Implementing Gaussian elimination with partial pivoting [closed] - matlab

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I am writing a program to implement Gaussian elimination with partial pivoting in MATLAB. I created an integer array to store the interchange of rows, instead of directly exchanging the rows.
However, I could not obtain the correct result and I could not figure out the problem. How should I modify my code to get the right answer?
A=[1, -2, 1; 2, 1, -3; 4, -7, 1];
b=[0, 5, 1];
b=b';
function x = GE(A,b)
[m,n]= size(A);
if m ~= n
disp('Not a square');
end
for p=1:n
array(p)=p;
endfor
A = [A,b];
%elimination
for i = 1:n-1
pivot = i;
%select pivot
for j = i+1:n
if abs(A(array(i),i)) < abs(A(array(i),i)) %row interchange
temp = array(i);
array(i) = array(j);
array(j) = temp;
end
end
while (pivot <= n && A(pivot,i)== 0)
pivot = pivot+1;
end
if pivot > n
disp('No unique solution');
break
else
if pivot > i
tem = array(i);
array(i) = pivot
pivot= tem;
end
end
for j = i+1:n
m = -A(array(j),i)/A(array(i),i);
for k = i+1:n+1
A(array(j),k) = A(array(j),k) + m*A(array(i),k);
end
end
end
if A(n,n) == 0
disp('No unique solution');
return
end
%backward substitution
x(n) = A(array(n),n+1)/A(array(n),n);
for i = n - 1:-1:1
sum = 0;
for j = i+1:n
sum = sum + A(array(i),j)*x(j);
end
x(i) = (A(array(i),n+1) - sum)/A(array(i),i);
end
endfunction

Answer 1

Your error is pretty simple. You're not pivoting properly - specifically here inside your if statement:
for j = i+1:n
if abs(A(array(i),i)) < abs(A(array(i),i)) %row interchange <-------
temp = array(i);
array(i) = array(j);
array(j) = temp;
end
end
Your check to see which coefficient to pivot from is not correct because you are using the index i for checking along the columns when you need to use j. Therefore, simply change the other side of your Boolean condition so that it uses j:
for j = i+1:n
if abs(A(array(i),i)) < abs(A(array(j),j)) %// CHANGE HERE
temp = array(i);
array(i) = array(j);
array(j) = temp;
end
end
With your example A and b, the answer I get is x = [2 1 0], which agrees with MATLAB's ldivide operation: x = A \ b.