def calc_covariance_matrix(coord=None, weights=None):
"""Calculate the covariance matrix for the structures.
@keyword coord: The list of coordinates of all models to superimpose. The first index is the models, the second is the atomic positions, and the third is the xyz coordinates.
@type coord: list of numpy rank-2, Nx3 arrays
@keyword weights: The weights for each structure.
@type weights: list of float
@return: The covariance matrix and the deviation matrix.
@rtype: numpy rank-2 3Nx3N array, numpy rank-2 MxNx3 array
"""
# Init.
M = len(coord)
N = len(coord[0])
if weights == None:
weights = ones(M, float64)
else:
weights = array(weights, float64)
covariance_matrix = zeros((N * 3, N * 3), float64)
deviations = zeros((M, N, 3), float64)
mean_struct = zeros((N, 3), float64)
# Calculate the mean structure.
calc_mean_structure(coord, mean_struct, weights=weights)
# Loop over the models.
for i in range(M):
# The deviations from the mean.
deviations[i] = coord[i] - mean_struct
# Sum the covariance element.
covariance_matrix += weights[i] * (outer(deviations[i], deviations[i]))
# Average.
covariance_matrix /= weights.sum()
# Return the matrix.
return covariance_matrix, deviations
def calc_covariance_matrix(coord=None, weights=None):
"""Calculate the covariance matrix for the structures.
@keyword coord: The list of coordinates of all models to superimpose. The first index is the models, the second is the atomic positions, and the third is the xyz coordinates.
@type coord: list of numpy rank-2, Nx3 arrays
@keyword weights: The weights for each structure.
@type weights: list of float
@return: The covariance matrix and the deviation matrix.
@rtype: numpy rank-2 3Nx3N array, numpy rank-2 MxNx3 array
"""
# Init.
M = len(coord)
N = len(coord[0])
if weights == None:
weights = ones(M, float64)
else:
weights = array(weights, float64)
covariance_matrix = zeros((N * 3, N * 3), float64)
deviations = zeros((M, N, 3), float64)
mean_struct = zeros((N, 3), float64)
# Calculate the mean structure.
calc_mean_structure(coord, mean_struct, weights=weights)
# Loop over the models.
for i in range(M):
# The deviations from the mean.
deviations[i] = coord[i] - mean_struct
# Sum the covariance element.
covariance_matrix += weights[i] * (outer(deviations[i], deviations[i]))
# Average.
covariance_matrix /= weights.sum()
# Return the matrix.
return covariance_matrix, deviations
def fit_to_mean(models=None, coord=None, centroid=None, verbosity=1):
"""Superimpose a set of structural models using the fit to first algorithm.
@keyword models: The list of models to superimpose.
@type models: list of int
@keyword coord: The list of coordinates of all models to superimpose. The first index is the models, the second is the atomic positions, and the third is the xyz coordinates.
@type coord: list of numpy rank-2, Nx3 arrays
@keyword centroid: An alternative position of the centroid to allow for different superpositions, for example of pivot point motions.
@type centroid: list of float or numpy rank-1, 3D array
@keyword verbosity: The amount of information to print out. If 0, nothing will be printed.
@type verbosity: int
@return: The lists of translation vectors, rotation matrices, and rotation pivots.
@rtype: list of numpy rank-1 3D arrays, list of numpy rank-2 3D arrays, list of numpy rank-1 3D arrays
"""
# Print out.
if verbosity:
print("\nSuperimposition of structural models %s using the 'fit to mean' algorithm." % models)
# Duplicate the coordinates.
orig_coord = deepcopy(coord)
# Initialise the displacement lists.
T_list = []
R_list = []
pivot_list = []
# Initialise the mean structure.
N = len(coord[0])
mean = zeros((N, 3), float64)
# Iterative fitting to mean.
converged = False
iter = 0
while not converged:
# Print out.
if verbosity:
print("\nIteration %i of the algorithm." % iter)
print("%-10s%-25s%-25s" % ("Model", "Translation (Angstrom)", "Rotation (deg)"))
# Calculate the mean structure.
calc_mean_structure(coord, mean)
# Fit each model to the mean.
converged = True
for i in range(len(models)):
# Calculate the displacements (Kabsch algorithm).
trans_vect, trans_dist, R, axis, angle, pivot = kabsch(name_from='model %s'%models[0], name_to='mean', coord_from=coord[i], coord_to=mean, centroid=centroid, verbosity=0)
# Table printout.
if verbosity:
print("%-10i%25.3g%25.3g" % (i, trans_dist, (angle / 2.0 / pi * 360.0)))
# Shift the coordinates.
for j in range(N):
# Translate.
coord[i][j] += trans_vect
# The pivot to atom vector.
coord[i][j] -= pivot
# Rotation.
coord[i][j] = dot(R, coord[i][j])
# The new position.
coord[i][j] += pivot
# Convergence test.
if trans_dist > 1e-10 or angle > 1e-10:
converged = False
# Increment the iteration number.
iter += 1
# Perform the fit once from the original coordinates to obtain the full transforms.
for i in range(len(models)):
# Calculate the displacements (Kabsch algorithm).
trans_vect, trans_dist, R, axis, angle, pivot = kabsch(name_from='model %s'%models[i], name_to='the mean structure', coord_from=orig_coord[i], coord_to=mean, centroid=centroid, verbosity=0)
# Store the transforms.
T_list.append(trans_vect)
R_list.append(R)
pivot_list.append(pivot)
# Return the transform data.
return T_list, R_list, pivot_list
def fit_to_mean(models=None,
coord=None,
centre_type="centroid",
elements=None,
centroid=None,
verbosity=1):
"""Superimpose a set of structural models using the fit to first algorithm.
@keyword models: The list of models to superimpose.
@type models: list of int
@keyword coord: The list of coordinates of all models to superimpose. The first index is the models, the second is the atomic positions, and the third is the xyz coordinates.
@type coord: list of numpy rank-2, Nx3 arrays
@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 to allow for different superpositions, for example of pivot point motions.
@type centroid: list of float or numpy rank-1, 3D array
@keyword verbosity: The amount of information to print out. If 0, nothing will be printed.
@type verbosity: int
@return: The lists of translation vectors, rotation matrices, and rotation pivots.
@rtype: list of numpy rank-1 3D arrays, list of numpy rank-2 3D arrays, list of numpy rank-1 3D arrays
"""
# Print out.
if verbosity:
print(
"\nSuperimposition of structural models %s using the 'fit to mean' algorithm."
% models)
# Duplicate the coordinates.
orig_coord = deepcopy(coord)
# Initialise the displacement lists.
T_list = []
R_list = []
pivot_list = []
# Initialise the mean structure.
N = len(coord[0])
mean = zeros((N, 3), float64)
# Iterative fitting to mean.
converged = False
iter = 0
while not converged:
# Print out.
if verbosity:
print("\nIteration %i of the algorithm." % iter)
print("%-10s%-25s%-25s" %
("Model", "Translation (Angstrom)", "Rotation (deg)"))
# Calculate the mean structure.
calc_mean_structure(coord, mean)
# Fit each model to the mean.
converged = True
for i in range(len(models)):
# Calculate the displacements (Kabsch algorithm).
trans_vect, trans_dist, R, axis, angle, pivot = kabsch(
name_from='model %s' % models[0],
name_to='mean',
coord_from=coord[i],
coord_to=mean,
centre_type=centre_type,
elements=elements,
centroid=centroid,
verbosity=0)
# Table printout.
if verbosity:
print("%-10i%25.3g%25.3g" % (i, trans_dist,
(angle / 2.0 / pi * 360.0)))
# Shift the coordinates.
for j in range(N):
# Translate.
coord[i][j] += trans_vect
# The pivot to atom vector.
coord[i][j] -= pivot
# Rotation.
coord[i][j] = dot(R, coord[i][j])
# The new position.
coord[i][j] += pivot
# Convergence test.
if trans_dist > 1e-10 or angle > 1e-10:
converged = False
# Increment the iteration number.
iter += 1
# Perform the fit once from the original coordinates to obtain the full transforms.
for i in range(len(models)):
# Calculate the displacements (Kabsch algorithm).
trans_vect, trans_dist, R, axis, angle, pivot = kabsch(
name_from='model %s' % models[i],
name_to='the mean structure',
coord_from=orig_coord[i],
coord_to=mean,
centre_type=centre_type,
elements=elements,
centroid=centroid,
verbosity=0)
# Store the transforms.
T_list.append(trans_vect)
R_list.append(R)
pivot_list.append(pivot)
# Return the transform data.
return T_list, R_list, pivot_list
