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
explicit zero entries	1,387,472
nonzero pattern symmetry	symmetric
numeric value symmetry	symmetric
type	complex
structure	Hermitian
Cholesky candidate?	yes
positive definite?	no

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:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	2,070,437,023
Cholesky flop count	4.2e+13
nnz(L+U), no partial pivoting, with AMD	4,140,582,038
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	3,742,233,527
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	7,912,859,348

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 1387472 explicit zero entries.

For a description of the statistics displayed above, click here.

Maintained by Tim Davis, last updated 12-Mar-2014.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.