How can I expand a matrix by replacing its elements?

%mod p multiplication%
p=5;
a=0:p-1;
b=repmat(a,p,1);
s=mod(b.*b',p);

the above code generates the matrix s as
s=[0 0 0 0 0;0 1 2 3 4;0 2 4 1 3;0 3 1 4 2;0 4 3 2 1]

Now i need to expand the matrix s of size 5 by 5 to a matrix of size 5 by 25 by replacing the elements in it as:

0 as 10000,
1 as 01000,
2 as 00100,
3 as 00010,
4 as 00001.

so that the new expanded matrix is:

[10000       10000       10000       10000       10000
 10000       01000       00100       00010       00001
 10000       00100       00001       01000       00010
 10000       00010       01000       00001       00100
 10000       00001       00010       00100       01000]

I tried doing it using reshape and re-size of matrix but failed to do it.

Is there any way to expand it?

Thank you.

[Jan]

The resulting matrix does not look like a 5 by 25 matrix. Do you mean:

[1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0; ...
etc

or:

{'10000', '10000', '10000', '10000', '10000'; ...

?

Answer 1

[Jan]

s      = [0 0 0 0 0;0 1 2 3 4;0 2 4 1 3;0 3 1 4 2;0 4 3 2 1]
List   = {'10000', '01000', '00100', '00010', '00001'}
Result = List(s + 1);

Answer 2

[Azzi Abdelmalek]

out=arrayfun(@(x) circshift('10000',[0 x]),s,'un',0)

[Pragathi]

The code now gives result for any p.

p=7;
a=0:p-1;
b=repmat(a,p,1);
s=mod(b.*b',p);
out=arrayfun(@(x) circshift('10000',[0 x]),s,'un',0)

Thanks a lot.

Answer 3

[Andrei Bobrov]

q = num2cell(eye(5),2);
out = cell2mat(q(s+1));

or

p=5;
a=0:p-1;
s = rem(a'*a,p) + 1;
ii = bsxfun(@plus,s,p*a);
jj= ndgrid(a+1);
out = zeros(p,p^2);
out(sub2ind([p,p^2],jj,ii)) = 1;

Answer 4

[Osama AlThahab]

the matrix for example is still 5*5 matrix, and you can replace the numbers 0,1,2,3,4, by making a program with (if statement) like

%mod p multiplication%
for i=1:5
  for j=1:5
      if a(i,j)=0
          a(i,j)=10000
      else if a(i,j)=1
              a(i,j)=01000
              .
              .
              .
              .
          end
      end
  end

[Jan]

What do you mean by "a(i,j)=01000"? Leading zeros are not meaningful in Matlab for numbers.

Answer 5

[Azzi Abdelmalek]

p=5;
a=0:p-1;
b=repmat(a,p,1);
s=mod(b.*b',p);
s1=arrayfun(@num2str,s,'un',0)
s1=strrep(s1,'0','x0')
s1=strrep(s1,'1','x1')
s1=strrep(s1,'4','00001');
s1=strrep(s1,'3','00010');
s1=strrep(s1,'2','00100');
s1=strrep(s1,'x1','01000')
s1=strrep(s1,'x0','10000')