How summation of two matrix so that one element of A matrix summed with B matrix and save in M(1,1)?

Hi every one.

I want to make summation of two A and B matrices so that one element summed with all elements of B matrix and save in M matrix.

for example for two 3*3 A and B matrix,

I wrote some codes for two 2*2 A and B matrices, and they worked,but I couldn't expand them for two N*N A and B matrices. help me?!!

Codes:

 clc
 clear all
 close all

 n=4;
 m=2;
 A=[1 2; 4 5];
 B=[3 8; 6 9];

 M=ones(n,n);

 M1=zeros(m,m);
 M2=zeros(m,m);
 M3=zeros(m,m);
 M4=zeros(m,m);

 for i=1:m
     for j=1:m
         M1(i,j)=A(1,1)+B(i,j);
     end
 end

 for i=1:m
     for j=1:m
         M2(i,j)=A(1,2)+B(i,j);
     end
 end

 for i=1:m
     for j=1:m
         M3(i,j)=A(2,1)+B(i,j);
     end
 end

 for i=1:m
     for j=1:m
         M4(i,j)=A(2,2)+B(i,j);
     end
 end

 for i=1:m
     for j=1:m
         M(i,j)=M1(i,j);
     end
 end
 for i=1:m
     for j=m+1:n
         M(i,j)=M2(i,j-m);
     end
 end
 for i=m+1:n
     for j=1:m
         M(i,j)=M3(i-m,j);
     end
 end
 for i=m+1:n
     for j=m+1:n
         M(i,j)=M4(i-m,j-m);
     end
 end

Answer 1

[Jan]

What about:

reshape(bsxfun(@plus, reshape(B, [m,1,m,1]), reshape(A, [1,m,1,m])), n, n)

[Habib]

Thanks.

[Habib]

Mr. Jan Simon,

your codes worked, but I can't understand how it works, can you explain it for me?

Answer 2

[Andrei Bobrov]

M = kron(ones(size(A)),B)+kron(A,ones(size(B)));

[Habib]

Hi Abderi Borov,

Thank you for your replying. By M= kron(A,B), we can calculate the product of A and B matrices by way method that I described but I want two summation, not product of them.

what must I do?

[Andrei Bobrov]

Yes, my mistake. Corrected.