def test_can_transform_a_3_x_3(self):
a = array([[1.0000, 0.0000, 0.0000],
[0.0000, 1.0000, 0.0000],
[0.0000, 0.0000, 1.0000]])
b = array([[0.0000, 1.0000, 0.0000],
[-1.0000, 0.0000, 0.0000],
[0.0000, 0.0000, 1.0000]])
ans = array([[0.0000, 1.0000, 0.0000],
[-1.0000, 0.0000, 0.0000],
[0.0000, 0.0000, 1.0000]])
rotation, _, _, _, _ = besttransformation(a, b)
assert_almost_equal(ans, rotation)
def setUp(self):
a = array([[1.0000, 0.0000, 0.0000],
[0.0000, 1.0000, 0.0000],
[0.0000, 0.0000, 1.0000],
[-1.0000, 0.0000, 0.0000],
[0.0000, -1.0000, 0.0000],
[0.0000, 0.0000, -1.0000]])
b = array([[0.0000, 1.0000, 0.0000],
[-1.0000, 0.0000, 0.0000],
[0.0000, 0.0000, 1.0000],
[0.0000, -1.0000, 0.0000],
[1.0000, 0.0000, 0.0000],
[0.0000, 0.0000, -1.0000]])
self.transformation, _, _, _, _ = besttransformation(a, b)
def test_can_transform_a_4_x_3_45degreezrotation(self):
theta = numpy.pi/4.0
ans = array([[numpy.cos(theta), -1*numpy.sin(theta), 0.0000],
[numpy.sin(theta), numpy.cos(theta), 0.0000],
[0.0000, 0.0000, 1.0000]])
a = array([[3.0000, 7.0000, 1.0000],
[5.0000, 9.0000, 2.0000],
[7.0000, 4.0000, 6.0000],
[1.0000, 1.0000, 1.0000]])
J = numpy.ones((4, 4))
meana = numpy.dot(J,a)/4.0
b = numpy.dot(a-meana,ans)
rotation, _, _, _, _ = besttransformation(a, b)
assert_almost_equal(ans, rotation)
angle = angle_of_rotation(rotation)
assert_almost_equal(angle, 45.0*numpy.pi/180.)
def infer_hydrogens(self):
"""Infer the coordinates of the hydrogen atoms of this component.
Currently, it only works for RNA with .sequence
"""
if self.sequence not in defs.RNAbaseheavyatoms:
return None
R = []
S = []
baseheavy = defs.RNAbaseheavyatoms[self.sequence]
for atom in self.atoms(name=baseheavy):
coordinates = atom.coordinates()
R.append(coordinates)
S.append(defs.RNAbasecoordinates[self.sequence][atom.name])
R = np.array(R)
R = R.astype(np.float)
S = np.array(S)
try:
rotation_matrix, fitted, base_center, rmsd, sse = \
besttransformation(R, S)
except:
return None
self.rotation_matrix = rotation_matrix
hydrogens = defs.RNAbasehydrogens[self.sequence]
coordinates = defs.RNAbasecoordinates[self.sequence]
for hydrogenatom in hydrogens:
hydrogencoordinates = coordinates[hydrogenatom]
newcoordinates = base_center + \
np.dot(hydrogencoordinates, np.transpose(rotation_matrix))
self._atoms.append(
Atom(name=hydrogenatom,
x=newcoordinates[0, 0],
y=newcoordinates[0, 1],
z=newcoordinates[0, 2]))
def test_can_transform_a_4_x_3_generalrotation(self):
theta1 = numpy.pi/4.0
theta2 = numpy.pi/3.0
theta3 = numpy.pi/9.0
R1 = array([[1.0000, 0.0000, 0.0000],
[0.0000, numpy.cos(theta1), -1*numpy.cos(theta1)],
[0.0000, numpy.sin(theta1), numpy.cos(theta1)]])
R2 = array([[numpy.cos(theta2), 0.0000, numpy.sin(theta2)],
[0.0000, 1.0000, 0.0000],
[-1*numpy.sin(theta2), 0.0000, numpy.cos(theta2)]])
R3 = array([[numpy.cos(theta3), -1*numpy.sin(theta3), 0.0000],
[numpy.sin(theta3), numpy.cos(theta3), 0.0000],
[0.0000, 0.0000, 1.0000]])
ans = numpy.dot(numpy.dot(R1,R2),R3)
a = array([[3.0000, 7.0000, 1.0000],
[5.0000, 9.0000, 2.0000],
[7.0000, 4.0000, 6.0000],
[1.0000, 1.0000, 1.0000]])
J = numpy.ones((4, 4))
meana = numpy.dot(J,a)/4.0
b = numpy.dot(a-meana,ans)
rotation, _, _, _, _ = besttransformation(a, b)
assert_almost_equal(ans, rotation)
def infer_hydrogens(self):
"""Infer the coordinates of the hydrogen atoms of this component.
Currently, it only works for RNA with .sequence
"""
if self.sequence not in defs.RNAbaseheavyatoms:
return None
R = []
S = []
baseheavy = defs.RNAbaseheavyatoms[self.sequence]
for atom in self.atoms(name=baseheavy):
coordinates = atom.coordinates()
R.append(coordinates)
S.append(defs.RNAbasecoordinates[self.sequence][atom.name])
R = np.array(R)
R = R.astype(np.float)
S = np.array(S)
try:
rotation_matrix, fitted, base_center, rmsd, sse = \
besttransformation(R, S)
except:
return None
self.rotation_matrix = rotation_matrix
hydrogens = defs.RNAbasehydrogens[self.sequence]
coordinates = defs.RNAbasecoordinates[self.sequence]
for hydrogenatom in hydrogens:
hydrogencoordinates = coordinates[hydrogenatom]
newcoordinates = base_center + \
np.dot(hydrogencoordinates, np.transpose(rotation_matrix))
self._atoms.append(Atom(name=hydrogenatom,
x=newcoordinates[0, 0],
y=newcoordinates[0, 1],
z=newcoordinates[0, 2]))
def calculate_rotation_matrix(self):
"""Calculate a rotation matrix that will rotate the atoms in an RNA
base into a standard orientation in the xy plane with the Watson-
Crick edge in the positive x and y quadrant.
"""
if self.sequence not in defs.NAbaseheavyatoms and \
self.sequence not in defs.modified_nucleotides:
return None
R = [] # 3d coordinates of observed base
S = [] # 3d coordinates of standard base in xy plane
if self.sequence in defs.NAbaseheavyatoms:
baseheavy = defs.NAbaseheavyatoms[self.sequence]
for atom in self.atoms(name=baseheavy):
R.append(atom.coordinates())
S.append(defs.NAbasecoordinates[self.sequence][atom.name])
if self.sequence in defs.modified_nucleotides:
current = defs.modified_nucleotides[self.sequence]
standard_coords = defs.NAbasecoordinates[current["standard"]]
for atom in self.atoms(name=current["atoms"].keys()):
R.append(atom.coordinates())
S.append(standard_coords[atom.name])
R = np.array(R)
R = R.astype(np.float)
S = np.array(S)
S = S.astype(np.float)
try:
rotation_matrix, fitted, meanR, rmsd, sse, meanS = \
besttransformation(R, S)
except:
if len(R) != len(S):
print(
"%s Rotation matrix calculation failed, sizes %d and %d" %
(self.unit_id(), len(R), len(S)))
elif len(R) < 3:
print("%s Rotation matrix calculation failed, %d new atoms" %
(self.unit_id(), len(R)))
elif len(S) < 3:
print(
"%s Rotation matrix calculation failed, %d standard atoms"
% (self.unit_id(), len(S)))
else:
print("%s Rotation matrix calculation failed, not sure why" %
self.unit_id())
return None
self.rotation_matrix = rotation_matrix
# map the origin out to where the center of the base should be
if self.sequence in defs.NAbaseheavyatoms:
# standard bases are designed to have meanS zero; less work
self.base_center = meanR
else:
# some modified bases are missing some heavy atoms, meanS not zero
# this comes out as a numpy matrix? different than meanR above
base_center = np.subtract(meanR, np.dot(rotation_matrix, meanS))
self.base_center = np.array(
[base_center[0, 0], base_center[0, 1], base_center[0, 2]])
""" For the life of me, I could not figure out any other way of
