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: return torsion else: torsion = 360-torsion if torsion == 360: torsion = 0.0 return torsion
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 test_norm(self): """norm: should return vector or matrix norm""" self.assertFloatEqual(norm(array([2,3,4,5])),sqrt(54)) self.assertEqual(norm(array([1,1,1,1])),2) self.assertFloatEqual(norm(array([[2,3],[4,5]])),sqrt(54)) self.assertEqual(norm(array([[1,1],[1,1]])),2)