coords.py 7.38 KiB
import numpy as np
from scipy.optimize import newton
def minimizeRmsd(coordsB, coordsA, weights=None, maxIter=100):
## Going through many iterations wasn't really needed
tol = 1
count = 0
R = np.eye(3)
comB = np.zeros([3,])
cNext = coordsB
while tol > 1e-6:
q,cB,comA = _minimizeRmsd(cNext,coordsA, weights)
R = R.dot(quaternion_to_matrix(q))
assert( np.all(np.isreal( R )) )
comB += cB
cLast = cNext
cNext = (coordsB-comB).dot(R)
tol = np.sum(((cNext-cLast)**2)[:]) / np.max(np.shape(coordsB))
if count > maxIter:
Exception("Exceeded maxIter (%d)" % maxIter)
count += 1
print("%d iterations",count)
return R, comB, comA
def minimizeRmsd(coordsB, coordsA, weights=None):
q,comA,comB = _minimizeRmsd(coordsB, coordsA, weights)
assert( np.all(np.isreal( q )) )
return quaternion_to_matrix(q),comA,comB
## http://onlinelibrary.wiley.com/doi/10.1002/jcc.21439/full
def _minimizeRmsd(coordsB, coordsA, weights=None):
A = coordsA
B = coordsB
shapeA,shapeB = [np.shape(X) for X in (A,B)]
for s in (shapeA,shapeB): assert( len(s) == 2 )
A,B = [X.T if s[1] > s[0] else X for X,s in zip([A,B],(shapeA,shapeB))] # TODO: print warning
shapeA,shapeB = [np.shape(X) for X in (A,B)]
assert( shapeA == shapeB )
for X,s in zip((A,B),(shapeA,shapeB)):
assert( s[1] == 3 and s[0] >= s[1] )
# if weights is None: weights = np.ones(len(A))
if weights is None:
comA,comB = [np.mean( X, axis=0 ) for X in (A,B)]
else:
assert( len(weights[:]) == len(B) )
W = np.diag(weights)
comA,comB = [np.sum( W.dot(X), axis=0 ) / np.sum(W) for X in (A,B)]
A = np.array( A-comA )
B = np.array( B-comB )
if weights is None:
s = A.T.dot(B)
else:
s = A.T.dot(W.dot(B))
sxx,sxy,sxz = s[0,:]
syx,syy,syz = s[1,:]
szx,szy,szz = s[2,:]
K = [[ sxx+syy+szz, syz-szy, szx-sxz, sxy-syx],
[syz-szy, sxx-syy-szz, sxy+syx, sxz+szx],
[szx-sxz, sxy+syx, -sxx+syy-szz, syz+szy],
[sxy-syx, sxz+szx, syz+szy, -sxx-syy+szz]]
K = np.array(K)
# GA = np.trace( A.T.dot(W.dot(A)) )
# GB = np.trace( B.T.dot(W.dot(B)) )
## Finding GA/GB can be done more quickly
# I = np.eye(4)
# x0 = (GA+GB)*0.5
# vals = newtoon(lambda x: np.det(K-x*I), x0 = x0)
vals, vecs = np.linalg.eig(K)
i = np.argmax(vals)
q = vecs[:,i]
# RMSD = np.sqrt( (GA+GB-2*vals[i]) / len(A) )
# print("CHECK:", K.dot(q)-vals[i]*q )
return q, comB, comA
def quaternion_to_matrix(q):
assert(len(q) == 4)
## It looks like the wikipedia article I used employed a less common convention for q (see below
## http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions#Rotation_matrix_.E2.86.94_quaternion
# q1,q2,q3,q4 = q
# R = [[1-2*(q2*q2 + q3*q3), 2*(q1*q2 - q3*q4), 2*(q1*q3 + q2*q4)],
# [ 2*(q1*q2 + q3*q4), 1-2*(q1*q1 + q3*q3), 2*(q2*q3 - q1*q4)],
# [ 2*(q1*q3 - q2*q4), 2*(q1*q4 + q2*q3), 1-2*(q2*q2 + q1*q1)]]
q0,q1,q2,q3 = q
R = [[1-2*(q2*q2 + q3*q3), 2*(q1*q2 - q3*q0), 2*(q1*q3 + q2*q0)],
[ 2*(q1*q2 + q3*q0), 1-2*(q1*q1 + q3*q3), 2*(q2*q3 - q1*q0)],
[ 2*(q1*q3 - q2*q0), 2*(q1*q0 + q2*q3), 1-2*(q2*q2 + q1*q1)]]
return np.array(R)
def quaternion_from_matrix( R ):
e1 = R[0]
e2 = R[1]
e3 = R[2]
# d1 = 0.5 * np.sqrt( 1+R[0,0]+R[1,1]+R[2,2] )
# d2 = 0.5 * np.sqrt( 1+R[0,0]-R[1,1]-R[2,2] )
# d2 = 0.5 * np.sqrt( 1+R[0,0]-R[1,1]-R[2,2] )
# d2 = 0.5 * np.sqrt( 1+R[0,0]-R[1,1]-R[2,2] )
d1 = 1+R[0,0]+R[1,1]+R[2,2]
d2 = 1+R[0,0]-R[1,1]-R[2,2]
d3 = 1-R[0,0]+R[1,1]-R[2,2]
d4 = 1-R[0,0]-R[1,1]+R[2,2]
maxD = max((d1,d2,d3,d4))
d = 0.5 / np.sqrt(maxD)
if d1 == maxD:
return np.array(( 1.0/(4*d),
d * (R[2,1]-R[1,2]),
d * (R[0,2]-R[2,0]),
d * (R[1,0]-R[0,1]) ))
elif d2 == maxD:
return np.array(( d * (R[2,1]-R[1,2]),
1.0/(4*d),
d * (R[0,1]+R[1,0]),
d * (R[0,2]+R[2,0]) ))
elif d3 == maxD:
return np.array(( d * (R[0,2]-R[2,0]),
d * (R[0,1]+R[1,0]),
1.0/(4*d),
d * (R[1,2]+R[2,1]) ))
elif d4 == maxD:
return np.array(( d * (R[1,0]-R[0,1]),
d * (R[0,2]+R[2,0]),
d * (R[1,2]+R[2,1]),
1.0/(4*d) ))
def rotationAboutAxis(axis,angle, normalizeAxis=True):
if normalizeAxis: axis = axis / np.linalg.norm(axis)
angle *= 0.5 * np.pi/180
cos = np.cos( angle )
sin = np.sin( angle )
q = [cos] + [sin*x for x in axis]
return quaternion_to_matrix(q)
def readArbdCoords(fname):
coords = []
with open(fname) as fh:
for line in fh:
coords.append([float(x) for x in line.split()[1:]])
return np.array(coords)
def readAvgArbdCoords(psf,pdb,dcd,rmsdThreshold=3.5):
import mdtraj as md
## align trajectory to pdb
ref = md.load(pdb, top=pdb)
sel = md.load(dcd, top=pdb)
# return ref.xyz[0,:,:]*10
# ref = sel[-1]
ids = ref.topology.select("name =~ 'D.*'")
assert(len(ids) > 3)
# r0 = ref.xyz[0,ids,:]
r0 = sel.xyz[-1,ids,:]
t = -1 # in case dcd_frames < 3
for t in range(len(sel.xyz)-2,-1,-1):
# print(t)
R,comA,comB = minimizeRmsd(sel.xyz[t,ids,:],r0)
sel.xyz[t,:,:] = np.array( [(r-comA).dot(R)+comB for r in sel.xyz[t]] )
rmsd = np.mean( (sel.xyz[t,ids,:]-r0)**2 )
if rmsd > (0.1*rmsdThreshold)**2:
break
t0=t+1
print( "Averaging coordinates in %s after frame %d" % (dcd, t0) )
pos = sel.xyz[t0:,:,:]
pos = np.mean(pos, axis=0)
return 10*pos # convert to Angstroms
# def readAvgArbdCoords(psf,pdb,dcd,rmsdThreshold=3.5):
# import MDAnalysis as md
# ## align trajectory to pdb
# from pdb import set_trace
# set_trace()
# uref = md.Universe(psf, pdb)
# usel = md.Universe(psf, dcd)
# ref = uref.select_atoms("name 'd*'")
# sel = usel.select_atoms("name 'd*'")
# # r0 = ref.xyz[0,ids,:]
# ts = usel.trajectory[-1]
# ts.frame
# r0 = sel.positions
# for t in range(ts.frame-1,-1,-1):
# print(t)
# usel.trajectory[t]
# R,comA,comB = minimizeRmsd(sel.positions,r0)
# sel.positions = np.array( [(r-comA).dot(R)+comB for r in sel.positions] )
# rmsd = np.mean( (sel.positions-r0)**2 )
# if rmsd > (0.1*rmsdThreshold)**2:
# break
# t0=t+1
# print( "Averaging coordinates in %s after frame %d" % (dcd, t0) )
# pos = sel.xyz[t0:,:,:]
# pos = np.mean(pos, axis=0)
# return 10*pos # convert to Angstroms
def unit_quat_conversions():
for axis in [[0,0,1],[1,1,1],[1,0,0],[-1,-2,0]]:
for angle in np.linspace(-180,180,10):
R = rotationAboutAxis(axis, angle)
R2 = quaternion_to_matrix( quaternion_from_matrix( R ) )
if not np.all( np.abs(R-R2) < 0.01 ):
import pdb
pdb.set_trace()
quaternion_to_matrix( quaternion_from_matrix( R ) )
if __name__ == "__main__":
unit_quat_conversions()