Decreasing data points by half via downsampling - matlab

Question

Let say I have a 6x5 matrix (my actual data is way bigger)
A B C D E
1 5 7 2 3
2 1 9 8 5
3 1 2 3 1
4 1 3 4 2
5 2 9 0 1
6 5 3 4 3
I have to make a plot with A on the x-axis and B,C,D on the y-axis. If I want to reduce the data points by half (by averaging each adjacent pair of data points), how do I do it? What if I want to decrease the points even further by averaging every five (or n) points?
I looked at the MATLAB help document but I'm still confused
I got what I needed, thanks for the input guys, it really helped

Answer 1

There you go:
M = [1 5 7 2 3
2 1 9 8 5
3 1 2 3 1
4 1 3 4 2
5 2 9 0 1
6 5 3 4 3]; % data
>>result = (M(1:2:end-1,:) + M(2:2:end,:))/2;
result =
1.5000 3.0000 8.0000 5.0000 4.0000
3.5000 1.0000 2.5000 3.5000 1.5000
5.5000 3.5000 6.0000 2.0000 2.0000

Answer 2

An even number of rows scenario is straightforward, using mean to do the work:
>> M = magic(4)
M =
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
>> reshape(mean(reshape(M,2,[]),1),[],size(M,2))
ans =
10.5000 6.5000 6.5000 10.5000
6.5000 10.5000 10.5000 6.5000
For the odd number of rows scenario, let's say you want to retain the last row. Here's a general even/odd solution:
>> M = magic(5) % 5 rows!
M =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
>> Mp = [M; repmat(M(end,:),mod(size(M,1),2),1)]; % replicate last row if odd
>> Mthin = reshape(mean(reshape(Mp,2,[]),1),[],size(Mp,2))
Mthin =
20.0000 14.5000 4.0000 11.0000 15.5000
7.0000 9.0000 16.0000 20.5000 12.5000
11.0000 18.0000 25.0000 2.0000 9.0000
Alternatively, if you want to throw away the last row when encountered with an odd number of rows:
>> Mp = M(1:end-mod(size(M,1),2),:);
>> Mthin = reshape(mean(reshape(Mp,2,[]),1),[],size(Mp,2))
Mthin =
20.0000 14.5000 4.0000 11.0000 15.5000
7.0000 9.0000 16.0000 20.5000 12.5000
Now for averaging n points, retaining the average of the mod(size(M,1),n) last rows:
n = 5;
M = rand(972,5); % or whatever
p = mod(size(M,1),n);
r = repmat(mean(M(end-p+1:end,:),1),(p>0)*(n-p),1);
Mp = [M; r];
Mthin = reshape(mean(reshape(Mp,n,[]),1),[],size(Mp,2));
And for throwing out the last mod(size(M,1),n) rows:
Mp = M(1:end-mod(size(M,1),n),:);
Mthin = reshape(mean(reshape(Mp,n,[]),1),[],size(Mp,2));

Answer 3

>>> A= magic(5) %some "random" data
A =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
>>> B=(A(1:2:end-1,:)+A(2:2:end,:))/2
B =
20.0000 14.5000 4.0000 11.0000 15.5000
7.0000 9.0000 16.0000 20.5000 12.5000
Takes average of each pair of rows, ignores the last row if row count is not even.
And some general solution:
%input data data
X=randi(30,30,5)
step=7
%extend matrix, until size matches step (could be done faster using repmat)
while(mod(size(X,1),step)~=0)
X(end+1,:)=X(end,:)
end
%Split data into segments of size "step"
C=mat2cell(X,repmat(step,floor(size(X,1)/step),1),size(X,2))
%Average over each segment:
AVG=cell2mat(cellfun(#(x)(mean(x,1)),C,'UniformOutput',false))