Implement this pseudo code with Java.

n is the size of the matrix for an n x n matrix.

k is the pivot.

i is the equation being eliminated.

j is the term you're working with.

Gaussian Elimination with Scaled Partial Pivoting

// Forward Elimination

function SPPFwdElimination(coeff : array(n,n), const : vector(n), ind : vector(n)) scaling := new vector(n) // vector of scaling factors // Initialize index and scaling vectors for i = 1 to n smax := 0 for j = 1 to n smax := max(smax,|coeff[i][j]|) // find coefficient with greatest absolute value end for scaling[i] := smax end for for k = 1 to n - 1 rmax := 0 maxInd := k for i = k to n r := |coeff[ind[i]][k] / scaling[ind[i]]| // ratio of coefficient to scaling factor if (r > rmax) then rmax := r maxInd := i end if end for swap(ind[maxInd], ind[k]) for i = k + 1 to n mult := coeff[ind[i]][k] / coeff[ind[k]][k] for j = k + 1 to n coeff[ind[i]][j] := coeff[ind[i]][j] - mult * coeff[ind[k]][j] end for const[ind[i]] := const[ind[i]] - mult * const[ind[k]] end for end for end function

// Back Substitution

function SPPBackSubst(coeff : array(n,n), const : vector(n), sol : vector(n), ind : vector(n)) sol[n] := const[ind[n]] / coeff[ind[n]][n] for i = n - 1 to 1 sum := const[ind[i]] for j = i + 1 to n sum := sum - coeff[ind[i]][j] * sol[j] end for sol[i] := sum / coeff[ind[i]][i] end for end function

// SPP Gaussian Algorithm

function SPPGaussian(coeff : array(n,n), const : vector(n)) sol := new array(n,n) ind := new vector(n) for i = 1 to n ind[i] := i end for call SPPFwdElimination(coeff,const,ind) call SPPBackSubst(coeff,const,sol,ind) end function