How to separate two matrices from a single matrice?

Hi, I would like to extract two matrix B and C from a matrix A to get A=B+C, where A=sparse(N,N) with N is a number.

Since index of A has two types : index = index_1 + index_2,

so the matrix B and C should be like

B= [A(i,j) , for i∈index_1 and j∈index;

0 otherwise]

C = [A(i,j) , for i∈index_2 and j∈index;

0 otherwise]

For example A= sparse(9,9):

A = [ 1 2 3

5 6 7

8 9 10];

index = {1,2,...,9}, index_1 = {2,4,6,8}, index_2={1,3,5,9}

how to write in matlab

B = sparse(9,9); C=sparse(9,9);

B = A(index_1,:) and C = A(index_2,:)

to get

B = [ 0 2 0

5 0 7

0 9 0];

C = [ 1 0 3

0 6 0

8 0 10];

Answer 1

[the cyclist]

Here is one way:

% Inputs
A = [ 1 2  3 
      5 6  7 
      8 9 10];

index_1 = [2,4,6,8];
index_2 = [1,3,5,9];

% Get the dimensions of A
[m,n] = size(A);

% Initialize the B and C as sparse arrays that are the size of A
[B,C] = deal(sparse(m,n));

% Assign index_1 elements to B
B(index_1) = A(index_1)

B = 
   (2,1)        5
   (1,2)        2
   (3,2)        9
   (2,3)        7

% Assign index_2 elements to C
C(index_2) = A(index_2)

C = 
   (1,1)        1
   (3,1)        8
   (2,2)        6
   (3,3)       10

[Yamina chbak]

Thank you, @the cyclist, for your assistance. I completed it, however as you can see from my example, it is not working. I find that : A ~= A I + A B

Just enough for the first column!

[Yamina chbak]

Now i can fix it , just edit code from @the cyclist

 
% Assign index_1 elements to B
B(index_1,[1:n]) = A(index_1,[1:n])
% Assign index_2 elements to C
C(index_2,[1:n]) = A(index_2,[1:n])