rref.ts

// elementary row operations

function interchange(A: number[][], i1: number, i2: number) {
  [A[i1], A[i2]] = [A[i2], A[i1]];
}

function scaling(A: number[][], i: number, f: number = 1) {
  const n = A[0].length;

  for (let j = 0; j < n; j++) {
    A[i][j] *= f;
  }
}

function rowAddition(A: number[][], si: number, di: number, f: number = 1) {
  const n = A[0].length;

  for (let j = 0; j < n; j++) {
    A[di][j] += f * A[si][j];
  }
}

// transforms A into reduced row echelon form
function rref(A: number[][]) {
  const m = A.length;
  const n = A[0].length;

  // forward pass
  for (let pi = 0, pj = 0; pi < m && pj < n; undefined) {
    if (A[pi][pj] === 0) {
      let ti = A.findIndex((row, i) => i > pi && row[pj] !== 0);

      if (ti === -1) {
        pj++;
        continue;
      }

      interchange(A, pi, ti);
    }
    
    scaling(A, pi, 1 / A[pi][pj]);

    for (let i = pi + 1; i < m; i++) {
      rowAddition(A, pi, i, -A[i][pj]);
    }

    pi++, pj++;
  }

  // backward pass
  for (let pi = m - 1; pi >= 0; pi--) {
    let pj = A[pi].findIndex((col) => col !== 0);

    if (pj === -1) {
      continue;
    }

    for (let i = pi - 1; i >= 0; i--) {
      rowAddition(A, pi, i, -A[i][pj]);
    }
  }
}

let A = [
  [1, 2, -1, 2, 1, 2],
  [-1, -2, 1, 2, 3, 6],
  [2, 4, -3, 2, 0, 3],
  [-3, -6, 2, 0, 3, 9],
];

rref(A);

console.log(A);