Building up a Matrix using for LOOP and summation

Hello fellows,

I am trying to make this equation but I couldn't do the summaiton part , i tried to use the double for loop but still not sure how to do the summation part,

I have the matrix " a " already defined 4x4 also initial l and u matrices are defiend l=eye(N),u=zeros(N,N);

any hints?

Answer 1

[David Hill]

I believe the below is correct.

I=eye(4);
u=zeros(4);
u(1,1:4)=a(1,1:4);
I(1:4,1)=a(1:4,1);
for i=2:4
    for j=1:4
        u(i,j)=a(i,j)-sum(I(i,1:i-1).*u(1:i-1,j)');
        if i<j
            I(j,i)=(I(j,i)-sum(I(j,1:i-1).*u(1:i-1,i)'))/u(i,i);
        end
    end
end

[Abdulrahman Odhah]

I think its the correct one also, I'll try it on some values,

thanks a lot, for your suuport,

[Abdulrahman Odhah]

I've applied the code on some known values, this code is supposed to find the lu matrices of a matrix A, using the above expression

what i've got from the code given by you is the following,

I =

6.0000 0 0 0

4.0000 1.0000 0 0

-2.0000 -0.5333 1.0000 0

3.0000 0.8000 0.0845 1.0000

u =

6.0000 4.0000 2.0000 1.0000

-20.0000 -15.0000 -8.0000 -2.0000

-0.6667 2.0000 4.7333 8.9333

1.0563 1.8310 4.0000 -1.1549

I thing that the code representing the mathematical expression has to produce the following

I =

1.0000 0 0 0

0.6667 -0.5000 0.5000 1.0000

-0.3333 1.0000 0 0

0.5000 0 1.0000 0

u=

6.0000 4.0000 2.0000 1.0000

0 3.3333 5.6667 8.3333

0 0 3.0000 0.5000

0 0 0 5.2500

Thanks again for your suuport.