% Lecture 36: SPECIAL MATRICES

% using sparse matrices

a = sparse(3,4,5,10,10);
spy(a);
a = sparse([3,3,3,3],[4,5,7,8],[5,4,3,2],10,10);
spy(a);
a(3,5);
a(3,5)

ans =

     4

a(1,1)

ans =

     0

% Pascal matrix 
p10 = pascal(10);
p10 = mod(p10,2);
spy(p10);

% convert to a sparse matrix 
s10 = sparse(p10);
[i,j,v] = find(s10); % make the table of entries of s10
norm(p10-s10)

ans =

     0

% Triagonal marices
i = [1:6 2:6 1:5];
j = [1:6 1:5 2:6];
v = [2*ones(1,6) ones(1,5) 3*ones(1,5)];
d3 = sparse(i,j,v);
spy(d3);


% NETWORK

cd h:
fschange('H:\nodes.m');
A = ones(12); 
[x,y]=nodes(12);
hold on
gplot(A,[x' y']); % the complete graph

% make the adjacency matrix for network with 
% all odd nodes linked to #1 and all even - to #8
A = spalloc(12,12,12);
for i=1:12
if mod(i,2)==0
A(i,8)=1;
else A(i,1)=1;
end;
end;
A(1,1)=0;
A(8,8)=0;
A = A + A';
openvar('A', A);
figure
[x,y]=nodes(12);
gplot(A, [x' y']);
[x,y]=nodes(12);
hold on
gplot(A, [x' y']);
A(1,8)=1;
A(8,1)=1;
gplot(A, [x' y']);
diary off