function c=mul(a,b)

    [a_n1 a_n2 a_n3]=size(a);
    [b_n1 b_n2 b_n3]=size(b);
    c=zeros(a_n1,b_n2,a_n3);
    A=cell(a_n3,1);
    B=cell(b_n3,1);
    
    for i=1:a_n3
        A{i}=a(:,:,i);
        B{i}=b(:,:,i);
    end

    index_up=zeros(1,a_n3);
    index_down=zeros(1,a_n3);
    for i=1:a_n3    
        index_up(i)=a_n3-i+1;
        index_down(i)=i;
    end
    
    s=cell(a_n3,a_n3);
    for i=1:a_n3
        for j=1:a_n3
            if i==j
                s{i,j}=A{1};
            end       
            if j>i
                s{i,j}=A{index_up(j-i)};
            end       
            if j<i
                s{i,j}=A{index_down(i-j+1)};
            end      
        end   
    end
    
    re=cell(a_n3,1);
    for i=1:a_n3
        re{i}=zeros(a_n1,b_n2);
    end

    for i=1:a_n3
        for j=1:a_n3
            for k=1:1
                re{i,k}=re{i,k}+s{i,j}*B{j,k};
            end
        end    
    end

    for i=1:a_n3
        c(:,:,i)=re{i};        
    end
    
end

function a=transpos(b)    
    [n1 n2 n3]=size(b);
    a=zeros(n2,n1,n3);
    for i=1:n3
        a(:,:,i)=b(:,:,i)';
    end
end

clear all;
close all;
clc;
n1=3;
n2=3;
n3=3;

A(:,:,1)=[10 23 34;43 55 63;72 85 96];
A(:,:,2)=[24 17 35;52 36 55;81 94 75];
A(:,:,3)=[65 16 52;21 47 78;92 33 43];
%A=imread('s.jpg');

D=fft(A,[],3);

for i=1:n3
    [q r]=qr(D(:,:,i));
    %[u s v]=svd(D(:,:,i));
    Q(:,:,i)=q;
    R(:,:,i)=r;
    %S(:,:,i)=s;
end
Q=ifft(Q,[],3);
R=ifft(R,[],3);
%S=ifft(S,[],3);


B(:,:,1)=eye(n1,n2);
B(:,:,2)=zeros(n1,n2);
B(:,:,3)=zeros(n1,n2);


%c=mul(mul(U,S),transpos(V));
c=mul(Q,R);
c