Matrix properties
number of rows	4,147,110
number of columns	4,147,110
nonzeros	316,548,962
structural full rank?	yes
structural rank	4,147,110
# of blocks from dmperm	149,447
# strongly connected comp.	149,447
explicit zero entries	12,950,322
nonzero pattern symmetry	symmetric
numeric value symmetry	symmetric
type	real
structure	symmetric
Cholesky candidate?	yes
positive definite?	yes

author	C. Janna, M. Ferronato
editor	T. Davis
date	2014
kind	2D/3D problem
2D/3D problem?	yes

Notes:

Janna/Queen_4147: 3D structural problem                        
                                                               
Authors: Carlo Janna and Massimiliano Ferronato                
Symmetric Positive Definite Matrix                             
# equations:     4,147,110                                     
# non-zeroes:  329,499,288                                     
                                                               
The matrix Queen_4147 is obtained from the 3D discretizaion    
of a structural problem by isoparametric hexahedral Finite     
Elements. The solid material is strongly heterogeneous and     
several elements exhibit shape distortion thus producing an    
ill-conditioned stiffness matrix.                              
                                                               
Further information may be found in the following paper:       
                                                               
1) C. Janna, M. Ferronato, G. Gambolati. "The use of supernodes
in factored sparse approximate inverse preconditioning". SIAM  
Journal on Scientific Computing, submitted.                    

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	64,402,387,996
Cholesky flop count	4.9e+15
nnz(L+U), no partial pivoting, with AMD	128,800,628,882
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	70,146,293,583
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	123,868,718,534

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 12950322 explicit zero entries.

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

Maintained by Tim Davis, last updated 04-Jun-2015.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.