How can I use bsxfun to replace for-loop in this code?

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Shi Shi
Shi Shi 2017-5-19
评论： Shi Shi 2017-5-23
Dear all,
I want to use the function 'bsxfun' instead of inner for-loop. My code is as following. However, the result, matrix B, calculated by 'bsxfun' is error. I feel very confused with how 'bsxfun' works. Could anyone help me to understand the result and use 'bsxfun' correctly instead of inner for-loop?
Thanks very much!
sequence = [1,2,3,4,5];
avg = @(i, j) mean(sequence(i:j));
for i = 1:4
for j = i+1:5
A(i,j) = avg(i,j);
end
B(i, i+1:5) = bsxfun(avg, i, i+1:5);
end
  2 个评论
Adam
Adam 2017-5-19
What is the end result you are looking for? You should state that clearly ahead of being focused entirely on using a specific function.
Shi Shi
Shi Shi 2017-5-19
Thanks for your answer. The result calculated by inner for-loop is just what I want. For each pair (i,j), where i<j, I want to calculate the average of sequence(i:j).

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Guillaume
Guillaume 2017-5-19
"I want to use the function 'bsxfun' instead of inner for-loop" Rather than fixating on a function that may not be a solution to your problem, tell us what you want to do. See XY problem.
Your avg function cannot be used with bsxfun. The documentation of bsxfun is very explicit: fun must support scalar expansion. There is no way to support scalar expansion with an expression that includes a colon. So bsxfun is not an option at all.
There might be some obscure way to generate your A array without a loop (some weird combination of cumsum, toeplitz, and some other functions maybe) but honestly, you're better off with your loop approach. It will be a lot clearer and most likely, just as fast.
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Guillaume
Guillaume 2017-5-22
The reason you can't use your avg function with bsxfun and the reason it returns 3.5 are all down to the : (colon) operator.
As per the documentation of colon, "If you specify nonscalar arrays, then MATLAB interprets j:i:k as j(1):i(1):k(1)." So it interprets [3, 3] : [4, 5] simply as 3 : 4, whose mean is indeed 3.5.
In effect your function ignores all but the first element of any vector that it is passed. Hence, why it does not work with bsxfun.

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Walter Roberson
Walter Roberson 2017-5-19
https://www.mathworks.com/help/matlab/ref/bsxfun.html#inputarg_fun
"Binary function to apply, specified as a function handle. fun must be a binary (two-input) element-wise function of the form C = fun(A,B) that accepts arrays A and B with compatible sizes. For more information, see Compatible Array Sizes for Basic Operations. fun must support scalar expansion, such that if A or B is a scalar, then C is the result of applying the scalar to every element in the other input array."
In practice what this means for bxfun(@fun, A, B) is:
  1. if A and B are the same size(), fun(A,B) is called directly and size(A) = size(B) outputs are expected
  2. if either A or B are scalars and the other is not, then fun(A,B) is called directly and size() of the non-scalar is the expected output size
  3. otherwise fun(A(:,K), B(K)) is called once for each column K in A with size(A,1)x1 expected output size
Your case matches the first of those, so avg(i, i+1:5) is going to be called -- but your avg code expects the second input to be a scalar rather than a vector.
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Shi Shi
Shi Shi 2017-5-19
Thanks very much for your reply. When avg(i, i+1:5) is called, I hope the result would be the same as arrayfun(avg, repmat(i, length(i+1:5)), i+1:5), because the document says "Whenever a dimension of A or B is singleton (equal to one), bsxfun virtually replicates the array along that dimension to match the other array". But the result is not as I thought. Actually,I have no idea what happens here of my bsxfun.
Shi Shi
Shi Shi 2017-5-19
Thanks very much. It works on small sample very well. I will try it on a large sample later, in size of million.

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