```#!/usr/bin/env python
#
# dihedral.py
#
# Calculates dihedral angles.
#

"""Dihedral angle calculation module.

K. Rother

Two functions are provided (see documentation of each function for
a more detailed description):

angle (v1,v2) - returns the angle between two 2D or 3D numpy arrays
dihedral (v1,v2,v3,v4) - returns the dihedral angle between four 3D vectors
(in degrees)

The vectors that dihedral uses can be lists, tuples or numpy arrays.
Scientific.Geometry.Vector objects behave differently on Win and Linux,
and they are therefore not supported (but may work anyway).
"""

__author__ = "Kristian Rother"
__contributors__ = ["Kristian Rother", "Sandra Smit"]
__credits__ = ["Janusz Bujnicki", "Daniel McDonald"]
__version__ = "1.5.3"
__maintainer__ = "Kristian Rother"
__email__ = "krother@rubor.de"
__status__ = "Production"

from numpy import array, cross, pi, cos, arccos as acos
from cogent.util.array import norm
from cogent.maths.stats.special import fix_rounding_error

class DihedralGeometryError(Exception): pass
class AngleGeometryError(Exception): pass

def scalar(v1,v2):
"""
calculates the scalar product of two vectors
v1 and v2 are numpy.array objects.
returns a float for a one-dimensional array.
"""
return sum(v1*v2)

def angle(v1,v2):
"""
calculates the angle between two vectors.
v1 and v2 are numpy.array objects.
returns a float containing the angle in radians.
"""
length_product = norm(v1)*norm(v2)
if length_product == 0:
raise AngleGeometryError(\
"Cannot calculate angle for vectors with length zero")
cosine = scalar(v1,v2)/length_product
angle = acos(fix_rounding_error(cosine))
return angle

def calc_angle(vec1,vec2,vec3):
"""Calculates a flat angle from three coordinates."""
if len(vec1) == 3:
v1, v2, v3 = map(create_vector,[vec1,vec2,vec3])
else:
v1, v2, v3 = map(create_vector2d,[vec1,vec2,vec3])
v12 = v2 - v1
v23 = v2 - v3
return angle(v12, v23)

def create_vector2d(vec):
"""Returns a vector as a numpy array."""
return array([vec[0],vec[1]])

def create_vector(vec):
"""Returns a vector as a numpy array."""
return array([vec[0],vec[1],vec[2]])

def create_vectors(vec1,vec2,vec3,vec4):
"""Returns dihedral angle, takes four
Scientific.Geometry.Vector objects
(dihedral does not work for them because
the Win and Linux libraries are not identical.
"""
return map(create_vector,[vec1,vec2,vec3,vec4])

def dihedral(vec1,vec2,vec3,vec4):
"""
Returns a float value for the dihedral angle between
the four vectors. They define the bond for which the
torsion is calculated (~) as:
V1 - V2 ~ V3 - V4

The vectors vec1 .. vec4 can be array objects, lists or tuples of length
three containing floats.
For Scientific.geometry.Vector objects the behavior is different
on Windows and Linux. Therefore, the latter is not a featured input type
even though it may work.

If the dihedral angle cant be calculated (because vectors are collinear),
the function raises a DihedralGeometryError
"""
# create array instances.
v1,v2,v3,v4 =create_vectors(vec1,vec2,vec3,vec4)
all_vecs = [v1,v2,v3,v4]

# rule out that two of the atoms are identical
# except the first and last, which may be.
for i in range(len(all_vecs)-1):
for j in range(i+1,len(all_vecs)):
if i>0 or j<3: # exclude the (1,4) pair
equals = all_vecs[i]==all_vecs[j]
if equals.all():
raise DihedralGeometryError(\
"Vectors #%i and #%i may not be identical!"%(i,j))

# calculate vectors representing bonds
v12 = v2-v1
v23 = v3-v2
v34 = v4-v3

# calculate vectors perpendicular to the bonds
normal1 = cross(v12,v23)
normal2 = cross(v23,v34)

# check for linearity
if norm(normal1) == 0 or norm(normal2)== 0:
raise DihedralGeometryError(\
"Vectors are in one line; cannot calculate normals!")

# normalize them to length 1.0
normal1 = normal1/norm(normal1)
normal2 = normal2/norm(normal2)

# calculate torsion and convert to degrees
torsion = angle(normal1,normal2) * 180.0/pi

# take into account the determinant
# (the determinant is a scalar value distinguishing
# between clockwise and counter-clockwise torsion.
if scalar(normal1,v34) >= 0: