function exercise_1_6_5()
% 
%
% Written by:
% -- 
% John L. Weatherwax                2006-12-13
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; 

airfoil

% Part (a):
%
figure; spy(A); title( 'airfoil' ); 
tic, R = chol(A); t=toc; 
fprintf('Time to directly Cholesky factor airfoil = %f\n', t ); 
fprintf( 'Number of non zeros of the Cholesky factor of airfoil = %d (=%f percent)\n', nnz(R), nnz(R)/prod(size(A)) ); 
figure; spy(R); title( 'Cholesky factor of airfoil' ); 

pause; close all; 

% Part (b):
%
p = symrcm(A);
arcm = A(p,p); 
figure; spy(arcm); title( 'Reverse Cuthill-McKee ordered version of airfoil' ); 
tic, R = chol(arcm); t=toc;
fprintf('Time to factor the reverse Cuthill-McKee ordered Cholesky factor airfoil = %f\n', t ); 
fprintf( 'Number of non zeros of the Cholesky factor of airfoil = %d (=%f percent)\n', nnz(R), nnz(R)/prod(size(A)) ); 
figure; spy(R); title( 'Cholesky factor of reverse cuthill-McKee ordered airfoil' ); 

% Part (c):
%
pause; close all; 

%p = symmmd(A);
p = symamd(A);
ammd = A(p,p); 
figure; spy(ammd); title( 'Minimum degree ordering of airfoil' ); 
tic, R = chol(ammd); t=toc;
fprintf('Time to factor the minimum degree ordering Cholesky factor airfoil = %f\n', t ); 
fprintf( 'Number of non zeros of the Cholesky factor of airfoil = %d (=%f percent)\n', nnz(R), nnz(R)/prod(size(A)) ); 
figure; spy(R); title( 'Cholesky factor of the minimum degree ordering of airfoil' ); 

pause; close all; 

return;