Matrix properties
number of rows	29,282
number of columns	29,282
nonzeros	406,084
structural full rank?	yes
structural rank	29,282
# of blocks from dmperm	1
# strongly connected comp.	1
entries not in dmperm blocks	0
explicit zero entries	0
nonzero pattern symmetry	symmetric
numeric value symmetry	0%
type	complex
structure	unsymmetric
Cholesky candidate?	no
positive definite?	no

author	H. Dehghani
editor	T. Davis
date	2007
kind	electromagnetics problem
2D/3D problem?	yes

Additional fields	size and type
b	sparse 29282-by-1
Q	sparse 14641-by-1
nodes	full 14641-by-3
elements	full 28800-by-3

Notes:

% The problem is solving the fluence (PHI) of light in soft tissue using
% a simplified 3rd spherical harmonic expansion (SPN3) of the Radiative 
% Transport Equation.  There are two coupled equations to solve:        
% M1*phi1 = Q + (M2*phi2)                                   eq(1)       
% (M4 - (M3*inv(M1)*M2))*phi2 = -2/3*Q + M3*inv(M1)*Q       eq(2)       
% PHI = phi1 - (1/3).*phi2                                  eq(3)       
                                                                        
Problem = UFget ('Dehghani/light_in_tissue') ;                          
A = Problem.A ;                   % get the problem                     
Q = Problem.aux.Q ;                                                     
k = size (A,1) / 2 ;                                                    
M1 = A (1:k,1:k) ;                                                      
M2 = A (1:k,k+1:end) ;                                                  
M3 = A (k+1:end, 1:k) ;                                                 
M4 = A (k+1:end, k+1:end) ;                                             
elements = Problem.aux.elements ;                                       
nodes = Problem.aux.nodes ;                                             
                                                                        
Q2 = (-(2/3).*Q) + (M3*(M1\Q)) ;  % create rhs for equation 2           
Q2 = [sparse(k,1) ; Q2] ;                                               
phi2 = A\Q2 ;                     % solve for phi2                      
phi2 = phi2 (end/2+1:end,:) ;                                           
Q1 = Q + M2*phi2 ;                % calculate rhs for equation 1        
phi1 = M1\Q1;                     % solve for phi1                      
PHI = phi1 - (1/3).*phi2;                                               
figure (1) ; clf                  % plot results                        
trisurf(elements, nodes(:,1), nodes(:,2), nodes(:,3), log(abs(PHI))) ;  
shading interp ;                                                        
view (2) ;                                                              
colorbar('horiz') ;                                                     
axis equal ;                                                            
axis off ;                                                              
colormap hot ;                                                          

Ordering statistics:	AMD	METIS
nnz(chol(P*(A+A'+s*I)*P'))	1,390,043	1,433,663
Cholesky flop count	2.0e+08	1.9e+08
nnz(L+U), no partial pivoting	2,750,804	2,838,044
nnz(V) for QR, upper bound nnz(L) for LU	2,925,391	2,792,783
nnz(R) for QR, upper bound nnz(U) for LU	5,672,099	5,340,581

Maintained by Tim Davis, last updated 30-Sep-2008.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.