Saving Matricies from a Loop

I'm creating a function to create an inverse matrix of some [A] following LU Factorization, and I have the correct loops to generate the columns of the inverse (defined by p), but the loop happens "n" times where n is the number of rows/columns in the square matrix. The problem is that "p" is overwritten each time the loop goes through, and I need to save the values from each time the loop happens so I can eventually piece the rows together into a final matrix: inverse A. I did some research and came across cells, but I was unsuccessful trying to implement it into my own code shown below. Any help is appreciated!

Thanks,

-Kyle

 %%Taking Apart Identity Matrix
L=[1,0,0;2.56,1,0;5.76,3.5,1]
U=[25,5,1;0,-4.8,-1.56;0,0,0.7]
w=length(L)
I=eye(w)
b=[1;0;0]
n=length(L)
for i=1:w
    b=I(:,i)
    %%Gauss Elim L
    n=length(L);
    m=zeros(n,1);
    x=zeros(n,1);
    for k =1:n-1;
          %compute the kth column of M
          m(k+1:n) = L(k+1:n,k)/L(k,k);
          %compute
          %An=Mn*An-1;
          %bn=Mn*bn-1;
          for i=k+1:n
              L(i, k+1:n) = L(i,k+1:n)-m(i)*L(k,k+1:n);
          end;
          b(k+1:n)=b(k+1:n)-b(k)*m(k+1:n);
    end
    W= triu(L);
    %BACKWARD ELIMINATION
    x(n)=b(n)/L(n,n);
    for k =n-1:-1:1;
          b(1:k)=b(1:k)-x(k+1)* W(1:k,k+1);
          x(k)=b(k)/W(k,k)
    end

    %%Gauss Elim U
    n=length(U);
    m=zeros(n,1);
    p=zeros(n,1);
    for k =1:n-1;
          %compute the kth column of M
          m(k+1:n) = U(k+1:n,k)/U(k,k);
          %compute
          %An=Mn*An-1;
          %bn=Mn*bn-1;
          for i=k+1:n
              U(i, k+1:n) = U(i,k+1:n)-m(i)*U(k,k+1:n);
          end;
          x(k+1:n)=x(k+1:n)-x(k)*m(k+1:n);
    end
    W= triu(U);
    %BACKWARD ELIMINATION
    p(n)=x(n)/U(n,n);
    for k =n-1:-1:1;
          x(1:k)=x(1:k)-p(k+1)* W(1:k,k+1);
          p(k)=x(k)/W(k,k)
    end
end

[Stephen23]

https://www.mathworks.com/help/matlab/matlab_prog/preallocating-arrays.html

Answer 1

[Mukul Rao]

Hello, I made some minor changes. Note that you had reused "i" as a loop-variable inside a nested for-loop, I renamed these to "j" to not corrupt the value of "i" in the outermost loop. Finally, initializing p to a square matrix of zeros and replacing all p(k) s with p(k,i)s does the trick.

%%Taking Apart Identity Matrix
L=[1,0,0;2.56,1,0;5.76,3.5,1]
U=[25,5,1;0,-4.8,-1.56;0,0,0.7]
w=length(L)
I=eye(w)
b=[1;0;0]
n=length(L)
p = zeros(w,w);
for i=1:w
    b=I(:,i)
    %%Gauss Elim L
    n=length(L);
    m=zeros(n,1);
    x=zeros(n,1);
    for k =1:n-1;
          %compute the kth column of M
          m(k+1:n) = L(k+1:n,k)/L(k,k);
          %compute
          %An=Mn*An-1;
          %bn=Mn*bn-1;
          for j=k+1:n
              L(j, k+1:n) = L(j,k+1:n)-m(j)*L(k,k+1:n);
          end;
          b(k+1:n)=b(k+1:n)-b(k)*m(k+1:n);
    end
    W= triu(L);
    %BACKWARD ELIMINATION
    x(n)=b(n)/L(n,n);
    for k =n-1:-1:1;
          b(1:k)=b(1:k)-x(k+1)* W(1:k,k+1);
          x(k)=b(k)/W(k,k)
    end
    %%Gauss Elim U
    n=length(U);
    m=zeros(n,1);
    for k =1:n-1;
          %compute the kth column of M
          m(k+1:n) = U(k+1:n,k)/U(k,k);
          %compute
          %An=Mn*An-1;
          %bn=Mn*bn-1;
          for j=k+1:n
              U(j, k+1:n) = U(j,k+1:n)-m(j)*U(k,k+1:n);
          end;
          x(k+1:n)=x(k+1:n)-x(k)*m(k+1:n);
    end
    W= triu(U);
    %BACKWARD ELIMINATION
    p(n,i)=x(n)/U(n,n);
    for k =n-1:-1:1
          x(1:k)=x(1:k)-p(k+1,i)* W(1:k,k+1);
          p(k,i)=x(k)/W(k,k);
    end

end

>> p

p =

    0.0476   -0.0833    0.0357
   -0.9524    1.4167   -0.4643
    4.5714   -5.0000    1.4286

>> (L*U)*p

ans =

    1.0000         0         0
    0.0000    1.0000    0.0000
    0.0000   -0.0000    1.0000