# This is statement is required by the build system to query build info
if __name__ == '__build__':
	raise Exception


import Numeric

def vv3(x, y):
	return Numeric.add.reduce(x*y)

def vxv3(a, b):
	return Numeric.array([
		a[1] * b[2] - a[2] * b[1],
		a[2] * b[0] - a[0] * b[2],
		a[0] * b[1] - a[1] * b[0]
		])

def dist3(x,y):
	return Numeric.sqrt(Numeric.add.reduce((y-x)**2))

def angle(x,y,z):
	d1 = dist3(x,y)
	d2 = dist3(z,y)
	if (d1 <= 0 or d2 <= 0):
		return 0.0

	acc = Numeric.add.reduce((y-x) * (y-z)) / (d1*d2)

	if (acc > 1):
		acc = 1.
	elif (acc < -1):
		acc = -1.

	return Numeric.arccos(acc)

def dihedral(crds):
	q = crds[1] - crds[0]
	r = crds[1] - crds[2]
	s = crds[2] - crds[3]

	t = vxv3(q, r)
	u = vxv3(s, r)
	v = vxv3(u, t)

	w = vv3(v, r)
	z = Numeric.zeros(3, Numeric.Float)
	acc = angle(t, z, u)
	ang = acc / Numeric.pi * 180.

	if (w < 0):
		ang = 360-ang

	return ang