Moving Norm using Vectorization

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.

Answer 1

[Oleg Komarov]

% 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));

[Jrand]

Thank you. nV should be numel(v).

[Oleg Komarov]

Edited.

[Walter Roberson]

What if numel(v) < w ? :-)

[Oleg Komarov]

MATLAB will start swearing uncomprehensible stuff :).

DISCLAIMER: no checks.

Answer 2

[Walter Roberson]

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!

[bym]

@Walter - I was just working on an answer that involved hankel, glad you beat me to the punch +1 vote