Extend a vector by extending its elements

I have a vector of dimension d: (1,2,...,d) (it's (x_1,x_2,...,x_n) but I removed the 'x_' for simplicity). Now I would like to extend it (in a fast manner) to obtain a d*d vector of the form:

(1,1,...,1,2,...,2,...,d,d,...,d)

where each element repeat d times.

I looked at this page: http://www.mathworks.fr/fr/help/wavelet/ref/wextend.html but it seems to me that the function does not handle this kind of extension.

Thank you for your help.

Answer 1

[Udit Gupta]

If your vector is X.

    reshape(repmat(X,d,1),1,[])

should do the trick.

Example -

>> X = [1 2 3 4];

>> d=4;

>> reshape(repmat(X,d,1),1,[])

ans =

     1     1     1     1     2     2     2     2     3     3     3     3     4     4     4     4

[f10w]

Thanks, Udit. If X is a column vector, then is there a way to avoid transposing and then re-transposing again the final vector?

[Udit Gupta]

reshape(repmat(X,d,1),[],1) will give you a column vector. But in this case you will have to transpose the original vector. SO you will apply -

reshape(repmat(X',d,1),[],1)

[f10w]

Thanks, Udit!

Answer 2

[George Papazafeiropoulos]

If X is a column vector:

% initial data
d=10;
% engine
X=(1:d)';
ind=ones(d^2,1);
ind(d+1:d:d^2)=1-d;
% result
output_vector=X(cumsum(ind))

If X is a row vector:

% initial data
d=10;
% engine
X=1:d;
ind=ones(d^2,1);
ind(d+1:d:d^2)=1-d;
% result
output_vector=X(cumsum(ind))

without the need to reshape or repmat!

[f10w]

Thanks, George. I will compare with Udit's solution and get back to you.

Answer 3

[Jos (10584)]

A slower but nice alternative to repmat:

X = [10 20 30 40] 
d = 4
Y = kron(X, ones(1,d))

Answer 4

[Jos (10584)]

A fast and also nice alternative:

X = [10 ; 20 ; 30 ; 40]
d = 3 

Y = X(ceil((1:d*numel(X))/d))

[f10w]

Thanks, Jos. I will compare with Udit's solution and get back to you.