def print_axis_system_full(self):
"""Print out of the full system to file."""
# Open the file.
file = open(self.save_path+sep+'axis_system', 'w')
# Header.
file.write("\n")
file.write("The motional axis system\n")
file.write("========================\n")
# The full axis system.
file.write("\nThe full axis system:\n")
string = ''
for i in range(3):
string += '['
for j in range(3):
string += "%24.20f" % self.axes[i, j]
string += ']\n'
file.write(string)
# The Euler angles.
a, b, g = R_to_euler_zyz(self.axes)
file.write("\nEuler angles of the system:\n")
file.write(" alpha: %.20f\n" % a)
file.write(" beta: %.20f\n" % b)
file.write(" gamma: %.20f\n" % g)
# The spherical angle system.
r, t, p = cartesian_to_spherical(self.axes[:, 2])
file.write("\nSpherical angles of the z-axis:\n")
file.write(" theta: %.20f\n" % t)
file.write(" phi: %.20f\n" % wrap_angles(p, 0, 2*pi))
def eigen_system():
"""Recreate the eigensystem parameters."""
# The centre of masses of each domain (from the system_create.log file).
N_COM = array([41.739, 6.03, -0.764], float64)
C_COM = array([26.837, -12.379, 28.342], float64)
# The Z-axis as the inter CoM vector.
z_axis = C_COM - N_COM
disp = norm(z_axis)
z_axis /= disp
# The eigenframe (partly from the system_create.log file).
eigensystem = transpose(
array([[
-7.778375610280605e-01, 6.284649244351433e-01,
-7.532653237683726e-04
], [-0.487095774865268, -0.60362450312215, -0.63116968030708], z_axis],
float64))
# Convert to Euler angles.
a, b, g = R_to_euler_zyz(eigensystem)
# Return the parameters.
return a, b, g, disp
def calc_euler(rotation):
"""Calculate the zyz notation Euler angles.
@param rotation: The rotation matrix.
@type rotation: numpy 3D, rank-2 array
@return: The Euler angles alpha, beta, and gamma in zyz notation.
@rtype: tuple of float
"""
return R_to_euler_zyz(rotation)
def tensor_eigen_system(tensor):
"""Determine the eigenvalues and vectors for the tensor, sorting the entries.
@return: The eigenvalues, rotation matrix, and the Euler angles in zyz notation.
@rtype: 3D rank-1 array, 3D rank-2 array, float, float, float
"""
# Eigenvalues.
R, Di, A = svd(tensor)
D_diag = zeros((3, 3), float64)
for i in range(3):
D_diag[i, i] = Di[i]
# Reordering structure.
reorder_data = []
for i in range(3):
reorder_data.append([Di[i], i])
reorder_data.sort()
# The indices.
reorder = zeros(3, int)
Di_sort = zeros(3, float)
for i in range(3):
Di_sort[i], reorder[i] = reorder_data[i]
# Reorder columns.
R_new = zeros((3, 3), float64)
for i in range(3):
R_new[:, i] = R[:, reorder[i]]
# Switch from the left handed to right handed universes (if needed).
if norm(cross(R_new[:, 0], R_new[:, 1]) - R_new[:, 2]) > 1e-7:
R_new[:, 2] = -R_new[:, 2]
# Reverse the rotation.
R_new = transpose(R_new)
# Euler angles (reverse rotation in the rotated axis system).
gamma, beta, alpha = R_to_euler_zyz(R_new)
# Collapse the pi axis rotation symmetries.
if alpha >= pi:
alpha = alpha - pi
if gamma >= pi:
alpha = pi - alpha
beta = pi - beta
gamma = gamma - pi
if beta >= pi:
alpha = pi - alpha
beta = beta - pi
# Return the values.
return Di_sort, R_new, alpha, beta, gamma
def rotation_hypersphere(self):
"""Random rotation using 4D hypersphere point picking and return of torsion-tilt angles."""
# Generate a random rotation.
R_random_hypersphere(self.rot)
# Rotate the frame.
frame = dot(self.eig_frame_T, dot(self.rot, EIG_FRAME))
# Decompose the frame into the zyz Euler angles.
alpha, beta, gamma = R_to_euler_zyz(frame)
# Convert to tilt and torsion angles (properly wrapped) and return them.
theta = beta
phi = wrap_angles(gamma, -pi, pi)
sigma = wrap_angles(alpha + gamma, -pi, pi)
return theta, phi, sigma
def rotation_z_axis(self):
"""Random rotation around the z-axis and return of torsion-tilt angles"""
# Random angle between -pi and pi.
angle = uniform(-pi, pi)
# Generate the rotation matrix.
axis_angle_to_R(self.z_axis, angle, self.rot)
# Decompose the rotation into the zyz Euler angles.
alpha, beta, gamma = R_to_euler_zyz(self.rot)
# Rotate the frame.
self.rot = dot(EIG_FRAME, dot(self.rot, self.eig_frame_T))
# Convert to tilt and torsion angles (properly wrapped) and return them.
theta = beta
phi = wrap_angles(gamma, -pi, pi)
sigma = wrap_angles(alpha + gamma, -pi, pi)
return theta, phi, sigma
def build_axes_pivot_com(self):
"""A standard axis system for the CaM system with the z-axis along the pivot-com axis."""
# The z-axis for the rotations (the pivot point to CoM axis).
axis_z = self.COM - self.PIVOT
axis_z = axis_z / norm(axis_z)
# The y-axis (to check the torsion angle).
axis_y = cross(axis_z, array([0, 0, 1]))
axis_y = axis_y / norm(axis_y)
# The x-axis.
axis_x = cross(axis_y, axis_z)
axis_x = axis_x / norm(axis_x)
# The eigenframe.
self.axes = transpose(array([axis_x, axis_y, axis_z]))
alpha, beta, gamma = R_to_euler_zyz(self.axes)
# Printout.
print("CoM-pivot axis: %s, norm = %s" % (repr(axis_z), norm(axis_z)))
print("Rotation axis: %s, norm = %s" % (repr(self.axes[:, 2]), norm(self.axes[:, 2])))
print("Full axis system:\n%s" % self.axes)
print("Full axis system Euler angles:\n\talpha: %s\n\tbeta: %s\n\tgamma: %s" % (repr(alpha), repr(beta), repr(gamma)))
def build_axes_alt(self):
"""An alternative axis system for the CaM system."""
# The z-axis for the rotations (the pivot point to CoM axis).
axis_z = self.COM - self.PIVOT
axis_z = axis_z / norm(axis_z)
# The y-axis (to check the torsion angle).
axis_y = cross(axis_z, array([0, 0, 1]))
axis_y = axis_y / norm(axis_y)
# The x-axis.
axis_x = cross(axis_y, axis_z)
axis_x = axis_x / norm(axis_x)
# The eigenframe.
axes = transpose(array([axis_x, axis_y, axis_z]))
# Init a rotation matrix.
R = zeros((3, 3), float64)
# Tilt the axes system by x degrees.
tilt_axis = cross(axis_z, array([0, 0, 1]))
tilt_axis = tilt_axis / norm(tilt_axis)
axis_angle_to_R(tilt_axis, self.TILT_ANGLE * 2.0 * pi / 360.0, R)
# Rotate the eigenframe.
self.axes = dot(R, axes)
alpha, beta, gamma = R_to_euler_zyz(self.axes)
# Printout.
print("Tilt axis: %s, norm = %s" % (repr(tilt_axis), norm(tilt_axis)))
print("CoM-pivot axis: %s, norm = %s" % (repr(axis_z), norm(axis_z)))
print("Rotation axis: %s, norm = %s" % (repr(self.axes[:, 2]), norm(self.axes[:, 2])))
print("Full axis system:\n%s" % self.axes)
print("Full axis system Euler angles:\n\talpha: %s\n\tbeta: %s\n\tgamma: %s" % (repr(alpha), repr(beta), repr(gamma)))
def kabsch(name_from=None,
name_to=None,
coord_from=None,
coord_to=None,
centre_type="centroid",
elements=None,
centroid=None,
verbosity=1):
"""Calculate the rotational and translational displacements between the two given coordinate sets.
This uses the U{Kabsch algorithm<http://en.wikipedia.org/wiki/Kabsch_algorithm>}.
@keyword name_from: The name of the starting structure, used for the printouts.
@type name_from: str
@keyword name_to: The name of the ending structure, used for the printouts.
@type name_to: str
@keyword coord_from: The list of atomic coordinates for the starting structure.
@type coord_from: numpy rank-2, Nx3 array
@keyword coord_to: The list of atomic coordinates for the ending structure.
@type coord_to: numpy rank-2, Nx3 array
@keyword centre_type: The type of centre to superimpose over. This can either be the standard centroid superimposition or the CoM could be used instead.
@type centre_type: str
@keyword elements: The list of elements corresponding to the atoms.
@type elements: list of str
@keyword centroid: An alternative position of the centroid, used for studying pivoted systems.
@type centroid: list of float or numpy rank-1, 3D array
@return: The translation vector T, translation distance d, rotation matrix R, rotation axis r, rotation angle theta, and the rotational pivot defined as the centroid of the ending structure.
@rtype: numpy rank-1 3D array, float, numpy rank-2 3D array, numpy rank-1 3D array, float, numpy rank-1 3D array
"""
# Calculate the centroids.
if centroid is not None:
centroid_from = centroid
centroid_to = centroid
elif centre_type == 'centroid':
centroid_from = find_centroid(coord_from)
centroid_to = find_centroid(coord_to)
else:
centroid_from, mass_from = centre_of_mass(pos=coord_from,
elements=elements)
centroid_to, mass_to = centre_of_mass(pos=coord_to, elements=elements)
# The translation.
trans_vect = centroid_to - centroid_from
trans_dist = norm(trans_vect)
# Calculate the rotation.
R = kabsch_rotation(coord_from=coord_from,
coord_to=coord_to,
centroid_from=centroid_from,
centroid_to=centroid_to)
axis, angle = R_to_axis_angle(R)
a, b, g = R_to_euler_zyz(R)
# Print out.
if verbosity >= 1:
print(
"\n\nCalculating the rotational and translational displacements from %s to %s using the Kabsch algorithm.\n"
% (name_from, name_to))
if centre_type == 'centroid':
print("Start centroid: [%20.15f, %20.15f, %20.15f]" %
(centroid_from[0], centroid_from[1], centroid_from[2]))
print("End centroid: [%20.15f, %20.15f, %20.15f]" %
(centroid_to[0], centroid_to[1], centroid_to[2]))
else:
print("Start CoM: [%20.15f, %20.15f, %20.15f]" %
(centroid_from[0], centroid_from[1], centroid_from[2]))
print("End CoM: [%20.15f, %20.15f, %20.15f]" %
(centroid_to[0], centroid_to[1], centroid_to[2]))
print("Translation vector: [%20.15f, %20.15f, %20.15f]" %
(trans_vect[0], trans_vect[1], trans_vect[2]))
print("Translation distance: %.15f" % trans_dist)
print("Rotation matrix:")
print(" [[%20.15f, %20.15f, %20.15f]" % (R[0, 0], R[0, 1], R[0, 2]))
print(" [%20.15f, %20.15f, %20.15f]" % (R[1, 0], R[1, 1], R[1, 2]))
print(" [%20.15f, %20.15f, %20.15f]]" % (R[2, 0], R[2, 1], R[2, 2]))
print("Rotation axis: [%20.15f, %20.15f, %20.15f]" %
(axis[0], axis[1], axis[2]))
print("Rotation euler angles: [%20.15f, %20.15f, %20.15f]" %
(a, b, g))
print("Rotation angle (deg): %.15f" % (angle / 2.0 / pi * 360.0))
# Return the data.
return trans_vect, trans_dist, R, axis, angle, centroid_to
def permute_axes(permutation='A'):
"""Permute the axes of the motional eigenframe to switch between local minima.
@keyword permutation: The permutation to use. This can be either 'A' or 'B' to select between the 3 permutations, excluding the current combination.
@type permutation: str
"""
# Check that the model is valid.
allowed = MODEL_LIST_ISO_CONE + MODEL_LIST_PSEUDO_ELLIPSE
if cdp.model not in allowed:
raise RelaxError(
"The permutation of the motional eigenframe is only valid for the frame order models %s."
% allowed)
# Check that the model parameters are setup.
if cdp.model in MODEL_LIST_ISO_CONE:
if not hasattr(cdp, 'cone_theta') or not is_float(cdp.cone_theta):
raise RelaxError("The parameter values are not set up.")
else:
if not hasattr(cdp, 'cone_theta_y') or not is_float(cdp.cone_theta_y):
raise RelaxError("The parameter values are not set up.")
# The iso cones only have one permutation.
if cdp.model in MODEL_LIST_ISO_CONE and permutation == 'B':
raise RelaxError("The isotropic cones only have one permutation.")
# The angles.
cone_sigma_max = 0.0
if cdp.model in MODEL_LIST_RESTRICTED_TORSION:
cone_sigma_max = cdp.cone_sigma_max
elif cdp.model in MODEL_LIST_FREE_ROTORS:
cone_sigma_max = pi
if cdp.model in MODEL_LIST_ISO_CONE:
angles = array([cdp.cone_theta, cdp.cone_theta, cone_sigma_max],
float64)
else:
angles = array([cdp.cone_theta_x, cdp.cone_theta_y, cone_sigma_max],
float64)
x, y, z = angles
# The axis system.
axes = generate_axis_system()
# Start printout for the isotropic cones.
if cdp.model in MODEL_LIST_ISO_CONE:
print("\nOriginal parameters:")
print("%-20s %20.10f" % ("cone_theta", cdp.cone_theta))
print("%-20s %20.10f" % ("cone_sigma_max", cone_sigma_max))
print("%-20s %20.10f" % ("axis_theta", cdp.axis_theta))
print("%-20s %20.10f" % ("axis_phi", cdp.axis_phi))
print("%-20s\n%s" % ("cone axis", axes[:, 2]))
print("%-20s\n%s" % ("full axis system", axes))
print("\nPermutation '%s':" % permutation)
# Start printout for the pseudo-ellipses.
else:
print("\nOriginal parameters:")
print("%-20s %20.10f" % ("cone_theta_x", cdp.cone_theta_x))
print("%-20s %20.10f" % ("cone_theta_y", cdp.cone_theta_y))
print("%-20s %20.10f" % ("cone_sigma_max", cone_sigma_max))
print("%-20s %20.10f" % ("eigen_alpha", cdp.eigen_alpha))
print("%-20s %20.10f" % ("eigen_beta", cdp.eigen_beta))
print("%-20s %20.10f" % ("eigen_gamma", cdp.eigen_gamma))
print("%-20s\n%s" % ("eigenframe", axes))
print("\nPermutation '%s':" % permutation)
# The axis inversion structure.
inv = ones(3, float64)
# The starting condition x <= y <= z.
if x <= y and y <= z:
# Printout.
print("%-20s %-20s" % ("Starting condition", "x <= y <= z"))
# The cone angle and axes permutations.
if permutation == 'A':
perm_angles = [0, 2, 1]
perm_axes = [2, 1, 0]
inv[perm_axes[2]] = -1.0
else:
perm_angles = [1, 2, 0]
perm_axes = [2, 0, 1]
# The starting condition x <= z <= y.
elif x <= z and z <= y:
# Printout.
print("%-20s %-20s" % ("Starting condition", "x <= z <= y"))
# The cone angle and axes permutations.
if permutation == 'A':
perm_angles = [0, 2, 1]
perm_axes = [2, 1, 0]
inv[perm_axes[2]] = -1.0
else:
perm_angles = [2, 1, 0]
perm_axes = [0, 2, 1]
inv[perm_axes[2]] = -1.0
# The starting condition z <= x <= y.
elif z <= x and x <= y:
# Printout.
print("%-20s %-20s" % ("Starting condition", "z <= x <= y"))
# The cone angle and axes permutations.
if permutation == 'A':
perm_angles = [2, 0, 1]
perm_axes = [1, 2, 0]
else:
perm_angles = [2, 1, 0]
perm_axes = [0, 2, 1]
inv[perm_axes[2]] = -1.0
# Cannot be here.
else:
raise RelaxFault
# Printout.
print("%-20s %-20s" % ("Cone angle permutation", perm_angles))
print("%-20s %-20s" % ("Axes permutation", perm_axes))
# Permute the angles.
if cdp.model in MODEL_LIST_ISO_CONE:
cdp.cone_theta = (angles[perm_angles[0]] +
angles[perm_angles[1]]) / 2.0
else:
cdp.cone_theta_x = angles[perm_angles[0]]
cdp.cone_theta_y = angles[perm_angles[1]]
if cdp.model in MODEL_LIST_RESTRICTED_TORSION:
cdp.cone_sigma_max = angles[perm_angles[2]]
elif cdp.model in MODEL_LIST_FREE_ROTORS:
cdp.cone_sigma_max = pi
# Permute the axes (iso cone).
if cdp.model in MODEL_LIST_ISO_CONE:
# Convert the y-axis to spherical coordinates (the x-axis would be ok too, or any vector in the x-y plane due to symmetry of the original permutation).
axis_new = axes[:, 1]
r, cdp.axis_theta, cdp.axis_phi = cartesian_to_spherical(axis_new)
# Permute the axes (pseudo-ellipses).
else:
axes_new = transpose(
array([
inv[0] * axes[:, perm_axes[0]], inv[1] * axes[:, perm_axes[1]],
inv[2] * axes[:, perm_axes[2]]
], float64))
# Convert the permuted frame to Euler angles and store them.
cdp.eigen_alpha, cdp.eigen_beta, cdp.eigen_gamma = R_to_euler_zyz(
axes_new)
# End printout.
if cdp.model in MODEL_LIST_ISO_CONE:
print("\nPermuted parameters:")
print("%-20s %20.10f" % ("cone_theta", cdp.cone_theta))
if cdp.model == MODEL_ISO_CONE:
print("%-20s %20.10f" % ("cone_sigma_max", cdp.cone_sigma_max))
print("%-20s %20.10f" % ("axis_theta", cdp.axis_theta))
print("%-20s %20.10f" % ("axis_phi", cdp.axis_phi))
print("%-20s\n%s" % ("cone axis", axis_new))
else:
print("\nPermuted parameters:")
print("%-20s %20.10f" % ("cone_theta_x", cdp.cone_theta_x))
print("%-20s %20.10f" % ("cone_theta_y", cdp.cone_theta_y))
if cdp.model == MODEL_PSEUDO_ELLIPSE:
print("%-20s %20.10f" % ("cone_sigma_max", cdp.cone_sigma_max))
print("%-20s %20.10f" % ("eigen_alpha", cdp.eigen_alpha))
print("%-20s %20.10f" % ("eigen_beta", cdp.eigen_beta))
print("%-20s %20.10f" % ("eigen_gamma", cdp.eigen_gamma))
print("%-20s\n%s" % ("eigenframe", axes_new))
CONE_SIGMA_MAX = 30.0 / 360.0 * 2.0 * pi
# Reconstruct the rotation axis.
AXIS = zeros(3, float64)
spherical_to_cartesian([1, AXIS_THETA, AXIS_PHI], AXIS)
# Create a full normalised axis system.
x = array([1, 0, 0], float64)
y = cross(AXIS, x)
y /= norm(y)
x = cross(y, AXIS)
x /= norm(x)
AXES = transpose(array([x, y, AXIS], float64))
# The Euler angles.
eigen_alpha, eigen_beta, eigen_gamma = R_to_euler_zyz(AXES)
# Printout.
print("Torsion angle: %s" % CONE_SIGMA_MAX)
print("Rotation axis: %s" % AXIS)
print("Full axis system:\n%s" % AXES)
print("cross(x, y) = z:\n %s = %s" % (cross(AXES[:, 0], AXES[:, 1]), AXES[:, 2]))
print("cross(x, z) = -y:\n %s = %s" % (cross(AXES[:, 0], AXES[:, 2]), -AXES[:, 1]))
print("cross(y, z) = x:\n %s = %s" % (cross(AXES[:, 1], AXES[:, 2]), AXES[:, 0]))
print("Euler angles (alpha, beta, gamma): (%.15f, %.15f, %.15f)" % (eigen_alpha, eigen_beta, eigen_gamma))
# Load the optimised rotor state for creating the pseudo-ellipse data pipes.
state.load(state='frame_order_true', dir='..')
# Set up the dynamic system.
value.set(param='ave_pos_x', val=AVE_POS_X)
def _calculate_rdc(self):
"""Calculate the averaged RDC for all states."""
# Open the output files.
if self.ROT_FILE:
rot_file = open_write_file('rotations', dir=self.save_path, compress_type=1, force=True)
# Printout.
sys.stdout.write("\n\nRotating %s states for the RDC:\n\n" % locale.format("%d", self.N**self.MODES, grouping=True))
# Turn off the relax interpreter echoing to allow the progress meter to be shown correctly.
self.interpreter.off()
# Set up some data structures for faster calculations.
interatoms = []
vectors = []
d = []
for interatom in interatomic_loop():
# Nothing to do.
if not hasattr(interatom, 'vector'):
continue
# Initialise the RDC structure (as a 1D numpy.float128 array for speed and minimising truncation artifacts).
interatom.rdc = {}
for tag in self._tensors:
interatom.rdc[tag] = zeros(1, float128)
# Pack the interatomic containers and vectors.
interatoms.append(interatom)
vectors.append(interatom.vector)
# Get the spins.
spin1 = return_spin(spin_id=interatom.spin_id1)
spin2 = return_spin(spin_id=interatom.spin_id2)
# Gyromagnetic ratios.
g1 = periodic_table.gyromagnetic_ratio(spin1.isotope)
g2 = periodic_table.gyromagnetic_ratio(spin2.isotope)
# Calculate the RDC dipolar constant (in Hertz, and the 3 comes from the alignment tensor), and append it to the list.
d.append(3.0/(2.0*pi) * dipolar_constant(g1, g2, interatom.r))
# Repackage the data for speed.
vectors = transpose(array(vectors, float64))
d = array(d, float64)
num_interatoms = len(vectors)
# Store the alignment tensors.
A = []
for i in range(len(self._tensors)):
A.append(cdp.align_tensors[i].A)
# Loop over each position.
for global_index, mode_indices in self._state_loop():
# The progress meter.
self._progress(global_index)
# Total rotation matrix (for construction of the frame order matrix).
total_R = eye(3)
# Data initialisation.
new_vect = vectors
# Loop over each motional mode.
for motion_index in range(self.MODES):
# Generate the distribution specific rotation.
self.rotation(mode_indices[motion_index], motion_index=motion_index)
# Rotate the NH vector.
new_vect = dot(self.R, new_vect)
# Decompose the rotation into Euler angles and store them.
if self.ROT_FILE:
a, b, g = R_to_euler_zyz(self.R)
rot_file.write('Mode %i: %10.7f %10.7f %10.7f\n' % (motion_index, a, b, g))
# Contribution to the total rotation.
total_R = dot(self.R, total_R)
# Loop over each alignment.
for i in range(len(self._tensors)):
# Calculate the RDC as quickly as possible.
rdcs = d * tensordot(transpose(new_vect), tensordot(A[i], new_vect, axes=1), axes=1)
# Store the values.
for j in range(len(interatoms)):
interatoms[j].rdc[self._tensors[i]][0] += rdcs[j, j]
# The frame order matrix component.
self.daeg += kron_prod(total_R, total_R)
# Print out.
sys.stdout.write('\n\n')
# Frame order matrix averaging.
self.daeg = self.daeg / self.N**self.MODES
# Write out the frame order matrix.
file = open(self.save_path+sep+'frame_order_matrix', 'w')
print_frame_order_2nd_degree(self.daeg, file=file, places=8)
# Reactive the interpreter echoing.
self.interpreter.on()
# Average the RDC and write the data.
for tag in self._tensors:
# Average.
for interatom in interatomic_loop():
interatom.rdc[tag] = interatom.rdc[tag][0] / self.N**self.MODES
# Save.
self.interpreter.rdc.write(align_id=tag, file='rdc_%s.txt'%tag, dir=self.save_path, force=True)
# Python module imports.
from numpy import array, float64, transpose, zeros
# relax module imports.
from lib.geometry.rotations import euler_to_R_zyz, R_to_euler_zyz
# Create a data pipe for the data.
pipe.create('displace', 'N-state')
# Load the structure.
structure.read_pdb('fancy_mol.pdb')
# First rotate.
R = zeros((3, 3), float64)
euler_to_R_zyz(1, 2, 3, R)
origin = array([1, 1, 1], float64)
structure.rotate(R=R, origin=origin)
# Then translate.
T = array([1, 2, 3], float64)
structure.translate(T=T)
# Write out the new structure.
structure.write_pdb('displaced.pdb', force=True)
# Printout of the inverted Euler angles of rotation (the solution).
a, b, g = R_to_euler_zyz(transpose(R))
print("alpha: %s" % a)
print("beta: %s" % b)
print("gamma: %s" % g)