Repeating the rows of an array by a number given by another array

Consider the array:

x=[linspace(1,4,4)' linspace(5,20,4)']

x = 4×2

1 5 2 10 3 15 4 20

I would like to repeat each row by a number given by another array such as

I=[2 3 2 1]'

I = 4×1

2 3 2 1

so that at the end the first row of x is repeat twice, the second row is repeated 3 times and so on.

Is this possible without using a loop?

Answer 1

[Jan]

Use repelem, which is the built-in efficient solution for repeating elements:

x = [linspace(1,4,4)' linspace(5,20,4)']

x = 4×2

1 5 2 10 3 15 4 20

I = [2 3 2 1];
y = repelem(x, I, 1)

y = 8×2

1 5 1 5 2 10 2 10 2 10 3 15 3 15 4 20

A speed comparison:

x = rand(1e4, 2);
I = repmat(1:10, 1, 1000);

tic
for k = 1:100
    C = cell(length(I),1) ; 
    for i = 1:length(C)
        C{i} = repmat(x(i,:),I(i),1) ;
    end
    C = cell2mat(C);
end
toc

tic
for k = 1:100  % Slightly modified for I is a row vector:
    idx = arrayfun(@(x,y)x*ones(1,y),1:numel(I),I,'UniformOutput',false);
    C = x([idx{:}],:);
end
toc

tic
for k = 1:100
    C = repelem(x, I, 1);
end
toc

% R2018b:
% Elapsed time is 3.676185 seconds.   loop
% Elapsed time is 6.848004 seconds.   arrayfun
% Elapsed time is 0.038391 seconds.   repelem

[Mike Croucher]

Nice!

[Saeid]

Wow, so there IS a difference! Thanks Jan!

Answer 2

[KSSV]

x=[linspace(1,4,4)' linspace(5,20,4)'] ;
I=[2 3 2 1]' ;
C = cell(length(I),1) ; 
for i = 1:length(C)
    C{i} = repmat(x(i,:),I(i),1) ;
end
C = cell2mat(C)

C = 8×2

1 5 1 5 2 10 2 10 2 10 3 15 3 15 4 20

[Mike Croucher]

That's got a loop though

[Saeid]

Yepp!

I am not completely opposed to loops if I cannot avoid them, but one beauty of MATLAB is how you both save time (dealing with very large datasets) and space when you avoid loops!

[Mike Croucher]

OK good! There has been a lot of work done by MathWorks in recent years on improving the efficiency of loops. You do not need to be afraid of them any more. In many cases, they are on par with vectorised methods.

If the algorithm can be expressed naturally as a loop, do so. Only worry about other methods if the performance is problematic.

[Saeid]

Thanks, Mike!