Vectorizing a MATLAB loop

Question

I'm trying to do my best and not use loops in Matlab, but I find it very hard sometimes .

For example I wrote this code :

vector = zeros(p,1);

diagDominantFlag = 1;
for row = 1:p
    for col = 1:q
        if(row ~= col)
            vector(row) = vector(row) + A(row,col);
        end
    end
    if(A(row,row) <= vector(row))
        diagDominantFlag = 0;
        break;
    end
end

Is it possible to vectorize that double for loop?

Thanks

I've edited the question, since "breaking" a loop means something totally different to "vectorizing" it. — NPE
– NPE, Commented May 30, 2012 at 17:18

Chris A. · Accepted Answer · 2012-05-30 17:22:56Z

2

Not an answer to your direct question, but, here's a loopless test for diagonal dominance (since you seem interested in that):

all(diag(A) >= (sum(abs(A),2)-abs(diag(A)) )

or for strict diagonal dominance:

all(diag(A) > (sum(abs(A),2)-abs(diag(A)) )

Also, in your above code, make sure you do abs() on the off-diagonal values.

answered May 30, 2012 at 17:22

Chris A.

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2 Comments

Eitan T Over a year ago

+1 for the abs() observation. Nevertheless, I'll stick to the OP's original code in my answer...

Chris A. Over a year ago

@EitanT I originally thought the same, but I've never seen a definition of diagonal dominance that didn't want the abs()

Eitan T · Accepted Answer · 2012-05-30 17:26:42Z

2

Adding to Ansari's answer, the diagDominantFlag can be calculated by:

diagDominantFlag = all(diag(A) >= (sum(A, 2) - diag(A)));

Thus replacing your double for loop with a one-liner.

answered May 30, 2012 at 17:26

Eitan T

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1 Comment

JAN Over a year ago

Okay,this is really nice.I'll try to remove all the loops from my code.

Ansari · Accepted Answer · 2012-05-30 17:33:16Z

2

You can replace the inner loop with

vector(row) = sum(A(row, :)) - A(row, row);

and in fact you can replace the whole thing by

vector = sum(A, 2) - diag(A);

To add the check you have in the outer loop, you can then do something like

f = find(diag(A) <= vector);
if length(f) > 0
    diagDominantFlag = 0;
    vector(f(1):end) = 0;
end

edited May 30, 2012 at 17:33

answered May 30, 2012 at 17:20

Ansari

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6 Comments

Eitan T Over a year ago

+1 for the calculation of vector. The inner loop can be replaced by a vectorized comparsion, though...

Ansari Over a year ago

Which inner loop? In the OPs question? That loop fills in the vector variable, so I don't see how a comparison would replace that .. can you elaborate?

Eitan T Over a year ago

Sorry for the misunderstanding. I meant to say that the whole ordeal can be replaced by one logical vectorized comparison. Note that the flag retains the value of 1 only if each element in the diagonal is greater or equal to the corresponding element in vector. It's called diagonal dominance.

JAN Over a year ago

@Ansari: Can I use abs somewhere here ? since I need to take the absolute value and the rest of the elements of each line , and compare the sum of the absolute value of them with a_ii . Thanks .

JAN Over a year ago

vector(row) = sum(abs(A(row, :))) - abs(A(row, row));

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