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ThreedfitMain.py
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ThreedfitMain.py
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#!/usr/bin/python
from __future__ import division
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import sys
import numpy as np
from numpy import linalg
from random import random
import sys
#number=sys.argv[1]
class EllipsoidTool:
"""Some stuff for playing with ellipsoids"""
def __init__(self): pass
def getMinVolEllipse(self, P=None, tolerance=0.01):
""" Find the minimum volume ellipsoid which holds all the points
Based on work by Nima Moshtagh
http://www.mathworks.com/matlabcentral/fileexchange/9542
and also by looking at:
http://cctbx.sourceforge.net/current/python/scitbx.math.minimum_covering_ellipsoid.html
Which is based on the first reference anyway!
Here, P is a numpy array of N dimensional points like this:
P = [[x,y,z,...], <-- one point per line
[x,y,z,...],
[x,y,z,...]]
Returns:
(center, radii, rotation)
"""
(N, d) = np.shape(P)
d = float(d)
# Q will be our working array
Q = np.vstack([np.copy(P.T), np.ones(N)])
QT = Q.T
# initializations
err = 1.0 + tolerance
u = (1.0 / N) * np.ones(N)
# Khachiyan Algorithm
while err > tolerance:
V = np.dot(Q, np.dot(np.diag(u), QT))
M = np.diag(np.dot(QT , np.dot(linalg.inv(V), Q))) # M the diagonal vector of an NxN matrix
j = np.argmax(M)
maximum = M[j]
step_size = (maximum - d - 1.0) / ((d + 1.0) * (maximum - 1.0))
new_u = (1.0 - step_size) * u
new_u[j] += step_size
err = np.linalg.norm(new_u - u)
u = new_u
# center of the ellipse
center = np.dot(P.T, u)
# the A matrix for the ellipse
A = linalg.inv(
np.dot(P.T, np.dot(np.diag(u), P)) -
np.array([[a * b for b in center] for a in center])
) / d
# Get the values we'd like to return
U, s, rotation = linalg.svd(A)
radii = 1.0/np.sqrt(s)
return (center, radii, rotation)
def getEllipsoidVolume(self, radii):
"""Calculate the volume of the blob"""
return 4./3.*np.pi*radii[0]*radii[1]*radii[2]
def plotEllipsoid(self, center, radii, rotation, ax=None, plotAxes=False, cageColor='b', cageAlpha=0.2):
"""Plot an ellipsoid"""
make_ax = ax == None
if make_ax:
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
u = np.linspace(0.0, 2.0 * np.pi, 100)
v = np.linspace(0.0, np.pi, 100)
# cartesian coordinates that correspond to the spherical angles:
x = radii[0] * np.outer(np.cos(u), np.sin(v))
y = radii[1] * np.outer(np.sin(u), np.sin(v))
z = radii[2] * np.outer(np.ones_like(u), np.cos(v))
# rotate accordingly
for i in range(len(x)):
for j in range(len(x)):
[x[i,j],y[i,j],z[i,j]] = np.dot([x[i,j],y[i,j],z[i,j]], rotation) + center
if plotAxes:
# make some purdy axes
axes = np.array([[radii[0],0.0,0.0],
[0.0,radii[1],0.0],
[0.0,0.0,radii[2]]])
# rotate accordingly
for i in range(len(axes)):
axes[i] = np.dot(axes[i], rotation)
# plot axes
for p in axes:
X3 = np.linspace(-p[0], p[0], 100) + center[0]
Y3 = np.linspace(-p[1], p[1], 100) + center[1]
Z3 = np.linspace(-p[2], p[2], 100) + center[2]
ax.plot(X3, Y3, Z3, color=cageColor)
# plot ellipsoid
ax.plot_wireframe(x, y, z, rstride=4, cstride=4, color=cageColor, alpha=cageAlpha)
if make_ax:
plt.show()
plt.close(fig)
del fig
fidX=open('SurfaceAreaVolumeX'+'.dat','w');
fidY=open('SurfaceAreaVolumeY'+'.dat','w');
fidZ=open('SurfaceAreaVolumeZ'+'.dat','w');
a=[249,243,199,191,182,171,160,146,139,134,136,134,115,107,102,91,84,81,59,65,47,51,157]
size=a+a
csize=np.cumsum(size)
atoms=sum(size)
chromosome=np.zeros((atoms+1,3),dtype=np.float)
for number in range(4001,10001,25):
print number
for fi in range(1,1+25):
f=open('Conf'+str(fi)+'/my/file'+str(number)+'.dat')
cont=f.readlines()
for i in range(5,len(cont)): ###8 check this line
l=cont[i].split()
if len(l)==6:
chromosome[int(l[0])]=[float(l[3]),float(l[4]),float(l[5])]
start=1
for i in range(1,47):
P=np.zeros((size[i-1],3),dtype=np.float)
for j in range(start,1+csize[i-1]):
P[j-start,:]=chromosome[j]
start=1+csize[i-1]
ET = EllipsoidTool()
(center, radii, rotation) = ET.getMinVolEllipse(P, .01)
#print center, radii, rotation
#plotEllipsoid( center, radii, rotation)
fidX.write(str(radii[0])+' ')
fidY.write(str(radii[1])+' ')
fidZ.write(str(radii[2])+' ')
fidX.write('\n')
fidY.write('\n')
fidZ.write('\n')