Is there a function like movsum which simply gets the values in a given sliding window rather than summing them?

If I have a sequence

x = [1 2 3 4 5 6 7 8 9 10];

What is the most efficient way to get sub-vectors in a sliding window, i.e., if the window is of length 2;

[1 2]
[2 3]
[3 4]
[4 6]

etc.

I ask this because I need get these values at multiple different window lengths.

Thank you in advance.

Answer 1

[Steven Lord]

Let's use some starting data that's a little more varied than 1:10.

x = [1 2 3 4 5 6 7 8 9 10].^2

x = 1×10

1 4 9 16 25 36 49 64 81 100

Define the window length.

windowLength = 2;

Where does each window start? There are windows starting with each element of x except for those that are too close to the end. "Too close" is less than windowLength-1 from the end; if we started at windowLength-2 from the end the window would extend past the end of the vector.

startingPoints = 1:numel(x)-(windowLength-1)

startingPoints = 1×9

1 2 3 4 5 6 7 8 9

Now we define the window offsets from the starting point. The first point in the window is the starting point + 0, the next is the starting point + 1, etc. up through starting point + window length - 1.

windowOffsets = (1:windowLength)-1

windowOffsets = 1×2

0 1

Use implicit expansion to define the window indices by adding the starting points and the offsets, with different orientations.

windowIndices = windowOffsets + startingPoints.'

windowIndices = 9×2

1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10

Get the corresponding elements from x.

x(windowIndices)

ans = 9×2

1 4 4 9 9 16 16 25 25 36 36 49 49 64 64 81 81 100

Answer 2

[David Hill]

b=1:10;
a=b;
n=5;%window size
for k=1:n-1
  a=[a;circshift(b,-k)];
end
a=a';
a=a(1:length(b)-n+1,:)

a = 6×5

1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 4 5 6 7 8 5 6 7 8 9 6 7 8 9 10

Answer 3

[Bora Eryilmaz]

If you have access to the Predictive Maintenance Toolbox, you can use the phaseSpaceReconstruction command:

x = [1 2 3 4 5 6 7 8 9 10];
sz = 2;
y = phaseSpaceReconstruction(x, 1, sz)

y = 9×2

1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10

sz = 4;
y = phaseSpaceReconstruction(x, 1, sz)

y = 7×4

1 2 3 4 2 3 4 5 3 4 5 6 4 5 6 7 5 6 7 8 6 7 8 9 7 8 9 10