Matrix properties
number of rows	5,489
number of columns	5,489
nonzeros	262,943
structural full rank?	yes
structural rank	5,489
# of blocks from dmperm	1
# strongly connected comp.	1
explicit zero entries	18,168
nonzero pattern symmetry	symmetric
numeric value symmetry	symmetric
type	real
structure	symmetric
Cholesky candidate?	yes
positive definite?	yes

author	R. Kouhia
editor	R. Boisvert, R. Pozo, K. Remington, B. Miller, R. Lipman, R. Barrett, J. Dongarra
date	1997
kind	structural problem
2D/3D problem?	yes

Additional fields	size and type
coord	full 5489-by-3

Notes:

%                                                                              
%FILE  s3rmq4m1.mtx                                                            
%TITLE Cyl shell R/t=1000 unif 30x30 quad mesh stab MITC4 elem with drill rot  
%KEY   s3rmq4m1                                                                
%                                                                              
%                                                                              
%CONTRIBUTOR Reijo Kouhia (reijo.kouhia@hut.fi)                                
%                                                                              
%REFERENCE   M. Benzi, R. Kouhia, M.Tuma: An assesment of some                 
%            preconditioning techniques in shell problems                      
%            Technical Report LA-UR-97-3892, Los Alamos National Laboratory    
%                                                                              
%BEGIN DESCRIPTION                                                             
% Matrix from a static analysis of a cylindrical shell                         
% Radius to thickness ratio R/t = 1000                                         
% Length to radius ratio    R/L = 1                                            
% One octant discretized with uniform 30 x 30 quadrilateral mesh               
% element:                                                                     
% facet-type shell element where the bending part is formulated                
% using the stabilized MITC theory (stabilization paramater 0.4)               
% the membrane part includes drilling rotations using                          
% the Hughes-Brezzi formulation with (regularizing parameter = G/1000,         
% where G is the shear modulus)                                                
% full 2x2 Gauss-Legendre integration                                          
% --------------------------------------------------------------------------   
% Note:                                                                        
% The sparsity pattern of the matrix is determined from the element            
% connectivity data assuming that the element matrix is full.                  
% Since this case the  material model is linear isotropically elastic          
% and the FE mesh is  uniform there exist some zeros.                          
% Since the removal of those zero elements is trivial                          
% but the reconstruction of the current sparsity                               
% pattern is impossible from the sparsified structure without any further      
% knowledge of the element connectivity, the zeros are retained in this file.  
% ---------------------------------------------------------------------------  
%END DESCRIPTION                                                               
%                                                                              
%                                                                              

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	848,498
Cholesky flop count	1.9e+08
nnz(L+U), no partial pivoting, with AMD	1,691,507
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	875,592
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	1,734,881

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 18168 explicit zero entries.

SVD-based statistics:
norm(A)	6874.52
min(svd(A))	3.89368e-07
cond(A)	1.76556e+10
rank(A)	5,489
sprank(A)-rank(A)	0
null space dimension	0
full numerical rank?	yes

singular values (MAT file):	click here
SVD method used:	s = svd (full (A)) ;
status:	ok

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.