Matrix properties
number of rows	1,391,349
number of columns	1,391,349
nonzeros	64,131,971
structural full rank?	yes
structural rank	1,391,349
# of blocks from dmperm	9,229
# strongly connected comp.	9,229
explicit zero entries	399,730
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	2011
kind	structural problem
2D/3D problem?	yes

Notes:

Authors: Carlo Janna and Massimiliano Ferronato                    
                                                                   
Symmetric Positive Definite Matrix                                 
# equations:   1,391,349                                           
# non-zeroes: 64,531,701                                           
Problem description: structural problem                            
                                                                   
The matrix Serena is obtained from a structural problem            
discretizing a gas reservoir with tetrahedral Finite Elements.     
The medium is strongly heterogeneous and characterized by a        
complex geometry consisting of alternating sequences of thin       
clay and sand layers.  Some further information may be found       
in the paper:                                                      
                                                                   
M. Ferronato, G. Gambolati, C. Janna, P. Teatini. "Geomechanical   
issues of anthropogenic CO2 sequestration in exploited gas fields",
Energy Conversion and Management, 51, pp. 1918-1928, 2010.         

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	7,502,311,154
Cholesky flop count	2.2e+14
nnz(L+U), no partial pivoting, with AMD	15,003,230,959
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	11,091,348,271
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	19,624,945,409

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 399730 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.