def test_compile_2nd_matrix_free_rotor_point2(self):
"""Check the operation of the compile_2nd_matrix_free_rotor() function."""
# The simulated free rotor 2nd degree frame order matrix (1e6 ensembles, axis=[2,1,3]).
real = array(
[[ 0.3367, -0.0100, -0.0307, -0.0100, 0.3521, -0.0152, -0.0307, -0.0152, 0.3112],
[ -0.0104, 0.3520, -0.0152, -0.2908, -0.0559, 0.2602, 0.1989, -0.1685, 0.0664],
[ -0.0306, -0.0155, 0.3112, 0.1991, -0.1683, 0.0666, 0.2399, 0.2092, 0.1989],
[ -0.0104, -0.2908, 0.1989, 0.3520, -0.0559, -0.1685, -0.0152, 0.2602, 0.0664],
[ 0.3520, -0.0563, -0.1684, -0.0563, 0.4362, -0.0841, -0.1684, -0.0841, 0.2118],
[ -0.0153, 0.2602, 0.0661, -0.1684, -0.0844, 0.2117, 0.2093, -0.0740, 0.0997],
[ -0.0306, 0.1991, 0.2399, -0.0155, -0.1683, 0.2092, 0.3112, 0.0666, 0.1989],
[ -0.0153, -0.1684, 0.2093, 0.2602, -0.0844, -0.0740, 0.0661, 0.2117, 0.0997],
[ 0.3113, 0.0663, 0.1991, 0.0663, 0.2117, 0.0993, 0.1991, 0.0993, 0.4770]])
# The cone axis.
r, theta, phi = cartesian_to_spherical([2, 1, 3])
# The Kronecker product of the eigenframe rotation.
Rx2_eigen = self.calc_Rx2_eigen_axis(theta, phi)
# Calculate the matrix.
f2 = compile_2nd_matrix_free_rotor(self.f2_temp, Rx2_eigen)
# Print out.
print_frame_order_2nd_degree(real, "real")
print_frame_order_2nd_degree(f2, "calculated")
print_frame_order_2nd_degree(real-f2, "difference")
# Check the values.
for i in range(9):
for j in range(9):
print("Element %s, %s; diff %s." % (i, j, f2[i, j] - real[i, j]))
self.assert_(abs(f2[i, j] - real[i, j]) < 1e-3)
def test_compile_2nd_matrix_free_rotor_point2(self):
"""Check the operation of the compile_2nd_matrix_free_rotor() function."""
# The simulated free rotor 2nd degree frame order matrix (1e6 ensembles, axis=[2,1,3]).
real = array(
[[ 0.3367, -0.0100, -0.0307, -0.0100, 0.3521, -0.0152, -0.0307, -0.0152, 0.3112],
[ -0.0104, 0.3520, -0.0152, -0.2908, -0.0559, 0.2602, 0.1989, -0.1685, 0.0664],
[ -0.0306, -0.0155, 0.3112, 0.1991, -0.1683, 0.0666, 0.2399, 0.2092, 0.1989],
[ -0.0104, -0.2908, 0.1989, 0.3520, -0.0559, -0.1685, -0.0152, 0.2602, 0.0664],
[ 0.3520, -0.0563, -0.1684, -0.0563, 0.4362, -0.0841, -0.1684, -0.0841, 0.2118],
[ -0.0153, 0.2602, 0.0661, -0.1684, -0.0844, 0.2117, 0.2093, -0.0740, 0.0997],
[ -0.0306, 0.1991, 0.2399, -0.0155, -0.1683, 0.2092, 0.3112, 0.0666, 0.1989],
[ -0.0153, -0.1684, 0.2093, 0.2602, -0.0844, -0.0740, 0.0661, 0.2117, 0.0997],
[ 0.3113, 0.0663, 0.1991, 0.0663, 0.2117, 0.0993, 0.1991, 0.0993, 0.4770]])
# The cone axis.
r, theta, phi = cartesian_to_spherical([2, 1, 3])
# The Kronecker product of the eigenframe rotation.
Rx2_eigen = self.calc_Rx2_eigen_axis(theta, phi)
# Calculate the matrix.
f2 = compile_2nd_matrix_free_rotor(self.f2_temp, Rx2_eigen)
# Print out.
print_frame_order_2nd_degree(real, "real")
print_frame_order_2nd_degree(f2, "calculated")
print_frame_order_2nd_degree(real-f2, "difference")
# Check the values.
for i in range(9):
for j in range(9):
print("Element %s, %s; diff %s." % (i, j, f2[i, j] - real[i, j]))
self.assert_(abs(f2[i, j] - real[i, j]) < 1e-3)
def _print_axis_system(self):
"""Print out of the full system."""
# 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 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 convert_axis_alpha_to_spherical(alpha=None, pivot=None, point=None):
"""Convert the axis alpha angle to spherical angles theta and phi.
@keyword alpha: The axis alpha angle, defined as the angle between a vector perpendicular to the pivot-CoM vector in the xy-plane and the rotor axis.
@type alpha: float
@keyword pivot: The pivot point on the rotation axis.
@type pivot: numpy rank-1 3D array
@keyword point: The reference point in space.
@type point: numpy rank-1 3D array
@return: The theta and phi spherical angles.
@rtype: float, float
"""
# Create the axis.
axis = create_rotor_axis_alpha(alpha=alpha, pivot=pivot, point=point)
# Coordinate system transform.
r, theta, phi = cartesian_to_spherical(axis)
# Return the angles.
return theta, phi
def convert_axis_alpha_to_spherical(alpha=None, pivot=None, point=None):
"""Convert the axis alpha angle to spherical angles theta and phi.
@keyword alpha: The axis alpha angle, defined as the angle between a vector perpendicular to the pivot-CoM vector in the xy-plane and the rotor axis.
@type alpha: float
@keyword pivot: The pivot point on the rotation axis.
@type pivot: numpy rank-1 3D array
@keyword point: The reference point in space.
@type point: numpy rank-1 3D array
@return: The theta and phi spherical angles.
@rtype: float, float
"""
# Create the axis.
axis = create_rotor_axis_alpha(alpha=alpha, pivot=pivot, point=point)
# Coordinate system transform.
r, theta, phi = cartesian_to_spherical(axis)
# Return the angles.
return theta, phi
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))
# Script for checking the free rotor frame order model. # Python module imports. from numpy import array, float64 from os import sep # relax module imports. from data_store import Relax_data_store; ds = Relax_data_store() from lib.geometry.coord_transform import cartesian_to_spherical from status import Status; status = Status() # Generate 3 orthogonal vectors. vect_z = array([2, 1, 3], float64) r, theta, phi = cartesian_to_spherical(vect_z) # Load the tensors. self._execute_uf(uf_name='script', file=status.install_path + sep+'test_suite'+sep+'system_tests'+sep+'scripts'+sep+'frame_order'+sep+'tensors'+sep+'free_rotor_axis2_1_3_rot_tensors.py') # Data init. cdp.ave_pos_beta = 0.5 cdp.ave_pos_gamma = 0.2 cdp.axis_theta = theta cdp.axis_phi = phi # Select the Frame Order model. self._execute_uf(uf_name='frame_order.select_model', model='free rotor') # Set the reference domain. self._execute_uf(uf_name='frame_order.ref_domain', ref='full')
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))
