Moving Norm using Vectorization
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Hi everyone,
I was wondering how to calculate the "moving norm" of a vector. For example, suppose I have a vector v1 = [a b c d e];
I want to calculate the moving norm involving 3 elements. The first element of the output will be incomplete because we haven't had time to "move over" the vector v1.
The first element of the output array is: norm([0 0 a])
The second element of the output array is: norm([0 a b])
The third element of the output array is: norm([a b c])
The fourth element of the output array is: norm([b c d])
...
The last element of the output array is: norm([e 0 0])
It would be good if all the elements are in one vector, and that vector could be calculated quickly using vectorization. I am already aware of solving this problem using a loop, but I am curious about how to do this faster.
Thank you very much for your help in advance.
采纳的回答
Oleg Komarov
2011-8-29
% Example input
v = rand(10,1);
% Window length
w = 3;
% Pad with zeros
o = zeros(w-1,1);
v = [o;v;o];
% Calculate index [0 0 a; 0 a b; ...]
pos = 0:numel(v)-w;
idx = bsxfun(@plus, pos.', pos(1:w)+1);
% Euclidean norm sqrt(a^2 + b^2 ...)
out = sqrt(sum(v(idx).^2,2));
4 个评论
Jrand
2011-8-29
Oleg Komarov
2011-8-30
Edited.
Walter Roberson
2011-8-30
What if numel(v) < w ? :-)
Oleg Komarov
2011-8-30
MATLAB will start swearing uncomprehensible stuff :).
DISCLAIMER: no checks.
更多回答（1 个）
Walter Roberson
2011-8-29
t = hankel([zeros(1,length(v1)-1) v1]);
out = sqrt(sum(t(1:length(v1),:).^2));
Knew I'd find a use for hankel() someday!
1 个评论
bym
2011-8-29
@Walter - I was just working on an answer that involved hankel, glad you beat me to the punch +1 vote
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