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
explicit zero entries	3,359,762
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 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:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	9.565681e+09
Cholesky flop count	4.3e+14
nnz(L+U), no partial pivoting, with AMD	1.913068e+10
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	1.648625e+10
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	3.444760e+10

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 3359762 explicit zero entries.

Maintained by Tim Davis, last updated 01-Apr-2011.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.