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# MDAnalysis --- https://www.mdanalysis.org
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# (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
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# 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 (2D) --- :mod:`MDAnalysis.visualization.streamlines`
=================================================================
:Authors: Tyler Reddy and Matthieu Chavent
:Year: 2014
:Copyright: GNU Public License v3
:Citation: [Chavent2014]_
The :func:`generate_streamlines` function can generate a 2D flow field from a
MD trajectory, for instance, lipid molecules in a flat membrane. It can make
use of multiple cores to perform the analyis in parallel (using
:mod:`multiprocessing`).
See Also
--------
MDAnalysis.visualization.streamlines_3D : streamplots in 3D
.. autofunction:: generate_streamlines
"""
from __future__ import absolute_import
from six.moves import zip
from six import raise_from
import multiprocessing
import numpy as np
import scipy
try:
import matplotlib
import matplotlib.path
except ImportError:
raise_from(
ImportError((
'2d streamplot module requires: matplotlib.path for its '
'path.Path.contains_points method. The installation '
'instructions for the matplotlib module can be found here: '
'http://matplotlib.org/faq/installing_faq.html?highlight=install'
)),
None)
import MDAnalysis
def produce_grid(tuple_of_limits, grid_spacing):
"""Produce a 2D grid for the simulation system.
The grid 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``
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]``
"""
x_min, x_max, y_min, y_max = tuple_of_limits
grid = np.mgrid[x_min:x_max:grid_spacing, y_min:y_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
square vertices that can be distributed to each core.
Parameters
----------
grid : numpy.array
2D array
num_cores : int
number of partitions to generate
Returns
-------
list_square_vertex_arrays_per_core : array of arrays
split the list of square vertices
``[[v1,v2,v3,v4],[v1,v2,v3,v4],...,...]`` into roughly equally-sized
sublists to be distributed over the available cores on the system
list_parent_index_values : array of arrays
arrays of `[[row, column], [row, column], ...]`` for each core
current_row : int
last row + 1
current_column : int
last column + 1
Note
----
Limited to 2D for now.
"""
# produce an array containing the cartesian coordinates of all vertices in the grid:
x_array, y_array = grid
grid_vertex_cartesian_array = np.dstack((x_array, y_array))
#the grid_vertex_cartesian_array has N_rows, with each row corresponding to a column of coordinates in the grid (
# so a given row has shape N_rows, 2); overall shape (N_columns_in_grid, N_rows_in_a_column, 2)
#although I'll eventually want a pure numpy/scipy/vector-based solution, for now I'll allow loops to simplify the
# division of the cartesian coordinates into a list of the squares in the grid
list_all_squares_in_grid = [] # should eventually be a nested list of all the square vertices in the grid/system
list_parent_index_values = [] # want an ordered list of assignment indices for reconstructing the grid positions
# in the parent process
current_column = 0
while current_column < grid_vertex_cartesian_array.shape[0] - 1:
# go through all the columns except the last one and account for the square vertices (the last column
# has no 'right neighbour')
current_row = 0
while current_row < grid_vertex_cartesian_array.shape[1] - 1:
# all rows except the top row, which doesn't have a row above it for forming squares
bottom_left_vertex_current_square = grid_vertex_cartesian_array[current_column, current_row]
bottom_right_vertex_current_square = grid_vertex_cartesian_array[current_column + 1, current_row]
top_right_vertex_current_square = grid_vertex_cartesian_array[current_column + 1, current_row + 1]
top_left_vertex_current_square = grid_vertex_cartesian_array[current_column, current_row + 1]
#append the vertices of this square to the overall list of square vertices:
list_all_squares_in_grid.append(
[bottom_left_vertex_current_square, bottom_right_vertex_current_square, top_right_vertex_current_square,
top_left_vertex_current_square])
list_parent_index_values.append([current_row, current_column])
current_row += 1
current_column += 1
#split the list of square vertices [[v1,v2,v3,v4],[v1,v2,v3,v4],...,...] into roughly equally-sized sublists to
# be distributed over the available cores on the system:
list_square_vertex_arrays_per_core = np.array_split(list_all_squares_in_grid, num_cores)
list_parent_index_values = np.array_split(list_parent_index_values, num_cores)
return [list_square_vertex_arrays_per_core, list_parent_index_values, current_row, current_column]
def per_core_work(topology_file_path, trajectory_file_path, list_square_vertex_arrays_this_core, MDA_selection,
start_frame, end_frame, reconstruction_index_list, maximum_delta_magnitude):
"""Run the analysis on one core.
The code to perform on a given core given the list of square vertices assigned to it.
"""
# obtain the relevant coordinates for particles of interest
universe_object = MDAnalysis.Universe(topology_file_path, trajectory_file_path)
list_previous_frame_centroids = []
list_previous_frame_indices = []
#define some utility functions for trajectory iteration:
def produce_list_indices_point_in_polygon_this_frame(vertex_coord_list):
list_indices_point_in_polygon = []
for square_vertices in vertex_coord_list:
path_object = matplotlib.path.Path(square_vertices)
index_list_in_polygon = np.where(path_object.contains_points(relevant_particle_coordinate_array_xy))
list_indices_point_in_polygon.append(index_list_in_polygon)
return list_indices_point_in_polygon
def produce_list_centroids_this_frame(list_indices_in_polygon):
list_centroids_this_frame = []
for indices in list_indices_in_polygon:
if not indices[0].size > 0: # if there are no particles of interest in this particular square
list_centroids_this_frame.append('empty')
else:
current_coordinate_array_in_square = relevant_particle_coordinate_array_xy[indices]
current_square_indices_centroid = np.average(current_coordinate_array_in_square, axis=0)
list_centroids_this_frame.append(current_square_indices_centroid)
return list_centroids_this_frame # a list of numpy xy centroid arrays for this frame
for ts in universe_object.trajectory:
if ts.frame < start_frame: # don't start until first specified frame
continue
relevant_particle_coordinate_array_xy = universe_object.select_atoms(MDA_selection).positions[..., :-1]
# only 2D / xy coords for now
#I will need a list of indices for relevant particles falling within each square in THIS frame:
list_indices_in_squares_this_frame = produce_list_indices_point_in_polygon_this_frame(
list_square_vertex_arrays_this_core)
#likewise, I will need a list of centroids of particles in each square (same order as above list):
list_centroids_in_squares_this_frame = produce_list_centroids_this_frame(list_indices_in_squares_this_frame)
if list_previous_frame_indices: # if the previous frame had indices in at least one square I will need to use
# those indices to generate the updates to the corresponding centroids in this frame:
list_centroids_this_frame_using_indices_from_last_frame = produce_list_centroids_this_frame(
list_previous_frame_indices)
#I need to write a velocity of zero if there are any 'empty' squares in either frame:
xy_deltas_to_write = []
for square_1_centroid, square_2_centroid in zip(list_centroids_this_frame_using_indices_from_last_frame,
list_previous_frame_centroids):
if square_1_centroid == 'empty' or square_2_centroid == 'empty':
xy_deltas_to_write.append([0, 0])
else:
xy_deltas_to_write.append(np.subtract(square_1_centroid, square_2_centroid).tolist())
#xy_deltas_to_write = np.subtract(np.array(
# list_centroids_this_frame_using_indices_from_last_frame),np.array(list_previous_frame_centroids))
xy_deltas_to_write = np.array(xy_deltas_to_write)
#now filter the array to only contain distances in the range [-8,8] as a placeholder for dealing with PBC
# issues (Matthieu seemed to use a limit of 8 as well);
xy_deltas_to_write = np.clip(xy_deltas_to_write, -maximum_delta_magnitude, maximum_delta_magnitude)
#with the xy and dx,dy values calculated I need to set the values from this frame to previous frame
# values in anticipation of the next frame:
list_previous_frame_centroids = list_centroids_in_squares_this_frame[:]
list_previous_frame_indices = list_indices_in_squares_this_frame[:]
else: # either no points in squares or after the first frame I'll just reset the 'previous' values so they
# can be used when consecutive frames have proper values
list_previous_frame_centroids = list_centroids_in_squares_this_frame[:]
list_previous_frame_indices = list_indices_in_squares_this_frame[:]
if ts.frame > end_frame:
break # stop here
return list(zip(reconstruction_index_list, xy_deltas_to_write.tolist()))
[docs]def generate_streamlines(topology_file_path, trajectory_file_path, grid_spacing, MDA_selection, start_frame,
end_frame, xmin, xmax, ymin, ymax, maximum_delta_magnitude, num_cores='maximum'):
r"""Produce the x and y components of a 2D 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
average_displacement : float
:math:`\frac{\sum\sqrt[]{dx^2 + dy^2}}{N}`
standard_deviation_of_displacement : float
standard deviation of :math:`\sqrt[]{dx^2 + dy^2}`
Examples
--------
Generate 2D streamlines and plot::
import matplotlib, matplotlib.pyplot, np
import MDAnalysis, MDAnalysis.visualization.streamlines
u1, v1, average_displacement, standard_deviation_of_displacement =
MDAnalysis.visualization.streamlines.generate_streamlines('testing.gro', 'testing_filtered.xtc',
grid_spacing=20, MDA_selection='name PO4', start_frame=2, end_frame=3,
xmin=-8.73000049591, xmax= 1225.96008301,
ymin= -12.5799999237, ymax=1224.34008789,
maximum_delta_magnitude=1.0, num_cores=16)
x = np.linspace(0, 1200, 61)
y = np.linspace(0, 1200, 61)
speed = np.sqrt(u1*u1 + v1*v1)
fig = matplotlib.pyplot.figure()
ax = fig.add_subplot(111, aspect='equal')
ax.set_xlabel('x ($\AA$)')
ax.set_ylabel('y ($\AA$)')
ax.streamplot(x, y, u1, v1, density=(10,10), color=speed, linewidth=3*speed/speed.max())
fig.savefig('testing_streamline.png',dpi=300)
.. image:: testing_streamline.png
References
----------
.. [Chavent2014] Chavent, M.*, Reddy, T.*, Dahl, C.E., Goose, J., Jobard,
B., and Sansom, M.S.P. Methodologies for the analysis of instantaneous
lipid diffusion in MD simulations of large membrane systems. *Faraday
Discussions* **169** (2014), 455–475. doi: `10.1039/c3fd00145h`_
.. _`10.1039/c3fd00145h`: https://doi.org/10.1039/c3fd00145h
See Also
--------
MDAnalysis.visualization.streamlines_3D.generate_streamlines_3d
"""
# 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_list_deltas = [] # collect all data from child processes here
def log_result_to_parent(delta_array):
parent_list_deltas.extend(delta_array)
tuple_of_limits = (xmin, xmax, ymin, ymax)
grid = produce_grid(tuple_of_limits=tuple_of_limits, grid_spacing=grid_spacing)
list_square_vertex_arrays_per_core, list_parent_index_values, total_rows, total_columns = \
split_grid(grid=grid,
num_cores=num_cores)
pool = multiprocessing.Pool(num_cores)
for vertex_sublist, index_sublist in zip(list_square_vertex_arrays_per_core, list_parent_index_values):
pool.apply_async(per_core_work, args=(
topology_file_path, trajectory_file_path, vertex_sublist, MDA_selection, start_frame, end_frame,
index_sublist, maximum_delta_magnitude), callback=log_result_to_parent)
pool.close()
pool.join()
dx_array = np.zeros((total_rows, total_columns))
dy_array = np.zeros((total_rows, total_columns))
#the parent_list_deltas is shaped like this: [ ([row_index,column_index],[dx,dy]), ... (...),...,]
for index_array, delta_array in parent_list_deltas: # go through the list in the parent process and assign to the
# appropriate positions in the dx and dy matrices:
#build in a filter to replace all values at the cap (currently between -8,8) with 0 to match Matthieu's code
# (I think eventually we'll reduce the cap to a narrower boundary though)
index_1 = index_array.tolist()[0]
index_2 = index_array.tolist()[1]
if abs(delta_array[0]) == maximum_delta_magnitude:
dx_array[index_1, index_2] = 0
else:
dx_array[index_1, index_2] = delta_array[0]
if abs(delta_array[1]) == maximum_delta_magnitude:
dy_array[index_1, index_2] = 0
else:
dy_array[index_1, index_2] = delta_array[1]
#at Matthieu's request, we now want to calculate the average and standard deviation of the displacement values:
displacement_array = np.sqrt(dx_array ** 2 + dy_array ** 2)
average_displacement = np.average(displacement_array)
standard_deviation_of_displacement = np.std(displacement_array)
return (dx_array, dy_array, average_displacement, standard_deviation_of_displacement)