# Getting B+ matrix (Warshall algorithm) in Matlab

Pseudocode:

// B = nxn binary matrix
// Bm = resulting matrix
for (i=1; i<=n; i++)
{
for (j=1; j<=n; j++)
{
if (B[i,j] == 1)
{
for (k=1; k<=n; k++)
{
Bm[i,j] = B[i,j] | B[k,j];
}
}
}
}


This is the Warshall algorithm written (in my way):

B = [1 1 0 0 0; 0 0 0 1 0; 0 0 0 0 1; 0 1 0 0 0; 0 0 0 0 0];

n = 5;

Bm = zeros(n);

for i = 1:n
for j = 1:n
if B(i,j) == 1
for k = 1:n
Bm(i,k) = B(i,k) | B(k,j);
end
end
end
end


It works but, how can I improve the matrix loops?

• Did you mean Bm(i,j) = B(i,k) | B(k,j)? – Quentin Pradet May 7 '13 at 13:48

## 1 Answer

This post may help you in removing a loop: http://mathforum.org/kb/message.jspa?messageID=845980

Furthermore, one way to speed up your code is to use a short circuit logical operator:

B(i,k) || B(k,j);


Also it seems to have a small effect if you use a logical matrix as input rather than a double:

B = logical(b);


Last and least, it would be nicer to initialize Bm with the datatype that it will have:

Bm = false(n)