Write a matlab function to execute gaussian elimination with scaled partial pivoting based off of the following psuedo code:

input variables: n (some number), a_ij (nxn coefficient array), l_i (the index array)

other terms and variables used s_i (scale array), denotes replacement of value with what is on the left, I believe in matlab an equal sign is what we're looking for.

Psuedo code:

function Gauss(n, (a_ij), (l_i))

integer i, j, k, n

real r, rmax, smax, xmult

real array (a_ij)_{1:n x 1:n}, (l_i)_1:n; real array allocate (s_i)_1:n

%in the first loop the index array is being established l_i=i then scale array is computed

for i = 1 to n

l_ii

smax 0

for j =1 to n

smax max(smax, abs.value(a_ij)

end for

si smax

end for

for k = 1 to n-1 % initiating principle outer loop

%k is the subscript of the variable whose coefficients will be made 0 in the array (a_ij) in other words, k is the index of the %column in which ne 0's are being created

rmax 0

for i = k to n

% r is the ratio between the the array and scale array and used to determined the correct pivot row

r abs. value (a_ij/s_{l_i}) %l_i = l_i

%calculating the gratest ratio rmax and the index j where it occurs

if (r > rmax) then

rmax r

j i

end if

end for

% l_j and l_k are swapped in array l_i

l_jl_k

%next loop makes the arithmetic modifications to a_ij due to subtracting multiples of row l_k from rows l_k+1, l_k+2,..., l_n. First the multiplier is computed and stored; then the subtraction occurs in a loop.

for i = k +1 to n

xmult a_{l_i,k}/a_{l_k,k}

a_{l_i,k} xmult

for j = k+1 to n

a_{l_i,j} a_{l_i,j} -(xmult)*a_{l_k,j}

end for

end for

end for

deallocate array (s_i)

end function Gauss