Matrix Partial Pivoting, Gauss Elimination

Original Question:

Function: gauss_banded.m

Modify the Gauss Elimination with Partial Pivoting algorithm we’ve developed to take advantage of the lower bandwidth to prevent any unneccesary computation. That is, no arithmetic should be performed on any element that is known to be zero.

Inputs: A The coefficient matrix.

b The right-hand-side vector

lb The lower bandwidth, i.e., the number of stripes below the matrix diagonal that have non-zero elements.

Outputs:

U The upper triangular result

d The transformed right-hand-side vector

. .

.

This is what I have so far:

%hw7_#3

function G = gauss_banded( A, b, 1b)

%A = coefficient matrix; b= right hand side vector; 1b= lower bandwith

format short

m= length(A(:,1)); %number rows

n= length(A(1,:)); % number of columns

for p= 1:m-1

    a_max_p= max(abs(A(p:m,p)));  

    if a_max_p == 0

        q=p;

    else;

        q= find(A(:,p)== a_max_p);

        if isempty(q)

            q= find(A(:,p)== -a_max_p);

        end

    end

temp= A(q,:);

A(q,:)= A(p,:);

A(p,:)= temp;

end

if A(p,p) ~= 0

    for i= ((p+1):m 

        Lij = A(i,p)/A(p,p);

        for j= p:n

            A(i,j) = A(i,j) - Lij*A(p,j);
        end
    end
end
end
G= A

Im really not sure how to get the outputs