# A Collection of classes and (eventually) functions.  The main use of this module
# will be in graphics (2D and 3D) applications
import math
import numbers       # to look for instances of the numbers.Number type

class VectorN(object):
	""" A General-purpose n-dimensional vector class. """
	def __init__(self, param):
		""" param can be a
		    a) positive non-zero integer (in which case, this
			becomes a vector of that size (all 0's).  Or
			b) it can be a sequence-like list of values.  The size of the
			vector is deduced from the length of that sequence """
		if isinstance(param, int) and param > 0:
			self.dim = param
			self.data = [0.0] * param
		elif hasattr(param, "__len__") and hasattr(param, "__getitem__"):
			self.dim = len(param)
			self.data = []
			for val in param:
				# Note: This *could* fail (if say, there is a "ABC" element in
				# the sequence).  In this case, though, I'll let python handle it...
				self.data.append(float(val))
		else:
			raise ValueError("param must be a positive non-zero int (dimension) \
				or a sequence-like object with initial values")

	def __str__(self):
		""" Returns a printable version of this object """
		s = "<Vector" + str(self.dim) + ": "
		for i in range(len(self.data)-1):
			s += str(self.data[i]) + ", "
		s += str(self.data[-1]) + ">"
		return s

	def __len__(self):
		""" Returns the number of elements in this 'sequence' (i.e. self.data)"""
		return self.dim

	def __getitem__(self, index):
		""" Returns the index'th element of this 'sequence' """
		if not isinstance(index, int) or index < 0 or index >= self.dim:
			raise IndexError("Invalid Index#: " + str(index))
		return self.data[index]

	def __setitem__(self, index, newVal):
		""" Sets the index'th element of this 'sequence' to newVal """
		if not isinstance(index, int) or index < 0 or index >= self.dim:
			raise IndexError("Invalid Index#: " + str(index))
		self.data[index] = float(newVal)

	def copy(self):
		""" Returns a new copy of this vector """
		cp = VectorN(self)
		# The following line is necessary to make the types match for derived
		# classes (e.g. Vector2)
		cp.__class__ = self.__class__
		return cp

#### NEW in LAB3 ####
	def __neg__(self):
		""" Returns the vector negation of this vector """
		rval = self.copy()
		for i in range(self.dim):
			rval[i] = -rval[i]
		return rval

	def length(self):
		""" Returns the vector length (magnitude) of this vector """
		mag = 0.0
		for i in range(self.dim):
			mag += self.data[i] ** 2
		return mag ** 0.5

	def __mul__(self, scalar):
		""" Returns the product of this vectorN and the given scalar """
		if not isinstance(scalar, numbers.Number):
			raise TypeError("This VectorN can only be multiplied by a scalar.")
		rval = VectorN(self.dim)
		for i in range(self.dim):
			rval[i] = self.data[i] * scalar
		return rval

	def __rmul__(self, scalar):
		""" Returns the product of the given scalar and this VectorN """
		# Since vector-scalar multiplication is commutative, we can just call __mul__
		return self.__mul__(scalar)

	def __truediv__(self, scalar):
		""" Returns the result of dividing this vector by the given scalar """
		if not isinstance(scalar, numbers.Number):
			raise TypeError("This VectorN can only be multiplied by a scalar.")
		rval = VectorN(self.dim)
		for i in range(self.dim):
			rval[i] = self.data[i] / scalar
		return rval

	def __add__(self, otherVect):
		""" Returns the vector sum of this vector and otherVect (which must be
			of the same size """
		if not isinstance(otherVect, VectorN) or otherVect.dim != self.dim:
			raise TypeError("You can only add an equally-sized vectorN to this vectorN")
		rval = VectorN(self.dim)
		for i in range(self.dim):
			rval[i] = self.data[i] + otherVect[i]
		return rval

	def __sub__(self, otherVect):
		""" Returns the result of subtracting otherVect (which must be the same
			size as this VectorN) from this vector. """
		return self + (-otherVect)

	def normalized(self):
		""" Returns a normalized copy of this vector (but does not change this
			vector """
		mag = self.length()
		if mag == 0:
			raise ZeroDivisionError("You can't normalize a zero-vector")
		rval = VectorN(self.dim)
		for i in range(self.dim):
			rval[i] = self.data[i] / mag
		return rval


class Vector2(VectorN):
	""" A specialized variant of VectorN that always has two values (useful
	    for 2D applications """
	def __init__(self, x=0, y=0):
		""" Creates two values in the Vector """
		VectorN.__init__(self, (x, y))

	@property
	def x(self):
		""" Returns the x-value (the first element in the list of numbers) """
		return self.data[0]

	@x.setter
	def x(self, newVal):
		""" Sets the first element of the list to newVal """
		self[0] = float(newVal)     # Calls VectorN.__setitem___

	@property
	def y(self):
		""" Returns the y-value (the second element in the list of numbers) """
		return self.data[1]

	@y.setter
	def y(self, newVal):
		""" Sets the second element of the list to newVal """
		self[1] = float(newVal)     # Calls VectorN.__setitem___


if __name__ == "__main__":
	v = VectorN((1, "3", -2))
	w = VectorN((5, 0, 4))

	z = -v                     # To python: z = v.__neg__()
	print(z)                   # <Vector3: -1.0, -3.0, 2.0>
	print(v)                   # <Vector3: 1.0, 3.0, -2.0>
	zMag = z.length()
	print(zMag)                # 3.7416573867739413     (a scalar)

	z = v * 3                  # To python: z = v.__mul__(3)
	print(z)                   # <Vector3: 3.0, 9.0, -6.0>
	#z = v * "ABC"             # ERROR!
	#z = v * w                 # ERROR!
	z = 3 * v                  # To python: z = 3.__mul__(v)
	                           #    Which will fail.  Python then tries
	                           #    z = v.__rmul__(3)
	print(z)                   # <Vector3: 3.0, 9.0, -6.0>
	z = v / 2                  # To python: z = v.__truediv__(2)
	print(z)                   # <Vector3: 0.5, 1.5, -1.0>
	#z = 2 / v                 # ERROR!
	z = v.normalized()
	print(z)                   # <Vector3: 0.2672612419124244, 0.8017837257372732, -0.5345224838248488>
	print(z.length())          # 1.0

	z = v + w                  # To python: z = v.__add__(w)
	# z = v + 3.0              # ERROR!
	print(z)                   # <Vector3: 6.0, 3.0, 2.0>
	z = v - w                  # To python: z = v.__sub__(w)
	print(z)                   # <Vector3: -4.0, 3.0, -6.0>
	z = v + (-w)               # To python: z = v.__add__(w.__neg__())
	print(z)                   # <Vector3: -4.0, 3.0, -6.0>