MDAnalysis distance selection commands like 'around' and 'sphzere' selects atoms from periodic image (I am using a rectangular box).
universe.select_atoms("name OW and around 4 (resid 20 and name O2)")
However, the coordinates of the atoms from the PBC box reside on the other side of the box. In other words, I have to manually translate the atoms to ensure that they actually are withing the 4 Angstrom distance.
Is there a selection feature to achieve this using the select_atoms function?
If I well understand, you would like to get the atoms around a given selection in the image that is the closest to that selection.
universe.select_atoms does not modify the coordinates, and I am not aware of a function that gives you what you want. The following function could work for an orthorhombic box like yours:
def pack_around(atom_group, center):
"""
Translate atoms to their periodic image the closest to a given point.
The function assumes that the center is in the main periodic image.
"""
# Get the box for the current frame
box = atom_group.universe.dimensions
# The next steps assume that all the atoms are in the same
# periodic image, so let's make sure it is the case
atom_group.pack_into_box()
# AtomGroup.positions is a property rather than a simple attribute.
# It does not always propagate changes very well so let's work with
# a copy of the coordinates for now.
positions = atom_group.positions.copy()
# Identify the *coordinates* to translate.
sub = positions - center
culprits = numpy.where(numpy.sqrt(sub**2) > box[:3] / 2)
# Actually translate the coordinates.
positions[culprits] -= (u.dimensions[culprits[1]]
* numpy.sign(sub[culprits]))
# Propagate the new coordinates.
atom_group.positions = positions
Using that function, I got the expected behavior on one of MDAnalysis test files. You need MDAnalysisTests to be installed to run the following piece of code:
import numpy
import MDAnalysis as mda
from MDAnalysisTests.datafiles import PDB_sub_sol
u = mda.Universe(PDB_sub_sol)
selection = u.select_atoms('around 15 resid 32')
center = u.select_atoms('resid 32').center_of_mass()
# Save the initial file for latter comparison
u.atoms.write('original.pdb')
selection.write('selection_original.pdb')
# Translate the coordinates
pack_around(selection, center)
# Save the new coordinates
u.atoms.write('modified.pdb')
selection.write('selection_modified.pdb')
Related
I use sympy plotting backends library to create plots directly from sympy expressions. I chose this library because it gives more options for plots fine tunning compared to standart sympy plotting module.
As backend in choosen library i use matplotlib.
My aim is to get resulting plot as svg string in order to insert it in the web page later. I need to do it programmatically. I use the code below:
from spb import plot, MB
import io
from sympy import symbols, sin, cos
x = symbols("x")
# create plot
p1 = plot(
(sin(x), "a", dict(color="k", linestyle=":")),
(cos(x), "b"),
backend=MB, show=False)
# buffer:
f = io.StringIO()
# save plot in buffer as svg string:
p1._fig.savefig(f, format = "svg")
# return result as svg string to insert it in web page later:
return f.getvalue()
The problem is that i get an exception:
'NoneType' object has no attribute 'savefig'
p1._fig.savefig(f, format = "svg")
But if i slightly modify the code:
...
# buffer:
f = io.StringIO()
# show plot:
p1.show()
# save plot in buffer as svg string:
p1._fig.savefig(f, format = "svg")
...
Everything works just fine. But the problem is that i do not want to show the plot, i need to save it as svg string. Anyone knows how to solve this task?
Here I am, the developer of that module.
That error is caused by the fact that when you create a plot with MatplotlibBackend and show=False, the figure is not created (too long to explain why); this behavior is specific to MatplotlibBackend, the other backends should not be affected by it. So, p1.fig is None.
However, the plotting function exposes the save method, which is nothing more than a wrapper to a specific plotting library "save" functionality. If you look at the source code, you'll see that MatplotlibBackend.save calls matplotlib's savefig, but first it checks if the figure has been created. If not, it forces the creation.
So, all you have to do is:
p1.save(f, format = "svg")
One final note. If possible, do not use attributes or methods starting with _ (underscore). They represent private attributes and the names might change from version to version. If you really need to retrieve the matplotlib figure, use p1.fig.
EDIT to answer the question in the comment about performance:
For back-compatibility reasons, the new module uses an adaptive algorithm for line plots by default, which is different from the one used on SymPy. On the one hand it can be easily applied to a wider set of applications, on the other hand it is slower.
You have two options: either way you might want to change the configuration file of the module.
Option 1: the adaptive algorithm minimizes some loss function (loss_fn) and stops when a threshold (adaptive_goal) has been reached. We can increase this threshold (which by default is set to 0.01), thus improving performance but sacrificing the smooth quality of lines.
from spb.defaults import cfg, set_defaults
# it requires a few tries to find an appropriate value
cfg["adaptive"]["goal"] = 0.02
set_defaults(cfg)
# restart the kernel to load the new configuration
Option 2: don't use the adaptive algorithm and switch to the uniform meshing algorithm which uses Numpy and vectorization (usually done with adaptive=False and possibly setting an appropriate number of discretization points n=something)! This is very very fast in comparison to the adaptive algorithm.
Think about it: generally, our plots are relatively small in comparison to the screen size. 1000 points per line (or whatever number you decide to use) should create smooth-enough lines.
So, you can deactivate the adaptive algorithm on a plot-by-plot basis (with adaptive=False), or you can set the module to always use the uniform meshing algorithm (this is the setup that I use on my machine).
from spb.defaults import cfg, set_defaults
# disable adaptive algorithm
cfg["adaptive"]["used_by_default"] = False
set_defaults(cfg)
# restart the kernel to load the new configuration
Then, when you create a plot and you feel like it should be smoother, simply increase the number of discretization points by setting n=something (default value is 1000).
You can find more customization options on this documentation page.
Edit: I've now fixed the problem I asked about. The spheres were leaving the box in the corners, where the if statements (in the while loop shown below) got confused. In the bits of code that reverse the individual components of velocity on contact with walls, some elif statements were used. When elif is used (as far as I can tell) if the sphere exceeds more than one position limit at a time, the program only reverses the velocity component for one of them. This is rectified when replacing elif with simply if. I'm not sure if I quite understand the reason behind this, so hopefully someone cleverer than I will comment such information, but for now, if anyone has the same problem, I hope my limited input helps!
Some context first:
I'm trying to build a model of the kinetic theory of gases in VPython, as a revision exercise for my (Physics) degree. This involves me building a hollow box and putting a bunch of spheres in it, randomly positioned throughout the box. I then need to assign each of the spheres its own random velocity and then use a loop to adjust the position of each sphere with reference to its velocity vector and a time step.
The spheres should also undergo elastic collisions with each wall and all other spheres.
When a sphere meets a wall in the x-direction, its x-velocity component is reversed and similarly in the y and z directions.
When a sphere meets another sphere, they swap velocities.
Currently, my code works so far as creating the right number of spheres and distributing them randomly and giving each sphere its own random velocity. The spheres also move as they should, except for collisions. The spheres should all stay inside the box as they should bounce off all the walls. They appear to be bouncing off each other, however, occasionally a sphere or two will go straight through the box.
I am extremely new to programming and I don't quite understand what's going on here or why it's happening but I'd be very grateful if someone could help me.
Below is the code I have so far (I've tried to comment what I'm doing at each step):
##########################################################
# This code is meant to create an empty box and then create
# a certain number of spheres (num_spheres) that will sit inside
# the box. Each sphere will then be assigned a random velocity vector.
# A loop will then adjust the position of each sphere to make them
# move. The spheres will undergo elastic collisions with the box walls
# and also with the other spheres in the box.
##########################################################
from visual import *
import random as random
import numpy as np
num_spheres = 15
fps = 24 #fps of while loop (later)
dt = 1.0/fps #time step
l = 40 #length of box
w = 2 #width of box
radius = 0.5 #radius of spheres
##########################################################
# Creating an empty box with sides length/height l, width w
wallR = box(pos = (l/2.0,0,0), size=(w,l,l), color=color.white, opacity=0.25)
wallL = box(pos = (-l/2.0,0,0), size=(w,l,l), color=color.white, opacity=0.25)
wallU = box(pos = (0,l/2.0,0), size=(l,w,l), color=color.white, opacity=0.25)
wallD = box(pos = (0,-l/2.0,0), size=(l,w,l), color=color.white, opacity=0.25)
wallF = box(pos = (0,0,l/2.0), size=(l,l,w), color=color.white, opacity=0.25)
wallB = box(pos = (0,0,-l/2.0), size=(l,l,w), color=color.white, opacity=0.25)
#defining a function that creates a list of 'num_spheres' randomly positioned spheres
def create_spheres(num):
global l, radius
particles = [] # Create an empty list
for i in range(0,num): # Loop i from 0 to num-1
v = np.random.rand(3)
particles.append(sphere(pos= (3.0/4.0*l) * (v - 0.5), #pos such that spheres are inside box
radius = radius, color=color.red, index=i))
# each sphere is given an index for ease of referral later
return particles
#defining a global variable = the array of velocities for the spheres
velarray = []
#defining a function that gives each sphere a random velocity
def velocity_spheres(sphere_list):
global velarray
for sphere in spheres:
#making the sign of each velocity component random
rand = random.randint(0,1)
if rand == 1:
sign = 1
else:
sign = -1
mu = 10 #defining an average for normal distribution
sigma = 0.1 #defining standard deviation of normal distribution
# 3 random numbers form the velocity vector
vel = vector(sign*random.normalvariate(mu, sigma),sign*random.normalvariate(mu, sigma),
sign*random.normalvariate(mu, sigma))
velarray.append(vel)
spheres = create_spheres(num_spheres) #creating some spheres
velocity_spheres(spheres) # invoking the velocity function
while True:
rate(fps)
for sphere in spheres:
sphere.pos += velarray[sphere.index]*dt
#incrementing sphere position by reference to its own velocity vector
if abs(sphere.pos.x) > (l/2.0)-w-radius:
(velarray[sphere.index])[0] = -(velarray[sphere.index])[0]
#reversing x-velocity on contact with a side wall
elif abs(sphere.pos.y) > (l/2.0)-w-radius:
(velarray[sphere.index])[1] = -(velarray[sphere.index])[1]
#reversing y-velocity on contact with a side wall
elif abs(sphere.pos.z) > (l/2.0)-w-radius:
(velarray[sphere.index])[2] = -(velarray[sphere.index])[2]
#reversing z-velocity on contact with a side wall
for sphere2 in spheres: #checking other spheres
if sphere2 != sphere:
#making sure we aren't checking the sphere against itself
if abs(sphere2.pos-sphere.pos) < (sphere.radius+sphere2.radius):
#if the other spheres are touching the sphere we are looking at
v1 = velarray[sphere.index]
#noting the velocity of the first sphere before the collision
velarray[sphere.index] = velarray[sphere2.index]
#giving the first sphere the velocity of the second before the collision
velarray[sphere2.index] = v1
#giving the second sphere the velocity of the first before the collision
Thanks again for any help!
The elif statements within the while loop in the code given in the original question are/were the cause of the problem. The conditional statement, elif, is only applicable if the original, if, condition is not satisfied. The circumstance wherein a sphere meets the corner of the box satisfies at least two of the conditions for reversing velocity components. This means that, while one would expect (at least) two velocity components to be reversed, only one is. That is, the direction specified by the if statement is reversed, whereas the component(s) mentioned in the elif statement(s) are not, as the first condition has been satisfied and, hence, the elif statements are ignored.
If each elif is changed to be a separate if statement, the code works as intended.
I'm looking for a more efficient way to draw continuous lines in PsychoPy. That's what I've come up with, for now...
edit: the only improvement I could think of is to add a new line only if the mouse has really moved by adding if (mspos1-mspos2).any():
ms = event.Mouse(myWin)
lines = []
mspos1 = ms.getPos()
while True:
mspos2 = ms.getPos()
if (mspos1-mspos2).any():
lines.append(visual.Line(myWin, start=mspos1, end=mspos2))
for j in lines:
j.draw()
myWin.flip()
mspos1 = mspos2
edit: I tried it with Shape.Stim (code below), hoping that it would work better, but it get's edgy even more quickly..
vertices = [ms.getPos()]
con_line = visual.ShapeStim(myWin,
lineColor='red',
closeShape=False)
myclock.reset()
i = 0
while myclock.getTime() < 15:
new_pos = ms.getPos()
if (vertices[i]-new_pos).any():
vertices.append(new_pos)
i += 1
con_line.vertices=vertices
con_line.draw()
myWin.flip()
The problem is that it becomes too ressource demanding to draw those many visual.Lines or manipulate those many vertices in the visual.ShapeStim on each iteration of the loop. So it will hang on the draw (for Lines) or vertex assignment (for ShapeStim) so long that the mouse has moved enough for the line to show discontinuities ("edgy").
So it's a performance issue. Here are two ideas:
Have a lower threshold for the minimum distance travelled by the mouse before you want to add a new coordinate to the line. In the example below I impose a the criterion that the mouse position should be at least 10 pixels away from the previous vertex to be recorded. In my testing, this compressed the number of vertices recorded per second to about a third. This strategy alone will postpone the performance issue but not prevent it, so on to...
Use the ShapeStim solution but regularly use new ShapeStims, each with fewer vertices so that the stimulus to be updated isn't too complex. In the example below I set the complexity at 500 pixels before shifting to a new stimulus. There might be a small glitch while generating the new stimulus, but nothing I've noticed.
So combining these two strategies, starting and ending mouse drawing with a press on the keyboard:
# Setting things up
from psychopy import visual, event, core
import numpy as np
# The crucial controls for performance. Adjust to your system/liking.
distance_to_record = 10 # number of pixels between coordinate recordings
screenshot_interval = 500 # number of coordinate recordings before shifting to a new ShapeStim
# Stimuli
myWin = visual.Window(units='pix')
ms = event.Mouse()
myclock = core.Clock()
# The initial ShapeStim in the "stimuli" list. We can refer to the latest
# as stimuli[-1] and will do that throughout the script. The others are
# "finished" and will only be used for draw.
stimuli = [visual.ShapeStim(myWin,
lineColor='white',
closeShape=False,
vertices=np.empty((0, 2)))]
# Wait for a key, then start with this mouse position
event.waitKeys()
stimuli[-1].vertices = np.array([ms.getPos()])
myclock.reset()
while not event.getKeys():
# Get mouse position
new_pos = ms.getPos()
# Calculating distance moved since last. Pure pythagoras.
# Index -1 is the last row.index
distance_moved = np.sqrt((stimuli[-1].vertices[-1][0]-new_pos[0])**2+(stimuli[-1].vertices[-1][1]-new_pos[1])**2)
# If mouse has moved the minimum required distance, add the new vertex to the ShapeStim.
if distance_moved > distance_to_record:
stimuli[-1].vertices = np.append(stimuli[-1].vertices, np.array([new_pos]), axis=0)
# ... and show it (along with any "full" ShapeStims
for stim in stimuli:
stim.draw()
myWin.flip()
# Add a new ShapeStim once the old one is too full
if len(stimuli[-1].vertices) > screenshot_interval:
print "new shapestim now!"
stimuli.append(visual.ShapeStim(myWin,
lineColor='white',
closeShape=False,
vertices=[stimuli[-1].vertices[-1]])) # start from the last vertex
Space is a premium for a set of subplots that I am automating in which there is sometimes many curves in one subplot. I want to split the legend into two boxes and then optimize the location of the second legend box (the location of the first is provided with loc='best').
Here is am simple example that demonstrates what I am attempting -
lines = []
leg = ['test','test1','test2']
lines.append(plot(np.array([1,20]), label = 'test')[0])
lines.append(plot(np.array([1,20]), label = 'test1')[0])
lines.append(plot(np.array([1,20]), label = 'test2')[0])
pltleg1 = plt.legend(lines[:2],leg[:2],loc='best')
# QUESTION: Here I want to put the second legend in the 2nd best location
# or if I could get the location decided upon for pltleg1, I can just add it
# the opposite corner.
pltleg2 = plt.legend(lines[2:],leg[2:],loc='best')
gca().add_artist(pltleg1)
So, I am hoping to find the second best location or if I could retrieve the chosen legend location than it would be okay to choose an alternative. For the second case, it is okay if there is curve overlap. How can this be done?
!I have values in the form of (x,y,z). By creating a list_plot3d plot i can clearly see that they are not quite evenly spaced. They usually form little "blobs" of 3 to 5 points on the xy plane. So for the interpolation and the final "contour" plot to be better, or should i say smoother(?), do i have to create a rectangular grid (like the squares on a chess board) so that the blobs of data are somehow "smoothed"? I understand that this might be trivial to some people but i am trying this for the first time and i am struggling a bit. I have been looking at the scipy packages like scipy.interplate.interp2d but the graphs produced at the end are really bad. Maybe a brief tutorial on 2d interpolation in sagemath for an amateur like me? Some advice? Thank you.
EDIT:
https://docs.google.com/file/d/0Bxv8ab9PeMQVUFhBYWlldU9ib0E/edit?pli=1
This is mostly the kind of graphs it produces along with this message:
Warning: No more knots can be added because the number of B-spline
coefficients
already exceeds the number of data points m. Probably causes:
either
s or m too small. (fp>s)
kx,ky=3,3 nx,ny=17,20 m=200 fp=4696.972223 s=0.000000
To get this graph i just run this command:
f_interpolation = scipy.interpolate.interp2d(*zip(*matrix(C)),kind='cubic')
plot_interpolation = contour_plot(lambda x,y:
f_interpolation(x,y)[0], (22.419,22.439),(37.06,37.08) ,cmap='jet', contours=numpy.arange(0,1400,100), colorbar=True)
plot_all = plot_interpolation
plot_all.show(axes_labels=["m", "m"])
Where matrix(c) can be a huge matrix like 10000 X 3 or even a lot more like 1000000 x 3. The problem of bad graphs persists even with fewer data like the picture i attached now where matrix(C) was only 200 x 3. That's why i begin to think that it could be that apart from a possible glitch with the program my approach to the use of this command might be totally wrong, hence the reason for me to ask for advice about using a grid and not just "throwing" my data into a command.
I've had a similar problem using the scipy.interpolate.interp2d function. My understanding is that the issue arises because the interp1d/interp2d and related functions use an older wrapping of FITPACK for the underlying calculations. I was able to get a problem similar to yours to work using the spline functions, which rely on a newer wrapping of FITPACK. The spline functions can be identified because they seem to all have capital letters in their names here http://docs.scipy.org/doc/scipy/reference/interpolate.html. Within the scipy installation, these newer functions appear to be located in scipy/interpolate/fitpack2.py, while the functions using the older wrappings are in fitpack.py.
For your purposes, RectBivariateSpline is what I believe you want. Here is some sample code for implementing RectBivariateSpline:
import numpy as np
from scipy import interpolate
# Generate unevenly spaced x/y data for axes
npoints = 25
maxaxis = 100
x = (np.random.rand(npoints)*maxaxis) - maxaxis/2.
y = (np.random.rand(npoints)*maxaxis) - maxaxis/2.
xsort = np.sort(x)
ysort = np.sort(y)
# Generate the z-data, which first requires converting
# x/y data into grids
xg, yg = np.meshgrid(xsort,ysort)
z = xg**2 - yg**2
# Generate the interpolated, evenly spaced data
# Note that the min/max of x/y isn't necessarily 0 and 100 since
# randomly chosen points were used. If we want to avoid extrapolation,
# the explicit min/max must be found
interppoints = 100
xinterp = np.linspace(xsort[0],xsort[-1],interppoints)
yinterp = np.linspace(ysort[0],ysort[-1],interppoints)
# Generate the kernel that will be used for interpolation
# Note that the default version uses three coefficients for
# interpolation (i.e. parabolic, a*x**2 + b*x +c). Higher order
# interpolation can be used by setting kx and ky to larger
# integers, i.e. interpolate.RectBivariateSpline(xsort,ysort,z,kx=5,ky=5)
kernel = interpolate.RectBivariateSpline(xsort,ysort,z)
# Now calculate the linear, interpolated data
zinterp = kernel(xinterp, yinterp)