How can I use "for loop" for this script?

Hi, I have a random matrix with large dimension and I have to form augmented matrix. My script for given dimensions is good but for random and large matrices I need a "for loop". For example:

X = rand(3,5);

[n,m]=size(X);

A0=X(:,m);

A1=[X(:,m-1); A0];

A2=[X(:,m-2); A1];

A3=[X(:,m-3); A2];

A4=[X(:,m-4); A3];

Now, A4 gives the first column of augmented matrix. The other columns can be calculated in the same way. But I need a loop to calculate all the columns regardless of the dimension of X. Assume that X is 3*100. How can I calculate the augmented matrix?

Answer 1

[Mohammad Abouali]

Looking at your code:

A0=X(:,m);
A1=[X(:,m-1); A0];
A2=[X(:,m-2); A1];
A3=[X(:,m-3); A2];
A4=[X(:,m-4); A3];

A0 is the last column of X, A1 is the last two column of X (in one long vector), A2 is the last three column of X (shown in one long vector) and so on.

if you just want the last A, i.e. A4 or in case if X is (3x100) then A99 then all you need to do is:

A4 = X(:); % or reshape(X,[],1);

or

A99 = X(:) % or reshape(X,[],1);

otherwise, you could write a function like this:

function AN=getAN(X,n)
  if (n<0 || n>(size(X,2)-1))
    error('wrong n');
  end

    AN=reshape(X(:,end-n:end),[],1);
  end

so now if you want A0

A0=getAN(X,0);

or if you want A4 do

A4=getAN(X,4);

you can do this in a loop as follow:

for n=0:4
  A{n+1}=getAN(X,n);
end

NOTE: it is not a good idea to name your variabl A0, A1, ... Try to use cell, tables, arrays, and other structures.

Answer 2

[mili ss]

Thanks a lot,

But I have a problem to create the augmented matrix. "X(:)" is useful for first column, but what can I do to create the other columns? please see this images to understand what I want. The example contains a 3*5 matrix and augmented matrix will be 9*3. For a large matrix how can I calculate "XD"? If "X" is "n*m", then I need a loop to be iterated until "m-2".

Thank you for your help

[Mohammad Abouali]

The definition of XD seems to be different than what you explained.

X(:) gives only the step 1, which was based on your code.

Based on the XD definition in 02.jpg here how you can do it:

XD=[ reshape(X(:,1:end-2),[],1), ...
     reshape(X(:,2:end-1),[],1), ...
     reshape(X(:,3:end),[],1)]

Here is an example:

X=reshape(1:15,3,5)

X =

       1     4     7    10    13
       2     5     8    11    14
       3     6     9    12    15

XD=[ reshape(X(:,1:end-2),[],1), ...
     reshape(X(:,2:end-1),[],1), ...
     reshape(X(:,3:end),[],1)]

XD =

       1     4     7
       2     5     8
       3     6     9
       4     7    10
       5     8    11
       6     9    12
       7    10    13
       8    11    14
       9    12    15