Assignment with Repeated Indices

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Repeated Indices with a Single Assignment

I initialize an output matrix to zeros and create two vectors, one with locations (indices) and one for the corresponding data. Now let's look at the results of an indexed assignment.

A = zeros(3);
loc = [1 3 7 9 1];
data = 1:5;
A(loc) = A(loc) + data

A =
     5     0     3
     0     0     0
     2     0     4

You see in this case that even though index 1 was repeated, its output value is only 5, and not 6. Let me reset A so I can show you what's going on.

A = zeros(3);

Here's what "essentially" happens during an assignment in MATLAB. On the right-hand side, A(loc) is created.

A(loc)

ans =
     0     0     0     0     0

This means that there are 2 copies of A(1) currently and an element of data will be added to each of these. The important thing to realize is that now the values for the right-hand side have been calculated and set.

A(loc) + data

ans =
     1     2     3     4     5

Following this, the 5-element right-hand side is assigned into A(loc) on the left-hand side. Values are currently placed into the output vector by marching down the left-hand side locations, replacing one element at a time. So the first element gets replaced not once, but twice, with the final one being the value that you see.

A(loc) = A(loc) + data

A =
     5     0     3
     0     0     0
     2     0     4

Repeated Indices Using a for Loop for the Assignment

Here's another way to do the assignment, but in this case, the

B = zeros(3);
for n = 1:length(loc)
  B(loc(n)) = B(loc(n)) + data(n);
end
B

B =
     6     0     3
     0     0     0
     2     0     4

Notice that the output here for B does not match that from the vectorized assignment above. This is because the values for the right-hand side get updated one at a time, and can therefore accumulate as additions made to a particular index.

isequal(A,B)

ans =
     0

Using accumarray to Accumulate Results with Repeated Indices

What if you want the accumulation effect, but you'd prefer to use vectorized code? That's what the function accumarray is for.

C = accumarray(loc',data,[9 1]);
C = reshape(C,[3 3])

C =
     6     0     3
     0     0     0
     2     0     4

We see the same results here as those from the for loop example.

isequal(B,C)

ans =
     1

Repeated Index Usage

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Published with MATLAB® 7.4