Gaussian Elimination in Egglang

main.egg

do(
  define(math, import("modules/math.egg")),
  define(matrix, get(math, "matrix")),
  define(mset, get(math, "mset")),
  define(mprint, get(math, "mprint")),
  define(mreduce, get(math, "mreduce")),

  # m: [
  #  [5, -3, 1, 14],
  #  [2, 3,  3, 15],
  #  [3, 2, -4, 3],
  # ]

  define(m, matrix(3, 4)),
  mset(m, 0, 0, 5),
  mset(m, 1, 0, 2),
  mset(m, 2, 0, 3),
  mset(m, 0, 1, -3),
  mset(m, 1, 1, 3),
  mset(m, 2, 1, 2),
  mset(m, 0, 2, 1),
  mset(m, 1, 2, 3),
  mset(m, 2, 2, -4),
  mset(m, 0, 3, 14),
  mset(m, 1, 3, 15),
  mset(m, 2, 3, 3),

  print("Original matrix:"),
  mprint(m),

  print("Reduced matrix:"),
  mprint(mreduce(m))
)

math.egg

dict(
  "min", define(min, fun(a, b, do(
    if (<(a, b), a, b)
  ))),

  "abs", define(abs, fun(a, do(
    if (<(a, 0), -(0, a), a)
  ))),

  "matrix", define(matrix, fun(n, m, do(
    define(values, dict()),
    define(i, 0),
    while(<(i, n), do(
      define(j, 0),
      while(<(j, m), do(
        push(values, +(i, +(",", j)), 0),
        define(j, +(j, 1))
      )),
      define(i, +(i, 1))
    )),
    dict(
      "n", n,
      "m", m,
      "_get", fun(i, j, get(values, +(i, +(",", j)))),
      "_set", fun(i, j, value, push(values, +(i, +(",", j)), value)),
      "_print", fun(print(values))
    )
  ))),

  "mget", define(mget, fun(mx, i, j, do(
    get(mx, "_get")(i, j)
  ))),

  "mset", define(mset, fun(mx, i, j, value, do(
    get(mx, "_set")(i, j, value)
  ))),

  "mprint", define(mprint, fun(mx, do(
    get(mx, "_print")()
  ))),

  "mreduce", define(mreduce, fun(mx, do(
    define(n, get(mx, "n")),
    define(m, get(mx, "m")),
    define(k, 0),
    while(<(k, min(n, m)), do(
      define(p, _pivot(mx, k, n)),
      _swap(mx, k, p),
      define(i, +(k, 1)),
      while(<(i, n), do(
        define(f, /(mget(mx, i, k), mget(mx, k, k))),
        define(j, +(k, 1)),
        while(<(j, m), do(
          mset(mx, i, j, -(mget(mx, i, j), *(mget(mx, k, j), f))),
          define(j, +(j, 1))
        )),
        mset(mx, i, k, 0),
        define(i, +(i, 1))
      )),
      define(k, +(k, 1))
    )),
    mx
  ))),

  "_pivot", define(_pivot, fun(mx, k, n, do(
    define(best, -1),
    define(p, -1),
    define(i, k),
    while(<(i, n), do(
      define(candidate, abs(mget(mx, i, k))),
      if(<(best, candidate), do(
        define(best, candidate),
        define(p, i)
      ), do(
        ""
      )),
      define(i, +(i, 1))
    )),
    p
  ))),

  "_swap", define(_swap, fun(mx, k, p, do(
    define(m, get(mx, "m")),
    define(j, 0),
    while(<(j, m), do(
      define(t, mget(mx, k, j)),
      mset(mx, k, j, mget(mx, p, j)),
      mset(mx, p, j, t),
      define(j, +(j, 1))
    ))
  )))
)