public void toReducedRowEchelonForm() {
InvertibleBinaryOperation<T> addition = ring.addition();
InvertibleBinaryOperation<T> multiplication =
(InvertibleBinaryOperation<T>) ring.multiplication();
toRowEchelonForm();
int j = 0;
for (int i = 0; i < m; i++) {
while (j < n) {
T aij = get(i, j);
if (!aij.equals(zero)) {
aij = multiplication.inverse(aij);
for (int k = j + 1; k < n; k++) {
T aik = multiplication.op(get(i, k), aij);
set(i, k, aik);
for (int l = 0; l < i; l++)
set(
l,
k,
addition.op(get(l, k), addition.inverse(multiplication.op(aik, get(l, j)))));
}
set(i, j, one);
for (int l = 0; l < i; l++) set(l, j, zero);
j++;
break;
}
j++;
}
}
}
public Matrix<T> getRowEchelonForm() {
Matrix<T> rowEchelonForm = copy();
rowEchelonForm.toRowEchelonForm();
return rowEchelonForm;
}