defmodule Vector do

  # Scalar multiplication.
  def smul({x1, x2, x3}, s) do
    {x1 * s, x2 * s, x3 * s}
  end

  # Addition and subtarction.
  def sub({x1, x2, x3}, {y1, y2, y3}) do
    {x1 - y1, x2 - y2, x3 - y3}
  end

  def add({x1, x2, x3}, {y1, y2, y3}) do
    {x1 + y1, x2 + y2, x3 + y3}
  end

  # Dot product.
  def dot({x1, x2, x3}, {y1, y2, y3}) do
    x1 * y1 + x2 * y2 + x3 * y3
  end

  # Scaling a vector to a specified length.
  def scale(x, l) do
    n = norm(x)
    # this will crash if N == 0!
    smul(x, l / n)
  end

  # Normalize by scaling to norm 1.
  def normalize(x) do
    scale(x, 1)
  end

  # Square of a vector.
  def sq(x) do
    dot(x, x)
  end

  # The norm (length) of a vector.
  def norm({x1, x2, x3}) do
    :math.sqrt(x1 * x1 + x2 * x2 + x3 * x3)
  end

  # Cross product, used to find a vector that as ortogonal to 
  # both x and y.
  def cross({x1, x2, x3}, {y1, y2, y3}) do
    {x2 * y3 - x3 * y2, x3 * y1 - x1 * y3, x1 * y2 - x2 * y1}
  end

end