<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def piece_wise_linear(scale, points):
 """Create a palette that is piece-wise linear given some colors at points."""

  assert len(points) >= 2
  assert points[0][0] == 0
  assert points[-1][0] == 1
  assert all(i < j for i, j in zip(points[:-1], points[1:]))
  out = numpy.zeros((scale, 3))
  p1, c1 = points[0]
  p2, c2 = points[1]
  next_pt = 2

  for i in range(1, scale):
    v = i / scale
    if v > p2:
      p1, c1 = p2, c2
      p2, c2 = points[next_pt]
      next_pt += 1
    frac = (v - p1) / (p2 - p1)
    out[i, :] = c1 * (1 - frac) + c2 * frac
  return out