import numpy as np

class smberror(Exception):
  """
    this is a silly little exception subclass
  """
  def __init__(self, val):
    self.value = val
  def __str__(self):
    return repr(self.value)

def rms(errors):
  """
    root mean square calculation
  """
  r = 0.0
  for i in errors:
    r += np.power(i, 2)
  r = np.sqrt(r / len(errors))
  return r

def exact_func(x, y):
  """
    the exact function used from baker's article (for testing)
  """
  return np.power((np.sin(x * np.pi) * np.cos(y * np.pi)), 2)

def exact_func_3D(X):
  """
    the exact function (3D) used from baker's article (for testing)
  """
  x = X[0]
  y = X[1]
  z = X[2]
  return np.power((np.sin(x * np.pi / 2.0) * np.sin(y * np.pi / 2.0) * np.sin(z * np.pi / 2.0)), 2)