Source code for MDAnalysis.visualization.streamlines

'''
Multicore 2D streamplot Python library for MDAnalysis --- :mod:`MDAnalysis.visualization.streamlines`
=====================================================================================================

:Authors: Tyler Reddy and Matthieu Chavent
:Year: 2014
:Copyright: GNU Public License v3
:Citation: [Chavent2014]_

.. autofunction:: generate_streamlines

'''

try:
    import matplotlib 
    import matplotlib.path
except ImportError:
    raise 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') 

import MDAnalysis
import multiprocessing
import numpy
import scipy

def produce_grid(tuple_of_limits,grid_spacing):
    '''Produce a grid for the simulation system based on the tuple of Cartesian Coordinate limits calculated in an earlier step.'''
    x_min, x_max, y_min, y_max = tuple_of_limits
    grid = numpy.mgrid[x_min:x_max:grid_spacing,y_min:y_max:grid_spacing]
    return grid

def split_grid(grid,num_cores):
    '''Take the overall grid for the system and split it into lists of square vertices that can be distributed to each core. 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 = numpy.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 = numpy.array_split(list_all_squares_in_grid,num_cores)
    list_parent_index_values = numpy.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(coordinate_file_path,trajectory_file_path,list_square_vertex_arrays_this_core,MDA_selection,start_frame,end_frame,reconstruction_index_list,maximum_delta_magnitude):
    '''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(coordinate_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 = numpy.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 = numpy.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.selectAtoms(MDA_selection).coordinates()[...,:-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(numpy.subtract(square_1_centroid,square_2_centroid).tolist())



            #xy_deltas_to_write = numpy.subtract(numpy.array(list_centroids_this_frame_using_indices_from_last_frame),numpy.array(list_previous_frame_centroids))
            xy_deltas_to_write = numpy.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 = numpy.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 zip(reconstruction_index_list,xy_deltas_to_write.tolist())

[docs]def generate_streamlines(coordinate_file_path,trajectory_file_path,grid_spacing,MDA_selection,start_frame,end_frame,xmin,xmax,ymin,ymax,maximum_delta_magnitude,num_cores='maximum'): '''Produce the x and y components of a 2D streamplot data set. :Parameters: **coordinate_file_path** : str Absolute path to the coordinate 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 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, 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: :: import matplotlib, matplotlib.pyplot, numpy 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 = numpy.linspace(0,1200,61) y = numpy.linspace(0,1200,61) speed = numpy.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 .. [Chavent2014] Chavent, M.\*, Reddy, T.\*, Dahl, C.E., Goose, J., Jobard, B., and Sansom, M.S.P. (2014) Methodologies for the analysis of instantaneous lipid diffusion in MD simulations of large membrane systems. *Faraday Discussions* **169**: **Accepted** ''' #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." numpy.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 = (coordinate_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 = numpy.zeros((total_rows,total_columns)) dy_array = numpy.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 = numpy.sqrt(dx_array ** 2 + dy_array ** 2) average_displacement = numpy.average(displacement_array) standard_deviation_of_displacement = numpy.std(displacement_array) return (dx_array,dy_array,average_displacement,standard_deviation_of_displacement) #if __name__ == '__main__': #execute the main control function only if this file is called as a top-level script #will probably mostly use this for testing on a trajectory: