Meaning of : in the parentheses

[jasoncurious]

Hi guys, I am currently doing a Matlab program for partial pivoting. I looked at my friend's example:

% Partial Pivoting
for i=1:n-1
for j = i+1:n
if (a(j,i)) > (a(i,i))
u=a(i,:);
a(i,:)=a(j,:);
a(j,:)=u;
v=b(i,1);
b(i,1)=b(j,1);
b(j,1)=v;
end
end
end

I was wondering what's the meaning of the : in the parentheses. Is it some sort of Matlab keyword? Thanks for helping

 

[Simon Bridge]

The colon stands for a whole line in the matrix. Observe:

octave:117> m=magic(4)
m =

   16    2    3   13
    5   11   10    8
    9    7    6   12
    4   14   15    1

octave:118> m(2,:)
ans =

    5   11   10    8

octave:119> m(:,2)
ans =

    2
   11
    7
   14

... see?
... so m(2,:) says to take the entire second row while the m(:,2) says take the second column.
http://volga.eng.yale.edu/sohrab/matlab_tutorial.html#selecting_parts_of_vectors_and_matrices__the_colon_operator
(Matlab works the same way...)

 

[jasoncurious]

Thanks bro.

 

[Simon Bridge]

No worries ;)
Generally, you can try out the confusing operations you see on some random matrix and see what happens ... the magic-square function is very useful for this.