Matrix inversion and LU Decomposition. Having issues with the for loops and how they reference inputs.

function output =myMatrixInversion(A)

%% Problem Setup

i=1;

n=size(A);

AInv=zeros(n,n);

L=eye(n);

I=eye(n);

%% Forward Elimination w/ Multiplier Recording

% Reminder 1: Use nested loops

% Reminder 2: Use MATLAB vector/matrix operations wherever appropriate to replace unnecessary loops and simplify your code

% Reminder 3: Do not forget to display the updated coefficient matrix at the end of each FE step

for i=1:n-1 % run through each of the rows

for j=i+1:n % run through each of the columns

A(j,i+1:n)=A(j,i+1:n)-x*A(i,i+1:n)); % take the number and divide it

L(j,i)=A(j,i)/A(i,i); %simultaneously fill in L matrix

end

fprintf('\n\nIteration #%2d:\n', i)

fprintf(' The matrix is %.4e\n', A)

end

%% Forward Substitution

% Reminder 1: Use nested loops

% Reminder 2: Use MATLAB vector/matrix operations wherever appropriate to replace unnecessary loops and simplify your code

for i=1:1:n

sum=0;

for j=(i-1):1:n

sum=sum-L(i,j)*z(i,j);

end

z(i,j)=sum/L(i,i);

end

%% Backward Substitution

% Reminder 1: Use nested loops

% Reminder 2: Use MATLAB vector/matrix operations wherever appropriate to replace unnecessary loops and simplify your code

for a=1:n

for i=n:-1:1

sum=z(i,a);

for j=(i+1):1:n

sum=sum-U(i,j)*x(j,a);

end

x(i,j)=sum/U(i,i);

end

end

%% Final Output and Display

output=[L, U, z, x];

end

[John D'Errico]

What issues do you have? What exactly is your question?

[Susanna Westersund]

I'm struggling with my first set of nested for loops, and don't really know how to go about fixing the i and j values, like if I am referencing them right to create the upper and lower triangular matrix?

Answer 1

[Divija Aleti]

Hi Susanna,

I understand that you want to obtain the upper and lower triangular matrices and solve the equation 'Ax=I', to find the inverse of matrix 'A'. Do refer to the following links to get to know about the MATLAB functions that can be used to achieve this.

https://www.mathworks.com/help/symbolic/lu.html

https://www.mathworks.com/help/symbolic/linsolve.html