# Efficient Weighted Moving average

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### Accepted Answer

John BG
on 16 Mar 2017

Edited: John BG
on 16 Mar 2017

Hi Matlab User

1.

simulating data

clear all,clc

V=zeros(25,3);x=V(:,1);y=V(:,2);

w=randi([1 9],25,1);

w=w/sum(w);V(:,3)=w

V(:,1)=randi([-10 10],25,1) % x

V(:,2)=randi([-10 10],25,1) % y

V(:,3)=w;

.

the data

format short

V =

-3.0000 3.0000 0.0857

-5.0000 8.0000 0.0190

-10.0000 3.0000 0.0476

-2.0000 -1.0000 0.0476

4.0000 1.0000 0.0571

0 3.0000 0.0190

1.0000 -7.0000 0.0190

10.0000 -1.0000 0.0857

10.0000 -1.0000 0.0762

-6.0000 -3.0000 0.0762

-5.0000 -9.0000 0.0381

0 4.0000 0.0095

-7.0000 1.0000 0.0190

-8.0000 -10.0000 0.0286

3.0000 8.0000 0.0381

-4.0000 -4.0000 0.0095

2.0000 6.0000 0.0190

-9.0000 0 0.0095

5.0000 6.0000 0.0286

-4.0000 -2.0000 0.0286

-10.0000 6.0000 0.0667

-9.0000 -2.0000 0.0381

-9.0000 1.0000 0.0095

7.0000 4.0000 0.0476

9.0000 -6.0000 0.0762

2.

averaging with the shifting window and applying the weight V(:,:,3)

N=25

R=zeros(N,1)

for k=3:1:N-2

s=[k-2 k-1 k k+1 k+2]

R(k)= mean(.5*(V(s,2)+V(s,1)).*V(s,3))

end

R =

0

0

-0.0133

-0.0076

-0.0248

0.0857

0.1686

0.0714

0.0124

0.0276

-0.0610

-0.1810

-0.0705

-0.0248

-0.0133

-0.0105

0.0724

0.0133

-0.0057

-0.0629

-0.0619

-0.0410

-0.0010

0

0

This does not apply the shifting window on the first 2 and last 2 sames, there aren't 5 samples to apply the window on head and tail anyway, aren't they?

if you find this answer useful would you please be so kind to mark my answer as Accepted Answer?

To any other reader, please if you find this answer

please click on the thumbs-up vote link

thanks in advance

John BG

##### 9 Comments

dpb
on 20 Mar 2017

Edited: dpb
on 21 Mar 2017

However is fine... :) I've noticed quite a few have typed 'dpd' rather than the trailing 'b'; I'm not sure why. I kinda' like the geometry of lower case string however as being mirror image/rotations of a single basic form...

"Addendum. An addendum, in general, is an addition required to be made to a document by its author subsequent to its printing or publication. It comes from the Latin verbal phrase addendum est, being the gerundive form of the verb addo, addere, addidi, additum, "to give to, add to", meaning "(that which) must be added"."

### More Answers (2)

dpb
on 13 Mar 2017

Edited: dpb
on 17 Mar 2017

N=5;

yavN=conv(v(:,2).*v(:,3),ones(1,N)/N,'valid');

discarding the zero-padded end values. See

doc conv % for other options, details...

ADDENDUM

If not clear how to use mean in the above, simply compute it "on the fly" as well instead of using just a single column from V...note the use of the optional DIM second argument to the MEAN function...

C=conv(mean(V(:,1:2),2).*V(:,3),ones(1,N)/N,'valid');

##### 1 Comment

Jan
on 20 Mar 2017

Edited: Jan
on 20 Mar 2017

Some further speed measurements:

function speedtest

N = 10000;

tic; for k = 1:N; R = test1(V); end, toc

tic; for k = 1:N; R = test2(V); end, toc

tic; for k = 1:N; R = test3(V); end, toc

tic; for k = 1:N; R = test4(V); end, toc

function R = test1(V) % John BG

N=size(V, 1);

R=zeros(N,1);

for k=3:1:N-2

s=[k-2 k-1 k k+1 k+2];

R(k)= mean(.5*(V(s,2)+V(s,1)).*V(s,3));

end

function R = test2(V) % Jan

% 1. repeated calcultations moved outside the loop

% 2. Indexing by a:b is much faster than using a pre-calculated vector

N = size(V, 1);

R = zeros(N,1);

X = 0.5 * sum(V(:, 1:2), 2) .* V(:, 3);

for k = 3:1:N-2

R(k) = sum(X(k-2:k+2)) * 0.2;

end

function R = test3(V) % dpb

N = 5;

R = conv(mean(V(:,1:2), 2) .* V(:,3), ones(1,N) / N,'valid');

function R = test4(V) % dpb without MEAN()

N = 5;

R = conv(0.5 * (V(:,1) + V(:, 2)) .* V(:,3), ones(1,N) / N, 'valid');

Results (R2016b/64, Core2Duo):

Elapsed time is 3.138929 seconds. John BG

Elapsed time is 0.444694 seconds. Improved loop

Elapsed time is 0.193468 seconds. dpb

Elapsed time is 0.119400 seconds. dpb without MEAN()

What happens, if the input is not tiny:

V = rand(25000, 3);

N = 10;

Elapsed time is 3.667920 seconds.

Elapsed time is 0.418300 seconds.

Elapsed time is 0.018349 seconds.

Elapsed time is 0.014222 seconds.

Conclusion: Loops profit from smart indexing and avoiding repeated calculations, but conv rules. mean has a remarkable overhead.

##### 2 Comments

Jan
on 21 Mar 2017

Edited: Jan
on 21 Mar 2017

x = rand(1000, 2);

tic; for k = 1:100000; m = x(:, 1) + x(:, 2); end; toc

tic; for k = 1:100000; m = sum(x, 2); end; toc

Elapsed time is 0.120969 seconds.

Elapsed time is 0.156458 seconds.

The difference can be measured. SUM is parallelized for more than 88999 elements. Then the number of cores matter also.

x = rand(100000, 2);

tic; for k = 1:1000; m = x(:, 1) + x(:, 2); end; toc

tic; for k = 1:1000; m = sum(x, 2); end; toc

Elapsed time is 0.103634 seconds.

Elapsed time is 0.148599 seconds.

But rmember, we are talking about 0.00004 seconds. "sum(x,2)" can save minute of hourse during the debugging. Therefore I prefer sum and apply the dirty tricks like v(:,1)+v(:,2) only for bottlenecks and with an exhaustive documentation and a unit-test function, which specifically cares about these lines.

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