% m2_sparsity.m - playing with sparse matrices


clf, clear all

A = [1 2; 0 4]                      
whos                      

B = sparse(A)
whos

A = eye(100);
B = speye(100);
whos

spy(A)
spy(B)

B(40:60,[10 20 40]) = 3;
spy(B)
spy(B+B')
spy((B+B')^2)

A = sprandsym(7,.25)
full(A)
  
A = sprandsym(10000,.002);
spy(A)
zoom(2), zoom(2),...
zoom out

A = A + 10*speye(10000);
b = ones(10000,1);
x = A\b;

x = pcg(A,b);                                  
x = pcg(A,b,1e-12,200);                                 
norm(A*x-b)                                 

more on                                   
help sparfun                             

A = gallery('wathen',20,20);           
spy(A)                                
spy(A^2)                             
spy(A^3)