Setting Matrix Values based on 'symsum' formula

I am working on a Doolittle LU decomposition at the moment, which is useful for solving a system of linear algebraic equations.

For example:

3x-0.1y-0.2z = 7.85

0.1x+7y-0.3z = -19.3

0.3x-0.2y+10z = 71.4

A = [3 -0.1 -0.2; 0.1 7 -0.3; 0.3 -0.2 10]

B = [7.85; -19.3;71.4]

We can decompose matrix A into L and U matrices.

We can use the following general formulae to achieve this quickly for any NxN matrix (square matrix):

I've tried implementing this into a sample code as follows:

a = [3 -0.1 -0.2; 0.1 7 -0.3; 0.3 -0.2 10]
b = [7.85; -19.3;71.4]

U = zeros(height(a))
L = eye(height(a))

i=0;
j=0;

while(1)
   i=i+1;
   j=j+1;
   L(i,j) = a(i,j) - symsum(L(i,r)*U(r,j),r,1,j-1)
   %I have only included the L matrix for simplicity's sake
   if i==height(a)
       break,end
end

However, this outputs the following error:

Unrecognized function or variable 'r'.

Changing r to:

syms r 

also yields the following error:

Error using sym/subsindex (line 857)
Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must be symbolic
variables, and function body must be sym expression.

I do not understand the issue. Could someone please explain the error or suggest a possible solution?

Just in case: documentation for symsum

Thank you in advance for any help.

Answer 1

[Swetha Polemoni]

Hi Michael Jacobson

You cannot use symbolic variable as index to a matrix. However the following code snippet can help to get summation you want.

L=rand(10,10);
U=rand(10,10);
for k=0:9
    i=k+1;
    j=k+1;
    r=1:i;
   summation(i)= L(i,r)*U(r,j);
end

Hope this helps