U) for LU | 3.444760e+10 | - |
Note that all matrix statistics (except nonzero pattern symmetry) exclude the 3359762 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.