Deleting some columns of matrix and obtain the original column index.

Dear friends

I need really some help/advice. My problem is stated as follows.

The original data is a X=100*50 matrix. The dependent variable is a y=100*1 vector.

Step 1: I regress y on X and get the regression coefficient "b". (The statistic toolbox)

Step 2: Sorting the coefficient "b" and get the index "I".

Step 3: Delete the first column denoted by "I" and get the new matrix X.

Step 4: Repeat the procedures Step 1 -Step 3 20 times until the new matrix X contains only 100*30.

Step 5: How can use the for loop to get the original index of the new matrix X?

For example, let X be a 9*5 matrix and y=ones(9,1). My codes for "2 runs" are as follows:

 X=[4   8   11   10   14;  12   9   8   12   13;  10   5   7   10   13; 
   25   16   5   7   7 ;  12   7   8   17   12;  18   15   13   18   31;
    7   5   4   35   16;  6    14   10   15   4 ;   8   11   8   11   10]

Step 1:

 [b,bint,r] = regress(y,X);   %regress y on X, where b is the regression coefficient (Statistic Toolbox)

Step 2:

 [B, I]=sortrows(b)           %I is the original column index, in this case, I=[2 5 4 1 3]

Step 3:

 X(:,2)=[]                    %Delete the column 2 of old X after sorting b

Step 4:

 [b,bint,r] = regress(y,X);   %regress y on X again

Step 5:

 [B, I]=sortrows(b)           %I is the new column index, in this case, I=[4 3 1 2]

Step 6:

 X(:,4)=[]                    % Delete the column 4 of new X

Step 7: Thus, the new matrix contains only the columns 1,3,4 of the original matrix.

How can I get original index of X after deleting? In this case, just output [1 3 4]

What I need the code to do is the following:

Answer 1

[KSSV]

A = rand(100,50) ;   % some random data 
N = 20 ; 
C = zeros(N,1) ;
for i = 1:N
    [m,n] = size(A) ;
    b = rand(n,1) ;   % some random coefficients 
    [B,idx] = sort(b) ;
    % remove the column 
    A(:,idx(1)) = [] ;
    % save thew removed column 
    C(i) = idx(1) ;
end
% get the remained columns indics 
iwant = setdiff(1:size(A,2),C) ;

Answer 2

[Wan-Yi Chiu]

Thank you very much.

I have tried the codes offered.

However, in my case, I can not get the array [1 3 4]

I mean that: If the original matrix has 5 columns.

The first operation I remove the column 2 from the original matrix.

The second operation I remove the column 4 from the new matrix.

However, this column should be labelled by the column 5 from the original matrix.

Thus, the last matrix left after removing contains only the array [1 3 4] of the original matrix.

The answer should be [1 3 4] that is the original index of the matrix.

It is kind of you to check it again.