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# MDAnalysis --- https://www.mdanalysis.org
# Copyright (c) 2006-2017 The MDAnalysis Development Team and contributors
# (see the file AUTHORS for the full list of names)
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#
# Please cite your use of MDAnalysis in published work:
#
# R. J. Gowers, M. Linke, J. Barnoud, T. J. E. Reddy, M. N. Melo, S. L. Seyler,
# D. L. Dotson, J. Domanski, S. Buchoux, I. M. Kenney, and O. Beckstein.
# MDAnalysis: A Python package for the rapid analysis of molecular dynamics
# simulations. In S. Benthall and S. Rostrup editors, Proceedings of the 15th
# Python in Science Conference, pages 102-109, Austin, TX, 2016. SciPy.
# doi: 10.25080/majora-629e541a-00e
#
# N. Michaud-Agrawal, E. J. Denning, T. B. Woolf, and O. Beckstein.
# MDAnalysis: A Toolkit for the Analysis of Molecular Dynamics Simulations.
# J. Comput. Chem. 32 (2011), 2319--2327, doi:10.1002/jcc.21787
#
"""Streamplots (3D) --- :mod:`MDAnalysis.visualization.streamlines_3D`
===================================================================
:Authors: Tyler Reddy and Matthieu Chavent
:Year: 2014
:Copyright: GNU Public License v3
:Citation: [Chavent2014]_
The :func:`generate_streamlines_3d` function can generate a 3D flow field from
a MD trajectory, for instance, lipid molecules in a virus capsid. It can make
use of multiple cores to perform the analyis in parallel (using
:mod:`multiprocessing`).
See Also
--------
MDAnalysis.visualization.streamlines : streamplots in 2D
.. autofunction:: generate_streamlines_3d
"""
from __future__ import division, absolute_import
import six
from six.moves import range, zip
import multiprocessing
import numpy as np
import numpy.testing
import scipy
import scipy.spatial.distance
import MDAnalysis
def determine_container_limits(topology_file_path, trajectory_file_path, buffer_value):
"""Calculate the extent of the atom coordinates + buffer.
A function for the parent process which should take the input trajectory
and calculate the limits of the container for the system and return these
limits.
Parameters
----------
topology_file_path : str
topology file name
trajectory_file_path : str
trajectory file name
buffer_value : float
buffer value (padding) in +/- {x, y, z}
"""
universe_object = MDAnalysis.Universe(topology_file_path, trajectory_file_path)
all_atom_selection = universe_object.select_atoms('all') # select all particles
all_atom_coordinate_array = all_atom_selection.positions
x_min, x_max, y_min, y_max, z_min, z_max = [
all_atom_coordinate_array[..., 0].min(),
all_atom_coordinate_array[..., 0].max(), all_atom_coordinate_array[..., 1].min(),
all_atom_coordinate_array[..., 1].max(), all_atom_coordinate_array[..., 2].min(),
all_atom_coordinate_array[..., 2].max()]
tuple_of_limits = \
(
x_min - buffer_value,
x_max + buffer_value, y_min - buffer_value, y_max + buffer_value, z_min - buffer_value,
z_max + buffer_value) # using buffer_value to catch particles near edges
return tuple_of_limits
def produce_grid(tuple_of_limits, grid_spacing):
"""Produce a 3D grid for the simulation system.
The partitioning is based on the tuple of Cartesian Coordinate limits
calculated in an earlier step.
Parameters
----------
tuple_of_limits : tuple
``x_min, x_max, y_min, y_max, z_min, z_max``
grid_spacing : float
grid size in all directions in ångström
Returns
-------
grid : array
``numpy.mgrid[x_min:x_max:grid_spacing, y_min:y_max:grid_spacing, z_min:z_max:grid_spacing]``
"""
x_min, x_max, y_min, y_max, z_min, z_max = tuple_of_limits
grid = np.mgrid[x_min:x_max:grid_spacing, y_min:y_max:grid_spacing, z_min:z_max:grid_spacing]
return grid
def split_grid(grid, num_cores):
"""Split the grid into blocks of vertices.
Take the overall `grid` for the system and split it into lists of cube
vertices that can be distributed to each core.
Parameters
----------
grid : numpy.array
3D array
num_cores : int
number of partitions to generate
Returns
-------
list_dictionaries_for_cores : list of dict
total_cubes : int
num_sheets : int
delta_array_shape : tuple
"""
# unpack the x,y,z mgrid arrays
x, y, z = grid
num_z_values = z.shape[-1]
num_sheets = z.shape[0]
delta_array_shape = tuple(
[n - 1 for n in x.shape]) # the final target shape for return delta arrays is n-1 in each dimension
ordered_list_per_sheet_x_values = []
for x_sheet in x: # each x_sheet should have shape (25,23) and the same x value in each element
array_all_x_values_current_sheet = x_sheet.flatten()
ordered_list_per_sheet_x_values.append(array_all_x_values_current_sheet)
ordered_list_per_sheet_y_values = []
for y_columns in y:
array_all_y_values_current_sheet = y_columns.flatten()
ordered_list_per_sheet_y_values.append(array_all_y_values_current_sheet)
ordered_list_per_sheet_z_values = []
for z_slices in z:
array_all_z_values_current_sheet = z_slices.flatten()
ordered_list_per_sheet_z_values.append(array_all_z_values_current_sheet)
ordered_list_cartesian_coordinates_per_sheet = []
for x_sheet_coords, y_sheet_coords, z_sheet_coords in zip(ordered_list_per_sheet_x_values,
ordered_list_per_sheet_y_values,
ordered_list_per_sheet_z_values):
ordered_list_cartesian_coordinates_per_sheet.append(list(zip(x_sheet_coords, y_sheet_coords, z_sheet_coords)))
array_ordered_cartesian_coords_per_sheet = np.array(ordered_list_cartesian_coordinates_per_sheet)
#now I'm going to want to build cubes in an ordered fashion, and in such a way that I can track the index /
# centroid of each cube for domain decomposition / reconstruction and mayavi mlab.flow() input
#cubes will be formed from N - 1 base sheets combined with subsequent sheets
current_base_sheet = 0
dictionary_cubes_centroids_indices = {}
cube_counter = 0
while current_base_sheet < num_sheets - 1:
current_base_sheet_array = array_ordered_cartesian_coords_per_sheet[current_base_sheet]
current_top_sheet_array = array_ordered_cartesian_coords_per_sheet[
current_base_sheet + 1] # the points of the sheet 'to the right' in the grid
current_index = 0
while current_index < current_base_sheet_array.shape[0] - num_z_values:
# iterate through all the indices in each of the sheet arrays (careful to avoid extra
# points not needed for cubes)
column_z_level = 0 # start at the bottom of a given 4-point column and work up
while column_z_level < num_z_values - 1:
current_list_cube_vertices = []
first_two_vertices_base_sheet = current_base_sheet_array[current_index:current_index + 2, ...].tolist()
first_two_vertices_top_sheet = current_top_sheet_array[current_index:current_index + 2, ...].tolist()
next_two_vertices_base_sheet = current_base_sheet_array[current_index +
num_z_values: 2 +
num_z_values + current_index, ...].tolist()
next_two_vertices_top_sheet = current_top_sheet_array[current_index +
num_z_values: 2 +
num_z_values + current_index, ...].tolist()
for vertex_set in [
first_two_vertices_base_sheet, first_two_vertices_top_sheet,
next_two_vertices_base_sheet, next_two_vertices_top_sheet
]:
current_list_cube_vertices.extend(vertex_set)
vertex_array = np.array(current_list_cube_vertices)
assert vertex_array.shape == (8, 3), "vertex_array has incorrect shape"
cube_centroid = np.average(np.array(current_list_cube_vertices), axis=0)
dictionary_cubes_centroids_indices[cube_counter] = {
'centroid': cube_centroid,
'vertex_list': current_list_cube_vertices}
cube_counter += 1
current_index += 1
column_z_level += 1
if column_z_level == num_z_values - 1: # the loop will break but I should also increment the
# current_index
current_index += 1
current_base_sheet += 1
total_cubes = len(dictionary_cubes_centroids_indices)
#produce an array of pseudo cube indices (actually the dictionary keys which are cube numbers in string format):
pseudo_cube_indices = np.arange(0, total_cubes)
sublist_of_cube_indices_per_core = np.array_split(pseudo_cube_indices, num_cores)
#now, the split of pseudoindices seems to work well, and the above sublist_of_cube_indices_per_core is a list of
# arrays of cube numbers / keys in the original dictionary
#now I think I'll try to produce a list of dictionaries that each contain their assigned cubes based on the above
# per core split
list_dictionaries_for_cores = []
subdictionary_counter = 0
for array_cube_indices in sublist_of_cube_indices_per_core:
current_core_dictionary = {}
items_to_pop = len(array_cube_indices)
items_popped = 0
while items_popped < items_to_pop:
key, value = dictionary_cubes_centroids_indices.popitem()
current_core_dictionary.update({key: value})
items_popped += 1
list_dictionaries_for_cores.append(current_core_dictionary)
subdictionary_counter += 1
return list_dictionaries_for_cores, total_cubes, num_sheets, delta_array_shape
def per_core_work(start_frame_coord_array, end_frame_coord_array, dictionary_cube_data_this_core, MDA_selection,
start_frame, end_frame):
"""Run the analysis on one core.
The code to perform on a given core given the dictionary of cube data.
"""
list_previous_frame_centroids = []
list_previous_frame_indices = []
# define some utility functions for trajectory iteration:
def point_in_cube(array_point_coordinates, list_cube_vertices, cube_centroid):
"""Determine if an array of coordinates are within a cube."""
#the simulation particle point can't be more than half the cube side length away from the cube centroid in
# any given dimension:
array_cube_vertices = np.array(list_cube_vertices)
cube_half_side_length = scipy.spatial.distance.pdist(array_cube_vertices, 'euclidean').min() / 2.0
array_cube_vertex_distances_from_centroid = scipy.spatial.distance.cdist(array_cube_vertices,
cube_centroid[np.newaxis, :])
np.testing.assert_almost_equal(array_cube_vertex_distances_from_centroid.min(),
array_cube_vertex_distances_from_centroid.max(), decimal=4,
err_msg="not all cube vertex to centroid distances are the same, "
"so not a true cube")
absolute_delta_coords = np.absolute(np.subtract(array_point_coordinates, cube_centroid))
absolute_delta_x_coords = absolute_delta_coords[..., 0]
indices_delta_x_acceptable = np.where(absolute_delta_x_coords <= cube_half_side_length)
absolute_delta_y_coords = absolute_delta_coords[..., 1]
indices_delta_y_acceptable = np.where(absolute_delta_y_coords <= cube_half_side_length)
absolute_delta_z_coords = absolute_delta_coords[..., 2]
indices_delta_z_acceptable = np.where(absolute_delta_z_coords <= cube_half_side_length)
intersection_xy_acceptable_arrays = np.intersect1d(indices_delta_x_acceptable[0],
indices_delta_y_acceptable[0])
overall_indices_points_in_current_cube = np.intersect1d(intersection_xy_acceptable_arrays,
indices_delta_z_acceptable[0])
return overall_indices_points_in_current_cube
def update_dictionary_point_in_cube_start_frame(array_simulation_particle_coordinates,
dictionary_cube_data_this_core):
"""Basically update the cube dictionary objects assigned to this core to contain a new key/value pair
corresponding to the indices of the relevant particles that fall within a given cube. Also, for a given cube,
store a key/value pair for the centroid of the particles that fall within the cube."""
cube_counter = 0
for key, cube in six.iteritems(dictionary_cube_data_this_core):
index_list_in_cube = point_in_cube(array_simulation_particle_coordinates, cube['vertex_list'],
cube['centroid'])
cube['start_frame_index_list_in_cube'] = index_list_in_cube
if len(index_list_in_cube) > 0: # if there's at least one particle in this cube
centroid_particles_in_cube = np.average(array_simulation_particle_coordinates[index_list_in_cube],
axis=0)
cube['centroid_of_particles_first_frame'] = centroid_particles_in_cube
else: # empty cube
cube['centroid_of_particles_first_frame'] = 'empty'
cube_counter += 1
def update_dictionary_end_frame(array_simulation_particle_coordinates, dictionary_cube_data_this_core):
"""Update the cube dictionary objects again as appropriate for the second and final frame."""
cube_counter = 0
for key, cube in six.iteritems(dictionary_cube_data_this_core):
# if there were no particles in the cube in the first frame, then set dx,dy,dz each to 0
if cube['centroid_of_particles_first_frame'] == 'empty':
cube['dx'] = 0
cube['dy'] = 0
cube['dz'] = 0
else: # there was at least one particle in the starting cube so we can get dx,dy,dz centroid values
new_coordinate_array_for_particles_starting_in_this_cube = array_simulation_particle_coordinates[
cube['start_frame_index_list_in_cube']]
new_centroid_for_particles_starting_in_this_cube = np.average(
new_coordinate_array_for_particles_starting_in_this_cube, axis=0)
cube['centroid_of_paticles_final_frame'] = new_centroid_for_particles_starting_in_this_cube
delta_centroid_array_this_cube = new_centroid_for_particles_starting_in_this_cube - cube[
'centroid_of_particles_first_frame']
cube['dx'] = delta_centroid_array_this_cube[0]
cube['dy'] = delta_centroid_array_this_cube[1]
cube['dz'] = delta_centroid_array_this_cube[2]
cube_counter += 1
#now that the parent process is dealing with the universe object & grabbing required coordinates, each child
# process only needs to take the coordinate arrays & perform the operations with its assigned cubes (no more file
# opening and trajectory iteration on each core--which I'm hoping will substantially reduce the physical memory
# footprint of my 3D streamplot code)
update_dictionary_point_in_cube_start_frame(start_frame_coord_array, dictionary_cube_data_this_core)
update_dictionary_end_frame(end_frame_coord_array, dictionary_cube_data_this_core)
return dictionary_cube_data_this_core
def produce_coordinate_arrays_single_process(topology_file_path, trajectory_file_path, MDA_selection, start_frame,
end_frame):
"""Generate coordinate arrays.
To reduce memory footprint produce only a single MDA selection and get
desired coordinate arrays; can later send these coordinate arrays to all
child processes rather than having each child process open a trajectory and
waste memory.
"""
universe_object = MDAnalysis.Universe(topology_file_path, trajectory_file_path)
relevant_particles = universe_object.select_atoms(MDA_selection)
# pull out coordinate arrays from desired frames:
for ts in universe_object.trajectory:
if ts.frame > end_frame:
break # stop here
if ts.frame == start_frame:
start_frame_relevant_particle_coordinate_array_xyz = relevant_particles.positions
elif ts.frame == end_frame:
end_frame_relevant_particle_coordinate_array_xyz = relevant_particles.positions
else:
continue
return (start_frame_relevant_particle_coordinate_array_xyz, end_frame_relevant_particle_coordinate_array_xyz)
[docs]def generate_streamlines_3d(topology_file_path, trajectory_file_path, grid_spacing, MDA_selection, start_frame,
end_frame, xmin, xmax, ymin, ymax, zmin, zmax, maximum_delta_magnitude=2.0,
num_cores='maximum'):
r"""Produce the x, y and z components of a 3D streamplot data set.
Parameters
----------
topology_file_path : str
Absolute path to the topology file
trajectory_file_path : str
Absolute path to the trajectory file. It will normally be desirable
to filter the trajectory with a tool such as GROMACS
:program:`g_filter` (see [Chavent2014]_)
grid_spacing : float
The spacing between grid lines (angstroms)
MDA_selection : str
MDAnalysis selection string
start_frame : int
First frame number to parse
end_frame : int
Last frame number to parse
xmin : float
Minimum coordinate boundary for x-axis (angstroms)
xmax : float
Maximum coordinate boundary for x-axis (angstroms)
ymin : float
Minimum coordinate boundary for y-axis (angstroms)
ymax : float
Maximum coordinate boundary for y-axis (angstroms)
maximum_delta_magnitude : float
Absolute value of the largest displacement tolerated for the
centroid of a group of particles ( angstroms). Values above this
displacement will not count in the streamplot (treated as
excessively large displacements crossing the periodic boundary)
num_cores : int or 'maximum' (optional)
The number of cores to use. (Default 'maximum' uses all available
cores)
Returns
-------
dx_array : array of floats
An array object containing the displacements in the x direction
dy_array : array of floats
An array object containing the displacements in the y direction
dz_array : array of floats
An array object containing the displacements in the z direction
Examples
--------
Generate 3D streamlines and visualize in `mayavi`_::
import numpy as np
import MDAnalysis
import MDAnalysis.visualization.streamlines_3D
import mayavi, mayavi.mlab
# assign coordinate system limits and grid spacing:
x_lower,x_upper = -8.73, 1225.96
y_lower,y_upper = -12.58, 1224.34
z_lower,z_upper = -300, 300
grid_spacing_value = 20
x1, y1, z1 = MDAnalysis.visualization.streamlines_3D.generate_streamlines_3d(
'testing.gro', 'testing_filtered.xtc',
xmin=x_lower, xmax=x_upper,
ymin=y_lower, ymax=y_upper,
zmin=z_lower, zmax=z_upper,
grid_spacing=grid_spacing_value, MDA_selection = 'name PO4',
start_frame=2, end_frame=3, num_cores='maximum')
x, y, z = np.mgrid[x_lower:x_upper:x1.shape[0]*1j,
y_lower:y_upper:y1.shape[1]*1j,
z_lower:z_upper:z1.shape[2]*1j]
# plot with mayavi:
fig = mayavi.mlab.figure(bgcolor=(1.0, 1.0, 1.0), size=(800, 800), fgcolor=(0, 0, 0))
for z_value in np.arange(z_lower, z_upper, grid_spacing_value):
st = mayavi.mlab.flow(x, y, z, x1, y1, z1, line_width=1,
seedtype='plane', integration_direction='both')
st.streamline_type = 'tube'
st.tube_filter.radius = 2
st.seed.widget.origin = np.array([ x_lower, y_upper, z_value])
st.seed.widget.point1 = np.array([ x_upper, y_upper, z_value])
st.seed.widget.point2 = np.array([ x_lower, y_lower, z_value])
st.seed.widget.resolution = int(x1.shape[0])
st.seed.widget.enabled = False
mayavi.mlab.axes(extent = [0, 1200, 0, 1200, -300, 300])
fig.scene.z_plus_view()
mayavi.mlab.savefig('test_streamplot_3D.png')
# more compelling examples can be produced for vesicles and other spherical systems
.. image:: test_streamplot_3D.png
See Also
--------
MDAnalysis.visualization.streamlines.generate_streamlines
.. _mayavi: http://docs.enthought.com/mayavi/mayavi/
"""
# work out the number of cores to use:
if num_cores == 'maximum':
num_cores = multiprocessing.cpu_count() # use all available cores
else:
num_cores = num_cores # use the value specified by the user
# assert isinstance(num_cores,(int,long)), "The number of specified cores must (of course) be an integer."
np.seterr(all='warn', over='raise')
parent_cube_dictionary = {} # collect all data from child processes here
def log_result_to_parent(process_dict):
parent_cube_dictionary.update(process_dict)
#step 1: produce tuple of cartesian coordinate limits for the first frame
#tuple_of_limits = determine_container_limits(topology_file_path = topology_file_path,trajectory_file_path =
# trajectory_file_path,buffer_value=buffer_value)
tuple_of_limits = (xmin, xmax, ymin, ymax, zmin, zmax)
#step 2: produce a suitable grid (will assume that grid size / container size does not vary during simulation--or
# at least not beyond the buffer limit, such that this grid can be used for all subsequent frames)
grid = produce_grid(tuple_of_limits=tuple_of_limits, grid_spacing=grid_spacing)
#step 3: split the grid into a dictionary of cube information that can be sent to each core for processing:
list_dictionaries_for_cores, total_cubes, num_sheets, delta_array_shape = split_grid(grid=grid, num_cores=num_cores)
#step 3b: produce required coordinate arrays on a single core to avoid making a universe object on each core:
start_frame_coord_array, end_frame_coord_array = produce_coordinate_arrays_single_process(topology_file_path,
trajectory_file_path,
MDA_selection,
start_frame, end_frame)
#step 4: per process work using the above grid data split
pool = multiprocessing.Pool(num_cores)
for sub_dictionary_of_cube_data in list_dictionaries_for_cores:
pool.apply_async(per_core_work, args=(
start_frame_coord_array, end_frame_coord_array, sub_dictionary_of_cube_data, MDA_selection, start_frame,
end_frame), callback=log_result_to_parent)
pool.close()
pool.join()
#so, at this stage the parent process now has a single dictionary with all the cube objects updated from all
# available cores
#the 3D streamplot (i.e, mayavi flow() function) will require separate 3D np arrays for dx,dy,dz
#the shape of each 3D array will unfortunately have to match the mgrid data structure (bit of a pain): (
# num_sheets - 1, num_sheets - 1, cubes_per_column)
cubes_per_sheet = int(float(total_cubes) / float(num_sheets - 1))
#produce dummy zero arrays for dx,dy,dz of the appropriate shape:
dx_array = np.zeros(delta_array_shape)
dy_array = np.zeros(delta_array_shape)
dz_array = np.zeros(delta_array_shape)
#now use the parent cube dictionary to correctly substitute in dx,dy,dz values
current_sheet = 0 # which is also the current row
y_index_current_sheet = 0 # sub row
z_index_current_column = 0 # column
total_cubes_current_sheet = 0
for cube_number in range(0, total_cubes):
dx_array[current_sheet, y_index_current_sheet, z_index_current_column] = parent_cube_dictionary[cube_number][
'dx']
dy_array[current_sheet, y_index_current_sheet, z_index_current_column] = parent_cube_dictionary[cube_number][
'dy']
dz_array[current_sheet, y_index_current_sheet, z_index_current_column] = parent_cube_dictionary[cube_number][
'dz']
z_index_current_column += 1
total_cubes_current_sheet += 1
if z_index_current_column == delta_array_shape[2]:
# done building current y-column so iterate y value and reset z
z_index_current_column = 0
y_index_current_sheet += 1
if y_index_current_sheet == delta_array_shape[1]: # current sheet is complete
current_sheet += 1
y_index_current_sheet = 0 # restart for new sheet
z_index_current_column = 0
total_cubes_current_sheet = 0
# now set velocity component values greater than a certain cutoff to 0,
# because they tend to reflect spurious values (i.e., PBC jumping)
dx_array[abs(dx_array) >= maximum_delta_magnitude] = 1.0
dy_array[abs(dy_array) >= maximum_delta_magnitude] = 1.0
dz_array[abs(dz_array) >= maximum_delta_magnitude] = 1.0
return (dx_array, dy_array, dz_array)